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2023/Finding the Pillars of Strength for Multi-Head Attention/full.md

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+# Finding the Pillars of Strength for Multi-Head Attention
+
+Jinjie Ni and Rui Mao and Zonglin Yang and Han Lei and Erik Cambria
+
+Nanyang Technological University, Singapore
+
+{jinjie001,leih0003}@e.ntu.edu.sg,
+
+{rui.mao, zonglin.yang, cambria}@ntu.edu.sg
+
+# Abstract
+
+Recent studies have revealed some issues of Multi-Head Attention (MHA), e.g., redundancy and over-parameterization. Specifically, the heads of MHA were originally designed to attend to information from different representation subspaces, whereas prior studies found that some attention heads likely learn similar features and can be pruned without harming performance. Inspired by the minimum-redundancy feature selection, we assume that focusing on the most representative and distinctive features with minimum resources can mitigate the above issues and lead to more effective and efficient MHAs. In particular, we propose Grouped Head Attention, trained with a self-supervised group constraint that group attention heads, where each group focuses on an essential but distinctive feature subset. We additionally propose a Voting-to-Stay procedure to remove redundant heads, thus achieving a transformer with lighter weights. Moreover, our method achieves significant performance gains on three well-established tasks while considerably compressing parameters.
+
+# 1 Introduction
+
+Transformers have shown promising performance across various tasks. However, they have some issues, e.g., redundancy and over-parameterization, which is mainly caused by Multi-Head Attention (MHA) (Michel et al., 2019; Voita et al., 2019) and Feed-Forward Network (FFN) (Sukhbaatar et al., 2019; Wu et al., 2019, 2020) of transformer. We aim to mitigate the redundancy and over-parameterization issues by optimizing the MHA module. The multi-heads were originally designed to attend to different representation subspaces of input (Vaswani et al., 2017). However, prior works (Michel et al., 2019; Voita et al., 2019) have shown that the attention heads are highly redundant and over-parameterized after training because some heads can be switched off with a negligible performance drop.
+
+Such an issue is probably caused by their parallel design: the heads naturally work in the same way and likely attend to similar features (Cordonnier et al., 2020). The existing redundancy optimization methods are mainly based on homogenization, diversification, and head significance. However, they all have some limits. (1) The homogenization-based methods mitigate redundancy and over-parameterization by making heads similar and removing unnecessary parameters. Cordonnier et al. (2020) homogenized attention heads by sharing most weights between all heads, which reduced the redundant parameters but sacrificed the performance somewhat because of the lack of diversity. (2) The diversification-based methods diversify the heads to enrich features and reduce the inter-head redundancy. Li et al. (2018) found that diversifying attention heads by adding a regularization could force MHA to reduce inter-head information redundancy, yielding performance gains in Machine Translation. However, such strategy that retains all feature subsets is suboptimal, because it does not address the issue that MHA is over-parameterized. (3) The significance-based methods (Michel et al., 2019; Voita et al., 2019; Li et al., 2021) learn significance scores for the heads to prune unimportant ones. However, the retained important heads still remain inter-head redundancy without diversifying them.
+
+Considering the issues of the above-mentioned methods, we hypothesize that attending to the most representative and distinctive feature subsets with minimum resources leads to more effective and efficient MHAs, which is inspired by the minimum-redundancy feature selection (Cordonnier et al., 2020). Accordingly, we propose a divide-and-conquer strategy, including Group-Constrained Training (GCT) and Voting-to-Stay (V2S), to achieve the setting of our assumption and mitigate the above-mentioned issues. We illustrate them below.
+
+We first propose a strategy to group and distinguish attention heads, where a Grouped Head Attention (GHA) is obtained via the self-supervised GCT. By encouraging homogenization within a group and diversification between groups, the MHA is forced to divide its heads to work in several separate groups, where each group focuses on an essential but unique feature subset, being in line with the setting of our assumption. Note that the redundancy exists when the resources deployed by the model are more than enough to process current information (Cordonnier et al., 2020). GHA reduces the redundancy in two aspects:
+
+- The intra-group homogenization reduces redundancy by encouraging similar intra-group heads and only retaining the most representative one later to lower the resource deployment.  
+- The inter-group diversification reduces redundancy by forcing heads to attend to more diversified features (with less overlap between heads) so that the unique information to process increases and matches the resources deployed.
+
+Next, we show that GHA-PS (GHA with the Pillar of Strength), a lighter-weight GHA, can be achieved by excluding the redundant heads of GHA via the V2S procedure. V2S culls the redundant heads that share similar patterns with the most representative head (PS head) of a group, which is selected by voting on different training batches. Note that upon the convergence of the GCT, the heads are highly homogenized within a group, thus being redundant because they process similar information. As a result, once the redundant heads are culled, the PS heads can still achieve the essential utility of the original attention layer and yield comparable performance to the unculled model. The Lottery Ticket hypothesis (Frankle and Carbin, 2019) argues that subnetworks in an over-parameterized neural network can converge faster and achieve comparable or better performance than the original network. Our GHA-PS achieving better results is also in line with this hypothesis.
+
+Such a divide-and-conquer combination resolves the issues of previous redundancy optimization methods: (1) Our model achieves better parameter efficiency, resolving the issue of previous diversification-based methods; (2) The feature diversity is guaranteed and the inter-head redundancy is reduced, resolving the problems of previous homogenization- and significance-based methods.
+
+We evaluate our method on three benchmarking tasks. We denote the corresponding transformer architectures of GHA and GHA-PS as Grouped Head Transformers (GHT) and Grouped Head Transformers with the Pillars of Strength (GHT-PS), respectively. GHT and GHT-PS achieve significant improvements over the strong baselines in Machine Translation (MT) BLEU scores  $(+3.8\%)$  and  $+4.4\%$  averaged on 7 datasets), Language Modeling (LM) perplexity  $(-2.8\%)$  and  $-2.9\%$  ), and Abstractive summarization (AS) F1-Rouge  $(+6.7\%)$  and  $+7.0\%$  on average). GHT-PS exhibits higher efficiency in model size, inference speed, and floating-point operations (FLOPs). The light architecture of GHT-PS reduces  $63.6\%$  parameters of the vanilla transformer and yields comparable performance. The key contributions of our work are threefold:
+
+- We find that, in a certain range, higher compactness of attention heads (i.e., the intra-group heads become closer to each other and the inter-group ones become farther) improves MHA's performance, forcing MHA to focus on the most representative and distinctive features. It provides guidance for future architectural designs of MHA.  
+- We propose a divide-and-conquer strategy that consists of GCT and V2S. It mitigates the redundancy and over-parameterization issues of MHA. Our method uses fewer parameters and achieves better performance, outperforming the existing MHA redundancy/parameter reduction methods.  
+- We verify our methods on three well-established NLP tasks. The superior results on datasets with multiple languages, domains, and data sizes demonstrate the effectiveness of our method.
+
+# 2 Related Work
+
+Parameter efficiency. Different methods were proposed to achieve lightweight transformers: (1) replacing attention with lightweight modules, e.g., convolution modules, such as Dynamic Conv (Wu et al., 2019) and Lite Transformer (Wu et al., 2020); (2) removing or replacing the feed-forward layers, such as Sukhbaatar et al. (2019) and Wu et al. (2020); (3) pruning the model, such as Michel et al. (2019), Voita et al. (2019), and Li et al. (2021).
+
+Modified multi-head mechanism. Ahmed et al. (2017) learned to weight the projected output of different heads, performing weighted sum over them. Li et al. (2019) aggregated the output of different heads by dynamic routing; Cui et al. (2019) used different attention mechanisms, e.g., global/local and forward/backward attention for different heads; Shazeer et al. (2020) mixed different heads before and after the softmax operation in an attention function to achieve communication between heads.
+
+Head redundancy optimization. Michel et al. (2019) and Voita et al. (2019) found that only a subset of the attention heads have significant utilities in transformer, where the important heads could be identified by Expected Sensitivity and Layer-wise Relevance Propagation (LRP) (Ding et al., 2017). Upon this, Li et al. (2021) learned per-head importance scores and pruned the heads. Cordonnier et al. (2020) homogenized the attention heads by sharing a part of the weights between heads, which lowered the number of parameters but sacrificed performance. Li et al. (2018) found that diversifying attention heads by adding a regularization can force MHA to reduce inter-head redundancy, yielding performance gains for Machine Translation. However, previous methods either traded performance for efficiency or retained extra parameters.
+
+# 3 Methodology
+
+There are two core components in our method, namely the Group-Constrained Training (GCT) and the Voting-to-Stay (V2S) procedure. GHA (Figure 1) is developed with GCT that removes head redundancy; GHA-PS is developed by removing the redundant parameters of GHA in V2S. In this section, we detail the process of developing the GHA and finding its Pillars of Strength (PS).
+
+# 3.1 Grouped Head Attention with Hidden Units
+
+First, we detail the core module of GHT, the GHA with hidden units, which is built based on MHA via the GCT. The GCT divides the attention heads of MHA into several groups and makes heads within a group become more similar, whereas heads between groups become more different. Thus, MHA is forced to divide its heads to work in several separate groups, where each group focuses on an essential but unique feature subset to reduce head redundancy. We will show the effectiveness in § 5.
+
+![](images/53b72b653183e49e603e11dbdca2ac350e35556332f827885eef69eac197fd9d.jpg)  
+Figure 1: The Grouped Head Attention. The heads in a group are under self-supervision of the discovered group hidden units  $\mathbf{Z}$  (Eq.4). The non-PS heads (dashed gray boxes in a group) will be culled in the VS procedure (Algorithm 1).  $S_{k}$  denotes the  $k$ -th representation subspace;  $\mathrm{FM}_C$  denotes the  $C$ -th feature map group. The output of GHA is omitted for simplicity.
+
+Given a transformer model  $f(\mathbf{x};\theta)$  with  $n$  attention layers, the set of heads at attention layer  $l$  is denoted as  $\mathbf{H}_l = \{\mathbf{h}_{1,l},\dots,\mathbf{h}_{k,l}\}$ , where  $k$  is the number of heads. The outputs of the attention heads are concatenated and projected with  $W^{out}$  where the  $i$ -th head output  $\mathbf{o}_{i,l}$  in layer  $l$  results from the computation of the projection matrices  $W_{i,l}^{\mathbf{Q}}$ ,  $W_{i,l}^{\mathbf{K}}$ , and  $W_{i,l}^{\mathbf{V}}$  of this head:
+
+$$
+M H A _ {l} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = C o n c a t e \left(\mathbf {o} _ {1, l}, \dots , \mathbf {o} _ {k, l}\right) W ^ {\text {o u t}} \tag {1}
+$$
+
+$$
+\mathbf {o} _ {i, l} = \operatorname {s o f t m a x} \left(\frac {\left(\mathbf {Q} W _ {i , l} ^ {\mathbf {Q}}\right) \left(\mathbf {K} W _ {i , l} ^ {\mathbf {K}}\right) ^ {T}}{\sqrt {d _ {k}}}\right) \left(\mathbf {V} W _ {i, l} ^ {\mathbf {V}}\right). \tag {2}
+$$
+
+Three feature maps (FMs) of GHA are extracted for the self-supervised GCT: (1) the result of  $\mathbf{V}W_{l}^{\mathbf{V}}$ , denoted as  $\hat{\mathbf{V}}_l = \{\mathbf{v}_{1,l},\dots,\mathbf{v}_{k,l}\}$  (the value FM); (2) the attention weights of the  $l$ -th layer, denoted as  $\mathbf{A}_l = \{\mathbf{a}_{1,l},\dots,\mathbf{a}_{k,l}\}$  (the attention FM); (3) the output of the  $l$ -th layer before the output projection  $W^{out}$ , denoted as  $\mathbf{O}_l = \{\mathbf{o}_{1,l},\dots,\mathbf{o}_{k,l}\}$  (the head output FM). Moreover,  $\hat{\mathbf{V}} = \{\hat{\mathbf{V}}_1,\dots,\hat{\mathbf{V}}_l\}$ ,  $\mathbf{A} = \{\mathbf{A}_1,\dots,\mathbf{A}_l\}$ ,  $\mathbf{O} = \{\mathbf{O}_1,\dots,\mathbf{O}_l\}$ . Given the FMs, a Hidden Unit Discovery System (HUDS)  $\Omega$  assigns a hidden unit  $\mathbf{z}_{i,l}^j$  for each head to represent its group property, where  $i$  denotes the  $i$ -th head and  $j$  denotes the  $j$ -th group hidden unit.  $\mathbf{z}_{i,l}^j \in \hat{\mathbf{Z}}_l$ , where  $\hat{\mathbf{Z}}_l = \{\mathbf{z}_l^1,\dots,\mathbf{z}_l^C\}$  represents the hidden unit candidates, and the hidden units assigned to the heads are denoted as  $\mathbf{Z}_l = \{\mathbf{z}_{i,l},\dots,\mathbf{z}_{i,l}\}$ .
+
+$\mathbf{Z}_l$  is discovered by the HUDS  $\Omega$ :  $\mathbf{Z}_l = \Omega(\mathbf{E}_l)$ , where  $\mathbf{E}_l$  denotes either one of the  $\hat{\mathbf{V}}_l$ ,  $\mathbf{A}_l$ , or  $\mathbf{O}_l$ . Here  $\Omega(\cdot)$  is an unsupervised algorithm that divides the heads into  $C$  groups given their FMs, such as  $\mathrm{K}$ -means<sup>2</sup>:
+
+$$
+\Omega (\mathbf {E} _ {l}) = \arg \min _ {\mathbf {Z} _ {l}} \sum_ {i = 1} ^ {C} \sum_ {\mathbf {x} \in \hat {\mathbf {E}} _ {l} ^ {i}} | | \mathbf {x} - \boldsymbol {\mu} _ {i} | | ^ {2}, (3)
+$$
+
+where  $\hat{\mathbf{E}}_l^i$  is the set of feature maps of the  $i$ -th head group in the  $l$ -th attention layer. Then, the feature map groups of the  $l$ -th attention layer are denoted as  $\hat{\mathbf{E}}_l = \{\hat{\mathbf{E}}_l^1,\dots,\hat{\mathbf{E}}_l^i,\dots,\hat{\mathbf{E}}_l^C\}$ .  $\mu_i$  is the mean of the feature map vectors in  $\hat{\mathbf{E}}_l^i$ . The hidden units  $\mathbf{Z} = \{\mathbf{Z}_1,\dots,\mathbf{Z}_l\}$  are  $C$ -class categorical variables (Eq.4(A)) or continuous vectors (Eq.4(B)) to supervise the GCT. The objective of the self-supervised GCT is termed as:
+
+$$
+\begin{array}{l} L _ {z} (\mathbf {f}; \mathbf {A}, \hat {\mathbf {V}}, \mathbf {O}, \mathbf {Z}) = \\ \left\{ \begin{array}{l} - \frac {1}{k n} \alpha \sum_ {l = 1} ^ {n} \sum_ {i = 1} ^ {k} \log p _ {z} \left(\mathbf {z} _ {i, l} \mid \mathbf {v} _ {i, l}, \mathbf {a} _ {i, l}, \mathbf {o} _ {i, l}\right) + \\ \frac {1}{(C - 1) k n} \beta \sum_ {l = 1} ^ {n} \sum_ {i = 1} ^ {k} \sum_ {j _ {2} \neq j _ {1}} \log p _ {z} \left(\mathbf {z} _ {l} ^ {j _ {2}} \mid \mathbf {v} _ {i, l} ^ {j _ {1}}, \mathbf {a} _ {i, l} ^ {j _ {1}}, \mathbf {o} _ {i, l} ^ {j _ {1}}\right) \\ \frac {1}{k n} \alpha \sum_ {l = 1} ^ {n} \sum_ {i = 1} ^ {k} \varphi \left(\mathbf {v} _ {i, l}, \mathbf {a} _ {i, l}, \mathbf {o} _ {i, l}; \mathbf {z} _ {i, l}\right) - \\ \frac {1}{\binom {C} {2} n} \beta \sum_ {l = 1} ^ {n} \sum_ {j _ {1} = 1} ^ {C - 1} \sum_ {j _ {2} = j _ {1} + 1} ^ {C} \varphi \left(\mathbf {z} _ {l} ^ {j _ {1}}; \mathbf {z} _ {l} ^ {j _ {2}}\right) \end{array} \right. \tag {B4} \\ \end{array}
+$$
+
+Either when  $\mathbf{Z}$  are categorical variables (Eq.4(A)) or continuous vectors (Eq.4(B)), the objective is composed of a homogenization term and a diversification term $^3$ .  $\mathbf{v}_{i,l}^j$ ,  $\mathbf{a}_{i,l}^j$ , and  $\mathbf{o}_{i,l}^j$  denote the feature maps of the  $i$ -th head belonging to the  $j$ -th group.  $p_z(\mathbf{z}_{i,l}|\mathbf{v}_{i,l},\mathbf{a}_{i,l},\mathbf{o}_{i,l})$  denotes the predicted probability of the assigned group hidden variable  $\mathbf{z}_{i,l}$ , given  $\mathbf{v}_{i,l}$ ,  $\mathbf{a}_{i,l}$ , and  $\mathbf{o}_{i,l}$ .  $\varphi (\mathbf{x};\mathbf{y})$  denotes a cosine similarity measurement between  $\mathbf{x}$  and  $\mathbf{y}$  (following Li et al. (2018)).  $\varphi (\mathbf{v}_{i,l},\mathbf{a}_{i,l},\mathbf{o}_{i,l};\mathbf{z}_{i,l}) = \tau_1\varphi (\mathbf{v}_{i,l};\mathbf{z}_{i,l}) + \tau_2\varphi (\mathbf{a}_{i,l};\mathbf{z}_{i,l}) + \tau_3\varphi (\mathbf{o}_{i,l};\mathbf{z}_{i,l})$  where  $\tau$  is a coefficient, determined by the specific settings for each dataset & task. When  $\mathbf{Z}$  are categorical variables, the grouping is a classification task whose classification heads project the output into  $C$  classes; when  $\mathbf{Z}$  are continuous vectors, the grouping process is a metric learning task whose
+
+similarity computations are conducted between  $\mathbf{Z}$  and the projected FM representations. In both conditions, GHA is supervised by  $\mathbf{Z}$  to make the heads in the same group yield similar patterns, whereas those in different groups repulse from each other. The overall objective is given by  $L = L_{t} + L_{z}$ , where  $L_{t}$  is the task-specific objective.
+
+# 3.2 The Pillars of Strength
+
+Being consistent with Lottery Ticket hypothesis (Frankle and Carbin, 2019), we establish the GHT-PS from GHT as its subnetwork by removing redundant heads from GHA to achieve higher parameter efficiency. We propose the V2S procedure to find the Pillars of Strength (PS) heads that constitute the core of the GHA and remove other heads. We first describe the V2S roughly. In GHA, the heads within each group exhibit similar patterns upon the convergence of the Group-Constrained Training (GCT). Then, we only keep the heads with the most explicit group patterns (the PS heads), and switch off the other ones within the same group via V2S. The main idea of V2S is to vote on all heads of the GHA, and only retain one head for each group – the head receiving the most votes. Specifically, it takes an entire epoch to collect the layer-wise votes  $\mathbf{m}_l^b\in \{0,1\} ^k$  from the whole training set (each data batch  $b$  creates one layer-wise vote  $\mathbf{m}_l^b$  per attention layer), where  $k$  denotes the head number; 0 indicates that the corresponding head should be switched off and 1 indicates that a head is retained.
+
+We assume that there are  $B$  mini-batches in the training set. Then, each attention layer receives  $B$  layer-wise votes within which each head-wise vote is denoted by either 0 or 1. For each group, the head receiving the most '1's are assigned a '1' in the final head mask  $\mathbf{m}_l \in \{0,1\}^k$  for attention layer  $l$ , indicating that this head will be retained. Following Michel et al. (2019) and Voita et al. (2019), we mask out the output of heads as the equivalent operation of head removal<sup>4</sup>. The V2S procedure is outlined in Algorithm 1. We detail some of its definitions below. (1)  $\rho$  indicates the full convergence of GHT, i.e., the hidden units found by  $\Omega$  have a center shift less than a threshold. (2) In Step 7-9, given feature maps  $\hat{\mathbf{V}}_l$ ,  $\mathbf{A}_l$ , and  $\mathbf{O}_l$  of the  $l$ -th attention layer, the vote vectors  $\mathbf{m}_{l,v}^b$ ,  $\mathbf{m}_{l,a}^b$ , and  $\mathbf{m}_{l,o}^b \in \{0,1\}^k$  are determined by the group pattern scores  $\eta_{i,l}$  of each head, indicating the explicitness of group patterns.
+
+Algorithm 1 The Voting-to-Stay (V2S) algorithm  
+1: Procedure Voting-to-Stay(f,  $\hat{\mathbf{V}}$ , A, O, Z)  
+2: if satisfy  $\rho$ , and  $\mathbf{m}$  is none then  
+3: Start voting epoch; Freeze  $\mathbf{f}$ .  
+4:  $\Gamma_l \gets [ ]$ $\triangleright$  Creat  $\Gamma_l$  to store votes  
+5: for batch  $b$  in  $B$  training batches do  
+6: for layer  $l$  in  $L$  layers do  
+7: for  $\mathbf{E}_l$  in  $\{\hat{\mathbf{V}}_l, \mathbf{A}_l, \mathbf{O}_l\}$  do  
+8: Based on  $\eta_l = \{\eta_{1,l}, \dots, \eta_{1,k}\}$ ,  
+9: create  $\mathbf{m}_{l,v}^b$ ,  $\mathbf{m}_{l,a}^b$ ,  $\mathbf{m}_{l,o}^b$ .  
+10: Add  $\mathbf{m}_{l,v}^b$ ,  $\mathbf{m}_{l,a}^b$ ,  $\mathbf{m}_{l,o}^b$  to  $\Gamma_l$ .  
+11: for  $l$  in  $n$  do  $\triangleright$  Vote at each attn layer  
+12:  $\mathbf{m}_l \gets VOTE(\Gamma_l)$   
+13:  $\mathbf{m} \gets [\mathbf{m}_1, \dots, \mathbf{m}_n]$ $\triangleright$  Stack layer votes  
+14: Unfreeze  $\mathbf{f}$ ; end voting epoch.  
+15:  $\mathbf{f} = \mathbf{f} \odot \mathbf{m} \triangleright$  Mask GHT outputs with  $\mathbf{m}$
+
+We set the corresponding digit in the vote vectors as 1 for the head achieving the highest  $\eta_{i,l}$  in its group, indicating the most representative head of the group. Here  $\eta_{i,l} = p_z(\mathbf{z}_{i,l}|\mathbf{e}_{i,l})$  if  $\mathbf{z}$  is categorical; otherwise  $\eta_{i,l} = -\varphi (\mathbf{e}_{i,l};\mathbf{z}_{i,l})$ .  $\mathbf{e}_{i,l}$  denotes the  $i$ -th head feature map (either one of the  $\mathbf{v}_{i,l}$ ,  $\mathbf{a}_{i,l}$ , or  $\mathbf{o}_{i,l}$ ). (3) VOTE means counting the '1's for each head based on the  $0-1$  votes in  $\Gamma_l$  and only keeping the heads with the highest counts<sup>5</sup>. After V2S, a finetuning is applied to adapt the pruned network.
+
+GHT-PS compresses considerable parameters. In the case of two head groups, GHT-PS reduces  $75\%$  parameters for an attention layer and  $32.1\%$  for the entire model<sup>6</sup>. We will show that V2S removing non-PS heads does not sacrifice model performance. Instead, it brings accuracy gains in some cases and improves inference speed.
+
+# 4 Experimental Setup
+
+In this section, we detail the key architectural configurations. Further training, model, dataset & evaluation setups are detailed in A.1, A.2, & A.3. We follow the transformer of Vaswani et al. (2017) as a backbone architecture for all datasets and tasks in our experiments. Following Wu et al. (2019, 2020), for Machine Translation and Abstractive Summarization, we adopt the same 8-head encoder-decoder architecture with 6 layers for both encoder
+
+and decoder, where the model dimension  $d_{model} = 512$  and feed-forward dimension  $d_f = 2048$ . For LM, we adopt the 16-head decoder-only architecture with 16 layers, where the model dimension  $d_{model} = 1024$  and feed-forward dimension  $d_f = 4096$ . The layer normalization is applied before the residual connection of each layer. The parameters of decoder input and output projections are shared. Our models are based on fairseq (Ott et al., 2019) implementations.
+
+We perform the GCT as a metric learning task because it does not introduce additional projection layers when the shapes of similarity inputs are identical (Eq.4(B)), which makes GHT weight-lighter. In addition, it performs better in our experiments compared to the classification-based grouping.
+
+# 5 Results and Analysis
+
+# 5.1 Machine Translation
+
+Ours vs. vanilla transformer. We first report results by comparing GHT and GHT-PS with the vanilla transformer (Vaswani et al., 2017) which is the backbone of our model. As shown in Table 1, the models are compared at different parameter levels<sup>7</sup>. GHT does not have weight reduction, keeping the same parameter size as the vanilla transformer (44M, the same setting as transformer base (Vaswani et al., 2017)). In contrast, GHT-PS is compressed to 30M parameters via V2S. For a fair comparison, we first compare GHT-PS with two lite architectures, Transformer-Lite1 and Transformer-Lite2, whose parameter numbers are 30M as well. Keeping other settings unchanged, the encoder and decoder of Transformer-Lite1 are reduced to 4 layers, respectively. Transformer-Lite2 reduces the model dimension  $d_{model}$  to 424, and  $d_f$  to 1696.
+
+GHT and GHT-PS consistently and significantly outperform their backbone models at the same parameter level across all datasets. On average, the GHT surpasses 44M vanilla transformer by  $3.8\%$  in BLEU (Papineni et al., 2002); GHT-PS surpasses Lite1 and Lite2 by  $4.9\%$  and  $4.4\%$ , respectively. Although GHT-PS reduces  $32.1\%$  parameters, it significantly outperforms both 44M and 30M vanilla transformers, which is comparable to GHT on all datasets. It shows that V2S reduces the parameter size of the original transformer without sacrificing accuracy on MT. Efficiency is analyzed later.
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Param ↓</td><td rowspan="2">Inference Speed ↑</td><td rowspan="2">FLOPs ↓</td><td colspan="2">BLEU ↑</td><td colspan="3">IWSLT</td><td colspan="2">WMT</td></tr><tr><td>de-en</td><td>it-en</td><td>en-de</td><td>en-it</td><td>en-fr</td><td>en-de</td><td>en-fr</td></tr><tr><td>Vanilla Transformer</td><td>44M</td><td>1012.1 sent/s</td><td>1996M</td><td>34.4</td><td>32.3</td><td>28.0</td><td>30.8</td><td>40.1</td><td>27.3</td><td>38.1</td></tr><tr><td>GHT (ours)</td><td>44M</td><td>1016.4 sent/s</td><td>1996M</td><td>35.4</td><td>32.8</td><td>29.1</td><td>31.6</td><td>41.5</td><td>28.6</td><td>40.7</td></tr><tr><td>Transformer-Lite1</td><td>30M</td><td>1175.4 sent/s</td><td>1549M</td><td>33.8</td><td>31.9</td><td>27.9</td><td>29.3</td><td>39.9</td><td>26.9</td><td>37.7</td></tr><tr><td>Transformer-Lite2</td><td>30M</td><td>1108.7 sent/s</td><td>1465M</td><td>34.0</td><td>32.2</td><td>28.2</td><td>29.5</td><td>40.0</td><td>26.7</td><td>37.8</td></tr><tr><td>GHT-PS (ours)</td><td>30M</td><td>1122.1 sent/s</td><td>1558M</td><td>35.2</td><td>32.7</td><td>28.9</td><td>31.6</td><td>41.4</td><td>28.2</td><td>40.5</td></tr></table>
+
+Table 1: Benchmark with vanilla transformer (backbone) on IWSLT and WMT Machine Translation datasets, measured by BLEU. All improvements are statistically significant with  $p < 0.05$  under t-test.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Param ↓</td><td rowspan="2">Inference Speed ↑</td><td rowspan="2">FLOPs ↓</td><td colspan="2">BLEU ↑</td><td colspan="4">IWSLT</td><td colspan="2">WMT</td></tr><tr><td>de-en</td><td>it-en</td><td>en-de</td><td>en-it</td><td>en-fr</td><td>en-de</td><td>en-fr</td><td></td></tr><tr><td>Cordonnier et al. (2020)</td><td>44M</td><td>416.6 sent/s</td><td>2054M</td><td>34.4</td><td>31.8</td><td>28.2</td><td>31.0</td><td>40.7</td><td>27.6</td><td>38.5</td><td></td></tr><tr><td>Li et al. (2018)</td><td>44M</td><td>1011.2 sent/s</td><td>1996M</td><td>34.7</td><td>31.8</td><td>28.5</td><td>30.7</td><td>40.7</td><td>27.3</td><td>39.3</td><td></td></tr><tr><td>GHT (ours)</td><td>44M</td><td>1016.4 sent/s</td><td>1996M</td><td>35.4*</td><td>32.8*</td><td>29.1*</td><td>31.6*</td><td>41.5*</td><td>28.6*</td><td>40.7*</td><td></td></tr><tr><td>Voita et al. (2019)</td><td>30M</td><td>1099.1 sent/s</td><td>1558M</td><td>32.2</td><td>30.8</td><td>26.5</td><td>30.3</td><td>39.8</td><td>22.0</td><td>34.0</td><td></td></tr><tr><td>Li et al. (2021)</td><td>30M</td><td>1116.9 sent/s</td><td>1558M</td><td>33.2</td><td>31.3</td><td>27.5</td><td>30.0</td><td>39.7</td><td>20.5</td><td>33.6</td><td></td></tr><tr><td>Dynamic conv</td><td>30M</td><td>1050.2 sent/s</td><td>1615M</td><td>34.8</td><td>32.7</td><td>28.7</td><td>31.1</td><td>40.6</td><td>24.0</td><td>36.5</td><td></td></tr><tr><td>Lite Transformer</td><td>30M</td><td>1096.6 sent/s</td><td>1809M</td><td>33.3</td><td>31.4</td><td>27.5</td><td>29.8</td><td>39.4</td><td>24.9</td><td>37.4</td><td></td></tr><tr><td>GHT-PS (ours)</td><td>30M</td><td>1122.1 sent/s</td><td>1558M</td><td>35.2*</td><td>32.7</td><td>28.9*</td><td>31.6*</td><td>41.4*</td><td>28.2*</td><td>40.5*</td><td></td></tr></table>
+
+Ours vs. efficient attention models. We compare GHT with two state-of-the-art (SOTA) MHA redundancy optimization baselines. Cordonnier et al. (2020) and Li et al. (2018) are respectively homogenization- and diversification-based methods. In addition, we compare GHT-PS with four SOTA baselines that made major contributions to attention parameter compression and redundancy optimization $^{8}$ . Voita et al. (2019) and Li et al. (2021) are significance-based pruning methods. Dynamic Conv (Wu et al., 2019) and Lite Transformer (Wu et al., 2020) modify the MHA arch to reduce parameters.
+
+Table 2 shows that GHT outperforms all its baselines on all datasets, exceeding the strongest baseline by  $2.9\%$  in averaged BLEU scores. GHT-PS outperforms all its baselines on 6 out of 7 datasets, exceeding the strongest baseline by  $4.4\%$  on average. Model compression of the baselines may sacrifice performance (especially on large datasets, e.g., WMT en-de and en-fr), while GHT-PS is al
+
+most not affected by the parameter reduction, even surpassing GHT's baselines with 44M parameters.
+
+Table 2: Benchmark with state-of-the-art MHA redundancy/parameter optimization baselines on IWSLT and WMT Machine Translation datasets at the same parameter level, measured by BLEU. * denotes the improvement is statistical significant with  $p < 0.05$  under t-test.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="5">BLEU ↑</td></tr><tr><td>de-en</td><td>it-en</td><td>en-de</td><td>en-it</td><td>en-fr</td></tr><tr><td>GHT</td><td>35.4</td><td>32.8</td><td>29.1</td><td>31.6</td><td>41.5</td></tr><tr><td>- w/o Diversifying</td><td>34.7</td><td>31.8</td><td>28.5</td><td>30.7</td><td>40.7</td></tr><tr><td>- w/o Homologizing</td><td>34.3</td><td>32.0</td><td>28.2</td><td>30.9</td><td>40.2</td></tr><tr><td>GHT-PS</td><td>35.2</td><td>32.7</td><td>28.9</td><td>31.6</td><td>41.4</td></tr><tr><td>- w/o GCT</td><td>33.8</td><td>31.9</td><td>28.1</td><td>30.5</td><td>39.8</td></tr><tr><td>- w/o GC</td><td>34.0</td><td>32.0</td><td>28.4</td><td>31.0</td><td>40.2</td></tr><tr><td>- w/o HUDS</td><td>33.7</td><td>32.0</td><td>28.1</td><td>30.9</td><td>40.3</td></tr><tr><td>- w/o PS stay</td><td>33.6</td><td>31.7</td><td>27.9</td><td>30.7</td><td>40.2</td></tr><tr><td>- w/ stage 2 GC</td><td>33.2</td><td>31.8</td><td>28.1</td><td>30.8</td><td>40.3</td></tr><tr><td>- w/ stage 1&amp; 2 GC</td><td>33.4</td><td>31.9</td><td>27.7</td><td>30.6</td><td>40.2</td></tr></table>
+
+Table 3: Ablation study on IWSLT'14. The results are statistically significant with  $p < {0.05}$  under t-test.
+
+Ablation Study. We evaluate the impacts of the features we choose for GHT and GHT-PS (Table 3). We first ablate the diversification/homogenization term of GCT (see Eq.4), which lowers the BLEU scores. Next, we show the importance of GCT for V2S. w/o GCT denotes that we directly perform V2S at the very beginning without GCT. w/o GC
+
+![](images/04e0e7365c98ee4918f12804a9c6a27571bd80cb5840b46171fb905c7f66af6f.jpg)  
+Figure 2: The final BLEU scores achieved by GHT (on IWSLT'14 dev set) first rise and then drop, as the final group patterns become more compact (indicated by the increasing SC and DI scores).
+
+denotes that V2S is employed after normal training without Group Constrain (GC). Both ablation models yield lower BLEU, because they do not homogenize unnecessary heads and prepare them for pruning. Next, we validate the power of Pillars of Strength. w/o HUDS denotes we replace HUDS with randomly switching off heads after GCT; w/o PS stay denotes we keep random group members instead of the Pillars of Strength after GCT. We observe lower BLEU in w/o HUDS and w/o PS stay. Finally, we find that GC only needs to be added before V2S. We denote the training stages before and after V2S as stages 1 and 2. We compare the proposed Stage 1-based GHT-PS with models that perform GCT at Stage 2 (w/ stage 2 GC) and at both stages (w/ stage 1& 2 GC). BLEU scores of both ablation models decrease.
+
+Effect of group compactness. We hypothesize that more compact group patterns bring performance gains to the GHT. Figure 2 shows the correlation between the compactness of the final group patterns and the final BLEU scores GHT achieved on 5 IWSLT'14 development sets when the GHT is fully converged in GCT. One data point corresponds to an independent run. We choose Silhouette Coefficient (SC) (Rousseeuw, 1987) and Dunn's Index (DI) (Bezdek and Pal, 1995) as the measurements of group pattern compactness, both of which increase as the intra-group samples become more similar and the inter-group ones become more separated. The SC and DI are computed with the FMs of GHA (\$3.1) and controlled by tuning the  $\alpha$  and  $\beta$  (Eq.4).
+
+![](images/ee9a92e2e14da481b38214ec5072ce84f48217b9f79495eae9409178168c1ac0.jpg)  
+Figure 3: The BLEUs of GHT and GHT-PS by different numbers of hidden units (groups) on IWSLT'14 dev set.
+
+Figure 2 shows that, within the normal range, the BLEU scores rise with higher SC/DI scores, which is in line with our assumption. The BLEUs start to drop after the peak as the SC/DI scores increase, because the very heavy group constraint prohibits the model from learning useful task-specific knowledge.
+
+Effect of group number. Figure 3 shows the performance trends of 16-head GHT and GHT-PS by different numbers of group hidden units. For GHT, different datasets have different optimal hidden unit quantities, while a similar trend is observed. The optimal group number is between 2 and 8, which is in line with the claim that our group strategy is superior to sole homogenization (1 group) or diversification (16 groups) strategies. For GHT-PS, when the group number is larger than 1, it shows comparable performance to GHT on most datasets. This also verifies that non-PS heads can be switched off without sacrificing performance.
+
+![](images/d7065dfc3e9c03a6f870e5fb8909cd27d26b8d13955eef70ea7654ee5ba8fc50.jpg)  
+Figure 4: Intra-group homogeneity (upper) and intergroup diversity (lower) of GHT and vanilla transformer by training steps.
+
+<table><tr><td>Model</td><td>Param ↓</td><td>Inference Speed ↑</td><td>FLOPs ↓</td><td>Rouge-1 ↑</td><td>Rouge-2 ↑</td><td>Rouge-L ↑</td></tr><tr><td>LSTM (Paulus et al., 2018)</td><td>-</td><td>-</td><td>-</td><td>38.30</td><td>14.81</td><td>35.49</td></tr><tr><td>CNN (Fan et al., 2018)</td><td>-</td><td>-</td><td>-</td><td>39.06</td><td>15.38</td><td>35.77</td></tr><tr><td>Light Conv (Wu et al., 2019)</td><td>86M</td><td>-</td><td>-</td><td>39.52</td><td>15.97</td><td>36.51</td></tr><tr><td>Dynamic Conv (Wu et al., 2019)</td><td>87M</td><td>-</td><td>-</td><td>39.84</td><td>16.25</td><td>36.73</td></tr><tr><td>Vanilla Transformer (Voita et al., 2019)</td><td>44M</td><td>208.77 sent/s</td><td>1996M</td><td>38.45</td><td>17.97</td><td>36.03</td></tr><tr><td>GHT (ours)</td><td>44M</td><td>208.77 sent/s</td><td>1996M</td><td>40.00</td><td>21.10</td><td>37.51</td></tr><tr><td>GHT-PS (ours)</td><td>30M</td><td>257.62 sent/s</td><td>1558M</td><td>40.01</td><td>21.31</td><td>37.62</td></tr></table>
+
+Group pattern trends. Figure 4 shows the trends of intra-group homogeneity (given by the  $1st$  term of Eq.4(B)) and inter-group diversity (given by the  $2nd$  term of Eq.4(B)) of GHT and vanilla transformer in the training process on five IWSLT datasets. By training, GHT yields higher intra-group homogeneity and inter-group diversity absolute values, leading to more compact groups, while the vanilla transformer shows flattened trends. It shows that GCT can effectively homogenize intra-group heads and diversify inter-group heads.
+
+Table 4: Abstractive Summarization results on CNN-DailyMail in terms of F1-Rouge and efficiency (parameter, inference speed, and FLOPs). All improvements are statistically significant with  $p < 0.05$  under t-test.  
+
+<table><tr><td>Model</td><td>BLEU↑</td><td>Param↓</td><td>Infer Speed↑</td><td>FLOPs↓</td></tr><tr><td>Transformer base</td><td>25.8</td><td>44M</td><td>1016.4 sent/s</td><td>1996M</td></tr><tr><td>Transformer big</td><td>26.4</td><td>176M</td><td>707.1 sent/s</td><td>6635M</td></tr><tr><td>Lite Conv</td><td>26.6</td><td>166M</td><td>722.1 sent/s</td><td>6184M</td></tr><tr><td>Dynamic Conv</td><td>26.9</td><td>176M</td><td>710.0 sent/s</td><td>6315M</td></tr><tr><td>GHT-PS-LITE (ours)</td><td>26.6</td><td>16M</td><td>1170.2 sent/s</td><td>1181M</td></tr></table>
+
+Efficiency analysis. In Tables 1 and 2, the efficiency metrics are controlled to be identical. Our models with higher inference speed and lower FLOPs show efficiency by culling redundant parameters. We also compare the efficiency metrics by controlling BLEU scores. In Table 5, we select models from the works in Table 1 and 2 that are reported to achieve close BLEU scores on new-stest2013 as the baselines. The GHT-PS-LITE is a light version of GHT-PS that has a  $d_{f}$  of 1024. Given BLEU ranges from 25.8 to 26.9, GHT-PS-LITE is much more efficient than the baselines. Noticeably, GHT-PS-LITE achieves  $90.36\%$  fewer parameters,  $62.05\%$  faster inference speed, and  $80.90\%$  fewer FLOPs against Lite Conv which yields the same BLEU as it.
+
+# 5.2 Abstractive Summarization
+
+We evaluate the ability of our model to process longer inputs via Abstractive Summarization on the CNN-DailyMail dataset. We take vanilla transformer as the backbone. Table 4 shows that both GHT and GHT-PS achieve higher F1-Rouge scores (Lin, 2004a) on this task. GHT-PS achieves  $4.1\%$  higher Rouge-1,  $18.6\%$  higher Rouge-2, and  $4.4\%$  higher Rouge-L against vanilla transformer. It also achieves  $0.4\%$  higher Rouge-1,  $31.1\%$  higher Rouge-2 and  $2.4\%$  higher Rouge-L against the best-performing baseline (Dynamic Conv). Meanwhile, GHT-PS only takes  $68.18\%$  parameters of the vanilla transformer and exhibits higher inference speed and fewer FLOPs.
+
+Table 5: Efficiency comparison by parameter, inference speed (averaged on five runs), and FLOPs. All results are generated with beam size 5, batch size 256, max decoding length 10 on a NVIDIA Quadro RTX A6000.  
+
+<table><tr><td>Model</td><td>Param↓</td><td>Infer Spd↑</td><td>FLOPs↓</td><td>Valid↓</td><td>Test↓</td></tr><tr><td>S4</td><td>249M</td><td>-</td><td>-</td><td>19.69</td><td>20.95</td></tr><tr><td>BERT-L-CAS</td><td>395M</td><td>-</td><td>-</td><td>19.67</td><td>20.42</td></tr><tr><td>GPT-2 Large</td><td>762M</td><td>-</td><td>-</td><td>-</td><td>22.05</td></tr><tr><td>VT w/ AI</td><td>201M</td><td>9.9 tok/s</td><td>6106M</td><td>19.03</td><td>19.14</td></tr><tr><td>GHT (ours)</td><td>201M</td><td>9.9 tok/s</td><td>6106M</td><td>18.57</td><td>18.60</td></tr><tr><td>GHT-PS (ours)</td><td>167M</td><td>19.0 tok/s</td><td>4573M</td><td>18.58</td><td>18.59</td></tr></table>
+
+Table 6: Language modeling results on WIKITEXT-103 by perplexity and efficiency (parameter, inference speed, and FLOPs). VT w/ AI denotes vanilla transformer with adaptive input. All improvements against the baselines are statistically significant with  $p < 0.05$  under t-test.
+
+# 5.3 Language Modeling
+
+We evaluate LM performance on WIKITTEXT-103 dataset. The backbone is a decoder-only transformer with 16 layers and adaptive inputs (Baevski and Auli, 2019). We compare with the backbone model, as well as comparable SOTA LM models, including S4 (Gu et al., 2022), BERT-Large-CAS (Wang et al., 2019), and GPT-2 Large (Radford et al., 2018).
+
+Table 6 shows that both GHT and GHT-PS achieve lower perplexity (Vajapeyam, 2014) than the baselines on both validation and test sets (2.9% and 9.0% less perplexity against the backbone and the best performing LM baseline, respectively). Meanwhile, GHT-PS achieves 16.92% parameter reduction, 2 times faster inference speed, and 75% FLOPs compared with the backbone.
+
+# 6 Conclusion
+
+In this paper, we assume that only focusing on the most representative and distinctive features with minimum resources may mitigate the redundancy and over-parameterization issues of MHA. Accordingly, we propose a divide-and-conquer strategy, including GCT and V2S to mitigate the issues. The improvements on three tasks and the extensive analysis verify our hypothesis and the effectiveness of our redundancy optimization methods. Our study may inspire future MHA design and training to achieve higher accuracy and efficiency.
+
+# Limitations
+
+In this work, we evaluate the proposed models for NLP tasks only. However, tasks in other fields such as Computer Vision may present a very different input inductive bias, thus affecting the performance. Moreover, our models are trained from scratch, hence it is unknown whether the same divide-and-conquer strategy works for pre-trained models. We will study these limitations in the future to give a more extensive exploration.
+
+# Ethics Statement
+
+This article follows the ACL Code of Ethics. The annotations are based on public datasets that do not contain private data. The algorithm we developed is an architectural optimization technique for improving model performance. To our best knowledge, there are no foreseeable potential risks to using this technique.
+
+# Acknowledgments
+
+This research is supported by the Agency for Science, Technology and Research (A\*STAR) under its AME Programmatic Funding Scheme (Project #A18A2b0046).
+
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+
+# A Appendix
+
+# A.1 Trainig Settings
+
+# A.1.1 Machine Translation
+
+We use Adam to optimize the MT models and set the  $\beta_{1} = 0.9, \beta_{2} = 0.98$ . We use the Inverse Square Root Schedule (Vaswani et al., 2017) where it first warms up for 4K steps until the learning rate reaches  $5 \times 10^{-4}$ , and then it exponentially decays the learning rate. We apply early stop as a termination condition. We apply a 0.3 dropout rate for all Machine Translation models. A weight decay of  $10^{-4}$  is used for all IWSLT 2014 models, whereas for WMT models we use a weight decay of 0. We apply a 0.1 label smoothing (Szegedy et al., 2016; Pereyra et al., 2017) for the uniform prior distribution over the vocabulary.
+
+# A.1.2 Language Modeling
+
+Following Baevski and Auli (2019), we use Nesterov's accelerated gradient method (Sutskever et al., 2013) with a momentum of 0.99. We clip the gradient norm if it exceeds 0.1 (Pascanu et al., 2013). The learning rate is linearly warmed up from  $10^{-7}$  to 1 for 16K steps and then annealed using a cosine learning rate schedule (Loshchilov and Hutter, 2017) with multiple cycles. Each cycle doubles the number of updates than the previous cycle and we shrink the maximum and minimum learning rates by 0.75 compared to the previous cycle. The initial minimum learning rate is  $10^{-4}$  and the maximum is 1. We apply 0.2 adaptive softmax dropout rate, 0.1 attention dropout rate, and 0.1 activation dropout rate.
+
+# A.1.3 Abstractive Summarization
+
+We use the same training setup with IWSLT 2014 models. We apply 0.1 clip norm and 0.2 attention dropout. The model is warmed up for 10K updates.
+
+# A.2 Further Model Settings
+
+Different  $\alpha$ ,  $\beta$ , and head feature maps ( $\hat{\mathbf{V}}$ ,  $\mathbf{A}$ , and  $\mathbf{O}$ ) are preferred for different datasets to achieve optimal performance. The Machine Translation configurations are detailed in Table 7; Language Modeling and Abstractive Summarization configurations are detailed in Table 8.
+
+Note that  $\varphi (\mathbf{v}_{i,l},\mathbf{a}_{i,l},\mathbf{o}_{i,l};\mathbf{z}_{i,l}) = \tau_1\varphi (\mathbf{v}_{i,l};\mathbf{z}_{i,l}) + \tau_2\varphi (\mathbf{a}_{i,l};\mathbf{z}_{i,l}) + \tau_3\varphi (\mathbf{o}_{i,l};\mathbf{z}_{i,l})$  , we set one of the  $\{\tau_1,\tau_2,\tau_3\}$  to be 1, the other to be O.
+
+# A.3 Datasets and Evaluation<sup>9</sup>
+
+# A.3.1 Efficiency Metrics settings
+
+Inference speed. All inference speed results are generated with beam size 5, batch size 256, maximum decoding length 10 on a single NVIDIA Quadro RTX A6000.
+
+FLOPs. We use the  $\mathrm{fvcore}^{10}$  to calculate the FLOPs, with a fixed input length of 30.
+
+# A.3.2 Machine Translation
+
+To fully evaluate the effectiveness of our methods, we evaluate seven MT datasets of IWSLT'14 and WMT 2014 benchmarks. We closely follow the setup of Vaswani et al. (2017) for data preparation. WMT 2014 English-German dataset consists of about 4.5M sentence pairs. It is encoded with byte-pair encoding (Britz et al., 2017), having a shared source-target vocabulary of about 40K tokens. Following the standard setting (Vaswani et al., 2017), we validate on newstest2013 and test on newstest2014 for experiments on this dataset. The WMT 2014 English-French dataset consists of 36M sentence pairs and is encoded with a joint source-target BPE of about 43K vocabularies. Following the standard split, we validate on a concatenation of newstest2012 and newstest2013 and test on newstest2014. For IWSLT'14 German to English, IWSLT'14 English to German, IWSLT'14 English to French, IWSLT'14 English to Italian and IWSLT'14 Italian to English, we encode the sentence pairs with joint source-target BPE. Following Edunov et al. (2018), the validation set is randomly splited from the training set with a ratio of 1:23. The testset consists TED.tst2010, TED.tst2011, TED.tst2012 and TED.dev2010, TEDX.dev2012 for IWSLT'14 German to English, IWSLT'14 English to German, and IWSLT'14 English to French; the TEDX.dev2012 is replaced by TEDX.dev2014 for IWSLT'14 English to Italian and IWSLT'14 Italian to English.
+
+For all Machine Translation datasets, we use detokenized BLEU. WMT 2014 English-German and WMT 2014 English-French are evaluated with a beam size 4 and length penalty 0.6; IWSLT'14 datasets are evaluated with a beam size 5 and without length penalty.
+
+<table><tr><td rowspan="2">Model</td><td colspan="5">IWSLT (α/β/FM)</td><td colspan="2">WMT (α/β/FM)</td></tr><tr><td>de-en</td><td>it-en</td><td>en-de</td><td>en-it</td><td>en-fr</td><td>en-de</td><td>en-fr</td></tr><tr><td>GHT</td><td>0.7/0.5/√V</td><td>0.3/0.5/√V</td><td>0.3/0.1/A</td><td>0.3/0.3/√V</td><td>0.7/0.7/√V</td><td>0.5/0.5/√V</td><td>0.3/0.3/√V</td></tr><tr><td>GHT-PS</td><td>0.5/0.7/O</td><td>0.3/0.3/A</td><td>0.3/0.7/O</td><td>0.3/1/√V</td><td>0.5/0.3/A</td><td>0.5/0.5/√V</td><td>0.3/0.3/√V</td></tr></table>
+
+Table 7: The configuration of  $\alpha ,\beta$  ,and Feature Maps (FM,including  $\widehat{\mathbf{V}}$  ,A,and  $\mathbf{O}$  ) for GHT and GHT-PS on different Machine Translation datasets.  
+
+<table><tr><td>Model</td><td>α/β/FM</td></tr><tr><td>GHT</td><td>0.5/0.5/ˆV</td></tr><tr><td>GHT-PS</td><td>0.5/0.5/ˆV</td></tr></table>
+
+Table 8: The configuration of  $\alpha$ ,  $\beta$ , and Feature Maps (FM, including  $\hat{\mathbf{V}}$ , A, and O) for GHT and GHT-PS in Abstractive Summarization and Language Modeling.
+
+# A.3.3 Language Modeling
+
+We evaluate LM on WIKITEXT-103 (Merit et al., 2017) which has about 100M tokens and a 260K BPE vocabulary. Following Baevski and Auli (2019), we use perplexity as an evaluation metric and a context window of 2047 at the inference stage.
+
+# A.3.4 Abstractive Summarization
+
+We also evaluate on CNN-DailyMail (Hermann et al., 2015) for AS to test the ability of GHT in hard tasks with long inputs. The dataset comprises over 280K news articles paired with multi-sentence summaries. Following Wu et al. (2019), articles are truncated to 512 tokens and encoded with 50K BPE. We use F1-Rouge (Lin, 2004b) to evaluate the performance, including Rouge-1, Rouge-2 and Rouge-L.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work?
+
+Section 7
+
+A2. Did you discuss any potential risks of your work?
+
+The study is theoretical. It does not involve human in the experiment or involve ethnic issues. It will not result in any potential risks.
+
+A3. Do the abstract and introduction summarize the paper's main claims?
+
+Section 1
+
+A4. Have you used AI writing assistants when working on this paper?
+
+Left blank.
+
+B Did you use or create scientific artifacts?
+
+Section 4; Appendix A.3
+
+B1. Did you cite the creators of artifacts you used?
+
+Section 4; Appendix A.3
+
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts?
+
+The tools are for public use.
+
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)?
+
+No specific intended use is specified by the artifact creators.
+
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it?
+
+They do not contain any information that names or uniquely identifies individual people or offensive content.
+
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.?
+
+Section 4; Appendix A.3
+
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.
+
+Appendix A.3
+
+C Did you run computational experiments?
+
+Section 5
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?
+
+Section 5; Appendix A.1
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?
+
+Section 4, 5; Appendix A.1, 2, 3
+
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+Section 5
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+Appendix A.1, 2, 3
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?
+
+Not applicable. Left blank.
+
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+Not applicable. Left blank.
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+Not applicable. Left blank.
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board?
+
+Not applicable. Left blank.
+
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+Not applicable. Left blank.

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+        "text": "Finding the SWEET Spot: Analysis and Improvement of Adaptive Inference in Low Resource Settings",
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+        "text": "Daniel Rotem $^{\\text{♥}}$  Michael Hassid $^{\\text{♥}}$  Jonathan Mamou $^{\\text{♣}}$  Roy Schwartz $^{\\text{♥}}$",
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+        "text": "{daniel.rotem, michael.hassid, roy.schwartz1}@mail.huji.ac.il jonathan.mamou@intel.com",
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+        "text": "Adaptive inference is a simple method for reducing inference costs. The method works by maintaining multiple classifiers of different capacities, and allocating resources to each test instance according to its difficulty. In this work, we compare the two main approaches for adaptive inference, Early-Exit and Multi-Model, when training data is limited. First, we observe that for models with the same architecture and size, individual Multi-Model classifiers outperform their Early-Exit counterparts by an average of  $2.3\\%$ . We show that this gap is caused by Early-Exit classifiers sharing model parameters during training, resulting in conflicting gradient updates of model weights. We find that despite this gap, Early-Exit still provides a better speed-accuracy trade-off due to the overhead of the Multi-Model approach. To address these issues, we propose SWEET, an Early-Exit fine-tuning method that assigns each classifier its own set of unique model weights, not updated by other classifiers. We compare SWEET's speed-accuracy curve to standard Early-Exit and Multi-Model baselines and find that it outperforms both methods at fast speeds while maintaining comparable scores to Early-Exit at slow speeds. Moreover, SWEET individual classifiers outperform Early-Exit ones by  $1.1\\%$  on average. SWEET enjoys the benefits of both methods, paving the way for further reduction of inference costs in NLP. We publicly release our code.",
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+        "text": "1 Introduction",
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+        "text": "Pre-trained Transformer-based language models such as BERT (Devlin et al., 2019), DeBERTa (He et al., 2020), and GPT3 (Brown et al., 2020) have become the go-to tool in NLP. Although powerful, the growing size of these models has been a major drawback (Thompson et al., 2020; Schwartz et al.,",
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+        "image_caption": [
+            "Figure 1: Illustration of the adaptive inference approaches compared in this work. In both methods, multiple classifiers of increasing sizes are run serially, until a confident prediction is made. In Early-Exit (left), a single model with multiple classifiers is used, such that early computations are reused by later classifiers. In Multi-Model (right), a sequence of independent models is used, allowing each classifier to decouple its parameters from other classifiers."
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+        "text": "2020a), making them costly to run. Various attempts to reduce inference cost have been proposed, including distillation (Hinton et al., 2015), pruning (LeCun et al., 1989) and quantization (Courbariaux et al., 2014). This work focuses on adaptive inference (Graves, 2016; Liu et al., 2020), a recent approach in which the variability of sample difficulty is leveraged toward a smarter allocation of computational resources. An appealing property of adaptive inference is that it enables dynamic control of the speed-accuracy trade-off.",
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+        "text": "There are two main approaches to adaptive inference, both using a set of classifiers of different sizes. In Early-Exit (Schwartz et al., 2020b; Xin et al., 2020), multiple classification heads are added to the same model at different layers, allowing for early exit during inference (Fig. 1, left). Another approach (henceforth Multi-Model) is to apply multiple independent classifiers of varying capacities serially until a prediction is made (Varshney and",
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+        "text": "$^{1}$ Separating Weights in Early Exit Transformers.",
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+        "text": "$^{2}$ https://github.com/schwartz-lab-NLP/SWEET",
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+        "text": "Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics",
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+        "text": "Baral, 2022a; Li et al., 2020, Fig. 1, right). These approaches have complementary benefits; Multi-Model allows for easier batching at inference time, and potentially larger savings due to using very efficient models (Mamou et al., 2023). Early-Exit on the other hand is more memory efficient, faster to train, and enables re-use of early computation if an early exit was not taken.",
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+        "text": "In this work, we compare the speed-accuracy behavior of the two approaches when training data is limited. We first observe that Early-Exit model weights are updated by multiple conflicting gradient signals throughout the training process (Fig. 2, left). We show that this leads to a decrease in performance of individual Early-Exit classifiers compared to Multi-Model ones (2.3% gap on average). We find that this gap is higher for the earliest classifiers (5.2% on average) than for later ones (1.4%).",
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+        "type": "text",
+        "text": "We also find that while each Multi-Model classifier outperforms its Early-Exit counterpart, it does not translate to an overall better speed-accuracy trade-off. Instead, we find that each method dominates performance in a different region: Multi-Model outperforms Early-Exit at fast inference speeds, while Early-Exit is better at slow speeds. Multi-Model downgraded scores at slow speeds are likely caused by the overhead of running models sequentially to predict hard samples.",
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+        "type": "text",
+        "text": "Inspired by our findings, we present SWEET, $^{4}$  an Early-Exit method for bridging the performance gap between standard Early-Exit and Multi-Model. In SWEET, each Early-Exit classifier only updates the parameters of layers preceding it up to the previous classifier. This way, each model parameter is updated by a single classifier, thus avoiding conflicting gradients during the training of Early-Exit models (Fig. 2, right).",
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+        "text": "We experiment with two established pretrained models: BERT (Devlin et al., 2019) and DeBERTa (He et al., 2020). We fine-tune Early-Exit models using SWEET on seven text classification tasks from GLUE (Wang et al., 2018) and compare them to Early-Exit and Multi-Model baselines. The speed-accuracy curve of SWEET dominates both baselines at fast speeds for 21 out of 28 experiments conducted. As for individual clas",
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+        "image_caption": [
+            "Figure 2: Left: standard Early-Exit fine-tuning, where lower layers get gradient updates from multiple classifiers. Right: our SWEET method, in which each layer parameters are updated only by the next classifier."
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+        "text": "sifiers, SWEET performs  $1.1\\%$  better on average than Early-Exit, mostly improving earlier classifiers, where conflicting gradients are more dominant.",
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+        "type": "text",
+        "text": "We summarise our main contributions: (1) We propose a way of measuring conflicting gradients, and show that they exist in Early-Exit training process; (2) We empirically compare Early-Exit and Multi-Model classifiers and show that conflicting gradients lead to individual Early-Exit classifiers being less accurate; (3) We propose a novel finetuning method, SWEET, which alleviates the conflicting gradients problem in Early-Exit, and leads to improved results at fast inference speeds; (4) We publicly release our code.",
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+        "text": "2 Background: Adaptive Inference",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Adaptive inference aims to reduce inference costs of deep neural nets by matching model and sample complexities. Sample difficulty usually varies in real-world data, meaning not all instances require processing by the most powerful classifier. Therefore, we can allocate fewer resources to easier instances, and reduce the average inference cost, potentially at the cost of performance degradation.",
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+        "text": "<sup>5</sup>https://github.com/schwartz-lab-NLP/SWEET",
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+        "text": "$^{3}$ Reducing inference costs is particularly helpful when computational resources are limited. Such conditions are often paired with restricted access to labeled data or a low budget for data annotation. To evaluate the effectiveness of adaptive inference methods in such scenarios, we limit training data size to a few thousand examples in all our experiments.",
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+    {
+        "type": "page_footnote",
+        "text": "4 Separating Weights for Early-Exit Transformers.",
+        "bbox": [
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+        "page_idx": 1
+    },
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+        "text": "14837",
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+    {
+        "type": "text",
+        "text": "Several exit strategies have been developed to control the speed-accuracy trade-off of a model by deciding when to make an early prediction and halt computation (Xin et al., 2020; Zhou et al., 2020; Xin et al., 2021; Schuster et al., 2021; Zhang et al., 2022). In this work, we mainly experiment with confidence-based exiting (Schwartz et al., 2020b), in which computation halts if the softmax probability assigned to a given label exceeds a predetermined threshold. Dynamic control of model's inference speed is gained through setting different threshold values. There are two main adaptive inference approaches, Early-Exit and Multi-Model, which we describe below.",
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+        "type": "text",
+        "text": "Early-Exit Early-Exit models are deep neural nets with multiple output points, following intermediate layers. In this work, we focus on Early-Exit implementation as presented in Schwartz et al. (2020b). During fine-tuning, instances are passed through the model, and a loss is calculated based on predictions made by all classifiers. This leads to some model weights being updated by gradient signals from multiple classifiers (Fig. 2, left).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "At inference time, an instance is passed through the model and its label is predicted sequentially until a decision to exit early is taken, and computation is halted. An appealing property of Early-Exit is that it allows for efficient re-use of previous computation from lower layers in higher classifiers. However, this means that some model parameters are updated by multiple classifiers, which may lead to sub-optimal performance of individual classifiers due to conflicting gradients. In this work, we study the effect of this property on Early-Exit models.",
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+    {
+        "type": "text",
+        "text": "Multi-Model In Multi-Model adaptive inference, a set of independent models of increasing capacity are fine-tuned separately for the same task. At inference time, the models are used sequentially from smallest to largest until a prediction meets some predetermined criterion or until the largest model has been used. This method is more robust than Early-Exit, being easier to extend and enabling the use of different architectures. Additionally, Multi-Model potentially allows for further computational savings by using models smaller than the smallest Early-Exit model (a single layer of the backbone",
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+    {
+        "type": "text",
+        "text": "model, Mamou et al., 2023). However, it may add overhead to the prediction time of hard instances, as those pass through multiple models with early computations being discarded, bringing the total runtime to exceed that of using the largest model.",
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+    {
+        "type": "text",
+        "text": "3 Early-Exit vs. Multi-Model",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 Conflicting Gradients in Early-Exit",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Unlike Multi-Model, when fine-tuning Early-Exit models, model weights are updated by multiple gradient signals, originating in different classification layers (Fig. 2, left). We hypothesize that this leads to sub-optimal performance for all classifiers involved, as gradient signals might conflict with one another and derail the classifiers from their goal. To test this hypothesis, we compare the gradient similarity of different Early-Exit classifiers.",
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+    {
+        "type": "text",
+        "text": "We fine-tune a  $\\mathrm{BERT}_{BASE}$  model with four exit points (following layers [1, 4, 6, 12]) for 400 training steps on the MNLI dataset (Williams et al., 2018), using a batch size of 16 with a learning rate of 2e-5. We pass a new training batch through the model, and inspect the gradients with respect to the last feed-forward matrix in each layer preceding a classifier. To measure the degree of alignment between gradient updates of different classifiers, we average the cosine similarity between the rows of gradient matrices for every pair of classifiers. High similarity indicates that the classifiers are updating the weights in a similar direction, while low similarity (in absolute values) suggests that the updates are close to orthogonal and potentially detrimental to both classifiers.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This section studies the strengths and weaknesses of both adaptive inference approaches. We start by describing a limitation of Early-Exit approaches: lower model layers are updated by conflicting gradient signals during training. We show that this leads to inferior performance of individual Early-Exit classifiers compared to corresponding Multi-Model classifiers. We then compare the effects of these performance drops on the speed-accuracy curve of Early-Exit models compared Multi-Model ones.",
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+    {
+        "type": "text",
+        "text": "Fig. 3 shows that the gradients of future classifiers are generally orthogonal to those of the current classifier for each examined Transformer block. This indicates that model weights indeed suffer",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>6</sup>Some works have pre-trained Early-Exit Models from scratch (Liu et al., 2021b) but due to budgetary constraints, it is common practice to fine-tune pre-trained models with the added classifiers on the downstream task (Liu et al., 2020; Xin et al., 2020; Schwartz et al., 2020b).",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>7</sup>We repeat this experiment with an additional batch. Results (Appendix B) show a very similar trend.",
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+    {
+        "type": "page_footnote",
+        "text": "Except for the last layer, updated by a single classifier.",
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+    {
+        "type": "page_number",
+        "text": "14838",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/c7d4a0182aafd37e17a3bc56755485f6155ae2af38b76d8ba4d12fac619246e3.jpg",
+        "image_caption": [
+            "Figure 3: Average cosine similarity between classifiers' gradient updates of model layers. C-i stands for Classifier  $i$ . Layer 1 (preceding C-1) is updated by 3 classifiers, while layers 4 (preceding C-2), and 6 (C-3) are updated by 3 & 2 classifiers respectively. For each layer, the gradient update of the following classifier is roughly orthogonal to those of future classifiers, whereas gradient updates of higher classifiers tend to better align with one another."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "from conflicting gradient updates during the training process, which might affect the performance of each individual classifier. Interestingly, when multiple future classifiers are present, they tend to align with each other, as indicated by the relatively high similarity between layer 1's gradient updates originating in classifiers 2, 3, and 4, and between layer 4's gradient updates from classifiers 3 and 4.",
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+    {
+        "type": "text",
+        "text": "3.2 Effects of Conflicting Gradients",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To evaluate the effect of conflicting gradients on individual Early-Exit classifiers, we compare the different classifiers of an Early-Exit model and a Multi-Model model. For a clean comparison, we use the same backbone model, exit points, hyperparameters, $^{9}$  and random seeds. As an example, for a given 12-layer Transformer model, an Early-Exit model with exit points following layers [4, 12] would be compared to a Multi-Model one consisting of two classifiers: the first four layers fit with a classification head, and a full (12 layer) model. The models differ only in the fact that for the Early-Exit model, model weights are updated by multiple future classifiers during the fine-tuning process, while each Multi-Model classifier is an independent model. To isolate the effect of conflicting gradients",
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+    {
+        "type": "table",
+        "img_path": "images/d1dcc21000b014b4408a02bdc867f3c939edef4c3f34f7e53ef17e54d1ac4477.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Size</td><td>Method</td><td colspan=\"4\">Exit Layer</td></tr><tr><td></td><td></td><td>1</td><td>4</td><td>6</td><td>12</td></tr><tr><td rowspan=\"3\">BASE</td><td>MM</td><td>60.90.6</td><td>71.40.1</td><td>74.71.2</td><td>79.90.9</td></tr><tr><td>EE</td><td>57.30.3</td><td>70.30.3</td><td>74.40.7</td><td>78.70.5</td></tr><tr><td>SWEET</td><td>60.90.5</td><td>71.60.5</td><td>74.00.4</td><td>77.40.6</td></tr><tr><td></td><td></td><td>1</td><td>6</td><td>12</td><td>24</td></tr><tr><td rowspan=\"3\">LARGE</td><td>MM</td><td>60.10.1</td><td>66.90.4</td><td>74.40.9</td><td>81.60.3</td></tr><tr><td>EE</td><td>56.60.3</td><td>65.60.9</td><td>74.00.6</td><td>79.91.9</td></tr><tr><td>SWEET</td><td>59.80.3</td><td>66.50.7</td><td>74.50.3</td><td>81.31.0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: Results of individual classification layers averaged across all tasks using BERT as a backbone model. Multi-Model (MM) classifiers outperform their Early-Exit (EE) counterparts, with the gap being the largest for early classifiers. SWEET closes much of this gap, especially for early classifiers. Standard deviation (across random seeds) is reported in subscript. Results for DeBERTa are presented in Table 3.",
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+    },
+    {
+        "type": "text",
+        "text": "on the classifiers, we evaluate each one separately on the entire validation set. The performance gap between each individual Multi-Model classifier and its corresponding Early-Exit classifier, allows us to directly measure the latter's downgrade in performance caused by conflicting gradients.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We experiment with BERT and DeBERTa {BASE ( $\\sim$ 110M parameters), and LARGE ( $\\sim$ 350M parameters)}. For BASE versions, we install classifiers following layers [1, 4, 6, 12]. For LARGE versions, we use layers [1, 6, 12, 24]. We fine-tune an Early-Exit model and a corresponding Multi-Model model on seven NLP tasks from the GLUE benchmark (Wang et al., 2019): SST-2 (Socher et al., 2013), MRPC (Dolan and Brockett, 2005), RTE (Dagan et al., 2006; Haim et al., 2006; Giampiccolo et al., 2007; Bentivogli et al., 2009), CoLA (Warstadt et al., 2019), MNLI (Williams et al., 2018), QNLI (Rajpurkar et al., 2016), and QQP (Iyer et al., 2016). We report accuracy for all tasks except for CoLA (Matthews corr.). We fine-tune the models for two epochs on all tasks. As our goal is to test Adaptive inference in a low resource setting, we limit the training set size for each task to  $6K$ . We report the mean validation scores and standard deviation across three random seeds. Other hyper-parameters are listed in Appendix A.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>10</sup>For datasets smaller than  $6K$ , we use the entire dataset. The training sets are randomly sampled for each random seed, and are shared across methods with the same seed.",
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+    {
+        "type": "page_footnote",
+        "text": "${}^{9}$  Except for the learning rate,which was tuned for each task and model individually.",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "14839",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 1 shows results for BERT classifiers, $^{11}$  averaged across all tasks. Our results show that multiple classifiers updating the same weights during fine-tuning diminishes the performance of Early Exit classifiers by  $2.3\\%$  on average (1.7% for BERT, 3.0% for DeBERTa), with earliest classifiers affected the most (3.5% for BERT, 7.0% for DeBERTa). The increased effect on early classifiers supports our hypothesis regarding conflicting gradients: parameters used by early classifiers receive updates from the largest number of classifiers, thus increasing the chance for conflicting gradients and leading to a larger decrease in performance.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 Speed-Accuracy Trad-eoff",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "So far we observed that Multi-Model classifiers outperform Early-Exit ones. On the other hand, we also note that there is considerable overhead when using a Multi-Model model. For Multi-Model, an instance that makes an exit on classifier  $C_i$ , runs all classifiers up to (including)  $C_i$ , each being an independent model, while Early-Exit early layer computations are reused by later classifiers. We turn to evaluate the trade-off between these two factors and compare the overall speed-accuracy curve of each adaptive inference method.",
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate model scores across different inference speeds using 11 threshold values, evenly spaced in the range  $\\left(\\frac{1}{\\# \\text{ of labels}}, 1\\right)$ . We note that  $t = \\frac{1}{\\# \\text{ of labels}}$  corresponds to the earliest classifier predicting all labels, while for  $t = 1$ , the final classifier is used on the entire validation set.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We compute the speedup ratio for each instance as the number of layers it passes through divided by the number of layers of the full backbone model (12 for BASE models, 24 for LARGE models), and average across all instances. As an example, for classifiers following layers [1, 4, 6, 12], an instance that exits on the third classifier (i.e., after layer 6), will have a speedup ratio of  $\\frac{6}{12}$  for Early-Exit and  $\\frac{11}{12}$  for Multi-Model  $(\\frac{6}{12} + \\frac{4}{12} + \\frac{1}{12})$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate models on the seven tasks listed in Section 3.2, and report the average scores across all tasks.  $\\mathrm{BERT}_{BASE}$  results are presented in Fig. 4, while the results for all other models can be found in Fig. 5. The speed-accuracy curves reveal two important observations. First, as expected, MultiModel achieves better scores at fast speeds (when most instances are predicted by early classifiers).",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/c3c10d4e89b0ca3e40881ee2e1342205ab1768d254d9ebed2e1d0115aef355b4.jpg",
+        "image_caption": [
+            "Figure 4: Speed-accuracy trade-off comparison of Multi-Model and Early-Exit. Multi-Model performs better only at fast inference times (up to  $\\frac{1}{4}$  of original run time), while Early-Exit dominates the remainder of the range. The graph shows the average task scores (y-axis) as a function of the speedup ratio (x-axis)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Second, although each Multi-Model classifier outperforms its corresponding Early-Exit one, the Multi-Model overhead leads to this approach being outperformed by Early-Exit at slow speeds (when more instances are predicted by later classifiers).",
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+    {
+        "type": "text",
+        "text": "4 SWEET: Separating Weights for Early-Exit Transformers",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Based on our findings, we aim to design an Early-Exit method that takes advantage of the benefits of both Multi-Model and Early-Exit approaches: making the lower Early-Exit classifiers as accurate as the Multi-Model ones, without the additional overhead of the Multi-Model approach.",
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+    {
+        "type": "text",
+        "text": "4.1 SWEET",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We present SWEET—a method for fine-tuning Early-Exit models that avoids the harmful impact of conflicting gradients. SWEET grants each classifier exclusive control over part of the model's parameters, such that each model parameter is only updated by a single classifier. This is done by truncating the loss signal from classifier  $C_i$  when reaching the Transformer layer corresponding to classifier  $C_{i - 1}$  (Fig. 2, right).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In SWEET, each classification head receives complete control over a portion of the Model's parameters and can alter them in a way that optimizes its own goals. Truncating future loss signals make the very first classifier an independent model, as",
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+    {
+        "type": "page_footnote",
+        "text": "11See Appendix C, Table 3 for DeBERTa results.",
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+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "Further experimental details can be found in Appendix A.",
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+    },
+    {
+        "type": "page_number",
+        "text": "14840",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8ff76a1b473522e37cd46613480350baa255c8d2678946bb23110590c7cd0cd9.jpg",
+        "image_caption": [
+            "Figure 5: Speed-accuracy tradeoff averaged across tasks. SWEET matches the performance of Multi-Model at fast speeds, while maintaining results comparable to Early-Exit at slow speeds."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "opposed to a model that shares its parameters with future classifiers. The following classifiers update only a subset of the model's parameters but are affected by early model parameters, allowing them to still make use of earlier computations when processing an instance. We clarify that all model weights are updated simultaneously, as opposed to training the classifiers (and their corresponding layers) sequentially, which would have led to significantly longer fine-tuning, matching that of a Multi-Model model.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 A Better Speeds-Accuracy Curve",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We turn to evaluate the speed-accuracy curve of SWEET. We use the same experimental setup as in Section 3.2; we fine-tune two pre-trained LMs (BERT and DeBERTa) in two sizes (BASE, LARGE) over the same seven text classification tasks. We use the same exit points and evaluate over the entire validation set using confidence-based exiting. We compare SWEET to two baselines: a standard Early-Exit model and a Multi-Model model. We compute the speedup ratio using the same method as described in Section 3.3. For further implementation details, see Appendix A.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Fig. 5 presents the speed-accuracy curves of all models, averaged across all tasks. The figure shows that at the fastest speeds, SWEET outperforms Early-Exit for all models and is comparable to, or outperforms, Multi-Model. However, for 3 out of the 4 models (all but  $\\mathrm{BERT}_{\\text{LARGE}}$ ), Early-Exit surpasses the performance of SWEET at slow speeds. SWEET's reduced scores at slow inference speeds are likely due to the lower capacity of the later classifiers, stemming from their restricted influence on early model parameters during fine-tuning.",
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+    {
+        "type": "text",
+        "text": "Fig. 6 presents results on individual tasks for",
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+    {
+        "type": "text",
+        "text": "$\\mathrm{BERT}_{BASE}$ . On five out of seven tasks, SWEET outperforms both baselines at fast speeds (up to a speedup ratio of  $1/2$ ), suggesting that SWEET improves the performance of lower Early-Exit classifiers by avoiding conflicting gradients during training. For two tasks (MRPC and CoLA), SWEET suffers a considerable decrease in performance at slow inference speeds. For the other five tasks SWEET maintains comparable results to Early-Exit.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It is also interesting to examine how SWEET affects individual Early-Exit classifiers. Table 1 shows the results of BERT's individual classifiers trained with SWEET compared to Early-Exit and Multi-Model. $^{14}$  SWEET classifiers close much of the gap between Early-Exit and Multi-Model: they outperform those of Early-Exit by  $1.1\\%$  on average  $(1.2\\%)$  for BERT,  $1.0\\%$  for DeBERTa), with the margin being larger for the earliest classifier  $(3.4\\%)$  for BERT,  $6.2\\%$  for DeBERTa). The final two classifiers trained with SWEET achieve lower scores than those of Early-Exit  $(0.9\\%)$  on average), probably due to the restricted influence those classifiers have on early model parameters. Our results hint that SWEET is able to effectively bridge the gap between Early-Exit and Multi-Model early classifiers, leading to a speed-accuracy curve favoring fast inference speeds.",
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+    {
+        "type": "text",
+        "text": "We note that during our experiments with Early-Exit and Multi-Model models, some models did not converge. In order to ensure the validity of our results, we repeated these experiments with different random seeds, which led to convergence. We emphasize that this did not occur during the training of models using SWEET.",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>13</sup>Fig. 10 in Appendix D shows individual results for the other models.",
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+    {
+        "type": "page_footnote",
+        "text": "14See Table 3 in Appendix C for DeBERTa results.",
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+        "text": "14841",
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+        "type": "image",
+        "img_path": "images/01108ddab7f9fa9cf895bcc9b8842ba40f2a87366cb172314bf4ddc52dd82be4.jpg",
+        "image_caption": [
+            "Figure 6: Speed-accuracy curve for individual tasks, using a  $\\mathrm{BERT}_{\\mathrm{BASE}}$  model. SWET outperforms both baselines at fast speeds (lower values of  $x$ ) on five out of seven tasks. See Fig. 10 for  $\\mathrm{BERT}_{\\mathrm{LARGE}}$  and DeBERTa results."
+        ],
+        "image_footnote": [],
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+        "image_caption": [
+            "Figure 7: Speed-Accuracy curves with the learning-to-exit strategy. As with confidence-based methods, SWEET outperforms both baselines at fast speeds, while maintaining comparable results at slow speeds."
+        ],
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+    {
+        "type": "text",
+        "text": "5 Further Analysis",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We turn to evaluate the robustness of our approach. We start with evaluating SWEET using a different exit strategy. We then test how our results generalize when using varying amounts of training data.",
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+        "type": "text",
+        "text": "A different exit strategy: Learning to Exit Our experiments so far have used a confidence-based exit strategy (Section 2). Here we consider a different strategy—learning to exit (Xin et al., 2021), in which a separate module is trained for each classifier, learning whether the classifier's prediction should be trusted, and an exit should be made. This method also allows for a natural extension to regression problems, unlike confidence-based methods that are limited to classification tasks.",
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+    {
+        "type": "text",
+        "text": "We use BERT {BASE, LARGE} as a backbone",
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+    {
+        "type": "text",
+        "text": "model and fine-tune in the same procedure described in Section 3.3. Our results (Fig. 7) reveal that the methods behave similarly to the confidence-based setup; SWEET outperforms both baselines at the early stage of the curve (fast speeds), while performing on par with Early-Exit at slow speeds. We also measure the performance of individual exit layers, as in Section 3.2, for models fine-tuned using learning-to-exit. Our results (Table 4 in Appendix E) reveal a similar behavior to that of models fine-tuned using confidence based early exiting: Multi-Model classifiers surpass the performance of Early-Exit classifiers. Moreover, SWEET's early classifiers outperform those of Early-Exit, while later ones show a slight decrease in performance.",
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+    {
+        "type": "text",
+        "text": "Varying data sizes Our experiments so far have focused on low-resource setups (a training set of several thousand examples). We now evaluate how SWEET performs as we vary the amount of training data. We fine-tune a BERT<sub>BASE</sub> model on different portions of the MNLI dataset using the same experimental setup as in Section 3.2. Our results, shown in Fig. 8, indicate that SWEET is mostly beneficial when training data is limited to a few thousand examples, but still somewhat useful even with as many as 60K training instances. Nonetheless, the effects of conflicting gradients on the earliest Early-Exit classifier tend to disappear when training on the full dataset (400K instances), making it as good as the smallest Multi-Model classifier. Moreover, in that setup, the use of SWEET seems to substan",
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+        "text": "14842",
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+        "img_path": "images/0f13d70cd97c2b81636f607e04efb7f0693cbc46fe5a3fff7bf4c4f888f3e6ff.jpg",
+        "image_caption": [
+            "BERTBASE",
+            "Figure 8: Speed-accuracy curves of  $\\mathrm{BERT}_{BASE}$  models trained on varying sizes of the MNLI dataset. The title of each plot describes the amount of training data used in the fine-tuning phase. The benefits of using SWEET vanish with large amounts of training data."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "tially decrease the performance of later classifiers, suggesting that the harm caused by limiting the influence of classifiers on model parameters may grow with the amount of training data.",
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+    {
+        "type": "text",
+        "text": "6 Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Several approaches have been proposed for reducing the inference time of large models (Treviso et al., 2022). These include knowledge distillation (Ba and Caruana, 2014; Hinton et al., 2015), in which the knowledge of a large teacher model is transferred to a smaller student model; pruning (LeCun et al., 1989; Frankle and Carbin, 2018), which removes unnecessary model parameters; and weight quantization (Jacob et al., 2018; Zafrir et al., 2019), which reduces the floating point precision of model weights. See (Treviso et al., 2023, Section 6), for a recent survey. Adaptive inference methods studied in this work are an orthogonal approach, which can be used in combination with these methods (Schwartz et al., 2020b).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The use of Adaptive inference in deep neural networks has been extensively studied, with successful implementations in various types of networks including recurrent neural networks (Graves, 2016) and convolutional neural networks (Teerapittayanon et al., 2016; Huang and Chen, 2018). In the context of this work, it has also been applied to existing backbone pre-trained language models: Xin et al. (2020) implemented early exit strategies on top of classification tasks. Zhou et al. (2020) Introduced a patience-based exiting, requiring sequential classifiers to agree on a label for a prediction to be made. Xin et al. (2021) extended the use of Early-Exit in Transformers to regression tasks, as well as addressed the issue of reduced performance of the final classifier through the use of an alter",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "nating training algorithm. Schuster et al. (2021) proposed a confidence-based early exit model with guarantees on the agreement between early exit predictions and the final classifier.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Liu et al. (2022) presented a strong baseline for efficient NLP by adding multiple classifiers to a BERT model during pre-training. Recently, Schuster et al. (2022) adjusted the Early-Exit method to language modeling for text generation, making dynamic computation at the single token level.",
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+    {
+        "type": "text",
+        "text": "Multi-Model approaches to adaptive inference have been proposed for vision tasks (Enomoro and Eda, 2021) as well as for NLP (Li et al., 2020; Varshney and Baral, 2022b). Mamou et al. (2023) introduced a two-tier design with a highly efficient model serving as the first model and a powerful model serving as the second, enabling the possibility of achieving extremely fast inference speed.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Finally, the concept of conflicting gradients has been mainly studied in the context of multi-task learning, where a single model is faced with solving different tasks (Yu et al., 2020; Liu et al., 2021a). To the best of our knowledge, no previous work examined this in the context of Early-Exit.",
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+    {
+        "type": "text",
+        "text": "7 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we analyzed the performance of two common adaptive inference methods—Early-Exit and Multi-Model. We found evidence that model weights are updated by conflicting gradients in the training process of Early-Exit models, causing classifiers to perform at a sub-optimal level. Despite this, we showed that regarding the entire speed-accuracy curve, Early-Exit is still favorable to Multi-Model due to the overhead of using independent model runs in a Multi-Model setup.",
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+    },
+    {
+        "type": "text",
+        "text": "To address these findings, we proposed SWEET,",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "14843",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "a novel Early-Exit method, which avoids conflicting gradients by allocating each Early-Exit classifier a subset of model weights which are updated solely by it. We found that for Early-Exit models trained with SWEET, early classifiers perform better than those of standard Early-Exit, but later classifiers of SWEET are not as good. These measures lead to SWEET outperforming both Early-Exit and Multi-Model in fast speeds, with slightly worse results than Early-Exit at slow speeds.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Overall, our results demonstrate that Early-Exit models can benefit from fine-tuning algorithms that are tailored to their architecture, and that SWEET is a promising approach for improving the speed-accuracy trade-off of Early-Exit models in the context of adaptive inference.",
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+    {
+        "type": "text",
+        "text": "8 Limitations",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work focuses on the effects of adaptive inference in a low-resource setting, specifically when training data is limited. Our experiments (Section 5) suggest that the negative impact of conflicting gradients may be less prominent when larger amount of training data is available.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our experiments were conducted using relatively small pre-trained language models ( $\\leq 350M$  parameters) due to computational constraints, and we defer the replication of our findings with larger, more powerful models to future work. Nonetheless, our results have important implications for the growing trend of increasingly large language models. We hope this work inspires further research on methods to reduce the computational cost of NLP.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work concentrates on evaluating the speed-accuracy trade-off of Multi-Model and Early-Exit at inference time. We recognize that there are additional factors, such as memory usage, batch processing, and training duration, that could be considered when comparing these methods.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Finally, we experimented with seven text classification tasks in English. We recognize that results may vary for other tasks and languages.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We acknowledge Yarden Tal for her early contributions to this work, and Gabriel Stanovsky for his advice and meaningful feedback. This work was supported in part by the Israel Science Foundation (grant no. 2045/21), NSF-BSF grant 2020793, and by a grant from Intel Labs.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+            "Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. 2020. Transformers: State-of-the-art natural language processing. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations, pages 38-45, Online. Association for Computational Linguistics.",
+            "Ji Xin, Raphael Tang, Jaejun Lee, Yaoliang Yu, and Jimmy Lin. 2020. DeeBERT: Dynamic early exiting for accelerating BERT inference. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 2246-2251, Online. Association for Computational Linguistics.",
+            "Ji Xin, Raphael Tang, Yaoliang Yu, and Jimmy Lin. 2021. BERxiT: Early exiting for BERT with better fine-tuning and extension to regression. In Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics:"
+        ],
+        "bbox": [
+            115,
+            85,
+            485,
+            917
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Main Volume, pages 91-104, Online. Association for Computational Linguistics.",
+            "Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine, Karol Hausman, and Chelsea Finn. 2020. Gradient surgery for multi-task learning. Advances in Neural Information Processing Systems, 33:5824-5836.",
+            "Ofir Zafrir, Guy Boudoukh, Peter Izsak, and Moshe Wasserblat. 2019. Q8bert: Quantized 8bit bert. 2019 Fifth Workshop on Energy Efficient Machine Learning and Cognitive Computing - NeurIPS Edition (EMC2-NIPS), pages 36-39.",
+            "Zhen Zhang, Wei Zhu, Jinfan Zhang, Peng Wang, Rize Jin, and Tae-Sun Chung. 2022. Pcee-bert: Accelerating bert inference via patient and confident early exiting. In *Findings of the Association for Computational Linguistics: NAACL* 2022, pages 327-338.",
+            "Wangchunshu Zhou, Canwen Xu, Tao Ge, Julian McAuley, Ke Xu, and Furu Wei. 2020. Bert loses patience: fast and robust inference with early exit. In Proceedings of the 34th International Conference on Neural Information Processing Systems, pages 18330-18341."
+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "14846",
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+    },
+    {
+        "type": "text",
+        "text": "A Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Further implementation details For fine-tuning BERT models, we use a batch size of 16. For fine-tuning DeBERTa, due to GPU memory constraints, we use a batch size of 16 for BASE and 8 for LARGE. We fine tune the models for two epochs with a maximal sequence length of 256. We use  $\\beta = 0.9$ , 0.999 for the AdamW optimizer with linear LR-decay. We optimize the initial learning rate for each method, model size & task by performing a search over five values {1e-5, 2e-5, 3e-5, 4e-5, 5e-5} and choose the value leading to the largest area under the speed-accuracy curve. Chosen LRs are presented in table Table 2",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "All experiments were run on a single NVIDIA A5000 GPU. The overall computational budget was  $\\sim 1000$  GPU hours. We implement all methods using the HuggingFace Transformer library (Wolf et al., 2020).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Speedup evaluation The speed-up ratio of the model when using exit threshold  $t$  is calculated using the formula:",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {s p e e d u p} _ {t} = \\frac {\\sum_ {i = 1} ^ {M} S _ {i} ^ {t} \\cdot L _ {i}}{L _ {M} \\cdot \\sum_ {i = 1} ^ {M} S _ {i} ^ {t}} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where  $M$  is the number of classifiers used for the model,  $L_{i}$  denotes the number of the layer preceding the  $i$ -th classification head and  $S_{i}^{t}$  denotes the number of samples classified by the  $i$ -th classifier when using threshold  $t$ .",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The same exit threshold can lead to different speedup ratios amongst models trained with different random seeds. We use linear interpolation to approximate the accuracy score at set speedup ratios. We evaluate at  $(1/12, 1/4, 1/2, 3/4, 1)^{15}$  and report the average across three random seeds as well as a  $95\\%$  confidence interval. $^{16}$  We use temperature scaling (Guo et al., 2017) to make classifiers confidence, and therefore early-exiting decisions, more reliable. Note that this scaling is monotonic and therefore does not influence predictions.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "B Conflicting Gradients",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We replicate the experiment done in Section 3.1 with another batch of size 16 to examine if our findings generalize. results presented in Fig. 9 show",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "a similar trend to Fig. 3: Gradient updates of current classifiers are roughly orthogonal to those of future classifiers, whereas future classifier updates are more aligned.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/2bc7a657c42144c9049f04337c6f7aaa4b25682b0c1cfd7e1eb6aecbe30931b8.jpg",
+        "image_caption": [
+            "Figure 9: Average cosine similarity between classifiers' gradient updates of model layers. C-i stands for Classifier  $i$ . Layer 1 (preceding C-1) is updated by 3 classifiers, while layers 4 (preceding C-2), and 6 (C-3) are updated by 3 & 2 classifiers respectively. For each layer, the gradient update of the following classifier is roughly orthogonal to those of future classifiers, whereas gradient updates of higher classifiers tend to better align with one another."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "C DeBERTa Individual Layer Comparison",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 3 Shows individual classifier results for DeBERTa models. As with the BERT results, Multi-Model classifiers outperform corresponding Early-Exit classifiers. SWEET early classifiers are better than Early-Exit ones, while later classifiers tend to downgrade in performance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "D Individual Task Results",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Fig. 10 shows results on individual tasks for BERTLARGE and DeBERTa (BASE & LARGE). For BERTLARGE, SWEET outperforms both baselines throughout the entire speed-accuracy curve over all tasks examined. For DeBERTa models, results are similar to those of BERTBASE, where SWEET performs better at high speeds (small speedup ratio) and is dominated at low speeds (where later classifiers do most of the heavy lifting).",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "15For LARGE models we evaluate at  $1 / 24$  as the fastest speedup ratio.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "16 For Multi-Model we also use  $(13 / 8,13 / 4)$  as overhead causes the model to perform at such \"speedup\" ratios.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "14847",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c23448f8a39989bc129223c54064a0f8048f5ca23d82fbc7d17a5cd74c44a22c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Size</td><td colspan=\"7\">Task</td></tr><tr><td></td><td></td><td>SST-2</td><td>MRPC</td><td>CoLA</td><td>MNLI</td><td>QQP</td><td>QNLI</td><td>RTE</td></tr><tr><td rowspan=\"2\">BERT</td><td>BASE</td><td>5\\5\\5</td><td>5\\3\\4</td><td>4\\4\\5</td><td>5\\5\\5</td><td>5\\5\\5</td><td>5\\4\\5</td><td>5\\5\\4</td></tr><tr><td>LARGE</td><td>4\\2\\2</td><td>4\\5\\4</td><td>4\\3\\4</td><td>4\\3\\4</td><td>5\\3\\4</td><td>4\\4\\3</td><td>3\\3\\3</td></tr><tr><td rowspan=\"2\">DeBERTa</td><td>BASE</td><td>3\\3\\3</td><td>4\\5\\5</td><td>4\\5\\4</td><td>2\\4\\3</td><td>4\\5\\5</td><td>3\\4\\3</td><td>2\\1\\4</td></tr><tr><td>LARGE</td><td>2\\4\\3</td><td>3\\2\\1</td><td>3\\3\\2</td><td>2\\2\\2</td><td>2\\2\\3</td><td>3\\2\\1</td><td>1\\2\\2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/0132e41e732fe157b59694a2757aa1db129df337fb027a284eebe254297c32fa.jpg",
+        "table_caption": [
+            "Table 2: Chosen initial learning rate to optimize area under the speed-accuracy curve of each model, size, task. All numbers should be multiplied by 1e-5.  $x \\backslash y \\backslash z$  represent the initial learning rate of Early-Exit\\Multi-Model\\SWEET respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Size</td><td>Method</td><td colspan=\"4\">Exit Layer</td></tr><tr><td></td><td></td><td>1</td><td>4</td><td>6</td><td>12</td></tr><tr><td rowspan=\"3\">BASE</td><td>MM</td><td>60.10.4</td><td>74.60.6</td><td>78.31.1</td><td>82.20.7</td></tr><tr><td>EE</td><td>52.30.4</td><td>70.90.6</td><td>77.90.8</td><td>81.70.1</td></tr><tr><td>SWEET</td><td>59.11.5</td><td>72.40.2</td><td>75.11.1</td><td>79.50.5</td></tr><tr><td></td><td></td><td>1</td><td>6</td><td>12</td><td>24</td></tr><tr><td rowspan=\"3\">LARGE</td><td>MM</td><td>61.90.1</td><td>76.20.4</td><td>80.20.9</td><td>86.80.2</td></tr><tr><td>EE</td><td>55.80.9</td><td>74.71.1</td><td>79.20.8</td><td>83.61.9</td></tr><tr><td>SWEET</td><td>61.30.7</td><td>76.00.5</td><td>77.80.4</td><td>82.70.4</td></tr></table>",
+        "bbox": [
+            114,
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+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/f679cedf9848c233f41ee614d15ec1a84414ccb819881a1b1c7370bd6db30bec.jpg",
+        "table_caption": [
+            "Table 3: Results of individual classification layers averaged over all tasks using DeBERTa as a backbone model. Best scores are highlighted in bold, standard deviation (across random seeds) is reported in subscript. The results for BERT models presented in Table 1."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Size</td><td>Method</td><td colspan=\"4\">Exit Layer</td></tr><tr><td></td><td></td><td>1</td><td>4</td><td>6</td><td>12</td></tr><tr><td rowspan=\"3\">BASE</td><td>MM</td><td>53.70.5</td><td>66.10.4</td><td>71.10.3</td><td>75.42.7</td></tr><tr><td>EE</td><td>49.51.1</td><td>63.00.2</td><td>70.00.6</td><td>75.30.4</td></tr><tr><td>SWEET</td><td>53.50.4</td><td>64.90.9</td><td>68.51.4</td><td>74.10.4</td></tr><tr><td></td><td></td><td>1</td><td>6</td><td>12</td><td>24</td></tr><tr><td rowspan=\"3\">LARGE</td><td>MM</td><td>51.60.3</td><td>59.90.4</td><td>67.62.6</td><td>77.90.8</td></tr><tr><td>EE</td><td>50.50.8</td><td>59.30.9</td><td>68.81.3</td><td>76.61.6</td></tr><tr><td>SWEET</td><td>53.90.5</td><td>60.60.2</td><td>69.50.4</td><td>75.811.0</td></tr></table>",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Results of individual classification layers averaged over all tasks using BERT as a backbone model, fine-tuned using learning-to-exit. Best scores are highlighted in bold, standard deviation (across random seeds) is reported in subscript.",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "E Learning-to-exit Individual Layer Comparison",
+        "text_level": 1,
+        "bbox": [
+            114,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Table 4 Shows individual classifier results for BERT models fine tuned with the learning to exit strategy. As with the confidence-based results, Multi-Model classifiers outperform corresponding Early-Exit classifiers. SWEET early classifiers are better than Early-Exit ones, while later classifiers tend to downgrade in performance.",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "page_number",
+        "text": "14848",
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+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/bc16d91f92dc31c537519873d571f956a0c710c5e20a2d2d51fb11e886a19432.jpg",
+        "image_caption": [
+            "Figure 10: Speed-accuracy curves for individual tasks. For  $\\text{BERT}_{\\text{LARGE}}$ , SWEET outperforms both baselines across the entire curve. For DeBERTa, SWEET performs better than Early-Exit at high speeds on 9 out of 14 experiments."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 13
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+    {
+        "type": "page_number",
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+    },
+    {
+        "type": "text",
+        "text": "A For every submission:",
+        "bbox": [
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+            322,
+            122
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "A1. Did you describe the limitations of your work? Section 8",
+            "A2. Did you discuss any potential risks of your work? Our work does not present any risks.",
+            "A3. Do the abstract and introduction summarize the paper's main claims? Section 1",
+            "A4. Have you used AI writing assistants when working on this paper? We used ChatGPT for assistance, purely with the language of the paper"
+        ],
+        "bbox": [
+            129,
+            126,
+            695,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "B Did you use or create scientific artifacts?",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Section 3 + 4",
+        "bbox": [
+            132,
+            321,
+            236,
+            334
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "B1. Did you cite the creators of artifacts you used? Section 3 + 4",
+            "B2. Did you discuss the license or terms for use and / or distribution of any artifacts? We use publicly available data sets which are commonly used during research",
+            "B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Such terms were not specified.",
+            "B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? We use publicly available data sets which are commonly used during research",
+            "B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? We use publicly available data sets which are commonly used during research",
+            "B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Section 3 + 4, Appendix A"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "C Did you run computational experiments?",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Section 3 + 4",
+        "bbox": [
+            132,
+            785,
+            236,
+            800
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Section 1 + 3, Appendix A",
+        "bbox": [
+            129,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "header",
+        "text": "ACL 2023 Responsible NLP Checklist",
+        "bbox": [
+            132,
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+            433,
+            99
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "page_footnote",
+        "text": "The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "page_number",
+        "text": "14850",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? Section 3 + 4, Appendix A",
+            "C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Section 3 + 4",
+            "C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Appendix A"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "D Did you use human annotators (e.g., crowdworkers) or research with human participants?",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Left blank.",
+        "bbox": [
+            132,
+            313,
+            213,
+            329
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? No response.",
+            "D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? No response.",
+            "D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? No response.",
+            "D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? No response.",
+            "D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? No response."
+        ],
+        "bbox": [
+            127,
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2023/Finding the SWEET Spot_ Analysis and Improvement of Adaptive Inference in Low Resource Settings/299364f1-0f55-4167-82d9-b2dbc57d8e7b_origin.pdf

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2023/Finding the SWEET Spot_ Analysis and Improvement of Adaptive Inference in Low Resource Settings/full.md

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+# Finding the SWEET Spot: Analysis and Improvement of Adaptive Inference in Low Resource Settings
+
+Daniel Rotem $^{\text{♥}}$  Michael Hassid $^{\text{♥}}$  Jonathan Mamou $^{\text{♣}}$  Roy Schwartz $^{\text{♥}}$
+
+$^{\text{©}}$ School of Computer Science & Engineering, Hebrew University of Jerusalem
+
+$\spadesuit$  Intel Labs, Israel
+
+{daniel.rotem, michael.hassid, roy.schwartz1}@mail.huji.ac.il jonathan.mamou@intel.com
+
+# Abstract
+
+Adaptive inference is a simple method for reducing inference costs. The method works by maintaining multiple classifiers of different capacities, and allocating resources to each test instance according to its difficulty. In this work, we compare the two main approaches for adaptive inference, Early-Exit and Multi-Model, when training data is limited. First, we observe that for models with the same architecture and size, individual Multi-Model classifiers outperform their Early-Exit counterparts by an average of  $2.3\%$ . We show that this gap is caused by Early-Exit classifiers sharing model parameters during training, resulting in conflicting gradient updates of model weights. We find that despite this gap, Early-Exit still provides a better speed-accuracy trade-off due to the overhead of the Multi-Model approach. To address these issues, we propose SWEET, an Early-Exit fine-tuning method that assigns each classifier its own set of unique model weights, not updated by other classifiers. We compare SWEET's speed-accuracy curve to standard Early-Exit and Multi-Model baselines and find that it outperforms both methods at fast speeds while maintaining comparable scores to Early-Exit at slow speeds. Moreover, SWEET individual classifiers outperform Early-Exit ones by  $1.1\%$  on average. SWEET enjoys the benefits of both methods, paving the way for further reduction of inference costs in NLP. We publicly release our code.
+
+# 1 Introduction
+
+Pre-trained Transformer-based language models such as BERT (Devlin et al., 2019), DeBERTa (He et al., 2020), and GPT3 (Brown et al., 2020) have become the go-to tool in NLP. Although powerful, the growing size of these models has been a major drawback (Thompson et al., 2020; Schwartz et al.,
+
+![](images/e02d2f143e8e6a9dbdce5b944abcf920e1fb215c7a99b9f4a4428e0afbcd70c8.jpg)  
+Early Exit
+
+![](images/f0aabbf61bc333253a8ce10012aed56327a395c2b9555c83d27220e936156953.jpg)  
+Figure 1: Illustration of the adaptive inference approaches compared in this work. In both methods, multiple classifiers of increasing sizes are run serially, until a confident prediction is made. In Early-Exit (left), a single model with multiple classifiers is used, such that early computations are reused by later classifiers. In Multi-Model (right), a sequence of independent models is used, allowing each classifier to decouple its parameters from other classifiers.
+
+2020a), making them costly to run. Various attempts to reduce inference cost have been proposed, including distillation (Hinton et al., 2015), pruning (LeCun et al., 1989) and quantization (Courbariaux et al., 2014). This work focuses on adaptive inference (Graves, 2016; Liu et al., 2020), a recent approach in which the variability of sample difficulty is leveraged toward a smarter allocation of computational resources. An appealing property of adaptive inference is that it enables dynamic control of the speed-accuracy trade-off.
+
+There are two main approaches to adaptive inference, both using a set of classifiers of different sizes. In Early-Exit (Schwartz et al., 2020b; Xin et al., 2020), multiple classification heads are added to the same model at different layers, allowing for early exit during inference (Fig. 1, left). Another approach (henceforth Multi-Model) is to apply multiple independent classifiers of varying capacities serially until a prediction is made (Varshney and
+
+Baral, 2022a; Li et al., 2020, Fig. 1, right). These approaches have complementary benefits; Multi-Model allows for easier batching at inference time, and potentially larger savings due to using very efficient models (Mamou et al., 2023). Early-Exit on the other hand is more memory efficient, faster to train, and enables re-use of early computation if an early exit was not taken.
+
+In this work, we compare the speed-accuracy behavior of the two approaches when training data is limited. We first observe that Early-Exit model weights are updated by multiple conflicting gradient signals throughout the training process (Fig. 2, left). We show that this leads to a decrease in performance of individual Early-Exit classifiers compared to Multi-Model ones (2.3% gap on average). We find that this gap is higher for the earliest classifiers (5.2% on average) than for later ones (1.4%).
+
+We also find that while each Multi-Model classifier outperforms its Early-Exit counterpart, it does not translate to an overall better speed-accuracy trade-off. Instead, we find that each method dominates performance in a different region: Multi-Model outperforms Early-Exit at fast inference speeds, while Early-Exit is better at slow speeds. Multi-Model downgraded scores at slow speeds are likely caused by the overhead of running models sequentially to predict hard samples.
+
+Inspired by our findings, we present SWEET, $^{4}$  an Early-Exit method for bridging the performance gap between standard Early-Exit and Multi-Model. In SWEET, each Early-Exit classifier only updates the parameters of layers preceding it up to the previous classifier. This way, each model parameter is updated by a single classifier, thus avoiding conflicting gradients during the training of Early-Exit models (Fig. 2, right).
+
+We experiment with two established pretrained models: BERT (Devlin et al., 2019) and DeBERTa (He et al., 2020). We fine-tune Early-Exit models using SWEET on seven text classification tasks from GLUE (Wang et al., 2018) and compare them to Early-Exit and Multi-Model baselines. The speed-accuracy curve of SWEET dominates both baselines at fast speeds for 21 out of 28 experiments conducted. As for individual clas
+
+![](images/652a69ab2635e220dde2eaac266bd74a0592eebecba4976a7c033a6a67cd1810.jpg)  
+Figure 2: Left: standard Early-Exit fine-tuning, where lower layers get gradient updates from multiple classifiers. Right: our SWEET method, in which each layer parameters are updated only by the next classifier.
+
+![](images/146761ab93be75ec31f06c845d1921225fda1725520086311ab96fbb67b39117.jpg)
+
+sifiers, SWEET performs  $1.1\%$  better on average than Early-Exit, mostly improving earlier classifiers, where conflicting gradients are more dominant.
+
+We summarise our main contributions: (1) We propose a way of measuring conflicting gradients, and show that they exist in Early-Exit training process; (2) We empirically compare Early-Exit and Multi-Model classifiers and show that conflicting gradients lead to individual Early-Exit classifiers being less accurate; (3) We propose a novel finetuning method, SWEET, which alleviates the conflicting gradients problem in Early-Exit, and leads to improved results at fast inference speeds; (4) We publicly release our code.
+
+# 2 Background: Adaptive Inference
+
+Adaptive inference aims to reduce inference costs of deep neural nets by matching model and sample complexities. Sample difficulty usually varies in real-world data, meaning not all instances require processing by the most powerful classifier. Therefore, we can allocate fewer resources to easier instances, and reduce the average inference cost, potentially at the cost of performance degradation.
+
+Several exit strategies have been developed to control the speed-accuracy trade-off of a model by deciding when to make an early prediction and halt computation (Xin et al., 2020; Zhou et al., 2020; Xin et al., 2021; Schuster et al., 2021; Zhang et al., 2022). In this work, we mainly experiment with confidence-based exiting (Schwartz et al., 2020b), in which computation halts if the softmax probability assigned to a given label exceeds a predetermined threshold. Dynamic control of model's inference speed is gained through setting different threshold values. There are two main adaptive inference approaches, Early-Exit and Multi-Model, which we describe below.
+
+Early-Exit Early-Exit models are deep neural nets with multiple output points, following intermediate layers. In this work, we focus on Early-Exit implementation as presented in Schwartz et al. (2020b). During fine-tuning, instances are passed through the model, and a loss is calculated based on predictions made by all classifiers. This leads to some model weights being updated by gradient signals from multiple classifiers (Fig. 2, left).
+
+At inference time, an instance is passed through the model and its label is predicted sequentially until a decision to exit early is taken, and computation is halted. An appealing property of Early-Exit is that it allows for efficient re-use of previous computation from lower layers in higher classifiers. However, this means that some model parameters are updated by multiple classifiers, which may lead to sub-optimal performance of individual classifiers due to conflicting gradients. In this work, we study the effect of this property on Early-Exit models.
+
+Multi-Model In Multi-Model adaptive inference, a set of independent models of increasing capacity are fine-tuned separately for the same task. At inference time, the models are used sequentially from smallest to largest until a prediction meets some predetermined criterion or until the largest model has been used. This method is more robust than Early-Exit, being easier to extend and enabling the use of different architectures. Additionally, Multi-Model potentially allows for further computational savings by using models smaller than the smallest Early-Exit model (a single layer of the backbone
+
+model, Mamou et al., 2023). However, it may add overhead to the prediction time of hard instances, as those pass through multiple models with early computations being discarded, bringing the total runtime to exceed that of using the largest model.
+
+# 3 Early-Exit vs. Multi-Model
+
+# 3.1 Conflicting Gradients in Early-Exit
+
+Unlike Multi-Model, when fine-tuning Early-Exit models, model weights are updated by multiple gradient signals, originating in different classification layers (Fig. 2, left). We hypothesize that this leads to sub-optimal performance for all classifiers involved, as gradient signals might conflict with one another and derail the classifiers from their goal. To test this hypothesis, we compare the gradient similarity of different Early-Exit classifiers.
+
+We fine-tune a  $\mathrm{BERT}_{BASE}$  model with four exit points (following layers [1, 4, 6, 12]) for 400 training steps on the MNLI dataset (Williams et al., 2018), using a batch size of 16 with a learning rate of 2e-5. We pass a new training batch through the model, and inspect the gradients with respect to the last feed-forward matrix in each layer preceding a classifier. To measure the degree of alignment between gradient updates of different classifiers, we average the cosine similarity between the rows of gradient matrices for every pair of classifiers. High similarity indicates that the classifiers are updating the weights in a similar direction, while low similarity (in absolute values) suggests that the updates are close to orthogonal and potentially detrimental to both classifiers.
+
+This section studies the strengths and weaknesses of both adaptive inference approaches. We start by describing a limitation of Early-Exit approaches: lower model layers are updated by conflicting gradient signals during training. We show that this leads to inferior performance of individual Early-Exit classifiers compared to corresponding Multi-Model classifiers. We then compare the effects of these performance drops on the speed-accuracy curve of Early-Exit models compared Multi-Model ones.
+
+Fig. 3 shows that the gradients of future classifiers are generally orthogonal to those of the current classifier for each examined Transformer block. This indicates that model weights indeed suffer
+
+![](images/c7d4a0182aafd37e17a3bc56755485f6155ae2af38b76d8ba4d12fac619246e3.jpg)  
+Figure 3: Average cosine similarity between classifiers' gradient updates of model layers. C-i stands for Classifier  $i$ . Layer 1 (preceding C-1) is updated by 3 classifiers, while layers 4 (preceding C-2), and 6 (C-3) are updated by 3 & 2 classifiers respectively. For each layer, the gradient update of the following classifier is roughly orthogonal to those of future classifiers, whereas gradient updates of higher classifiers tend to better align with one another.
+
+from conflicting gradient updates during the training process, which might affect the performance of each individual classifier. Interestingly, when multiple future classifiers are present, they tend to align with each other, as indicated by the relatively high similarity between layer 1's gradient updates originating in classifiers 2, 3, and 4, and between layer 4's gradient updates from classifiers 3 and 4.
+
+# 3.2 Effects of Conflicting Gradients
+
+To evaluate the effect of conflicting gradients on individual Early-Exit classifiers, we compare the different classifiers of an Early-Exit model and a Multi-Model model. For a clean comparison, we use the same backbone model, exit points, hyperparameters, $^{9}$  and random seeds. As an example, for a given 12-layer Transformer model, an Early-Exit model with exit points following layers [4, 12] would be compared to a Multi-Model one consisting of two classifiers: the first four layers fit with a classification head, and a full (12 layer) model. The models differ only in the fact that for the Early-Exit model, model weights are updated by multiple future classifiers during the fine-tuning process, while each Multi-Model classifier is an independent model. To isolate the effect of conflicting gradients
+
+<table><tr><td>Size</td><td>Method</td><td colspan="4">Exit Layer</td></tr><tr><td></td><td></td><td>1</td><td>4</td><td>6</td><td>12</td></tr><tr><td rowspan="3">BASE</td><td>MM</td><td>60.90.6</td><td>71.40.1</td><td>74.71.2</td><td>79.90.9</td></tr><tr><td>EE</td><td>57.30.3</td><td>70.30.3</td><td>74.40.7</td><td>78.70.5</td></tr><tr><td>SWEET</td><td>60.90.5</td><td>71.60.5</td><td>74.00.4</td><td>77.40.6</td></tr><tr><td></td><td></td><td>1</td><td>6</td><td>12</td><td>24</td></tr><tr><td rowspan="3">LARGE</td><td>MM</td><td>60.10.1</td><td>66.90.4</td><td>74.40.9</td><td>81.60.3</td></tr><tr><td>EE</td><td>56.60.3</td><td>65.60.9</td><td>74.00.6</td><td>79.91.9</td></tr><tr><td>SWEET</td><td>59.80.3</td><td>66.50.7</td><td>74.50.3</td><td>81.31.0</td></tr></table>
+
+Table 1: Results of individual classification layers averaged across all tasks using BERT as a backbone model. Multi-Model (MM) classifiers outperform their Early-Exit (EE) counterparts, with the gap being the largest for early classifiers. SWEET closes much of this gap, especially for early classifiers. Standard deviation (across random seeds) is reported in subscript. Results for DeBERTa are presented in Table 3.
+
+on the classifiers, we evaluate each one separately on the entire validation set. The performance gap between each individual Multi-Model classifier and its corresponding Early-Exit classifier, allows us to directly measure the latter's downgrade in performance caused by conflicting gradients.
+
+We experiment with BERT and DeBERTa {BASE ( $\sim$ 110M parameters), and LARGE ( $\sim$ 350M parameters)}. For BASE versions, we install classifiers following layers [1, 4, 6, 12]. For LARGE versions, we use layers [1, 6, 12, 24]. We fine-tune an Early-Exit model and a corresponding Multi-Model model on seven NLP tasks from the GLUE benchmark (Wang et al., 2019): SST-2 (Socher et al., 2013), MRPC (Dolan and Brockett, 2005), RTE (Dagan et al., 2006; Haim et al., 2006; Giampiccolo et al., 2007; Bentivogli et al., 2009), CoLA (Warstadt et al., 2019), MNLI (Williams et al., 2018), QNLI (Rajpurkar et al., 2016), and QQP (Iyer et al., 2016). We report accuracy for all tasks except for CoLA (Matthews corr.). We fine-tune the models for two epochs on all tasks. As our goal is to test Adaptive inference in a low resource setting, we limit the training set size for each task to  $6K$ . We report the mean validation scores and standard deviation across three random seeds. Other hyper-parameters are listed in Appendix A.
+
+Table 1 shows results for BERT classifiers, $^{11}$  averaged across all tasks. Our results show that multiple classifiers updating the same weights during fine-tuning diminishes the performance of Early Exit classifiers by  $2.3\%$  on average (1.7% for BERT, 3.0% for DeBERTa), with earliest classifiers affected the most (3.5% for BERT, 7.0% for DeBERTa). The increased effect on early classifiers supports our hypothesis regarding conflicting gradients: parameters used by early classifiers receive updates from the largest number of classifiers, thus increasing the chance for conflicting gradients and leading to a larger decrease in performance.
+
+# 3.3 Speed-Accuracy Trad-eoff
+
+So far we observed that Multi-Model classifiers outperform Early-Exit ones. On the other hand, we also note that there is considerable overhead when using a Multi-Model model. For Multi-Model, an instance that makes an exit on classifier  $C_i$ , runs all classifiers up to (including)  $C_i$ , each being an independent model, while Early-Exit early layer computations are reused by later classifiers. We turn to evaluate the trade-off between these two factors and compare the overall speed-accuracy curve of each adaptive inference method.
+
+We evaluate model scores across different inference speeds using 11 threshold values, evenly spaced in the range  $\left(\frac{1}{\# \text{ of labels}}, 1\right)$ . We note that  $t = \frac{1}{\# \text{ of labels}}$  corresponds to the earliest classifier predicting all labels, while for  $t = 1$ , the final classifier is used on the entire validation set.
+
+We compute the speedup ratio for each instance as the number of layers it passes through divided by the number of layers of the full backbone model (12 for BASE models, 24 for LARGE models), and average across all instances. As an example, for classifiers following layers [1, 4, 6, 12], an instance that exits on the third classifier (i.e., after layer 6), will have a speedup ratio of  $\frac{6}{12}$  for Early-Exit and  $\frac{11}{12}$  for Multi-Model  $(\frac{6}{12} + \frac{4}{12} + \frac{1}{12})$ .
+
+We evaluate models on the seven tasks listed in Section 3.2, and report the average scores across all tasks.  $\mathrm{BERT}_{BASE}$  results are presented in Fig. 4, while the results for all other models can be found in Fig. 5. The speed-accuracy curves reveal two important observations. First, as expected, MultiModel achieves better scores at fast speeds (when most instances are predicted by early classifiers).
+
+![](images/c3c10d4e89b0ca3e40881ee2e1342205ab1768d254d9ebed2e1d0115aef355b4.jpg)  
+Figure 4: Speed-accuracy trade-off comparison of Multi-Model and Early-Exit. Multi-Model performs better only at fast inference times (up to  $\frac{1}{4}$  of original run time), while Early-Exit dominates the remainder of the range. The graph shows the average task scores (y-axis) as a function of the speedup ratio (x-axis).
+
+Second, although each Multi-Model classifier outperforms its corresponding Early-Exit one, the Multi-Model overhead leads to this approach being outperformed by Early-Exit at slow speeds (when more instances are predicted by later classifiers).
+
+# 4 SWEET: Separating Weights for Early-Exit Transformers
+
+Based on our findings, we aim to design an Early-Exit method that takes advantage of the benefits of both Multi-Model and Early-Exit approaches: making the lower Early-Exit classifiers as accurate as the Multi-Model ones, without the additional overhead of the Multi-Model approach.
+
+# 4.1 SWEET
+
+We present SWEET—a method for fine-tuning Early-Exit models that avoids the harmful impact of conflicting gradients. SWEET grants each classifier exclusive control over part of the model's parameters, such that each model parameter is only updated by a single classifier. This is done by truncating the loss signal from classifier  $C_i$  when reaching the Transformer layer corresponding to classifier  $C_{i - 1}$  (Fig. 2, right).
+
+In SWEET, each classification head receives complete control over a portion of the Model's parameters and can alter them in a way that optimizes its own goals. Truncating future loss signals make the very first classifier an independent model, as
+
+![](images/8ff76a1b473522e37cd46613480350baa255c8d2678946bb23110590c7cd0cd9.jpg)  
+Figure 5: Speed-accuracy tradeoff averaged across tasks. SWEET matches the performance of Multi-Model at fast speeds, while maintaining results comparable to Early-Exit at slow speeds.
+
+opposed to a model that shares its parameters with future classifiers. The following classifiers update only a subset of the model's parameters but are affected by early model parameters, allowing them to still make use of earlier computations when processing an instance. We clarify that all model weights are updated simultaneously, as opposed to training the classifiers (and their corresponding layers) sequentially, which would have led to significantly longer fine-tuning, matching that of a Multi-Model model.
+
+# 4.2 A Better Speeds-Accuracy Curve
+
+We turn to evaluate the speed-accuracy curve of SWEET. We use the same experimental setup as in Section 3.2; we fine-tune two pre-trained LMs (BERT and DeBERTa) in two sizes (BASE, LARGE) over the same seven text classification tasks. We use the same exit points and evaluate over the entire validation set using confidence-based exiting. We compare SWEET to two baselines: a standard Early-Exit model and a Multi-Model model. We compute the speedup ratio using the same method as described in Section 3.3. For further implementation details, see Appendix A.
+
+Fig. 5 presents the speed-accuracy curves of all models, averaged across all tasks. The figure shows that at the fastest speeds, SWEET outperforms Early-Exit for all models and is comparable to, or outperforms, Multi-Model. However, for 3 out of the 4 models (all but  $\mathrm{BERT}_{\text{LARGE}}$ ), Early-Exit surpasses the performance of SWEET at slow speeds. SWEET's reduced scores at slow inference speeds are likely due to the lower capacity of the later classifiers, stemming from their restricted influence on early model parameters during fine-tuning.
+
+Fig. 6 presents results on individual tasks for
+
+$\mathrm{BERT}_{BASE}$ . On five out of seven tasks, SWEET outperforms both baselines at fast speeds (up to a speedup ratio of  $1/2$ ), suggesting that SWEET improves the performance of lower Early-Exit classifiers by avoiding conflicting gradients during training. For two tasks (MRPC and CoLA), SWEET suffers a considerable decrease in performance at slow inference speeds. For the other five tasks SWEET maintains comparable results to Early-Exit.
+
+It is also interesting to examine how SWEET affects individual Early-Exit classifiers. Table 1 shows the results of BERT's individual classifiers trained with SWEET compared to Early-Exit and Multi-Model. $^{14}$  SWEET classifiers close much of the gap between Early-Exit and Multi-Model: they outperform those of Early-Exit by  $1.1\%$  on average  $(1.2\%)$  for BERT,  $1.0\%$  for DeBERTa), with the margin being larger for the earliest classifier  $(3.4\%)$  for BERT,  $6.2\%$  for DeBERTa). The final two classifiers trained with SWEET achieve lower scores than those of Early-Exit  $(0.9\%)$  on average), probably due to the restricted influence those classifiers have on early model parameters. Our results hint that SWEET is able to effectively bridge the gap between Early-Exit and Multi-Model early classifiers, leading to a speed-accuracy curve favoring fast inference speeds.
+
+We note that during our experiments with Early-Exit and Multi-Model models, some models did not converge. In order to ensure the validity of our results, we repeated these experiments with different random seeds, which led to convergence. We emphasize that this did not occur during the training of models using SWEET.
+
+![](images/01108ddab7f9fa9cf895bcc9b8842ba40f2a87366cb172314bf4ddc52dd82be4.jpg)  
+Figure 6: Speed-accuracy curve for individual tasks, using a  $\mathrm{BERT}_{\mathrm{BASE}}$  model. SWET outperforms both baselines at fast speeds (lower values of  $x$ ) on five out of seven tasks. See Fig. 10 for  $\mathrm{BERT}_{\mathrm{LARGE}}$  and DeBERTa results.
+
+![](images/c6793d2840b9d00f1a774a08cede444aa4791440af8632c07dfe627e94e3cccc.jpg)  
+Figure 7: Speed-Accuracy curves with the learning-to-exit strategy. As with confidence-based methods, SWEET outperforms both baselines at fast speeds, while maintaining comparable results at slow speeds.
+
+# 5 Further Analysis
+
+We turn to evaluate the robustness of our approach. We start with evaluating SWEET using a different exit strategy. We then test how our results generalize when using varying amounts of training data.
+
+A different exit strategy: Learning to Exit Our experiments so far have used a confidence-based exit strategy (Section 2). Here we consider a different strategy—learning to exit (Xin et al., 2021), in which a separate module is trained for each classifier, learning whether the classifier's prediction should be trusted, and an exit should be made. This method also allows for a natural extension to regression problems, unlike confidence-based methods that are limited to classification tasks.
+
+We use BERT {BASE, LARGE} as a backbone
+
+model and fine-tune in the same procedure described in Section 3.3. Our results (Fig. 7) reveal that the methods behave similarly to the confidence-based setup; SWEET outperforms both baselines at the early stage of the curve (fast speeds), while performing on par with Early-Exit at slow speeds. We also measure the performance of individual exit layers, as in Section 3.2, for models fine-tuned using learning-to-exit. Our results (Table 4 in Appendix E) reveal a similar behavior to that of models fine-tuned using confidence based early exiting: Multi-Model classifiers surpass the performance of Early-Exit classifiers. Moreover, SWEET's early classifiers outperform those of Early-Exit, while later ones show a slight decrease in performance.
+
+Varying data sizes Our experiments so far have focused on low-resource setups (a training set of several thousand examples). We now evaluate how SWEET performs as we vary the amount of training data. We fine-tune a BERT<sub>BASE</sub> model on different portions of the MNLI dataset using the same experimental setup as in Section 3.2. Our results, shown in Fig. 8, indicate that SWEET is mostly beneficial when training data is limited to a few thousand examples, but still somewhat useful even with as many as 60K training instances. Nonetheless, the effects of conflicting gradients on the earliest Early-Exit classifier tend to disappear when training on the full dataset (400K instances), making it as good as the smallest Multi-Model classifier. Moreover, in that setup, the use of SWEET seems to substan
+
+![](images/0f13d70cd97c2b81636f607e04efb7f0693cbc46fe5a3fff7bf4c4f888f3e6ff.jpg)  
+BERTBASE  
+Figure 8: Speed-accuracy curves of  $\mathrm{BERT}_{BASE}$  models trained on varying sizes of the MNLI dataset. The title of each plot describes the amount of training data used in the fine-tuning phase. The benefits of using SWEET vanish with large amounts of training data.
+
+tially decrease the performance of later classifiers, suggesting that the harm caused by limiting the influence of classifiers on model parameters may grow with the amount of training data.
+
+# 6 Related Work
+
+Several approaches have been proposed for reducing the inference time of large models (Treviso et al., 2022). These include knowledge distillation (Ba and Caruana, 2014; Hinton et al., 2015), in which the knowledge of a large teacher model is transferred to a smaller student model; pruning (LeCun et al., 1989; Frankle and Carbin, 2018), which removes unnecessary model parameters; and weight quantization (Jacob et al., 2018; Zafrir et al., 2019), which reduces the floating point precision of model weights. See (Treviso et al., 2023, Section 6), for a recent survey. Adaptive inference methods studied in this work are an orthogonal approach, which can be used in combination with these methods (Schwartz et al., 2020b).
+
+The use of Adaptive inference in deep neural networks has been extensively studied, with successful implementations in various types of networks including recurrent neural networks (Graves, 2016) and convolutional neural networks (Teerapittayanon et al., 2016; Huang and Chen, 2018). In the context of this work, it has also been applied to existing backbone pre-trained language models: Xin et al. (2020) implemented early exit strategies on top of classification tasks. Zhou et al. (2020) Introduced a patience-based exiting, requiring sequential classifiers to agree on a label for a prediction to be made. Xin et al. (2021) extended the use of Early-Exit in Transformers to regression tasks, as well as addressed the issue of reduced performance of the final classifier through the use of an alter
+
+nating training algorithm. Schuster et al. (2021) proposed a confidence-based early exit model with guarantees on the agreement between early exit predictions and the final classifier.
+
+Liu et al. (2022) presented a strong baseline for efficient NLP by adding multiple classifiers to a BERT model during pre-training. Recently, Schuster et al. (2022) adjusted the Early-Exit method to language modeling for text generation, making dynamic computation at the single token level.
+
+Multi-Model approaches to adaptive inference have been proposed for vision tasks (Enomoro and Eda, 2021) as well as for NLP (Li et al., 2020; Varshney and Baral, 2022b). Mamou et al. (2023) introduced a two-tier design with a highly efficient model serving as the first model and a powerful model serving as the second, enabling the possibility of achieving extremely fast inference speed.
+
+Finally, the concept of conflicting gradients has been mainly studied in the context of multi-task learning, where a single model is faced with solving different tasks (Yu et al., 2020; Liu et al., 2021a). To the best of our knowledge, no previous work examined this in the context of Early-Exit.
+
+# 7 Conclusion
+
+In this work, we analyzed the performance of two common adaptive inference methods—Early-Exit and Multi-Model. We found evidence that model weights are updated by conflicting gradients in the training process of Early-Exit models, causing classifiers to perform at a sub-optimal level. Despite this, we showed that regarding the entire speed-accuracy curve, Early-Exit is still favorable to Multi-Model due to the overhead of using independent model runs in a Multi-Model setup.
+
+To address these findings, we proposed SWEET,
+
+a novel Early-Exit method, which avoids conflicting gradients by allocating each Early-Exit classifier a subset of model weights which are updated solely by it. We found that for Early-Exit models trained with SWEET, early classifiers perform better than those of standard Early-Exit, but later classifiers of SWEET are not as good. These measures lead to SWEET outperforming both Early-Exit and Multi-Model in fast speeds, with slightly worse results than Early-Exit at slow speeds.
+
+Overall, our results demonstrate that Early-Exit models can benefit from fine-tuning algorithms that are tailored to their architecture, and that SWEET is a promising approach for improving the speed-accuracy trade-off of Early-Exit models in the context of adaptive inference.
+
+# 8 Limitations
+
+This work focuses on the effects of adaptive inference in a low-resource setting, specifically when training data is limited. Our experiments (Section 5) suggest that the negative impact of conflicting gradients may be less prominent when larger amount of training data is available.
+
+Our experiments were conducted using relatively small pre-trained language models ( $\leq 350M$  parameters) due to computational constraints, and we defer the replication of our findings with larger, more powerful models to future work. Nonetheless, our results have important implications for the growing trend of increasingly large language models. We hope this work inspires further research on methods to reduce the computational cost of NLP.
+
+This work concentrates on evaluating the speed-accuracy trade-off of Multi-Model and Early-Exit at inference time. We recognize that there are additional factors, such as memory usage, batch processing, and training duration, that could be considered when comparing these methods.
+
+Finally, we experimented with seven text classification tasks in English. We recognize that results may vary for other tasks and languages.
+
+# Acknowledgements
+
+We acknowledge Yarden Tal for her early contributions to this work, and Gabriel Stanovsky for his advice and meaningful feedback. This work was supported in part by the Israel Science Foundation (grant no. 2045/21), NSF-BSF grant 2020793, and by a grant from Intel Labs.
+
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+
+# A Implementation Details
+
+Further implementation details For fine-tuning BERT models, we use a batch size of 16. For fine-tuning DeBERTa, due to GPU memory constraints, we use a batch size of 16 for BASE and 8 for LARGE. We fine tune the models for two epochs with a maximal sequence length of 256. We use  $\beta = 0.9$ , 0.999 for the AdamW optimizer with linear LR-decay. We optimize the initial learning rate for each method, model size & task by performing a search over five values {1e-5, 2e-5, 3e-5, 4e-5, 5e-5} and choose the value leading to the largest area under the speed-accuracy curve. Chosen LRs are presented in table Table 2
+
+All experiments were run on a single NVIDIA A5000 GPU. The overall computational budget was  $\sim 1000$  GPU hours. We implement all methods using the HuggingFace Transformer library (Wolf et al., 2020).
+
+Speedup evaluation The speed-up ratio of the model when using exit threshold  $t$  is calculated using the formula:
+
+$$
+\operatorname {s p e e d u p} _ {t} = \frac {\sum_ {i = 1} ^ {M} S _ {i} ^ {t} \cdot L _ {i}}{L _ {M} \cdot \sum_ {i = 1} ^ {M} S _ {i} ^ {t}} \tag {1}
+$$
+
+where  $M$  is the number of classifiers used for the model,  $L_{i}$  denotes the number of the layer preceding the  $i$ -th classification head and  $S_{i}^{t}$  denotes the number of samples classified by the  $i$ -th classifier when using threshold  $t$ .
+
+The same exit threshold can lead to different speedup ratios amongst models trained with different random seeds. We use linear interpolation to approximate the accuracy score at set speedup ratios. We evaluate at  $(1/12, 1/4, 1/2, 3/4, 1)^{15}$  and report the average across three random seeds as well as a  $95\%$  confidence interval. $^{16}$  We use temperature scaling (Guo et al., 2017) to make classifiers confidence, and therefore early-exiting decisions, more reliable. Note that this scaling is monotonic and therefore does not influence predictions.
+
+# B Conflicting Gradients
+
+We replicate the experiment done in Section 3.1 with another batch of size 16 to examine if our findings generalize. results presented in Fig. 9 show
+
+a similar trend to Fig. 3: Gradient updates of current classifiers are roughly orthogonal to those of future classifiers, whereas future classifier updates are more aligned.
+
+![](images/2bc7a657c42144c9049f04337c6f7aaa4b25682b0c1cfd7e1eb6aecbe30931b8.jpg)  
+Figure 9: Average cosine similarity between classifiers' gradient updates of model layers. C-i stands for Classifier  $i$ . Layer 1 (preceding C-1) is updated by 3 classifiers, while layers 4 (preceding C-2), and 6 (C-3) are updated by 3 & 2 classifiers respectively. For each layer, the gradient update of the following classifier is roughly orthogonal to those of future classifiers, whereas gradient updates of higher classifiers tend to better align with one another.
+
+# C DeBERTa Individual Layer Comparison
+
+Table 3 Shows individual classifier results for DeBERTa models. As with the BERT results, Multi-Model classifiers outperform corresponding Early-Exit classifiers. SWEET early classifiers are better than Early-Exit ones, while later classifiers tend to downgrade in performance.
+
+# D Individual Task Results
+
+Fig. 10 shows results on individual tasks for BERTLARGE and DeBERTa (BASE & LARGE). For BERTLARGE, SWEET outperforms both baselines throughout the entire speed-accuracy curve over all tasks examined. For DeBERTa models, results are similar to those of BERTBASE, where SWEET performs better at high speeds (small speedup ratio) and is dominated at low speeds (where later classifiers do most of the heavy lifting).
+
+<table><tr><td>Model</td><td>Size</td><td colspan="7">Task</td></tr><tr><td></td><td></td><td>SST-2</td><td>MRPC</td><td>CoLA</td><td>MNLI</td><td>QQP</td><td>QNLI</td><td>RTE</td></tr><tr><td rowspan="2">BERT</td><td>BASE</td><td>5\5\5</td><td>5\3\4</td><td>4\4\5</td><td>5\5\5</td><td>5\5\5</td><td>5\4\5</td><td>5\5\4</td></tr><tr><td>LARGE</td><td>4\2\2</td><td>4\5\4</td><td>4\3\4</td><td>4\3\4</td><td>5\3\4</td><td>4\4\3</td><td>3\3\3</td></tr><tr><td rowspan="2">DeBERTa</td><td>BASE</td><td>3\3\3</td><td>4\5\5</td><td>4\5\4</td><td>2\4\3</td><td>4\5\5</td><td>3\4\3</td><td>2\1\4</td></tr><tr><td>LARGE</td><td>2\4\3</td><td>3\2\1</td><td>3\3\2</td><td>2\2\2</td><td>2\2\3</td><td>3\2\1</td><td>1\2\2</td></tr></table>
+
+Table 2: Chosen initial learning rate to optimize area under the speed-accuracy curve of each model, size, task. All numbers should be multiplied by 1e-5.  $x \backslash y \backslash z$  represent the initial learning rate of Early-Exit\Multi-Model\SWEET respectively.  
+
+<table><tr><td>Size</td><td>Method</td><td colspan="4">Exit Layer</td></tr><tr><td></td><td></td><td>1</td><td>4</td><td>6</td><td>12</td></tr><tr><td rowspan="3">BASE</td><td>MM</td><td>60.10.4</td><td>74.60.6</td><td>78.31.1</td><td>82.20.7</td></tr><tr><td>EE</td><td>52.30.4</td><td>70.90.6</td><td>77.90.8</td><td>81.70.1</td></tr><tr><td>SWEET</td><td>59.11.5</td><td>72.40.2</td><td>75.11.1</td><td>79.50.5</td></tr><tr><td></td><td></td><td>1</td><td>6</td><td>12</td><td>24</td></tr><tr><td rowspan="3">LARGE</td><td>MM</td><td>61.90.1</td><td>76.20.4</td><td>80.20.9</td><td>86.80.2</td></tr><tr><td>EE</td><td>55.80.9</td><td>74.71.1</td><td>79.20.8</td><td>83.61.9</td></tr><tr><td>SWEET</td><td>61.30.7</td><td>76.00.5</td><td>77.80.4</td><td>82.70.4</td></tr></table>
+
+Table 3: Results of individual classification layers averaged over all tasks using DeBERTa as a backbone model. Best scores are highlighted in bold, standard deviation (across random seeds) is reported in subscript. The results for BERT models presented in Table 1.  
+
+<table><tr><td>Size</td><td>Method</td><td colspan="4">Exit Layer</td></tr><tr><td></td><td></td><td>1</td><td>4</td><td>6</td><td>12</td></tr><tr><td rowspan="3">BASE</td><td>MM</td><td>53.70.5</td><td>66.10.4</td><td>71.10.3</td><td>75.42.7</td></tr><tr><td>EE</td><td>49.51.1</td><td>63.00.2</td><td>70.00.6</td><td>75.30.4</td></tr><tr><td>SWEET</td><td>53.50.4</td><td>64.90.9</td><td>68.51.4</td><td>74.10.4</td></tr><tr><td></td><td></td><td>1</td><td>6</td><td>12</td><td>24</td></tr><tr><td rowspan="3">LARGE</td><td>MM</td><td>51.60.3</td><td>59.90.4</td><td>67.62.6</td><td>77.90.8</td></tr><tr><td>EE</td><td>50.50.8</td><td>59.30.9</td><td>68.81.3</td><td>76.61.6</td></tr><tr><td>SWEET</td><td>53.90.5</td><td>60.60.2</td><td>69.50.4</td><td>75.811.0</td></tr></table>
+
+Table 4: Results of individual classification layers averaged over all tasks using BERT as a backbone model, fine-tuned using learning-to-exit. Best scores are highlighted in bold, standard deviation (across random seeds) is reported in subscript.
+
+# E Learning-to-exit Individual Layer Comparison
+
+Table 4 Shows individual classifier results for BERT models fine tuned with the learning to exit strategy. As with the confidence-based results, Multi-Model classifiers outperform corresponding Early-Exit classifiers. SWEET early classifiers are better than Early-Exit ones, while later classifiers tend to downgrade in performance.
+
+![](images/bc16d91f92dc31c537519873d571f956a0c710c5e20a2d2d51fb11e886a19432.jpg)  
+Figure 10: Speed-accuracy curves for individual tasks. For  $\text{BERT}_{\text{LARGE}}$ , SWEET outperforms both baselines across the entire curve. For DeBERTa, SWEET performs better than Early-Exit at high speeds on 9 out of 14 experiments.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work? Section 8  
+A2. Did you discuss any potential risks of your work? Our work does not present any risks.  
+A3. Do the abstract and introduction summarize the paper's main claims? Section 1  
+A4. Have you used AI writing assistants when working on this paper? We used ChatGPT for assistance, purely with the language of the paper
+
+B Did you use or create scientific artifacts?
+
+Section 3 + 4
+
+B1. Did you cite the creators of artifacts you used? Section 3 + 4  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? We use publicly available data sets which are commonly used during research  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Such terms were not specified.  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? We use publicly available data sets which are commonly used during research  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? We use publicly available data sets which are commonly used during research  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Section 3 + 4, Appendix A
+
+C Did you run computational experiments?
+
+Section 3 + 4
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Section 1 + 3, Appendix A
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? Section 3 + 4, Appendix A  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Section 3 + 4  
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Appendix A
+
+# D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? No response.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? No response.  
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? No response.  
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? No response.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? No response.

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+        "type": "text",
+        "text": "junmshao@uestc.edu.cn",
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Pre-trained language models (PLMs) are known to be overly parameterized and have significant redundancy, indicating a small degree of freedom of the PLMs. Motivated by the observation, in this paper, we study the problem of re-parameterizing and fine-tuning PLMs from a new perspective: Discovery of intrinsic task-specific subspace. Specifically, by exploiting the dynamics of the fine-tuning process for a given task, the parameter optimization trajectory is learned to uncover its intrinsic task-specific subspace. A key finding is that PLMs can be effectively fine-tuned in the subspace with a small number of free parameters. Beyond, we observe some outlier dimensions emerging during fine-tuning in the subspace. Disabling these dimensions degrades the model performance significantly. This suggests that these dimensions are crucial to induce task-specific knowledge to downstream tasks.",
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+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Pre-trained Language Models (PLMs) have become the de facto methods for various natural language processing (NLP) tasks (Devlin et al., 2019; Radford et al., 2019; Liu et al., 2019). The typical paradigm is to pre-train a big language model on large-scale corpora and then fine-tune the model on small task-specific datasets to adapt to the downstream tasks. Despite the great success of this paradigm, two questions still come to our mind: (1) Why can a PLM with hundreds of millions of parameters be successfully fine-tuned on different downstream tasks using only hundreds or thousands of labeled samples? (2) Do we really need a full fine-tuning of all parameters of a PLM to reach state-of-the-art performance on downstream tasks? In this paper, we try to provide a new viewpoint on the two questions, and",
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+    {
+        "type": "text",
+        "text": "claim that: Fine-tuning happens only in some tiny task-specific subspaces, which can be effectively learned with a small number of free parameters.",
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+        "type": "text",
+        "text": "Recent studies have shown that PLMs are highly over-parameterized and robust to pruning (Frankle and Carbin, 2019; Chen et al., 2020; Prasanna et al., 2020; Gordon et al., 2020; Liang et al., 2021, 2022), and can be fine-tuned in parameter-efficient ways (Gong et al., 2022; Zaken et al., 2022; Mahabadi et al., 2021; Li and Liang, 2021). This emerging empirical evidence tends to point to one fact that there exist some intrinsic structures in PLMs that are responsible for inducing task-specific knowledge to downstream tasks. Notably, the recent work (Aghajanyan et al., 2021) provides a promising conclusion that PLMs can be re-parameterized and fine-tuned in random low-dimensional subspaces using random projection, and the dimensionality of the random subspace is orders of magnitude smaller than the dimensionality of the full parameter space. Their findings implicitly suggest the existence of such intrinsic structure in the PLMs, which is, however, understudied. To bridge this gap, we explicitly demonstrate that there exist task-specific low-dimensional subspaces in which PLMs can be effectively fine-tuned.",
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+        "text": "Inspired by the low dimensional landscape hypothesis (Li et al., 2022a) that a training trajectory of a neural network lies in a low-dimensional subspace, in this work, we thus resort to the fine-tuning trajectory to study the intrinsic task-specific subspaces of PLMs. We show that it is possible to uncover the intrinsic task-specific subspaces with a fine-tuning trajectory by finding its principal directions. The uncovered intrinsic task-specific subspaces usually have very low dimensionalities, but are quite effective in inducing task-specific knowledge. For example, by re-parameterizing the encoder and optimizing only 32 free parameters per",
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+        "type": "page_footnote",
+        "text": "* Canada CIFAR AI Chair.",
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+    {
+        "type": "page_footnote",
+        "text": "† Corresponding authors.",
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+    {
+        "type": "page_number",
+        "text": "1701",
+        "bbox": [
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+    {
+        "type": "footer",
+        "text": "Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics",
+        "bbox": [
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+    {
+        "type": "footer",
+        "text": "Volume 1: Long Papers, pages 1701-1713",
+        "bbox": [
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+    },
+    {
+        "type": "footer",
+        "text": "July 9-14, 2023 ©2023 Association for Computational Linguistics",
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+    {
+        "type": "text",
+        "text": "layer in the intrinsic task-specific subspace, the model allows achieving nearly the same performance as fine-tuning in the full parameter space. Moreover, we further show that the uncovered intrinsic task-specific subspaces have a certain transferability.",
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+        "type": "text",
+        "text": "Beyond this, we find that the model contains some outlier dimensions with abnormal spikes when fine-tuning in the intrinsic task-specific subspaces instead of a random subspace. Disabling these outlier dimensions degrades the model performance significantly. We believe that this phenomenon is related to the previously discovered outlier dimensions of PLMs (Luo et al., 2021; Kovaleva et al., 2021; Puccetti et al., 2022). However, there are essential differences between them, which we will discuss in the latter section.",
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+    {
+        "type": "text",
+        "text": "By exploring the intrinsic task-specific subspaces of PLMs, the main contributions of this paper are summarized as follows.",
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+    {
+        "type": "list",
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+        "list_items": [
+            "1. We interpret the ease of adapting PLMs to downstream tasks as fine-tuning happens in tiny intrinsic task-specific subspaces. Within this interpretation, we propose a method to uncover the subspaces by finding the principal directions of the fine-tuning trajectory.",
+            "2. We conduct extensive experiments on the GLUE benchmark using BERT and RoBERTa models to support our claims. We show that the models can be effectively fine-tuned with a very small number of parameters in the uncovered intrinsic task-specific subspaces.",
+            "3. We identify some outlier dimensions when fine-tuning in the intrinsic task-specific subspaces, and some empirical analysis is further given."
+        ],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Intrinsic Dimensionality. Li et al. (2018) first defined the intrinsic dimension of an objective function in the context of deep learning. They showed that various neural networks can be effectively re-parameterized and trained in random low-dimensional subspaces. Their findings shed light on understanding the high-dimensional landscape of complex neural networks. Following this, Aghajanyan et al. (2021) further measured the intrinsic dimensions of PLMs fine-tuning on downstream tasks. They showed that PLMs have very",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "low intrinsic dimensions ranging from hundreds to thousands. Qin et al. (2021) exploited the idea of intrinsic subspace and proposed a prompt tuning method for efficient training. In addition, the concept of intrinsic dimension is also related to the low-rank approximation of PLMs (Hu et al., 2022; Mahabadi et al., 2021; Chen et al., 2021), but their motivations are entirely different. The former aims to open the black box of models and explore the internal mechanisms of why they are effective, while the latter focuses on developing new methods to train the models efficiently.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The random projection has a long history in machine learning research community, and is a key tool to analyze the intrinsic dimension (Li et al., 2018; Aghajanyan et al., 2021). In the context of optimization, Gressmann et al. (2020) proposed a random bases descent algorithm to train neural networks in low-dimensional subspaces. However, the random projection inevitably introduces task-irrelevant information, and is not optimal for subspace learning. We believe that a more compact and task-specific subspace can be found in the model, which is the main motivation of this work. Gur-Ari et al. (2018) empirically found that gradient descent of neural networks happens in a tiny subspace, Li et al. (2022a) further developed a subspace learning algorithm DLDR that dynamically extracts the subspace from the optimization trajectory. Li et al. (2022b) leveraged the DLDR algorithm for adversarial training. However, to the best of our knowledge, there is no research on the discovery of non-random intrinsic task-specific subspace of PLMs.",
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+    {
+        "type": "text",
+        "text": "Outlier Dimensions in Pre-trained Language Models. Multiple studies have identified outlier dimensions in PLMs. Some works were motivated by calibrating the anisotropy behavior of hidden representation of PLMs (Timkey and van Schijndel, 2021; Ding et al., 2022; Luo et al., 2021; Su et al., 2021; Zhang et al., 2020). Another line of work identified certain outlier dimensions in PLMs that are very sensitive to the finetuning of downstream tasks (Kovaleva et al., 2021; Puccetti et al., 2022). Disabling these outlier dimensions degrades the model performance significantly. Luo et al. (2021) showed that the outlier dimensions are artefacts derived from positional embeddings and layer normalization. Puccetti et al. (2022) identified a correlation between outlier di",
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+    {
+        "type": "page_number",
+        "text": "1702",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "mensions and token frequency. It is worth noting that our findings differ largely from previous works in three ways: 1) The outlier dimensions in their context actually refer to output neurons. In our context, an outlier dimension refers to a specific model parameter. In other words, they consider abnormal outputs, while we consider abnormal weights. 2) The ways of identifying outlier dimensions are different. They identify outlier dimensions by examining abnormal outputs, while we find outlier dimensions by examining abnormal updates to weights. 3) The effects of disabling outlier dimensions are different. They show that disabling just one outlier neuron can result in a significant drop in performance. In contrast, disabling the top outlier weight has almost no effect on the model performance. However, the model performance will drop significantly if we disable more outlier weights. The reason for the emergence of these outlier dimensions remains unclear, and we aim to conduct further in-depth analysis in future work.",
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+    {
+        "type": "text",
+        "text": "3 Intrinsic Task-specific Subspaces Discovery in PLMs",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 Preliminary: Intrinsic Dimensionality",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The intrinsic dimension of an objective landscape is first defined by Li et al. (2018), which is the number of independent optimization variables with regard to minimizing the objective function. However, finding the exact intrinsic dimension is computationally intractable for complex objective functions like deep neural networks. Therefore, a random subspace training method is usually employed to estimate the intrinsic dimension (Li et al., 2018; Aghajanyan et al., 2021).",
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+    {
+        "type": "text",
+        "text": "Formally, let  $\\pmb{\\theta}^{D} \\in \\mathbb{R}^{D}$  be a parameter vector that parameterizes a model  $f(\\pmb{x};\\pmb{\\theta})$ . Take the BERT-base model as an example,  $\\pmb{\\theta}^{D}$  represents all BERT's parameters that are flattened into a 110M-dimensional vector.  $\\pmb{\\theta}_{0}^{D} \\in \\mathbb{R}^{D}$  denotes the initial parameterization,  $\\pmb{P} \\in \\mathbb{R}^{D \\times d}$  denotes a random projection matrix whose columns form an orthonormal basis for a randomly oriented  $d$ -dimensional subspace of  $\\mathbb{R}^{D}$ ,  $\\pmb{\\theta}^{d} \\in \\mathbb{R}^{d}$  denotes a parameter vector in a lower  $d$ -dimensional space. The model is fine-tuned in the lower  $d$ -dimensional subspace via the following reparameterization method:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\theta} ^ {D} = \\boldsymbol {\\theta} _ {0} ^ {D} + \\boldsymbol {P} \\boldsymbol {\\theta} ^ {d}. \\tag {1}\n$$\n",
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+    {
+        "type": "image",
+        "img_path": "images/71499a923b15013325fe1faa71e06c1d05bb8ccd45c6c86117c98b4a4bbe5449.jpg",
+        "image_caption": [
+            "Figure 1: An illustrative example of optimizing a model in the 3-dimensional space, while the optimization trajectory only lies in a 2-dimensional subspace. We call the subspace the intrinsic subspace for the model."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Note that  $\\theta_0^D$  and  $P$  are frozen during the training process, and only  $\\theta^d$  is trained by the gradient descent. In practice, the re-parameterization can be done in a layer-wise manner to save computational resources (Aghajanyan et al., 2021), and we also follow the layer-wise setting for our analysis.",
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+    {
+        "type": "text",
+        "text": "The intrinsic dimension of a PLM is estimated by grid searching the minimal  $d$  that makes the model reach  $90\\%$  of the full fine-tuning performance. Take the BERT-base model as an example, the intrinsic dimension for fine-tuning on the MRPC dataset is only 1861 (Aghajanyan et al., 2021), which is surprisingly small considering the original model has up to 110 million parameters.",
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+    {
+        "type": "text",
+        "text": "3.2 Finding Intrinsic Task-specific Subspaces",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Gur-Ari et al. (2018) showed strong empirical evidence that the gradient dynamically converges to a very small subspace in various large-scale deep-learning scenarios. The subspace is spanned by a few top eigenvectors of the Hessian, and the dimension is equal to the number of data classes. This also indicates that the training trajectory of neural networks lies in a low-dimensional subspace, which is in line with the conclusion of Li et al. (2022a). Considering an illustrative example in Fig. 1, the full parameter space contains three dimensions, but the training trajectory  $\\{\\pmb{\\theta}_i^D\\}_{i = 0,\\dots ,t}$  only lies in a 2-dimensional subspace  $S$  spanned by  $e_1$  and  $e_2$ . We call this subspace the intrinsic subspace because it has a minimal degree of freedom (Li et al., 2018) for the objective function to reach the optimum. The aforementioned random subspace can be seen as a naive estimation of  $S$ .",
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+    {
+        "type": "page_number",
+        "text": "1703",
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+    {
+        "type": "text",
+        "text": "We hypothesize that an intrinsic task-specific subspace exists for each downstream task when fine-tuning a PLM. Generally, it is intractable to search such an intrinsic task-specific subspace directly. However, if our hypothesis is true, the finetuning trajectory will lie in a low-dimensional subspace. Thus we can resort to the fine-tuning trajectory to obtain an approximation of the intrinsic task-specific subspace. Specifically, given a finetuning trajectory  $\\{\\pmb{\\theta}_i^D\\}_{i=0,\\dots,t}$  of a PLM on a downstream task, we stack it into a matrix  $\\mathbf{W} \\in \\mathbb{R}^{t \\times D}$ , and apply Singular Value Decomposition (SVD) on it.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {W} = \\boldsymbol {U} \\boldsymbol {\\Sigma} \\boldsymbol {V} ^ {T}, \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\pmb{\\Sigma} \\in \\mathbb{R}^{t \\times t}$  is the singular value matrix,  $U \\in \\mathbb{R}^{t \\times t}$  and  $V \\in \\mathbb{R}^{D \\times t}$  are two real orthogonal matrices whose columns are left and right singular vectors, respectively<sup>1</sup>. It is worth noting that the columns of  $V$  are actually the principal directions of the given trajectory if zero empirical means of columns, and these directions constitute an orthonormal basis of the subspace in which the trajectory lies. Theoretically, a  $(t-1)$ -dimensional subspace needs only  $t$  independent points to determine. We can regard this subspace as an approximation of the intrinsic task-specific subspace whose dimension is equal to the number of points in the trajectory. Thus, we can replace the random projection matrix  $P$  in Eq. (1) with  $V$  to re-parameterize the model.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.3 Fine-tuning in Intrinsic Task-specific Subspaces",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given an approximated intrinsic task-specific subspace  $V$ , we reformulate Eq. (1) by letting the model train in the subspace as follows.",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\theta} ^ {D} = \\boldsymbol {\\theta} _ {0} ^ {D} + \\boldsymbol {V} \\boldsymbol {\\theta} ^ {t}. \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "In our early exploration, we can achieve good performance close to full fine-tuning by Eq. (3). However, the performance is not stable, and sensitive to the initialization of  $\\pmb{\\theta}^{t}$ . To solve this problem, we propose an ensemble-like method that combines multiple  $\\pmb{\\theta}^{t}$  of different initialization to reduce variance, which is as follows.",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\theta} ^ {D} = \\boldsymbol {\\theta} _ {0} ^ {D} + \\boldsymbol {V} \\sum_ {i = 1} ^ {h} \\frac {1}{h} \\boldsymbol {\\theta} ^ {t (i)}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $h$  is the number of vectors to combine, and we set it as 16 in this paper. Note that although the ensemble increases the number of parameters to optimize, it does not change the intrinsic dimensionality of the subspace (i.e., the degree of freedom).",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "In the following experimental evaluation, we will investigate subspace fine-tuning in both transductive and inductive settings to verify our hypotheses. The former is to verify the existence of intrinsic task-specific subspaces when fine-tuning PLMs on the downstream tasks, and the effectiveness of our method to uncover the subspaces. The latter further examines how well the intrinsic task-specific subspaces can be transferred to other similar tasks.",
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+    {
+        "type": "text",
+        "text": "4 Experiment and Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 Experimental Settings",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets and models. We evaluate the performance of the methods on the commonly used GLUE benchmark (Wang et al., 2018; Warstadt et al., 2019; Socher et al., 2013; Dolan and Brockett, 2005; Cer et al., 2017; Williams et al., 2018; Rajpurkar et al., 2016). For evaluation metrics, we report the matched accuracy for MNLI, Matthews correlation for CoLA, Pearson correlation for STS-B, and accuracy for other tasks. We choose the publicly available pre-trained language models RoBERTa-base (Liu et al., 2019) and BERT-base-cased (Devlin et al., 2019) for analysis. All experimental results are averaged over 5 runs of different seeds.",
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+        "type": "text",
+        "text": "Implementation details. Our implementation is based on HuggingFace's Transformers toolkit (Wolf et al., 2020). We first need to produce a set of fine-tuning trajectories of GLUE tasks for calculating projection matrices. We use the default script in the toolkit for fine-tuning, and save a checkpoint every epoch to obtain optimization trajectories. We set the trajectory length to 32 except for the MNLI dataset, which is set to 64 since it is the largest dataset and needs more parameters to fit. We flatten all parameters in an encoder layer into a wide vector, and then stack all vectors of different checkpoints into a matrix to perform SVD. We compute independent projection matrices for all layers, resulting in 12 projection matrices. For transductive subspace fine-tuning, the projection matrix is calculated from the same task,",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>We assume  $t \\ll D$  and thus compact SVD is applied.",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "1704",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/16f5cda4aff688f555ac4ebab1282e9a8b097d9d24180975403c67102cc6c021.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CoLA</td><td>MRPC</td><td>SST-2</td><td>STS-B</td><td>QQP</td><td>MNLI</td><td>QNLI</td><td>RTE</td><td>Avg.</td></tr><tr><td>BERT-Full</td><td>59.37</td><td>84.46</td><td>91.95</td><td>89.08</td><td>91.07</td><td>83.39</td><td>90.77</td><td>66.93</td><td>82.13</td></tr><tr><td>BERT-Freeze</td><td>27.52</td><td>69.66</td><td>88.81</td><td>78.35</td><td>84.48</td><td>71.55</td><td>81.61</td><td>56.46</td><td>69.81</td></tr><tr><td>BERT-Random</td><td>37.89</td><td>70.78</td><td>89.47</td><td>81.41</td><td>85.86</td><td>72.91</td><td>83.38</td><td>58.63</td><td>72.54</td></tr><tr><td>BERT-Intrinsic</td><td>60.27</td><td>84.31</td><td>89.93</td><td>89.51</td><td>89.73</td><td>81.21</td><td>87.73</td><td>67.00</td><td>81.21</td></tr><tr><td>RoBERTa-Full</td><td>61.04</td><td>89.31</td><td>94.29</td><td>90.70</td><td>91.72</td><td>87.23</td><td>92.48</td><td>76.68</td><td>85.43</td></tr><tr><td>RoBERTa-Freeze</td><td>0.00</td><td>68.38</td><td>85.32</td><td>15.69</td><td>82.81</td><td>71.16</td><td>79.11</td><td>53.86</td><td>57.04</td></tr><tr><td>RoBERTa-Random</td><td>27.58</td><td>68.38</td><td>91.45</td><td>75.47</td><td>86.33</td><td>77.10</td><td>84.49</td><td>58.27</td><td>71.13</td></tr><tr><td>RoBERTa-Intrinsic</td><td>61.07</td><td>87.21</td><td>92.43</td><td>89.43</td><td>90.18</td><td>85.53</td><td>90.57</td><td>78.77</td><td>84.40</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Transductive intrinsic subspace fine-tuning on the GLUE benchmark. Full denotes fine-tuning in the full-parameter space. Freeze denotes fine-tuning with the encoder frozen. Random denotes fine-tuning in a random subspace. Intrinsic denotes fine-tuning in the intrinsic task-specific subspaces. The subspace dimension is set to 32 except MNLI is 64. The best results are marked in bold, and the second-best results are underlined.",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/ffc8363cc35eadc79654a4627f0070b0bc09882e1a5abaf40bdcb8d23e1c722a.jpg",
+        "image_caption": [
+            "Figure 2: Inductive intrinsic subspace fine-tuning on the GLUE benchmark. Columns are the target tasks to be fine-tuned, and rows are source tasks that provide the transferred subspaces. Numbers in cells are performance drop of fine-tuning target tasks with the subspaces provided by source tasks. The last column is the average of other columns. Note that the numbers cannot be compared across columns because they are in different metrics."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/7b2044ad67456248c8fcc648244f1d2aa3a52c023ef38c4e2834ed94d50aa743.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "while for inductive subspace fine-tuning, it is calculated from other tasks. We only re-parameterize the encoder layers into the subspaces and leave the embedding layer and the last classification layer in their original parameter space. We freeze the initial model  $\\theta_0^D$  and the projection matrix  $V$ , and only tune the low-dimensional vector  $\\theta^t$ . We keep the learning rate of the embedding and classification layers unchanged and set the learning rate of  $\\theta^t$  to 0.01.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.2 Transductive Intrinsic Subspace Fine-tuning",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 1 summarizes the experimental results. We can see that freezing the encoder significantly degrades the model performance as it serves as a naive baseline (Note that it implies fine-tuning in",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the null space, i.e.,  $V\\theta^t = 0$ , which brings no information to update the model). For intrinsic subspace fine-tuning, we can clearly see that it shows comparable performance to the full fine-tuning across all GLUE tasks and models. In contrast, random projection only yields a marginal improvement over the baseline, and significantly underperforms intrinsic subspace fine-tuning.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "From these empirical results, we first conclude that PLMs can be re-parameterized and fine-tuned in some low-dimensional subspaces. Secondly, there exist some subspaces in which the PLMs can most effectively adapt to downstream tasks, and we can uncover these subspaces by finding the principal directions of fine-tuning trajectories in the full parameter space. This conclusion in turn suggests that fine-tuning of PLMs happens in tiny",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "1705",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/86feb5f8e5dd90448ebea216ee240e49b22ad22b9544ee71a64df65efda33b38.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CoLA</td><td>MRPC</td><td>SST-2</td><td>STS-B</td><td>QQP</td><td>MNLI</td><td>QNLI</td><td>RTE</td><td>Avg.</td></tr><tr><td>BERT-Full</td><td>59.37</td><td>84.46</td><td>91.95</td><td>89.08</td><td>91.07</td><td>83.39</td><td>90.77</td><td>66.93</td><td>82.13</td></tr><tr><td>BERT-Random</td><td>32.49</td><td>70.15</td><td>88.65</td><td>79.29</td><td>84.84</td><td>71.75</td><td>82.29</td><td>57.11</td><td>70.82</td></tr><tr><td>BERT-Zeroshot</td><td>35.35</td><td>78.09</td><td>91.06</td><td>85.17</td><td>87.57</td><td>75.29</td><td>84.01</td><td>75.23</td><td>76.47</td></tr><tr><td>BERT-Unified</td><td>61.58</td><td>84.41</td><td>91.06</td><td>89.71</td><td>91.27</td><td>83.85</td><td>90.97</td><td>67.00</td><td>82.48</td></tr><tr><td>RoBERTa-Full</td><td>61.04</td><td>89.31</td><td>94.29</td><td>90.70</td><td>91.72</td><td>87.23</td><td>92.48</td><td>76.68</td><td>85.43</td></tr><tr><td>RoBERTa-Random</td><td>0.00</td><td>68.38</td><td>89.47</td><td>27.60</td><td>84.51</td><td>73.16</td><td>82.10</td><td>54.44</td><td>59.96</td></tr><tr><td>RoBERTa-Zeroshot</td><td>32.93</td><td>80.44</td><td>90.60</td><td>83.10</td><td>87.12</td><td>78.76</td><td>84.46</td><td>67.12</td><td>75.57</td></tr><tr><td>RoBERTa-Unified</td><td>63.80</td><td>89.12</td><td>93.55</td><td>90.88</td><td>91.85</td><td>87.20</td><td>92.36</td><td>77.91</td><td>85.83</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Intrinsic subspace fine-tuning in the unified task subspace. Random denotes fine-tuning in a random subspace (dim=8). Zereshot denotes fine-tuning in the unified task subspace with itself removed (dim=7). Unified denotes fine-tuning in the unified task subspace (dim=8).",
+        "bbox": [
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+            292
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "subspaces, which provides an explanation of the ease of adapting PLMs to downstream tasks.",
+        "bbox": [
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+            350
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 Inductive Intrinsic Subspace Fine-tuning",
+        "text_level": 1,
+        "bbox": [
+            112,
+            376,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Next, we conduct inductive intrinsic subspace finetuning to examine the transferability of the discovered subspaces. We generally follow the same training protocol as in the last section, except that we replace the projection matrices with the ones calculated from other tasks.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We can observe the performance drop using transferred task subspaces in Fig. 2. Generally, we can see that even though the models are finetuned in transferred subspaces, they still outperform the random subspace baseline, which suggests the transferability of intrinsic task-specific subspaces.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The transferability of subspaces seems to correlate with the scale of the transferred task. For example, big datasets like SST-2, QQP, MNLI and QNLI underperform small datasets like CoLA, MRPC, STS-B, and RTE in providing subspaces. This is because the intrinsic task-specific subspaces of complex tasks have higher dimensions and need more parameters to estimate.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "When comparing within one column, we can see significant difference between distinct subspaces used for fine-tuning one task. We assume similar tasks may have substantial subspace intersections and thus be easier to transfer. Still, this claim needs further analysis to confirm, we will leave it further study since transferability is not the main focus of this paper. In summary, we empirically show that the intrinsic task-specific subspace has a certain transferability.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4 Unified Intrinsic Task Subspace",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Qin et al. (2021) showed that a unified low-dimensional intrinsic task subspace can be constructed by a multi-task prompt tuning method. In our case, we can also construct a unified subspace by stacking the fine-tuning trajectories of different tasks into a matrix, and applying SVD on it. Specifically, we sample one checkpoint for each task and gather them to calculate the unified subspace, which forms an 8-dimensional subspace. And we additionally calculate a zero-shot subspace of a task for comparison, which is calculated by excluding the checkpoint of this task. The results are given in Table 2. We can see that the models can be effectively fine-tuned in the unified subspace. For the zero-shot setting, the model performance decreases significantly, but still outperforms the random baseline.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/20fef6782993afbd12ec69771f05760723f0d4ba880e00872a54316e3d0f657b.jpg",
+        "image_caption": [
+            "Figure 3: The cosine similarities between the low-dimensional parameter vectors  $\\pmb{\\theta}^t$  of different tasks in the unified intrinsic task subspace. Similarities are averaged over layers and ensembles."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            515,
+            626,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "1706",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/fee98878f24a83d5adce07984caf52dc14b67ee78fa3ca194ca123083c31de08.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            157,
+            85,
+            843,
+            259
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/926085918447465bfda2e47173e00e1f0138f842bb7389fcdb56f2e0aa9a421e.jpg",
+        "image_caption": [
+            "Figure 4: Visualization of product of  $V\\theta^t$  using the BERT model to fine-tune in the intrinsic task-specific subspace (top) and a random subspace (bottom) on the MRPC dataset. Outlier dimensions appear in the intrinsic subspace but not in a random subspace."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            263,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we take the BERT model as an example and examine the low-dimensional parameter vector  $\\theta^t$  learned within the unified intrinsic subspace. We calculate the cosine similarities between the  $\\theta^t$  vectors corresponding to different tasks and present the results in Fig. 3. As shown in the figure, the cosine similarities between different tasks are significantly low, indicating that the unified intrinsic subspace contains disentangled knowledge distributed in different dimensions, and the low-dimensional parameter vector  $\\theta^t$  serves as an (unnormized) probability distribution to induce task-specific knowledge.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Based on these empirical findings, we conclude that a unified intrinsic task subspace is feasible and it contains disentangled knowledge. However, in-domain knowledge still plays a crucial role in forming the subspace as we can see that the zero-shot setting still has a large perform gap.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5 Outlier Dimensions",
+        "text_level": 1,
+        "bbox": [
+            112,
+            848,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We find that PLMs have a small number of outlier dimensions exhibiting abnormal spikes when fine-tuning in the intrinsic task-specific subspaces.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We examine each dimension of the product of  $V\\theta^t$  and consider the dimension whose absolute value is greater than a threshold as outlier. Note that the product of  $V\\theta^t$  is the learned parameter update in the full parameter space and we re-parameterize the encoder of the PLM layer-wisely, thus it is a vector with the dimension equal to the number of all parameters of an encoder layer.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It is important to note that the outlier dimension in our context is different from the previous studies (Kovaleva et al., 2021; Luo et al., 2021; Puccetti et al., 2022). Previous studies use the outlier dimension to refer to the output channel (768 dimensions for BERT-base). In our context, we flatten all parameters of a layer into a vector (7,087,872 dimensions for BERT-base). Then an outlier dimension refers to a specific parameter weight in the layer. We use the BERT model and MRPC dataset for illustration, and visualize the product of  $V\\theta^{t}$  in Fig. 4 to show the outlier patterns. As we can see from the figure, when fine-tuning in the intrinsic task-specific subspace, the outlier patterns exist in all layers. In contrast, these outlier patterns disappear when fine-tuning in a random subspace.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "1707",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/79fefb5b3496cf3b51c43a7684d3928b367827e5ac52bc8b797ff7c26c86a327.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CoLA</td><td>MRPC</td><td>SST-2</td><td>STS-B</td><td>QQP</td><td>MNLI</td><td>QNLI</td><td>RTE</td></tr><tr><td>BERT-Full</td><td>59.37</td><td>84.46</td><td>91.95</td><td>89.08</td><td>91.07</td><td>83.39</td><td>90.77</td><td>66.93</td></tr><tr><td>BERT-Random</td><td>57.27</td><td>84.46</td><td>91.79</td><td>88.66</td><td>90.66</td><td>83.68</td><td>90.41</td><td>64.48</td></tr><tr><td>BERT-Outlier</td><td>0.00</td><td>68.38</td><td>50.92</td><td>0.00</td><td>63.18</td><td>33.64</td><td>49.89</td><td>52.71</td></tr><tr><td>RoBERTa-Full</td><td>61.04</td><td>89.31</td><td>94.29</td><td>90.70</td><td>91.72</td><td>87.23</td><td>92.48</td><td>76.68</td></tr><tr><td>RoBERTa-Random</td><td>58.80</td><td>87.65</td><td>93.95</td><td>89.52</td><td>91.29</td><td>87.76</td><td>92.61</td><td>68.88</td></tr><tr><td>RoBERTa-Outlier</td><td>0.00</td><td>70.49</td><td>50.92</td><td>28.05</td><td>63.67</td><td>36.15</td><td>49.89</td><td>52.71</td></tr></table>",
+        "bbox": [
+            115,
+            80,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/ec0920cb94e8a5cd438583d7f634a97a19932fd932eaf1110a92c940cba41616.jpg",
+        "table_caption": [
+            "Table 3: Evaluation on the GLUE benchmark when the outlier dimensions are zeroed. The results with the most performance loss are marked in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model component</td><td>Layer</td><td># of outliers each layer</td></tr><tr><td>attention.self.query.weight</td><td>1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12</td><td>3, 1, 1, 1, 4, 4, 8, 3, 3, 2, 4</td></tr><tr><td>attention.self.query.bias</td><td>1</td><td>1</td></tr><tr><td>attention.self.key.bias</td><td>10, 11</td><td>2, 1</td></tr><tr><td>attention.output LayerNorm.weight</td><td>1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12</td><td>1, 2, 3, 5, 4, 1, 2, 4, 1, 3, 2</td></tr><tr><td>attention.output LayerNorm.bias</td><td>1, 2, 3</td><td>1, 1, 1</td></tr><tr><td>intermediate.dense.weight</td><td>1, 12</td><td>2, 1</td></tr><tr><td>output.dense.weight</td><td>1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11</td><td>2, 6, 5, 4, 2, 4, 3, 2, 3, 4, 4</td></tr><tr><td>output LayerNorm.weight</td><td>5, 6, 7, 12</td><td>4, 1, 1, 3</td></tr></table>",
+        "bbox": [
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+            256,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Sampled outlier dimensions in the BERT model. The left column shows the model component containing outlier dimensions. The middle column shows the layer where the model component contains outlier dimensions. The right column shows the number of outlier dimensions in the corresponding layer.",
+        "bbox": [
+            112,
+            423,
+            882,
+            468
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This phenomenon is universal for different models and different datasets.",
+        "bbox": [
+            112,
+            492,
+            485,
+            524
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To investigate the effect of the outlier dimensions on the models, we disable them by setting them to zero and examine how this affects model performance. We first disable the top outlier dimension of each encoder layer and fine-tune the model in the full parameter space, which has almost no impact on model performance. This result is not surprising because disabling only one weight in a layer definitely has a negligible effect on the output than disabling an output channel as the previous studies do. We continue to disable more outlier dimensions, and these deviating at least  $3\\sigma$  from the mean are disabled. Approximately  $0.3\\%$  of encoder parameters are disabled. We also randomly sample and disable the same number of dimensions for comparison, and the results are shown in Table 3. We can see that disabling outlier dimensions degrades the model performance significantly while disabling random dimensions does not.",
+        "bbox": [
+            112,
+            527,
+            489,
+            850
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Next, we qualitatively examine the positions in which the outlier dimensions emerge. We sample each layer's top 10 outlier dimensions and record their positions in Table 4. We can see",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "that the outlier dimensions are ubiquitous in various model components. Then, we identify one outlier dimension  $O1$  that consistently produces high-magnitude weights in almost all BERT layers. Furthermore, we find that there is a considerable overlap in the outlier dimensions of each layer, which suggests that these dimensions can propagate through layers.",
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+        "type": "text",
+        "text": "Why do outlier dimensions emerge? Previous studies came up with several explanations like high-magnitude scaling factors (Kovaleva et al., 2021), LayerNorm and residual connection (Luo et al., 2021), and unbalanced token frequency (Puccetti et al., 2022). However, these explanations cannot apply to our case because the definitions of the outlier dimension are different. Recall that our approach to identifying outlier dimensions is actually examining re-parameterized parameter updates given the intrinsic task-specific subspace. The magnitude of the updates represents the importance of corresponding parameters with respect to solving the task. We have reason to believe that these dimensions play an important role in constituting the intrinsic subspace and are crucial to induce task-specific knowledge to adapt to downstream tasks.",
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+        "text": "1708",
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+    {
+        "type": "text",
+        "text": "5 Conclusion",
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+        "text": "In this paper, we claim that the fine-tuning of PLMs happens in tiny subspaces. To uncover such intrinsic task-specific subspaces, we exploit the fine-tuning trajectory to find its main direction. Our empirical experiments show that PLMs can effectively adapt to downstream tasks when re-parameterizing and training in the found subspaces, which well explains the ease of adapting PLMs to downstream tasks. Furthermore, we find outlier dimensions in PLMs during the subspace training. We consider that these dimensions are crucial to induce task-specific knowledge to downstream tasks. Still, we need further in-depth analysis to understand the reasons and impact of the emergence of outlier patterns.",
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+        "type": "text",
+        "text": "Limitations",
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+        "text": "Despite the insights obtained through our analysis, certain limitations persist, which we outline in this section.",
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+        "text": "With respect to the re-parameterization of parameters as presented in Eq. (3), we adopted the layer-wise setting as proposed by Aghajanyan et al. (2021) in order to alleviate memory and computational burdens. Nonetheless, such a setting restricts us to only identifying local subspaces, rather than discovering global subspaces within the entire parameter space of a pre-trained language model. The existence of a task-specific global subspace is yet to be ascertained. If such a subspace does exist, the correlation between this global subspace and the identified local subspaces needs to be explored in future research.",
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+        "type": "text",
+        "text": "In terms of experimental settings, the evaluation tasks are limited to natural language understanding tasks, with a lack of natural language generation tasks. On model architecture, decoder-only (e.g., GPT) and encoder-decoder (e.g., T5) models are not included. On model scale, we use basic-size models rather than large ones due to limited computational resources. Consequently, the conclusions drawn in this study may not be applicable to the above situations.",
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+        "type": "text",
+        "text": "The analysis presented in Section 4.5 demonstrates that pre-trained language models exhibit a small number of outlier dimensions when finetuning in the intrinsic task-specific subspaces. Although we have observed a significant decline in model performance when disabling these dimensions, the underlying mechanism responsible for",
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+        "type": "text",
+        "text": "the emergence of these outlier dimensions remains unclear.",
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+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
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+        "text": "This work is supported by the Sichuan key research program (22ZDYF3388), Fundamental Research Funds for the Central Universities (ZYGX2019Z014), National Natural Science Foundation of China (61976044, 52079026), Fok YingTong Education Foundation for Young Teachers in the Higher Education Institutions of China (161062), the Canada CIFAR AI Chair Program, and the Canada NSERC Discovery Grant (RGPIN-2021-03115).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References",
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+        "text": "Zhong Zhang, Chongming Gao, Cong Xu, Rui Miao, Qinli Yang, and Junming Shao. 2020. Revisiting representation degeneration problem in language modeling. In *Findings of the Association for Computational Linguistics: EMNLP* 2020, pages 518-527.",
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+        "type": "text",
+        "text": "A Appendix",
+        "text_level": 1,
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+        "text": "A.1 Hyperparameters",
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+        "type": "text",
+        "text": "We first fine-tune the BERT and RoBERTa models for calculating projection matrices. We use the fine-tuning script in the Transformers toolkit<sup>2</sup>. All hyperparameters remain default except for the number of epochs, which is set to 32 and 64 for the MNLI and all other tasks, respectively. For intrinsic subspace fine-tuning, the dimensionality of  $\\theta^t$  is set to 32 and 64 for the MNLI and all other tasks, respectively. The learning rate of  $\\theta^t$  is set to 0.01. The number of ensembles  $h$  is set to 16. Other hyperparameter are the same as those in the script. All experimental results are averaged over 5 runs of different seeds. Each experiment is conducted on a single GeForce RTX 2080Ti GPU with environment of Pytorch 1.11.0 + CUDA 11.3.1.",
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+        "type": "text",
+        "text": "A.2 Ablation study",
+        "text_level": 1,
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+        "text": "We conduct an ablation experiment over the number of dimensions of the subspaces. The results are given in Table 5 and Table 6. The performance increases as the number of dimensions increases.",
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+        "img_path": "images/908cd998bc960f8b14a8a287c4d02a44501f4d385b1b53516142a7d9d9825612.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Tasks</td><td>dim=8</td><td>dim=16</td><td>dim=32</td></tr><tr><td>CoLA</td><td>54.06</td><td>57.17</td><td>60.27</td></tr><tr><td>MRPC</td><td>75.05</td><td>77.94</td><td>84.31</td></tr><tr><td>SST-2</td><td>89.52</td><td>90.05</td><td>89.93</td></tr><tr><td>STS-B</td><td>87.95</td><td>89.02</td><td>89.51</td></tr><tr><td>QQP</td><td>87.61</td><td>89.12</td><td>89.73</td></tr><tr><td>MNLI</td><td>76.93</td><td>78.48</td><td>78.70</td></tr><tr><td>QNLI</td><td>86.54</td><td>86.83</td><td>87.73</td></tr><tr><td>RTE</td><td>65.41</td><td>66.07</td><td>67.00</td></tr></table>",
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+        "type": "table",
+        "img_path": "images/1d637de4446bbd3a0079a8f60f29db649c8bfc664b2c657cdd4f720ffe0ac079.jpg",
+        "table_caption": [
+            "Table 5: Ablation study for the BERT model."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Tasks</td><td>dim=8</td><td>dim=16</td><td>dim=32</td></tr><tr><td>CoLA</td><td>58.04</td><td>60.27</td><td>61.07</td></tr><tr><td>MRPC</td><td>75.59</td><td>78.20</td><td>87.21</td></tr><tr><td>SST-2</td><td>91.93</td><td>92.34</td><td>92.43</td></tr><tr><td>STS-B</td><td>84.10</td><td>88.10</td><td>89.43</td></tr><tr><td>QQP</td><td>87.58</td><td>89.25</td><td>90.18</td></tr><tr><td>MNLI</td><td>79.96</td><td>81.77</td><td>82.32</td></tr><tr><td>QNLI</td><td>89.35</td><td>89.14</td><td>90.57</td></tr><tr><td>RTE</td><td>74.30</td><td>78.56</td><td>78.77</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 6: Ablation study for the RoBERTa model.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{2}$ https://github.com/huggingface/ transformers/tree/main/examples/pytorch/text-classification",
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+    {
+        "type": "page_number",
+        "text": "1711",
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+    },
+    {
+        "type": "text",
+        "text": "A For every submission:",
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+        "page_idx": 11
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "A1. Did you describe the limitations of your work? Section Limitations.",
+            "A2. Did you discuss any potential risks of your work? Section Limitations.",
+            "A3. Do the abstract and introduction summarize the paper's main claims? Abstract, Section 1.",
+            "A4. Have you used AI writing assistants when working on this paper? Left blank."
+        ],
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B Did you use or create scientific artifacts?",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Section 4.",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "B1. Did you cite the creators of artifacts you used? Section 4.",
+            "B2. Did you discuss the license or terms for use and / or distribution of any artifacts? We use open-source artifacts which can be used for academic research purposes.",
+            "B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? We use the artifacts in compliance with their licenses.",
+            "B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? We use the open-source GLUE dataset which does not contain sensitive information.",
+            "B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.",
+            "B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Section 4."
+        ],
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+    {
+        "type": "text",
+        "text": "C Did you run computational experiments?",
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+        ],
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+    },
+    {
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+        "text": "Section 4.",
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Appendix.",
+        "bbox": [
+            129,
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+    },
+    {
+        "type": "header",
+        "text": "ACL 2023 Responsible NLP Checklist",
+        "bbox": [
+            132,
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+            99
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_footnote",
+        "text": "The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.",
+        "bbox": [
+            112,
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+    {
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+    },
+    {
+        "type": "list",
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+        "list_items": [
+            "C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? No response.",
+            "C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Section 4",
+            "C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Section 4"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.",
+        "bbox": [
+            112,
+            293,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? Not applicable. Left blank.",
+            "D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? Not applicable. Left blank.",
+            "D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? Not applicable. Left blank.",
+            "D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? Not applicable. Left blank.",
+            "D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? Not applicable. Left blank."
+        ],
+        "bbox": [
+            127,
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+        ],
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+]

2023/Fine-tuning Happens in Tiny Subspaces_ Exploring Intrinsic Task-specific Subspaces of Pre-trained Language Models/02cdb8da-2abe-4d81-a26c-6d3cb079eafb_origin.pdf

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2023/Fine-tuning Happens in Tiny Subspaces_ Exploring Intrinsic Task-specific Subspaces of Pre-trained Language Models/full.md

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+# Fine-tuning Happens in Tiny Subspaces: Exploring Intrinsic Task-specific Subspaces of Pre-trained Language Models
+
+Zhong Zhang $^{1,2}$ , Bang Liu $^{3,*,\dagger}$ , Junming Shao $^{1,2,\dagger}$
+
+<sup>1</sup>University of Electronic Science and Technology of China, Chengdu, China
+
+$^{2}$ Shenzhen Institute for Advanced Study, UESTC, Shenzhen, China
+
+<sup>3</sup>Mila & Université de Montréal, Montréal, Canada
+
+zhongzhang@std.uestc.edu.cn,
+
+bang.liu@umontreal.ca,
+
+junmshao@uestc.edu.cn
+
+# Abstract
+
+Pre-trained language models (PLMs) are known to be overly parameterized and have significant redundancy, indicating a small degree of freedom of the PLMs. Motivated by the observation, in this paper, we study the problem of re-parameterizing and fine-tuning PLMs from a new perspective: Discovery of intrinsic task-specific subspace. Specifically, by exploiting the dynamics of the fine-tuning process for a given task, the parameter optimization trajectory is learned to uncover its intrinsic task-specific subspace. A key finding is that PLMs can be effectively fine-tuned in the subspace with a small number of free parameters. Beyond, we observe some outlier dimensions emerging during fine-tuning in the subspace. Disabling these dimensions degrades the model performance significantly. This suggests that these dimensions are crucial to induce task-specific knowledge to downstream tasks.
+
+# 1 Introduction
+
+Pre-trained Language Models (PLMs) have become the de facto methods for various natural language processing (NLP) tasks (Devlin et al., 2019; Radford et al., 2019; Liu et al., 2019). The typical paradigm is to pre-train a big language model on large-scale corpora and then fine-tune the model on small task-specific datasets to adapt to the downstream tasks. Despite the great success of this paradigm, two questions still come to our mind: (1) Why can a PLM with hundreds of millions of parameters be successfully fine-tuned on different downstream tasks using only hundreds or thousands of labeled samples? (2) Do we really need a full fine-tuning of all parameters of a PLM to reach state-of-the-art performance on downstream tasks? In this paper, we try to provide a new viewpoint on the two questions, and
+
+claim that: Fine-tuning happens only in some tiny task-specific subspaces, which can be effectively learned with a small number of free parameters.
+
+Recent studies have shown that PLMs are highly over-parameterized and robust to pruning (Frankle and Carbin, 2019; Chen et al., 2020; Prasanna et al., 2020; Gordon et al., 2020; Liang et al., 2021, 2022), and can be fine-tuned in parameter-efficient ways (Gong et al., 2022; Zaken et al., 2022; Mahabadi et al., 2021; Li and Liang, 2021). This emerging empirical evidence tends to point to one fact that there exist some intrinsic structures in PLMs that are responsible for inducing task-specific knowledge to downstream tasks. Notably, the recent work (Aghajanyan et al., 2021) provides a promising conclusion that PLMs can be re-parameterized and fine-tuned in random low-dimensional subspaces using random projection, and the dimensionality of the random subspace is orders of magnitude smaller than the dimensionality of the full parameter space. Their findings implicitly suggest the existence of such intrinsic structure in the PLMs, which is, however, understudied. To bridge this gap, we explicitly demonstrate that there exist task-specific low-dimensional subspaces in which PLMs can be effectively fine-tuned.
+
+Inspired by the low dimensional landscape hypothesis (Li et al., 2022a) that a training trajectory of a neural network lies in a low-dimensional subspace, in this work, we thus resort to the fine-tuning trajectory to study the intrinsic task-specific subspaces of PLMs. We show that it is possible to uncover the intrinsic task-specific subspaces with a fine-tuning trajectory by finding its principal directions. The uncovered intrinsic task-specific subspaces usually have very low dimensionalities, but are quite effective in inducing task-specific knowledge. For example, by re-parameterizing the encoder and optimizing only 32 free parameters per
+
+layer in the intrinsic task-specific subspace, the model allows achieving nearly the same performance as fine-tuning in the full parameter space. Moreover, we further show that the uncovered intrinsic task-specific subspaces have a certain transferability.
+
+Beyond this, we find that the model contains some outlier dimensions with abnormal spikes when fine-tuning in the intrinsic task-specific subspaces instead of a random subspace. Disabling these outlier dimensions degrades the model performance significantly. We believe that this phenomenon is related to the previously discovered outlier dimensions of PLMs (Luo et al., 2021; Kovaleva et al., 2021; Puccetti et al., 2022). However, there are essential differences between them, which we will discuss in the latter section.
+
+By exploring the intrinsic task-specific subspaces of PLMs, the main contributions of this paper are summarized as follows.
+
+1. We interpret the ease of adapting PLMs to downstream tasks as fine-tuning happens in tiny intrinsic task-specific subspaces. Within this interpretation, we propose a method to uncover the subspaces by finding the principal directions of the fine-tuning trajectory.  
+2. We conduct extensive experiments on the GLUE benchmark using BERT and RoBERTa models to support our claims. We show that the models can be effectively fine-tuned with a very small number of parameters in the uncovered intrinsic task-specific subspaces.  
+3. We identify some outlier dimensions when fine-tuning in the intrinsic task-specific subspaces, and some empirical analysis is further given.
+
+# 2 Related Work
+
+Intrinsic Dimensionality. Li et al. (2018) first defined the intrinsic dimension of an objective function in the context of deep learning. They showed that various neural networks can be effectively re-parameterized and trained in random low-dimensional subspaces. Their findings shed light on understanding the high-dimensional landscape of complex neural networks. Following this, Aghajanyan et al. (2021) further measured the intrinsic dimensions of PLMs fine-tuning on downstream tasks. They showed that PLMs have very
+
+low intrinsic dimensions ranging from hundreds to thousands. Qin et al. (2021) exploited the idea of intrinsic subspace and proposed a prompt tuning method for efficient training. In addition, the concept of intrinsic dimension is also related to the low-rank approximation of PLMs (Hu et al., 2022; Mahabadi et al., 2021; Chen et al., 2021), but their motivations are entirely different. The former aims to open the black box of models and explore the internal mechanisms of why they are effective, while the latter focuses on developing new methods to train the models efficiently.
+
+The random projection has a long history in machine learning research community, and is a key tool to analyze the intrinsic dimension (Li et al., 2018; Aghajanyan et al., 2021). In the context of optimization, Gressmann et al. (2020) proposed a random bases descent algorithm to train neural networks in low-dimensional subspaces. However, the random projection inevitably introduces task-irrelevant information, and is not optimal for subspace learning. We believe that a more compact and task-specific subspace can be found in the model, which is the main motivation of this work. Gur-Ari et al. (2018) empirically found that gradient descent of neural networks happens in a tiny subspace, Li et al. (2022a) further developed a subspace learning algorithm DLDR that dynamically extracts the subspace from the optimization trajectory. Li et al. (2022b) leveraged the DLDR algorithm for adversarial training. However, to the best of our knowledge, there is no research on the discovery of non-random intrinsic task-specific subspace of PLMs.
+
+Outlier Dimensions in Pre-trained Language Models. Multiple studies have identified outlier dimensions in PLMs. Some works were motivated by calibrating the anisotropy behavior of hidden representation of PLMs (Timkey and van Schijndel, 2021; Ding et al., 2022; Luo et al., 2021; Su et al., 2021; Zhang et al., 2020). Another line of work identified certain outlier dimensions in PLMs that are very sensitive to the finetuning of downstream tasks (Kovaleva et al., 2021; Puccetti et al., 2022). Disabling these outlier dimensions degrades the model performance significantly. Luo et al. (2021) showed that the outlier dimensions are artefacts derived from positional embeddings and layer normalization. Puccetti et al. (2022) identified a correlation between outlier di
+
+mensions and token frequency. It is worth noting that our findings differ largely from previous works in three ways: 1) The outlier dimensions in their context actually refer to output neurons. In our context, an outlier dimension refers to a specific model parameter. In other words, they consider abnormal outputs, while we consider abnormal weights. 2) The ways of identifying outlier dimensions are different. They identify outlier dimensions by examining abnormal outputs, while we find outlier dimensions by examining abnormal updates to weights. 3) The effects of disabling outlier dimensions are different. They show that disabling just one outlier neuron can result in a significant drop in performance. In contrast, disabling the top outlier weight has almost no effect on the model performance. However, the model performance will drop significantly if we disable more outlier weights. The reason for the emergence of these outlier dimensions remains unclear, and we aim to conduct further in-depth analysis in future work.
+
+# 3 Intrinsic Task-specific Subspaces Discovery in PLMs
+
+# 3.1 Preliminary: Intrinsic Dimensionality
+
+The intrinsic dimension of an objective landscape is first defined by Li et al. (2018), which is the number of independent optimization variables with regard to minimizing the objective function. However, finding the exact intrinsic dimension is computationally intractable for complex objective functions like deep neural networks. Therefore, a random subspace training method is usually employed to estimate the intrinsic dimension (Li et al., 2018; Aghajanyan et al., 2021).
+
+Formally, let  $\pmb{\theta}^{D} \in \mathbb{R}^{D}$  be a parameter vector that parameterizes a model  $f(\pmb{x};\pmb{\theta})$ . Take the BERT-base model as an example,  $\pmb{\theta}^{D}$  represents all BERT's parameters that are flattened into a 110M-dimensional vector.  $\pmb{\theta}_{0}^{D} \in \mathbb{R}^{D}$  denotes the initial parameterization,  $\pmb{P} \in \mathbb{R}^{D \times d}$  denotes a random projection matrix whose columns form an orthonormal basis for a randomly oriented  $d$ -dimensional subspace of  $\mathbb{R}^{D}$ ,  $\pmb{\theta}^{d} \in \mathbb{R}^{d}$  denotes a parameter vector in a lower  $d$ -dimensional space. The model is fine-tuned in the lower  $d$ -dimensional subspace via the following reparameterization method:
+
+$$
+\boldsymbol {\theta} ^ {D} = \boldsymbol {\theta} _ {0} ^ {D} + \boldsymbol {P} \boldsymbol {\theta} ^ {d}. \tag {1}
+$$
+
+![](images/71499a923b15013325fe1faa71e06c1d05bb8ccd45c6c86117c98b4a4bbe5449.jpg)  
+Figure 1: An illustrative example of optimizing a model in the 3-dimensional space, while the optimization trajectory only lies in a 2-dimensional subspace. We call the subspace the intrinsic subspace for the model.
+
+Note that  $\theta_0^D$  and  $P$  are frozen during the training process, and only  $\theta^d$  is trained by the gradient descent. In practice, the re-parameterization can be done in a layer-wise manner to save computational resources (Aghajanyan et al., 2021), and we also follow the layer-wise setting for our analysis.
+
+The intrinsic dimension of a PLM is estimated by grid searching the minimal  $d$  that makes the model reach  $90\%$  of the full fine-tuning performance. Take the BERT-base model as an example, the intrinsic dimension for fine-tuning on the MRPC dataset is only 1861 (Aghajanyan et al., 2021), which is surprisingly small considering the original model has up to 110 million parameters.
+
+# 3.2 Finding Intrinsic Task-specific Subspaces
+
+Gur-Ari et al. (2018) showed strong empirical evidence that the gradient dynamically converges to a very small subspace in various large-scale deep-learning scenarios. The subspace is spanned by a few top eigenvectors of the Hessian, and the dimension is equal to the number of data classes. This also indicates that the training trajectory of neural networks lies in a low-dimensional subspace, which is in line with the conclusion of Li et al. (2022a). Considering an illustrative example in Fig. 1, the full parameter space contains three dimensions, but the training trajectory  $\{\pmb{\theta}_i^D\}_{i = 0,\dots ,t}$  only lies in a 2-dimensional subspace  $S$  spanned by  $e_1$  and  $e_2$ . We call this subspace the intrinsic subspace because it has a minimal degree of freedom (Li et al., 2018) for the objective function to reach the optimum. The aforementioned random subspace can be seen as a naive estimation of  $S$ .
+
+We hypothesize that an intrinsic task-specific subspace exists for each downstream task when fine-tuning a PLM. Generally, it is intractable to search such an intrinsic task-specific subspace directly. However, if our hypothesis is true, the finetuning trajectory will lie in a low-dimensional subspace. Thus we can resort to the fine-tuning trajectory to obtain an approximation of the intrinsic task-specific subspace. Specifically, given a finetuning trajectory  $\{\pmb{\theta}_i^D\}_{i=0,\dots,t}$  of a PLM on a downstream task, we stack it into a matrix  $\mathbf{W} \in \mathbb{R}^{t \times D}$ , and apply Singular Value Decomposition (SVD) on it.
+
+$$
+\boldsymbol {W} = \boldsymbol {U} \boldsymbol {\Sigma} \boldsymbol {V} ^ {T}, \tag {2}
+$$
+
+where  $\pmb{\Sigma} \in \mathbb{R}^{t \times t}$  is the singular value matrix,  $U \in \mathbb{R}^{t \times t}$  and  $V \in \mathbb{R}^{D \times t}$  are two real orthogonal matrices whose columns are left and right singular vectors, respectively<sup>1</sup>. It is worth noting that the columns of  $V$  are actually the principal directions of the given trajectory if zero empirical means of columns, and these directions constitute an orthonormal basis of the subspace in which the trajectory lies. Theoretically, a  $(t-1)$ -dimensional subspace needs only  $t$  independent points to determine. We can regard this subspace as an approximation of the intrinsic task-specific subspace whose dimension is equal to the number of points in the trajectory. Thus, we can replace the random projection matrix  $P$  in Eq. (1) with  $V$  to re-parameterize the model.
+
+# 3.3 Fine-tuning in Intrinsic Task-specific Subspaces
+
+Given an approximated intrinsic task-specific subspace  $V$ , we reformulate Eq. (1) by letting the model train in the subspace as follows.
+
+$$
+\boldsymbol {\theta} ^ {D} = \boldsymbol {\theta} _ {0} ^ {D} + \boldsymbol {V} \boldsymbol {\theta} ^ {t}. \tag {3}
+$$
+
+In our early exploration, we can achieve good performance close to full fine-tuning by Eq. (3). However, the performance is not stable, and sensitive to the initialization of  $\pmb{\theta}^{t}$ . To solve this problem, we propose an ensemble-like method that combines multiple  $\pmb{\theta}^{t}$  of different initialization to reduce variance, which is as follows.
+
+$$
+\boldsymbol {\theta} ^ {D} = \boldsymbol {\theta} _ {0} ^ {D} + \boldsymbol {V} \sum_ {i = 1} ^ {h} \frac {1}{h} \boldsymbol {\theta} ^ {t (i)}, \tag {4}
+$$
+
+where  $h$  is the number of vectors to combine, and we set it as 16 in this paper. Note that although the ensemble increases the number of parameters to optimize, it does not change the intrinsic dimensionality of the subspace (i.e., the degree of freedom).
+
+In the following experimental evaluation, we will investigate subspace fine-tuning in both transductive and inductive settings to verify our hypotheses. The former is to verify the existence of intrinsic task-specific subspaces when fine-tuning PLMs on the downstream tasks, and the effectiveness of our method to uncover the subspaces. The latter further examines how well the intrinsic task-specific subspaces can be transferred to other similar tasks.
+
+# 4 Experiment and Analysis
+
+# 4.1 Experimental Settings
+
+Datasets and models. We evaluate the performance of the methods on the commonly used GLUE benchmark (Wang et al., 2018; Warstadt et al., 2019; Socher et al., 2013; Dolan and Brockett, 2005; Cer et al., 2017; Williams et al., 2018; Rajpurkar et al., 2016). For evaluation metrics, we report the matched accuracy for MNLI, Matthews correlation for CoLA, Pearson correlation for STS-B, and accuracy for other tasks. We choose the publicly available pre-trained language models RoBERTa-base (Liu et al., 2019) and BERT-base-cased (Devlin et al., 2019) for analysis. All experimental results are averaged over 5 runs of different seeds.
+
+Implementation details. Our implementation is based on HuggingFace's Transformers toolkit (Wolf et al., 2020). We first need to produce a set of fine-tuning trajectories of GLUE tasks for calculating projection matrices. We use the default script in the toolkit for fine-tuning, and save a checkpoint every epoch to obtain optimization trajectories. We set the trajectory length to 32 except for the MNLI dataset, which is set to 64 since it is the largest dataset and needs more parameters to fit. We flatten all parameters in an encoder layer into a wide vector, and then stack all vectors of different checkpoints into a matrix to perform SVD. We compute independent projection matrices for all layers, resulting in 12 projection matrices. For transductive subspace fine-tuning, the projection matrix is calculated from the same task,
+
+<table><tr><td></td><td>CoLA</td><td>MRPC</td><td>SST-2</td><td>STS-B</td><td>QQP</td><td>MNLI</td><td>QNLI</td><td>RTE</td><td>Avg.</td></tr><tr><td>BERT-Full</td><td>59.37</td><td>84.46</td><td>91.95</td><td>89.08</td><td>91.07</td><td>83.39</td><td>90.77</td><td>66.93</td><td>82.13</td></tr><tr><td>BERT-Freeze</td><td>27.52</td><td>69.66</td><td>88.81</td><td>78.35</td><td>84.48</td><td>71.55</td><td>81.61</td><td>56.46</td><td>69.81</td></tr><tr><td>BERT-Random</td><td>37.89</td><td>70.78</td><td>89.47</td><td>81.41</td><td>85.86</td><td>72.91</td><td>83.38</td><td>58.63</td><td>72.54</td></tr><tr><td>BERT-Intrinsic</td><td>60.27</td><td>84.31</td><td>89.93</td><td>89.51</td><td>89.73</td><td>81.21</td><td>87.73</td><td>67.00</td><td>81.21</td></tr><tr><td>RoBERTa-Full</td><td>61.04</td><td>89.31</td><td>94.29</td><td>90.70</td><td>91.72</td><td>87.23</td><td>92.48</td><td>76.68</td><td>85.43</td></tr><tr><td>RoBERTa-Freeze</td><td>0.00</td><td>68.38</td><td>85.32</td><td>15.69</td><td>82.81</td><td>71.16</td><td>79.11</td><td>53.86</td><td>57.04</td></tr><tr><td>RoBERTa-Random</td><td>27.58</td><td>68.38</td><td>91.45</td><td>75.47</td><td>86.33</td><td>77.10</td><td>84.49</td><td>58.27</td><td>71.13</td></tr><tr><td>RoBERTa-Intrinsic</td><td>61.07</td><td>87.21</td><td>92.43</td><td>89.43</td><td>90.18</td><td>85.53</td><td>90.57</td><td>78.77</td><td>84.40</td></tr></table>
+
+Table 1: Transductive intrinsic subspace fine-tuning on the GLUE benchmark. Full denotes fine-tuning in the full-parameter space. Freeze denotes fine-tuning with the encoder frozen. Random denotes fine-tuning in a random subspace. Intrinsic denotes fine-tuning in the intrinsic task-specific subspaces. The subspace dimension is set to 32 except MNLI is 64. The best results are marked in bold, and the second-best results are underlined.
+
+![](images/ffc8363cc35eadc79654a4627f0070b0bc09882e1a5abaf40bdcb8d23e1c722a.jpg)  
+Figure 2: Inductive intrinsic subspace fine-tuning on the GLUE benchmark. Columns are the target tasks to be fine-tuned, and rows are source tasks that provide the transferred subspaces. Numbers in cells are performance drop of fine-tuning target tasks with the subspaces provided by source tasks. The last column is the average of other columns. Note that the numbers cannot be compared across columns because they are in different metrics.
+
+![](images/7b2044ad67456248c8fcc648244f1d2aa3a52c023ef38c4e2834ed94d50aa743.jpg)
+
+while for inductive subspace fine-tuning, it is calculated from other tasks. We only re-parameterize the encoder layers into the subspaces and leave the embedding layer and the last classification layer in their original parameter space. We freeze the initial model  $\theta_0^D$  and the projection matrix  $V$ , and only tune the low-dimensional vector  $\theta^t$ . We keep the learning rate of the embedding and classification layers unchanged and set the learning rate of  $\theta^t$  to 0.01.
+
+# 4.2 Transductive Intrinsic Subspace Fine-tuning
+
+Table 1 summarizes the experimental results. We can see that freezing the encoder significantly degrades the model performance as it serves as a naive baseline (Note that it implies fine-tuning in
+
+the null space, i.e.,  $V\theta^t = 0$ , which brings no information to update the model). For intrinsic subspace fine-tuning, we can clearly see that it shows comparable performance to the full fine-tuning across all GLUE tasks and models. In contrast, random projection only yields a marginal improvement over the baseline, and significantly underperforms intrinsic subspace fine-tuning.
+
+From these empirical results, we first conclude that PLMs can be re-parameterized and fine-tuned in some low-dimensional subspaces. Secondly, there exist some subspaces in which the PLMs can most effectively adapt to downstream tasks, and we can uncover these subspaces by finding the principal directions of fine-tuning trajectories in the full parameter space. This conclusion in turn suggests that fine-tuning of PLMs happens in tiny
+
+<table><tr><td></td><td>CoLA</td><td>MRPC</td><td>SST-2</td><td>STS-B</td><td>QQP</td><td>MNLI</td><td>QNLI</td><td>RTE</td><td>Avg.</td></tr><tr><td>BERT-Full</td><td>59.37</td><td>84.46</td><td>91.95</td><td>89.08</td><td>91.07</td><td>83.39</td><td>90.77</td><td>66.93</td><td>82.13</td></tr><tr><td>BERT-Random</td><td>32.49</td><td>70.15</td><td>88.65</td><td>79.29</td><td>84.84</td><td>71.75</td><td>82.29</td><td>57.11</td><td>70.82</td></tr><tr><td>BERT-Zeroshot</td><td>35.35</td><td>78.09</td><td>91.06</td><td>85.17</td><td>87.57</td><td>75.29</td><td>84.01</td><td>75.23</td><td>76.47</td></tr><tr><td>BERT-Unified</td><td>61.58</td><td>84.41</td><td>91.06</td><td>89.71</td><td>91.27</td><td>83.85</td><td>90.97</td><td>67.00</td><td>82.48</td></tr><tr><td>RoBERTa-Full</td><td>61.04</td><td>89.31</td><td>94.29</td><td>90.70</td><td>91.72</td><td>87.23</td><td>92.48</td><td>76.68</td><td>85.43</td></tr><tr><td>RoBERTa-Random</td><td>0.00</td><td>68.38</td><td>89.47</td><td>27.60</td><td>84.51</td><td>73.16</td><td>82.10</td><td>54.44</td><td>59.96</td></tr><tr><td>RoBERTa-Zeroshot</td><td>32.93</td><td>80.44</td><td>90.60</td><td>83.10</td><td>87.12</td><td>78.76</td><td>84.46</td><td>67.12</td><td>75.57</td></tr><tr><td>RoBERTa-Unified</td><td>63.80</td><td>89.12</td><td>93.55</td><td>90.88</td><td>91.85</td><td>87.20</td><td>92.36</td><td>77.91</td><td>85.83</td></tr></table>
+
+Table 2: Intrinsic subspace fine-tuning in the unified task subspace. Random denotes fine-tuning in a random subspace (dim=8). Zereshot denotes fine-tuning in the unified task subspace with itself removed (dim=7). Unified denotes fine-tuning in the unified task subspace (dim=8).
+
+subspaces, which provides an explanation of the ease of adapting PLMs to downstream tasks.
+
+# 4.3 Inductive Intrinsic Subspace Fine-tuning
+
+Next, we conduct inductive intrinsic subspace finetuning to examine the transferability of the discovered subspaces. We generally follow the same training protocol as in the last section, except that we replace the projection matrices with the ones calculated from other tasks.
+
+We can observe the performance drop using transferred task subspaces in Fig. 2. Generally, we can see that even though the models are finetuned in transferred subspaces, they still outperform the random subspace baseline, which suggests the transferability of intrinsic task-specific subspaces.
+
+The transferability of subspaces seems to correlate with the scale of the transferred task. For example, big datasets like SST-2, QQP, MNLI and QNLI underperform small datasets like CoLA, MRPC, STS-B, and RTE in providing subspaces. This is because the intrinsic task-specific subspaces of complex tasks have higher dimensions and need more parameters to estimate.
+
+When comparing within one column, we can see significant difference between distinct subspaces used for fine-tuning one task. We assume similar tasks may have substantial subspace intersections and thus be easier to transfer. Still, this claim needs further analysis to confirm, we will leave it further study since transferability is not the main focus of this paper. In summary, we empirically show that the intrinsic task-specific subspace has a certain transferability.
+
+# 4.4 Unified Intrinsic Task Subspace
+
+Qin et al. (2021) showed that a unified low-dimensional intrinsic task subspace can be constructed by a multi-task prompt tuning method. In our case, we can also construct a unified subspace by stacking the fine-tuning trajectories of different tasks into a matrix, and applying SVD on it. Specifically, we sample one checkpoint for each task and gather them to calculate the unified subspace, which forms an 8-dimensional subspace. And we additionally calculate a zero-shot subspace of a task for comparison, which is calculated by excluding the checkpoint of this task. The results are given in Table 2. We can see that the models can be effectively fine-tuned in the unified subspace. For the zero-shot setting, the model performance decreases significantly, but still outperforms the random baseline.
+
+![](images/20fef6782993afbd12ec69771f05760723f0d4ba880e00872a54316e3d0f657b.jpg)  
+Figure 3: The cosine similarities between the low-dimensional parameter vectors  $\pmb{\theta}^t$  of different tasks in the unified intrinsic task subspace. Similarities are averaged over layers and ensembles.
+
+![](images/fee98878f24a83d5adce07984caf52dc14b67ee78fa3ca194ca123083c31de08.jpg)
+
+![](images/926085918447465bfda2e47173e00e1f0138f842bb7389fcdb56f2e0aa9a421e.jpg)  
+Figure 4: Visualization of product of  $V\theta^t$  using the BERT model to fine-tune in the intrinsic task-specific subspace (top) and a random subspace (bottom) on the MRPC dataset. Outlier dimensions appear in the intrinsic subspace but not in a random subspace.
+
+Next, we take the BERT model as an example and examine the low-dimensional parameter vector  $\theta^t$  learned within the unified intrinsic subspace. We calculate the cosine similarities between the  $\theta^t$  vectors corresponding to different tasks and present the results in Fig. 3. As shown in the figure, the cosine similarities between different tasks are significantly low, indicating that the unified intrinsic subspace contains disentangled knowledge distributed in different dimensions, and the low-dimensional parameter vector  $\theta^t$  serves as an (unnormized) probability distribution to induce task-specific knowledge.
+
+Based on these empirical findings, we conclude that a unified intrinsic task subspace is feasible and it contains disentangled knowledge. However, in-domain knowledge still plays a crucial role in forming the subspace as we can see that the zero-shot setting still has a large perform gap.
+
+# 4.5 Outlier Dimensions
+
+We find that PLMs have a small number of outlier dimensions exhibiting abnormal spikes when fine-tuning in the intrinsic task-specific subspaces.
+
+We examine each dimension of the product of  $V\theta^t$  and consider the dimension whose absolute value is greater than a threshold as outlier. Note that the product of  $V\theta^t$  is the learned parameter update in the full parameter space and we re-parameterize the encoder of the PLM layer-wisely, thus it is a vector with the dimension equal to the number of all parameters of an encoder layer.
+
+It is important to note that the outlier dimension in our context is different from the previous studies (Kovaleva et al., 2021; Luo et al., 2021; Puccetti et al., 2022). Previous studies use the outlier dimension to refer to the output channel (768 dimensions for BERT-base). In our context, we flatten all parameters of a layer into a vector (7,087,872 dimensions for BERT-base). Then an outlier dimension refers to a specific parameter weight in the layer. We use the BERT model and MRPC dataset for illustration, and visualize the product of  $V\theta^{t}$  in Fig. 4 to show the outlier patterns. As we can see from the figure, when fine-tuning in the intrinsic task-specific subspace, the outlier patterns exist in all layers. In contrast, these outlier patterns disappear when fine-tuning in a random subspace.
+
+<table><tr><td></td><td>CoLA</td><td>MRPC</td><td>SST-2</td><td>STS-B</td><td>QQP</td><td>MNLI</td><td>QNLI</td><td>RTE</td></tr><tr><td>BERT-Full</td><td>59.37</td><td>84.46</td><td>91.95</td><td>89.08</td><td>91.07</td><td>83.39</td><td>90.77</td><td>66.93</td></tr><tr><td>BERT-Random</td><td>57.27</td><td>84.46</td><td>91.79</td><td>88.66</td><td>90.66</td><td>83.68</td><td>90.41</td><td>64.48</td></tr><tr><td>BERT-Outlier</td><td>0.00</td><td>68.38</td><td>50.92</td><td>0.00</td><td>63.18</td><td>33.64</td><td>49.89</td><td>52.71</td></tr><tr><td>RoBERTa-Full</td><td>61.04</td><td>89.31</td><td>94.29</td><td>90.70</td><td>91.72</td><td>87.23</td><td>92.48</td><td>76.68</td></tr><tr><td>RoBERTa-Random</td><td>58.80</td><td>87.65</td><td>93.95</td><td>89.52</td><td>91.29</td><td>87.76</td><td>92.61</td><td>68.88</td></tr><tr><td>RoBERTa-Outlier</td><td>0.00</td><td>70.49</td><td>50.92</td><td>28.05</td><td>63.67</td><td>36.15</td><td>49.89</td><td>52.71</td></tr></table>
+
+Table 3: Evaluation on the GLUE benchmark when the outlier dimensions are zeroed. The results with the most performance loss are marked in bold.  
+
+<table><tr><td>Model component</td><td>Layer</td><td># of outliers each layer</td></tr><tr><td>attention.self.query.weight</td><td>1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12</td><td>3, 1, 1, 1, 4, 4, 8, 3, 3, 2, 4</td></tr><tr><td>attention.self.query.bias</td><td>1</td><td>1</td></tr><tr><td>attention.self.key.bias</td><td>10, 11</td><td>2, 1</td></tr><tr><td>attention.output LayerNorm.weight</td><td>1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12</td><td>1, 2, 3, 5, 4, 1, 2, 4, 1, 3, 2</td></tr><tr><td>attention.output LayerNorm.bias</td><td>1, 2, 3</td><td>1, 1, 1</td></tr><tr><td>intermediate.dense.weight</td><td>1, 12</td><td>2, 1</td></tr><tr><td>output.dense.weight</td><td>1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11</td><td>2, 6, 5, 4, 2, 4, 3, 2, 3, 4, 4</td></tr><tr><td>output LayerNorm.weight</td><td>5, 6, 7, 12</td><td>4, 1, 1, 3</td></tr></table>
+
+Table 4: Sampled outlier dimensions in the BERT model. The left column shows the model component containing outlier dimensions. The middle column shows the layer where the model component contains outlier dimensions. The right column shows the number of outlier dimensions in the corresponding layer.
+
+This phenomenon is universal for different models and different datasets.
+
+To investigate the effect of the outlier dimensions on the models, we disable them by setting them to zero and examine how this affects model performance. We first disable the top outlier dimension of each encoder layer and fine-tune the model in the full parameter space, which has almost no impact on model performance. This result is not surprising because disabling only one weight in a layer definitely has a negligible effect on the output than disabling an output channel as the previous studies do. We continue to disable more outlier dimensions, and these deviating at least  $3\sigma$  from the mean are disabled. Approximately  $0.3\%$  of encoder parameters are disabled. We also randomly sample and disable the same number of dimensions for comparison, and the results are shown in Table 3. We can see that disabling outlier dimensions degrades the model performance significantly while disabling random dimensions does not.
+
+Next, we qualitatively examine the positions in which the outlier dimensions emerge. We sample each layer's top 10 outlier dimensions and record their positions in Table 4. We can see
+
+that the outlier dimensions are ubiquitous in various model components. Then, we identify one outlier dimension  $O1$  that consistently produces high-magnitude weights in almost all BERT layers. Furthermore, we find that there is a considerable overlap in the outlier dimensions of each layer, which suggests that these dimensions can propagate through layers.
+
+Why do outlier dimensions emerge? Previous studies came up with several explanations like high-magnitude scaling factors (Kovaleva et al., 2021), LayerNorm and residual connection (Luo et al., 2021), and unbalanced token frequency (Puccetti et al., 2022). However, these explanations cannot apply to our case because the definitions of the outlier dimension are different. Recall that our approach to identifying outlier dimensions is actually examining re-parameterized parameter updates given the intrinsic task-specific subspace. The magnitude of the updates represents the importance of corresponding parameters with respect to solving the task. We have reason to believe that these dimensions play an important role in constituting the intrinsic subspace and are crucial to induce task-specific knowledge to adapt to downstream tasks.
+
+# 5 Conclusion
+
+In this paper, we claim that the fine-tuning of PLMs happens in tiny subspaces. To uncover such intrinsic task-specific subspaces, we exploit the fine-tuning trajectory to find its main direction. Our empirical experiments show that PLMs can effectively adapt to downstream tasks when re-parameterizing and training in the found subspaces, which well explains the ease of adapting PLMs to downstream tasks. Furthermore, we find outlier dimensions in PLMs during the subspace training. We consider that these dimensions are crucial to induce task-specific knowledge to downstream tasks. Still, we need further in-depth analysis to understand the reasons and impact of the emergence of outlier patterns.
+
+# Limitations
+
+Despite the insights obtained through our analysis, certain limitations persist, which we outline in this section.
+
+With respect to the re-parameterization of parameters as presented in Eq. (3), we adopted the layer-wise setting as proposed by Aghajanyan et al. (2021) in order to alleviate memory and computational burdens. Nonetheless, such a setting restricts us to only identifying local subspaces, rather than discovering global subspaces within the entire parameter space of a pre-trained language model. The existence of a task-specific global subspace is yet to be ascertained. If such a subspace does exist, the correlation between this global subspace and the identified local subspaces needs to be explored in future research.
+
+In terms of experimental settings, the evaluation tasks are limited to natural language understanding tasks, with a lack of natural language generation tasks. On model architecture, decoder-only (e.g., GPT) and encoder-decoder (e.g., T5) models are not included. On model scale, we use basic-size models rather than large ones due to limited computational resources. Consequently, the conclusions drawn in this study may not be applicable to the above situations.
+
+The analysis presented in Section 4.5 demonstrates that pre-trained language models exhibit a small number of outlier dimensions when finetuning in the intrinsic task-specific subspaces. Although we have observed a significant decline in model performance when disabling these dimensions, the underlying mechanism responsible for
+
+the emergence of these outlier dimensions remains unclear.
+
+# Acknowledgments
+
+This work is supported by the Sichuan key research program (22ZDYF3388), Fundamental Research Funds for the Central Universities (ZYGX2019Z014), National Natural Science Foundation of China (61976044, 52079026), Fok YingTong Education Foundation for Young Teachers in the Higher Education Institutions of China (161062), the Canada CIFAR AI Chair Program, and the Canada NSERC Discovery Grant (RGPIN-2021-03115).
+
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+
+# A Appendix
+
+# A.1 Hyperparameters
+
+We first fine-tune the BERT and RoBERTa models for calculating projection matrices. We use the fine-tuning script in the Transformers toolkit<sup>2</sup>. All hyperparameters remain default except for the number of epochs, which is set to 32 and 64 for the MNLI and all other tasks, respectively. For intrinsic subspace fine-tuning, the dimensionality of  $\theta^t$  is set to 32 and 64 for the MNLI and all other tasks, respectively. The learning rate of  $\theta^t$  is set to 0.01. The number of ensembles  $h$  is set to 16. Other hyperparameter are the same as those in the script. All experimental results are averaged over 5 runs of different seeds. Each experiment is conducted on a single GeForce RTX 2080Ti GPU with environment of Pytorch 1.11.0 + CUDA 11.3.1.
+
+# A.2 Ablation study
+
+We conduct an ablation experiment over the number of dimensions of the subspaces. The results are given in Table 5 and Table 6. The performance increases as the number of dimensions increases.
+
+<table><tr><td>Tasks</td><td>dim=8</td><td>dim=16</td><td>dim=32</td></tr><tr><td>CoLA</td><td>54.06</td><td>57.17</td><td>60.27</td></tr><tr><td>MRPC</td><td>75.05</td><td>77.94</td><td>84.31</td></tr><tr><td>SST-2</td><td>89.52</td><td>90.05</td><td>89.93</td></tr><tr><td>STS-B</td><td>87.95</td><td>89.02</td><td>89.51</td></tr><tr><td>QQP</td><td>87.61</td><td>89.12</td><td>89.73</td></tr><tr><td>MNLI</td><td>76.93</td><td>78.48</td><td>78.70</td></tr><tr><td>QNLI</td><td>86.54</td><td>86.83</td><td>87.73</td></tr><tr><td>RTE</td><td>65.41</td><td>66.07</td><td>67.00</td></tr></table>
+
+Table 5: Ablation study for the BERT model.  
+
+<table><tr><td>Tasks</td><td>dim=8</td><td>dim=16</td><td>dim=32</td></tr><tr><td>CoLA</td><td>58.04</td><td>60.27</td><td>61.07</td></tr><tr><td>MRPC</td><td>75.59</td><td>78.20</td><td>87.21</td></tr><tr><td>SST-2</td><td>91.93</td><td>92.34</td><td>92.43</td></tr><tr><td>STS-B</td><td>84.10</td><td>88.10</td><td>89.43</td></tr><tr><td>QQP</td><td>87.58</td><td>89.25</td><td>90.18</td></tr><tr><td>MNLI</td><td>79.96</td><td>81.77</td><td>82.32</td></tr><tr><td>QNLI</td><td>89.35</td><td>89.14</td><td>90.57</td></tr><tr><td>RTE</td><td>74.30</td><td>78.56</td><td>78.77</td></tr></table>
+
+Table 6: Ablation study for the RoBERTa model.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work? Section Limitations.  
+A2. Did you discuss any potential risks of your work? Section Limitations.  
+A3. Do the abstract and introduction summarize the paper's main claims? Abstract, Section 1.  
+A4. Have you used AI writing assistants when working on this paper? Left blank.
+
+B Did you use or create scientific artifacts?
+
+Section 4.
+
+B1. Did you cite the creators of artifacts you used? Section 4.  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? We use open-source artifacts which can be used for academic research purposes.  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? We use the artifacts in compliance with their licenses.  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? We use the open-source GLUE dataset which does not contain sensitive information.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Section 4.
+
+C Did you run computational experiments?
+
+Section 4.
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Appendix.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? No response.  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Section 4  
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Section 4
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? Not applicable. Left blank.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? Not applicable. Left blank.  
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? Not applicable. Left blank.  
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? Not applicable. Left blank.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? Not applicable. Left blank.

2023/Fine-tuning Happens in Tiny Subspaces_ Exploring Intrinsic Task-specific Subspaces of Pre-trained Language Models/images.zip

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2023/Forgotten Knowledge_ Examining the Citational Amnesia in NLP/aad7c0d8-3cef-4a9b-a451-aebedd7604ff_origin.pdf

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2023/Forgotten Knowledge_ Examining the Citational Amnesia in NLP/full.md

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+# Forgotten Knowledge: Examining the Citational Amnesia in NLP
+
+Janvijay Singh\*, Mukund Rungta\*, Diyi Yang, Saif M. Mohammad
+
+$^{\diamond}$  Georgia Institute of Technology,  $^{\diamond}$ Stanford University,  $^{\Phi}$ National Research Council Canada {iamjanvijay, mrungta8}@gatech.edu, diyiy@cs.stanford.edu, saif.mohammad@nrc-cnrc.gc.ca
+
+# Abstract
+
+Citing papers is the primary method through which modern scientific writing discusses and builds on past work. Collectively, citing a diverse set of papers (in time and area of study) is an indicator of how widely the community is reading. Yet there is little work looking at broad temporal patterns of citation. This work, systematically and empirically examines: How far back in time do we tend to go to cite papers? How has that changed over time, and what factors correlate with this citational attention/amnesia? We chose NLP as our domain of interest, and analyzed  $\sim 71.5\mathrm{K}$  papers to show and quantify several key trends in citation. Notably,  $\sim 62\%$  of cited papers are from the immediate five years prior to publication, whereas only  $\sim 17\%$  are more than ten years old. Furthermore, we show that the median age and age diversity of cited papers was steadily increasing from 1990 to 2014, but since then the trend has reversed, and current NLP papers have an all-time low temporal citation diversity. Finally, we show that unlike the 1990s, the highly cited papers in the last decade were also papers with the least citation diversity; likely contributing to the intense (and arguably harmful) recency focus. Code, data, and a demo are available at the project homepage.
+
+# 1 Introduction
+
+Study the past if you would define the future.
+
+Confucius
+
+The goal of scientific research is to create a better future for humanity. To do this we innovate on ideas and knowledge from the past. Thus, a central characteristic of the scientific method and modern scientific writing is to discuss other work: to build on ideas, to critique or reject earlier conclusions,
+
+to borrow ideas from other fields, and to situate the proposed work. Even when proposing something that others might consider dramatically novel, it is widely believed that these new ideas have been made possible because of a number of older ideas (Verstak et al., 2014). Citation (referring to another paper in a prescribed format) is the primary mechanism to point the reader to these prior pieces of work and also to assign credit for shaping current work (Mohammad, 2020a; Rungta et al., 2022). Thus, we argue that examining citation patterns across time can lead to crucial insights into what we value, what we have forgotten, and what we should do in the future.
+
+Of particular interest is the extent to which good older work is being forgotten — citational amnesia. More specifically, for this paper, we define citational amnesia as shown below:
+
+Citational Amnesia: the tendency to not cite enough relevant good work from the past (more than a few years old).
+
+We cannot directly measure citational amnesia empirically because determining "enough", "relevance", and "good" require expert researcher judgment. However, what we can measure is the collective tendency of a field to cite older work. Such an empirical finding enables reflection on citational amnesia. A dramatic drop in our tendency to cite older work should give us cause to ponder whether we are putting enough effort to read older papers (and stand on the proverbial shoulders of giants).
+
+Note that we are not saying that old work should be cited simply because it exists. We are saying that we should consciously reflect on the diversity of the papers we explore when conducting research. Diversity can take many forms, including reading relevant papers from diverse fields, by authors from diverse regions, and relevant papers published from various time periods — the focus of this paper. Exploring a diverse set of papers allows us to ben
+
+efit from important and diverse research perspectives. Looking at older literature makes us privy to broader trends, and informs us in ways that are beneficial well beyond the immediate work.
+
+Historically, citational amnesia was impacted by various factors around access and invention. For example, the invention of the printing press in the year 1440 allowed a much larger number of people to access scientific writing (Eisenstein, 1985). The era of the internet and digitization of scientific literature that began in the 1990s also greatly increased the ease with which one could access past work (Verstak et al., 2014). However, other factors such as the birth of paradigm-changing technologies may also impact citation patterns; ushering in a trend of citing very new work or citing work from previously ignored fields of work. Such dramatic changes are largely seen as beneficial; however, strong tailwinds may also lead to a myopic focus on recent papers and those from only some areas, at the expense of benefiting from a wide array of work (Pan et al., 2018; Martin-Martín et al., 2016).
+
+We choose as our domain of interest, papers on Natural Language Processing (NLP), specifically those in the ACL Anthology. This choice is motivated by the fact that NLP (and other related fields of Artificial Intelligence) are in a period of dramatic change: There are notable and frequent gains on benchmark datasets; NLP technology is becoming increasingly ubiquitous in society; and new sub-fields of NLP such as Computational Social Science, Ethics and NLP, and Sustainable NLP are emerging at an accelerated rate. The incredibly short research-to-production cycle and move-fast-and-break-things attitude in NLP (and Machine Learning more broadly) has also led to considerable adverse outcomes for various sections of society, especially those with the least power (Buolamwini and Gebru, 2018; ARTICLE19, 2021; Mohammad, 2021). Thus reading and citing more broadly is especially important now.
+
+In this work, we compiled a temporal citation network of 71.5K NLP papers that were published between 1990 and 2021, along with their meta-information such as the number of citations they received in each of the years since they were published — the Age of Citations (AoC) dataset. We use AoC to answer a series of specific research questions on what we value, what we have forgotten, what factors are associated with this citational attention/amnesia, what are the citation patterns
+
+of different types of papers, and how these citation patterns have changed over time. Finally, we show that many of the highly cited papers from the past decade have very low temporal citation diversity; and because of their wide reach, may have contributed to the intense recency focus in NLP. All of the data and code associated with the project will be made freely available on the project homepage.
+
+# 2 Related Work
+
+In the broad area of Scientometrics (study of quantitative aspects of scientific literature), citations and their networks have been studied from several perspectives, including: paper quality (Buela-Casal and Zych, 2010), field of study (Costas et al., 2009), novelty, length of paper (Antoniou et al., 2015; Falagas et al., 2013), impact factor (Callaham et al., 2002), venue of publication (Callaham et al., 2002; Wahle et al., 2022), language of publication (Lira et al., 2013), and number of authors (Della Sala and Brooks, 2008; Bosquet and Combes, 2013), collaboration (Nomaler et al., 2013), self-citation (Costas et al., 2010), as well as author's reputation (Collet et al., 2014), affiliation (Sin, 2011; Lou and He, 2015), geographic location (Nielsen and Andersen, 2021; Lee et al., 2010; Pasterkamp et al., 2007; Paris et al., 1998), gender, race and age (Ayres and Vars, 2000; Leimu and Koricheva, 2005; Chatterjee and Werner, 2021; Llorens et al., 2021).
+
+However, there has been relatively little work exploring the temporal patterns of citation. Verstak et al. (2014) analyzed scholarly articles published in 1990-2013 to show that the percentage of older papers being cited steadily increased from 1990 to 2013, for seven of the nine fields of study explored. (They treated papers that were published more than ten years before a particular citation as old papers.) For Computer Science papers published in 2013, on average,  $28\%$  of the cited papers were published more than ten years before. This represented an increase of  $39\%$  from 1990. They attributed this increasing trend in citing old papers to the ease of access of scientific literature on the world wide web, as well as the then relatively new scientific-literature-aggregating services such as Google Scholar.
+
+Parolo et al. (2015) analyzed about 25 million papers from Clinical Medicine, Molecular Biology, Physics, and Chemistry published until 2014 to show that typically the number of citations a paper receives per year increases in the years after
+
+publication, reaches a peak, and then decays exponentially. Interestingly they showed that this rate of decay was increasing in the more recent papers of their study. They attribute this quicker decay (or more "forgetting" of recent papers) to the substantial increase in the number of publications; a lot more papers are being published, and due to the limited attention span of subsequent researchers, on average, papers are being forgotten faster.
+
+Past work on NLP papers and their citations includes work on gender bias (Schluter, 2018; Vogel and Jurafsky, 2012; Mohammad, 2020b), author location diversity (Rungta et al., 2022), author institution diversity (Abdalla et al., 2023), and on broad general trends such as average number of citations over time and by type of paper (Mohammad, 2020a,c; Wahle et al., 2022).
+
+Bollmann and Elliott (2020) were the first to explore the recency bias of citations in NLP papers. They showed that the ACL Anthology papers published between 2017 and 2019 cited more recent work than papers published between 2010 and 2014. Question 3 in Section 4 of our paper is of the same spirit that was explored in their work; however, our work examines a much larger spread of NLP papers (published between 1965 and 2021). This will shed light on the reproducibility of those findings and, more importantly, determine the broader trajectory of temporal citation patterns (from the start of ACL to present day). Additionally, our work introduces a new citation age diversity metric to quantify the degree of spread of citations over time, as well as an interactive online demo system to visualize the citation age diversity of any paper. Going beyond how overall citation patterns have changed over time, our work takes a deep dive into six other novel research questions, notably around temporal citation patterns in sub-areas of NLP, of cited topics, and across sparsely and highly cited papers.
+
+# 3 Dataset
+
+The ACL Anthology (AA) Citation Corpus (Rungta et al., 2022) contains meta data (paper title, year of publication, and venue, etc. for the 71,568 papers in the ACL Anthology repository (published until January 2022). We used the Semantic Scholar API to gather the references for each paper in the AA Citation Corpus, using the paper's unique Semantic Scholar ID (SSID). This allowed us to obtain
+
+![](images/18cd25eaba4f425d738c03b90490c619da26a7bbfe9a1dc9e43b69fcba9d7ca7.jpg)  
+Figure 1: Average number of unique references in an AA paper published in different years.
+
+<table><tr><td></td><td>Mean</td><td>Median</td></tr><tr><td>Journal</td><td>23.24</td><td>15</td></tr><tr><td>Conference</td><td>21.11</td><td>19</td></tr><tr><td>Workshop</td><td>19.07</td><td>17</td></tr><tr><td>Overall</td><td>20.63</td><td>18</td></tr></table>
+
+Table 1: Mean and median of the number of unique references in an AA paper.
+
+additional information about the cited papers, such as their title, year of publication, and venue of publication. Note that these cited papers may or may not be part of AA. To study the dynamics of citations over time, we constructed year-wise citation networks using the data collected. Specifically, we created the citation networks for every year from 1965 to 2001. This representation of citation data allows us to answer several interesting questions, such as the number of citations a paper receives in a particular year after its publication. We refer to this dataset as Age of Citations (AoC) dataset.
+
+# 4 Age of Citation
+
+We used the AoC dataset to answer a series of questions on how research papers are cited and the trends across years.
+
+Q1. What is the average number of unique references in the AA papers? How does this number vary by publication type, such as workshop, conference, and journal? Has this average stayed roughly the same or has it changed markedly over the years?
+
+Ans. We calculated the average number of unique references for all papers in the AoC dataset, as well as for each publication type (workshops, conferences, and journals). We then binned all papers by publication year, computed the mean and median for each bin for each year.
+
+Results The scores are shown in Table 1. Figure 1 shows how the mean has changed across the years.4 The graph shows a general upward trend. The trend seems roughly linear until the mid 2000s, at which point we see that the slope of the trend line increases markedly. Even just considering the last 7 years, there has been a  $41.74\%$  increase in referenced papers in 2021 compared to 2014.
+
+Similar overall trends can be observed when papers are grouped by publication type. Not surprisingly, the longer journal articles cite markedly more papers than conference and workshop papers. The plot for conferences and workshops is relatively smooth compared to journal articles. This is because the number of papers for each year in journals is far less. For example, in the year 2015, only 139 papers were published in journals, whereas 1709 and 983 papers were published in conferences and workshops respectively.
+
+Discussion The steady increase in the number of unique references from 1965 is likely because of the increasing number of relevant papers as the field develops and grows. However, it is interesting that this growth has not plateaued even after 55 years. By the late-2000s, with the advent of widely accessible electronic proceedings, *ACL venues started experimenting with more generous page limits: relaxing it from a strict 8 pages to first allowing one or two additional pages for references to eventually allowing unlimited pages for references.<sup>5</sup> Other factors that may have contributed to more papers being referred to (cited) within a paper, include: an additional page for incorporating reviewer comments, allowing Appendices, and the inclusion of an increasing number of experiments.
+
+# Q2. On average, how far back in time do we go to cite papers? As in, what is the average age of cited papers? What is the distribution of this age across all citations? How do these vary by publication type?
+
+Ans. If a paper  $x$  cites a paper  $y_{i}$ , then the age of the citation (AoC) is taken to be the difference between the year of publication (YoP) of  $x$  and  $y_{i}$ :
+
+$$
+A o C \left(x, y _ {i}\right) = Y o P (x) - Y o P \left(y _ {i}\right) \tag {1}
+$$
+
+We calculated the AoC for each of the citations in the AoC dataset. For each paper, we also calculated the mean  $AoC$  of all papers cited by it:
+
+$$
+m A o C (x) = \frac {1}{N} \sum_ {i = 1} ^ {N} A o C (x, y _ {i}) \tag {2}
+$$
+
+here  $N$  refers to the number of papers cited by  $x$ .
+
+Results The average mAoC for all the papers in the AoC dataset is 6.01. The scores were 7.16 for journal articles, 5.91 for conference papers, and 6.01 for workshop papers. Figure 2 shows the distribution of AoCs in the dataset across the years after the publication of the cited paper (overall, and across publication types). For example, the y-axis point for year 0 corresponds to the average of the percentage of citations papers received in the same year as it they were published. The y-axis point for year 1 corresponds to the average of percentage of citations the papers received in the year after they were published. And so on.
+
+Observe that the majority of the citations are for papers published one year prior,  $(\mathrm{AoC} = 1)$ . This is true for conference and workshop subsets as well, but in journal papers, the most frequent citations are for papers published two years prior. Overall though all the arcs have a similar shape, rising sharply from the number in year 0 to the peak value and then dropping off at an exponential rate in the years after the peak is reached. For the full set of citations, this exponential decay from the peak has a half life of about 4 years. Roughly speaking, the line plot for journals is shifted to the right by a year compared to the line plots for conferences and workshops. It also has a lower peak value and its citations for the years after the peak are at a higher percentage than those for conferences and workshops. Additionally, citations in workshop papers have the highest percentage of current year citations (age 0), whereas citations in journal article have the lowest percentage of current year citations.
+
+Analogous to Figure 2, Figure 3 presents the distribution of AoCs, albeit broken down by the total citations received by a paper. It is worth noting that the distribution leans more towards the right for papers with a higher number of citations. This shows that papers with a higher citation count continue to receive significant citations even far ahead in the future, which is intuitive.
+
+Discussion Overall, we observe that papers are cited most in years immediately after publication, and their chances of citation fall exponentially after
+
+![](images/32b90d99c297346119fc258947a1839500f0d32067e0d37b2b961a6866553811.jpg)  
+Figure 2: Distribution of  $AoC$  for papers in AA (overall and by publication type).
+
+![](images/f1fadf8ec10e05aec9bc1b80c2c47be3d04b0edf47e45c35a43cfb597a8686db.jpg)  
+Figure 3: Distribution of  $AoC$  for AA papers with different citation counts (shown in legend).
+
+that. The slight right-shift for the journal article citations is likely, at least in part, because journal submissions have a long turn-around time from the first submission to the date of publication (usually between 6 and 18 months). A list of the oldest papers cited by AA papers is available on the project's GitHub repository.
+
+# Q3. What is the trend in the variation of  $AoC$  over time and how does this variation differ across different publication venues in NLP?
+
+Ans. To answer this question, we split the papers into bins corresponding to the year of publication, and then examined the distribution of  $mAoC$  in each bin. We define a new metric called the Citation Age Diversity (CAD) Index, which measures the diversity in the  $mAoC$  for a set of papers. In simpler terms, a higher CAD Index indicates that  $mAoCs$  covers a broader range, implying that the cited papers span a wider time period of publication. This metric offers valuable insights into the temporal spread of scholarly influence and the long-term impact of research. Precisely, the CAD Index for a bin of papers  $b$ , is defined using the Gini
+
+![](images/2120a6dce781f53767627841f1c86e77c6a13ea040c7d83d52849aa85c618375.jpg)  
+Figure 4: Citation Age Diversity Index across years.
+
+Coefficient as follows:
+
+$$
+C A D (b) = 1 - \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {N} \frac {\left| m A o C \left(b _ {i}\right) - m A o C \left(b _ {j}\right) \right|}{2 N ^ {2} \bar {b}} \tag {3}
+$$
+
+here,  $b_{i}$  corresponds to  $i^{th}$  paper within bin  $b$ ,  $N$  denotes the total number of papers in bin  $b$  and  $\bar{b}$  represents the mean of  $mA_{oC}$  of papers' associated with bin  $b$ . A CAD Index close to 0 indicates minimum temporal diversity in citations (citing papers from just one year), whereas a CAD Index of 1 indicates maximum temporal diversity in citations (citing papers uniformly from past years). In addition to CAD Index, we also compute median  $mA_{oC}$  of each such yearly bin. The results for both CAD Index and median  $mA_{oC}$  have roughly identical trends across the years. We discuss the CAD Index analysis below. (The discussion of the median  $mA_{oC}$  results is in the Appendix A.1.)
+
+Results Figure 4 shows the CAD Index across years (higher CAD Index indicates high diversity), and across different publication types. The CAD Index plot of Figure 4 shows that the temporal diversity of citations had an increasing trend from 1990 to 2014, but the period from 1998 to 2004, and 2014 to 2021 (dramatically so) were periods of decline in temporal diversity (decreasing CAD Index scores). These intervals coincide with the year intervals in which we observed a decreasing trend in median  $mA_{o}C$  of published papers (discussed in the Appendix). This suggests that the increase or decrease in diversity is largely because of the decreased or increased focus on papers from recent years, respectively.
+
+The CAD Index plots by publication type all have similar trends, with journal paper submissions consistently having markedly higher scores (indicating markedly higher temporal diversity) across the years studied. However, they also seem to be
+
+![](images/35ad7f469baeb0f70ed3d4dc30ac825cd9620079e83f93e8f33aeb99aa7bbfe4.jpg)  
+Figure 5: Percentage of citations in AA papers where the cited paper is at least 10 years old.
+
+most impacted by the trend since 2014 to cite very recent papers. (CAD Index not only goes back to the 1990 level, but also undershoots beyond it.)
+
+Discussion Overall, we find that all the gains in temporal diversity of citations from 1990 to 2014 (a period of 35 years), have been negated in the 7 years from 2014. This change is driven largely by the deep neural revolution in the early 2010's and strengthened further by the substantial impact of transformers on NLP and Machine Learning. Interestingly, our results until 2013 are in line with what Verstak et al. (2014) found for many fields of study, but since 2014 there has been a marked shift in trends in NLP. We hope future work will explore whether similar shifts in trends have occurred in other fields. Our results add to (and are consistent with) the mean-citation age results found by Bollmann and Elliott (2020), who examined mean citation age between 2010 and 2019. Our analysis of the broader period (from 1965 to 2021), situates those results in the overall trajectory of how temporal citation patterns have evolved since the beginning of the Association of Computational Linguistics to the present period. Additionally, the new CAD Index metric quantifies the degree temporal citation diversity as opposed to the recency focus of citations captured by mean citation age.
+
+# Q4. What percentage of cited papers are old papers? How has this varied across years and publication venues?
+
+Ans. Just as Verstak et al. (2014), we define a cited paper as older if it was published at least ten years prior to the citing paper. We then divided all AA papers into groups based on the year in which they were published. For each AA paper, we determined the number of citations to older papers.
+
+Results Figure 5 shows the percentage of older papers cited by papers published in different years. Observe that this percentage increased steadily from 1990 to 1999, before decreasing until 2002. After 2002, the trend of citing older papers picked up again; reaching an all time high of  $\sim 30\%$  by 2014. However, since 2014, the percentage of citations to older papers has dropped dramatically, falling by  $12.5\%$  and reaching a historical low of  $\sim 17.5\%$  in 2021. Similar patterns are observed for different publication types. However, we note that a greater (usually around  $5\%$  more) percentage of a journal paper's citations are to older papers, than in conference and workshop papers.
+
+Discussion These results confirm that the trends in diversity discussed in Q2 are aligned with the trends in citing older papers. This dramatic drop in citing older papers since 2014 can largely be attributed to the explosion of paper count and the paradigm shift in the field of NLP brought on by deep learning and transformers.
+
+# Q5. What is the  $mAoC$  distribution for different areas within NLP? Relative to each other, which areas tend to cite more older papers and which areas have a strong bias towards recent papers?
+
+Ans. The ACL Anthology does not include metadata for sub-areas within NLP. Further, a paper may be associated with more than one area and the distinction between areas can often be fuzzy. Thus, we follow a rather simple approach used earlier in Mohammad (2020b): using paper title word bigrams as indicators of topics relevant to the paper. A paper with machine translation in the title is likely to be relevant to the area of machine translation. Using title bigrams for this analysis also allows for a finer analysis within areas. For example, two bigrams pertaining to finer subareas within the same area can be examined separately. (Papers in different sub-areas of an area need not be similar in terms of the age of the papers they cite.)
+
+We first compiled a list of the top 60 most frequent bigrams from the titles of AA papers. Next, for each of these bigrams, we created a bin containing all AA papers that had that bigram in their title. For each paper included in any of these bins, we computed  $mA_{o}C$ . Finally, we plotted the distribution of  $mA_{o}C$  values for the papers in each bin,
+
+![](images/c6885c85588c070608a8ff98684d0825da8d49dfd62c65db2ba43878a2ea7d2d.jpg)  
+Figure 6: Distribution of  $mA_{o}C$  for frequent bigrams appearing in the titles of citing papers.
+
+as shown in Figure 6. Note that, for the purpose of improving the visibility of the plot, only selected  $mAoC$  distributions are depicted in the figure 6. We then examined the distribution of  $mAoC$  for each of these bins.
+
+Results Figure 6 shows the  $mAoC$  violin plots for each of the bins pertaining to the title bigrams (in decreasing order of median  $mAoC$ ). Observe that papers with the title bigrams word alignment, parallel corpus/corpora, Penn Treebank, sense disambiguation and word sense (common in the word sense disambiguation area), speech tagging, coreference resolution, named entity and entity recognition (common in the named entity recognition area), and dependency parsing have some of the highest median  $mAoC$  (cite more older papers). In contrast, papers with the title bigrams glove vector, BERT pre, deep bidirectional, and bidirectional transformers (which correspond to new technologies) and papers with title bigrams reading comprehension, shared task, question answering, language inference, language models, and social media (which correspond to NLP subareas or domains) have some of the lowest median  $mAoC$  (cite more recent papers).
+
+Discussion The above results suggest that not all NLP subfields are equal in terms of the age of cited papers. In fact, some papers cited markedly more newer papers than others. This could be due to factors such as early adoption or greater applicability of the latest developments, the relative newness of the area itself (possibly enabled by new inventions such as social media), etc.
+
+# Q6. What topics are more pronounced in cited papers across different periods of time?
+
+Ans. To address this question, we partitioned the re
+
+search papers into those published between: 1990-1999, 2000-2009, 2010-2015, and 2016-2021. For papers from each period: we first extracted all unigrams and bigrams from the titles of the cited papers. Next, for the top 100 most frequent unigrams and bigrams, we calculated the percentage of all citations that had the respective ngram in the cited paper's title — the ngram citation percentage.
+
+Results Upon examining various bigram citation percentages, we found that bigrams pertaining to areas such as tree-adjoining grammars have been in decline since the 1990s (cited less as with every subsequent interval). Bigrams pertaining to areas such as conditional random fields and coreference resolution gained momentum in the middle periods (2000–2016) but have since lost popularity post-2016. On the other hand, techniques such as domain adaptation have consistently gained momentum since the 2010s. Post-2016 keywords related to deep learning technologies such as convolutional neural nets, deep bi-directional, deep learning, deep neural, Global vectors, and jointly learning experienced a substantial surge in popularity. Additionally, certain areas such as cross-lingual and entity recognition consistently gained momentum since the 1990s.
+
+Upon examining various unigram citation percentages, we found that deep-learning-related terms such as attention, bert, deep, neural, embeddings, and recurrent saw a substantial increase in citation post-2016. Furthermore, we observed that since the 1990s, there has been a growing trend in NLP papers towards citing research on the social aspects of language processing, as evidenced by the increasing popularity of keywords such as social and sentiment.
+
+Figures 9 and 10 in the Appendix show a number of unigrams and bigrams with the most notable changes in the ngram citation percentage across the chosen time intervals.
+
+# Q7. Do well-cited papers cite more old papers and have more AoC diversity?
+
+Ans. We introduce three hypotheses to explore the correlation between temporal citation patterns of target papers and the number of citations the target papers themselves get in the future.
+
+H1. The degree of citation has no correlation with temporal citation patterns of papers.  
+H2. Highly cited papers have more temporal citation diversity than less cited papers.  
+H3. Highly cited papers have less temporal citation diversity than less cited papers.
+
+Without an empirical experiment, it is difficult to know which hypothesis is true. H1 seemed likely, however, there were reasons to suspect H2 and H3 also. Perhaps cite more widely is correlated with other factors such the quality of work and thus correlates with higher citations (supporting H2). Or, perhaps, early work in a new area receives lots of subsequent citations and work in a new area often tends to have limited citation diversity as there is no long history of publications in the area (supporting H3).
+
+On, Nov 30, 2022, we used the Semantic Scholar API to extract the number of citations for each of the papers in the AoC dataset. We divided the AoC papers into nine different bins as per the number of citations: 0, 1–9, 10–49, 50–99, 100–499, 500–999, 1000–1999, 2000–4999, or  $5000+$  citations. For each bin, we calculated the mean of  $mAoC$  and  $CAD\ Index$ . We also computed the Spearman's Rank Correlation between the  $CAD\ Index$  of the citation bins and the mean of the citation range of each of these bins.
+
+Results Figure 7 shows the  $mAoC$  and  $CADIndex$  for each bin (a) for the full AoC dataset, and (b) for the subset of papers published between 1990 and 2000. (Figures 11a and 11b in the Appendix show plots for papers from two additional time periods.) On the full dataset (Figure 7a), we observe a clear pattern that the  $CADIndex$  decreases with increasing citation bin (with the exception of papers in the 1K-2K and 2K-5K bins). The mean  $mAoC$  follows similar trend w.r.t. the  $CADIndex$ .
+
+<table><tr><td>1990–99</td><td>2000-09</td><td>2010-15</td><td>1965-2021 (All)</td></tr><tr><td>0.16</td><td>-1.00*</td><td>-0.97*</td><td>-0.72*</td></tr></table>
+
+Table 2: Correlation between the mean number of citations received and CAD Index for papers from various time periods. The * indicates statistically significant correlation (p-value < 0.05).
+
+These results show that, for the full dataset, the higher citation count papers tend to have less temporal citation diversity than lower-citation count papers. However, on the 1990s subset (Figure 7b), the CAD Index decreased till the citation count  $< 50$  and increased markedly after that. This shows that during the 1990s, the highly cited papers also cited papers more widely in time. Plots for the 2000s and 2010s (Figure 11) follow a similar trend as the overall plot (Figure 7a), indicating that trend of highly cited papers having less temporally diverse citations started around the year 2000.
+
+The Spearman's rank Correlation Coefficients between the mean number of citations for a bin and the mean  $mA_{o}C$  of the citation bins are shown in Table 2. Observe that for the 1990's papers there is essentially no correlation, but there are strong correlations for the 2000s, 2010s, and the full dataset papers.
+
+Similar to Figure 7a, in Figure 12 (in the Appendix) we show how mean  $mA_{o}C$  and  $CAD$  Index of AA papers published between 1965 and 2021 but when broken down by research topics. This examination across various research topics consistently shows a trend: the higher the citations, the lower the age diversity of citations. This may be because "mainstream" work in an area tends to cite lots of other very recent work and brings in proportionately fewer ideas from the past. In contrast, "non-mainstream" work tends to incorporate proportionally more ideas from outside, yet receives fewer citations as there may be less future work in that space to cite it.
+
+Discussion Papers may receive high citations for a number of reasons; and those that receive high citations are not necessarily model research papers. While they may have some aspects that are appreciated by the community (leading to high citations), they also have flaws. High-citation papers (by definition) are more visible to the broader research community and are likely to influence early researchers more. Thus their strong recency focus in
+
+![](images/ade4e0f72baada46d7f89d7d92a71f6926f27520356e3bdf4a3978d281c68f66.jpg)  
+(a) Papers published between 1965 and 2021.
+
+![](images/4391803647c77f5b828fd0a0b44cc26a39524d97d71b646b3e676def48ae89c7.jpg)  
+(b) Papers published between 1990 and 2000.  
+Figure 7: Variation of mean  $mA_{o}C$  and Citation Age Diversity (CAD) Index (shown on y-axis) for papers with different citation counts (shown on x-axis).
+
+citations is a cause of concern. Multiple anecdotal incidents in the community have suggested how early researchers often consider papers that were published more than two or three years back as "old papers". This goes hand-in-hand with a feeling that they should not cite old papers and therefore, do not need to read them. The lack of temporal citation diversity in recent highly cited papers may be perpetuating such harmful beliefs.
+
+# 5 Demo: CAD Index of Your Paper
+
+To encourage authors to be more cognizant of the age of papers they cite, we created an online demonstration page where one can provide the Semantic Scholar ID of any paper and the system returns the number of papers referenced, mean Age of Citation (mAoC), top-5 oldest cited papers, and their years of publication. Notable, the demo also plots the distribution of mAoC for all the considered papers (all papers published till 2021) and compares it with mean Age of Citation of the input paper. Figure 13 in the Appendix shows a screenshot of the demo portal for an example input.
+
+# 6 Conclusions and Discussion
+
+This work looks at temporal patterns of citations by presenting a set of comprehensive analyses of the trend in the diversity of age of citations and the percentage of older papers cited in the field of NLP. To enable this analysis, we compiled a dataset of papers from the ACL Anthology and their meta-information; notably, the number of citations they received each year since they were published.
+
+We showed that both the diversity of age of citations and the percentage of older papers cited increased from 1990 to 2014, but since then there has been a dramatic reversal of the trend. By the year 2021 (the final year of analysis), both the diversity of age of citations and the percentage of older papers cited have reached historical lows. We also studied the correlation between the number of citations a paper receives and the diversity of age of cited papers, and found that while there was roughly no correlation in the 1990s, the 2000s marked the beginning of a period where the higher citation levels correlated strongly with lower temporal citation diversity.
+
+It is a common belief among researchers in the field that the advent of deep neural revolution in the early 2010's has led us to cite more recent papers than before. This analysis confirms and quantifies the extent to which temporal diversity is reduced in this recent period. In fact, it shows that the reduction in temporal diversity of citations is so dramatic that it has wiped out steady gains from 1990 to 2014. While some amount of increased focus on recent papers is expected (and perhaps beneficial) after large technological advances, an open question, now, is whether, as a community, we have gone too far, ignoring important older work. Our work calls for an urgent need for reflection on the intense recency focus in NLP: How are we contributing to this as researchers, advisors, reviewers, area chairs, and funding agencies?
+
+# 7 Ethics Statement
+
+This paper analyses scientific literature at an aggregate level. The ACL Anthology freely provides information about NLP papers, such as their title, authors, and year of publication. We do not make use of or redistribute any copyrighted information. All of the analyses in this work are at aggregate-level, and not about individual papers or authors. In fact, we desist from showing any breakdown of results involving 30 or fewer papers to avoid singling out a small group of papers.
+
+# 8 Limitation
+
+A limitation of this study is that it is based solely on papers published in the ACL Anthology, which primarily represents the international English-language NLP conference community. While the ACL Anthology is a reputable source of NLP research, it should be acknowledged that a significant amount of research is also published in other venues such as AAAI, ICLR, ICML, and WWW. Additionally, there are also vibrant local NLP communities and venues, often publishing in non-English languages, that are not represented in the ACL Anthology. As a result, the conclusions drawn from our experiments may not fully capture the global landscape of NLP research and further work is needed to explore the diversity of sub-communities and venues across the world.
+
+This work focuses on the aggregate trends of citing older work in NLP, but does not investigate the reasons for lower citation of certain older papers. There may be various factors that contribute to this, such as the accessibility to these older papers, the large number of recent papers, the applicability of these old works, and the technical relevance of the older work. Determining the relative impact of each reason is a challenging task. Therefore, more research is needed to fully understand the underlying mechanisms that influence the citation of older NLP papers.
+
+This study aims to investigate the factors that contribute to the citation of older works in the field of NLP. We have analyzed different factors such as the mean age of citation, diversity in the age of citations, venue of publication, and subfield of research. Our results indicate that these factors are associated with the citation of older works, but it should be noted that these associations do not establish any causal relationship between them.
+
+Lastly, it is important to note that citations can
+
+be heterogeneous and can be categorized in different ways. For example, some classifications of citations include background, method, and result citations. However, certain citations may be more important than others, as shown by previous research such as "Identifying Meaningful Citations" by (Valenzuela-Escarcega et al., 2015).
+
+# Acknowledgments
+
+Many thanks to Roland Kuhn, Rebecca Knowles, and Tara Small for thoughtful discussions.
+
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+
+# A Supplementary Statistics and Plots
+
+In addition to the primary results presented in the main body of the paper, here, we describe included supplementary material in the form of additional statistics and plots.
+
+# A.1 Q3 Results Supplement: Distribution of mAoC Over Years
+
+Figure 8 shows the violin plots for distributions of  $mA_{o}C$  across various years. If a paper  $x$  was published in year  $t$ , then  $mA_{o}C(x)$  will be a data point for plotting the distribution for year  $t$ . The median  $mA_{o}C$  for a given year (marked with a white dot within the grey rectangle) reflects the recency of citations, with a lower median  $mA_{o}C$  indicating that papers published in that year have cited relatively recent papers.
+
+The two halves of the grey rectangle on either side of the median correspond to the second and third quartiles. Observe that the third quartile is always longer (spread across more years than the second quartile. This shows that the rate at which papers are cited is higher in years before the median than in the years after the median. The violin plots indicate that the distributions have a single peak in each of the years considered.
+
+Observe that the median  $mA_{o}C$  has an increasing trend from 1990 to 2014 (a trend towards citing more older papers) with the exception of a period between 1998 and 2004 when the median decreased. However, most notably, from 2014 onward the median  $mA_{o}C$  decreased markedly with every year. (The median  $mA_{o}C$  in 2021 is nearly 2.5 years less than that of 2014.)
+
+<table><tr><td rowspan="2">Citation Bin</td><td colspan="4">Full AoC</td></tr><tr><td>1965–2021</td><td>1990–1999</td><td>2000–09</td><td>2010–15</td></tr><tr><td>0</td><td>5559</td><td>457</td><td>1062</td><td>1453</td></tr><tr><td>1–9</td><td>26794</td><td>1813</td><td>5354</td><td>7090</td></tr><tr><td>10–49</td><td>21926</td><td>1714</td><td>5804</td><td>6272</td></tr><tr><td>50–99</td><td>4843</td><td>515</td><td>1517</td><td>1275</td></tr><tr><td>100–499</td><td>3860</td><td>496</td><td>1296</td><td>954</td></tr><tr><td>500–999</td><td>332</td><td>45</td><td>105</td><td>94</td></tr><tr><td>1000–1999</td><td>123</td><td>26</td><td>26</td><td>49</td></tr><tr><td>2000+</td><td>106</td><td>21</td><td>34</td><td>27</td></tr></table>
+
+Table 3: Number of papers belonging to each citation bin on full AoC dataset, subset of papers published between 1990 to 2000, 2001 to 2010 and 2011 to 2016
+
+The blue line in Figure 8 is the mean  $mAoC$ . The mean follows a similar trend as the median, with slight variations. In particular, it is consistently higher than the median, indicating that the data is skewed to the right, with a few papers having large  $mAoC$  that significantly affect the mean.
+
+# A.2 Q6 Results Supplement: Pronounced Topics in the Cited Papers Across Year Intervals
+
+We investigated the distribution of the most frequent unigrams and bigrams (ngrams) found in the title of cited papers, grouped by the publication years of the citing paper. Figures 9 and 10 show the unigrams and bigrams with notable changes in citation percentages across the chosen time intervals. A single star  $(^{*})$  indicates that the change in the ngram's percentage from the minimum interval value to maximum interval value is more than  $1500\%$  for unigrams and  $3000\%$  for bigrams. A double star  $(^{**})$  denotes that the ngram was not cited at all in at least one of the intervals.
+
+# A.3 Q7 Results Supplement: Variation of mAoC and CAD Index Across Citation Count Bins
+
+Table 3 shows the number of papers in each citation bin for different segments of papers. We can see that for all the time periods most of the papers have a citation count  $< {50}$  .
+
+Figures 11a and 11b show the variation of mean  $mA_{o}C$  and  $CADIndex$  for subsets of papers published between 2001 to 2010 and 2011 to 2016, respectively. These two plots follow a similar pattern to Figure 7a on the full  $AoC$  dataset. The  $CADIndex$  decreases with increasing the citation bin and the mean  $mA_{o}C$  also varies inversely with the citation bin.
+
+![](images/3b37586f7b653bd2bbd6a311402a838defbbda34252719097584d1389dbe3002.jpg)  
+Figure 8: Distribution of  $mAoC$  for papers published between 1990 and 2021.
+
+![](images/773fdcf24137374b390fe5f38f8788577546f81df08877b8e0eefe9ac7f7c5cf.jpg)  
+Figure 9: Unigram citation percentages of some notable terms found in the titles of cited papers across different time intervals. For example, "Neural" occurred in  $11.41\%$  of the titles of cited papers in the 2016-2021 interval.
+
+<table><tr><td></td><td>90-99</td><td>00-09</td><td>10-15</td><td>16-21</td></tr><tr><td>Adjoining Grammars*</td><td>0.635</td><td>0.274</td><td>0.084</td><td>0.020</td></tr><tr><td>Alignment Models**</td><td>0.000</td><td>0.513</td><td>0.382</td><td>0.061</td></tr><tr><td>Bert Pre**</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.912</td></tr><tr><td>Bidirectional Transformers**</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.917</td></tr><tr><td>Conditional Random**</td><td>0.000</td><td>0.619</td><td>0.684</td><td>0.284</td></tr><tr><td>Convolutional Neural**</td><td>0.000</td><td>0.000</td><td>0.084</td><td>0.817</td></tr><tr><td>Coreference Resolution*</td><td>0.022</td><td>0.321</td><td>0.765</td><td>0.428</td></tr><tr><td>Cross Lingual*</td><td>0.019</td><td>0.133</td><td>0.408</td><td>1.165</td></tr><tr><td>Deep Bidirectional**</td><td>0.000</td><td>0.000</td><td>0.002</td><td>0.916</td></tr><tr><td>Deep Learning**</td><td>0.000</td><td>0.002</td><td>0.064</td><td>0.679</td></tr><tr><td>Deep Neural**</td><td>0.000</td><td>0.002</td><td>0.119</td><td>0.467</td></tr><tr><td>Distributed Representations*</td><td>0.009</td><td>0.005</td><td>0.158</td><td>0.594</td></tr><tr><td>Domain Adaptation*</td><td>0.002</td><td>0.124</td><td>0.612</td><td>0.506</td></tr><tr><td>Entity Recognition*</td><td>0.007</td><td>0.654</td><td>0.652</td><td>0.954</td></tr><tr><td>Error Rate*</td><td>0.007</td><td>0.343</td><td>0.523</td><td>0.078</td></tr><tr><td>Global Vectors**</td><td>0.000</td><td>0.000</td><td>0.038</td><td>0.527</td></tr><tr><td>Jointly Learning**</td><td>0.009</td><td>0.000</td><td>0.031</td><td>0.461</td></tr><tr><td>Language Inference*</td><td>0.034</td><td>0.011</td><td>0.030</td><td>0.520</td></tr><tr><td>Long Short**</td><td>0.000</td><td>0.005</td><td>0.035</td><td>0.656</td></tr><tr><td>Multi Task*</td><td>0.004</td><td>0.004</td><td>0.046</td><td>0.621</td></tr><tr><td>Named Entity*</td><td>0.028</td><td>1.052</td><td>0.965</td><td>1.052</td></tr><tr><td>Neural Machine**</td><td>0.019</td><td>0.000</td><td>0.031</td><td>3.313</td></tr><tr><td>Open Source*</td><td>0.002</td><td>0.343</td><td>0.829</td><td>0.420</td></tr><tr><td>Parts Program*</td><td>0.464</td><td>0.042</td><td>0.005</td><td>0.001</td></tr><tr><td>Phrase Parser*</td><td>0.464</td><td>0.042</td><td>0.005</td><td>0.001</td></tr><tr><td>Pre Training**</td><td>0.000</td><td>0.000</td><td>0.006</td><td>1.551</td></tr><tr><td>Reading Comprehension*</td><td>0.009</td><td>0.058</td><td>0.050</td><td>0.637</td></tr><tr><td>Recurrent Neural*</td><td>0.015</td><td>0.006</td><td>0.177</td><td>1.144</td></tr><tr><td>Reinforcement Learning*</td><td>0.007</td><td>0.099</td><td>0.155</td><td>0.593</td></tr><tr><td>Relation Extraction**</td><td>0.000</td><td>0.199</td><td>0.463</td><td>0.736</td></tr><tr><td>Semantic Role**</td><td>0.000</td><td>0.462</td><td>0.445</td><td>0.352</td></tr><tr><td>Semi Supervised**</td><td>0.000</td><td>0.209</td><td>0.713</td><td>0.522</td></tr><tr><td>Sentiment Analysis**</td><td>0.000</td><td>0.136</td><td>1.136</td><td>1.289</td></tr><tr><td>Sentiment Classification**</td><td>0.000</td><td>0.109</td><td>0.421</td><td>0.454</td></tr><tr><td>Sequence Learning**</td><td>0.006</td><td>0.000</td><td>0.020</td><td>0.513</td></tr><tr><td>Shared Task**</td><td>0.000</td><td>0.373</td><td>0.869</td><td>1.159</td></tr><tr><td>Short Term*</td><td>0.013</td><td>0.012</td><td>0.045</td><td>0.669</td></tr><tr><td>Social Media**</td><td>0.000</td><td>0.005</td><td>0.258</td><td>0.970</td></tr><tr><td>Source Toolkit*</td><td>0.002</td><td>0.151</td><td>0.487</td><td>0.224</td></tr><tr><td>Stochastic Optimization*</td><td>0.007</td><td>0.006</td><td>0.048</td><td>0.652</td></tr><tr><td>Stochastic Parts*</td><td>0.464</td><td>0.042</td><td>0.005</td><td>0.001</td></tr><tr><td>Support Vector*</td><td>0.004</td><td>0.825</td><td>0.652</td><td>0.188</td></tr><tr><td>Term Memory*</td><td>0.011</td><td>0.009</td><td>0.042</td><td>0.662</td></tr><tr><td>Transfer Learning**</td><td>0.000</td><td>0.010</td><td>0.045</td><td>0.463</td></tr><tr><td>Tree Adjoining*</td><td>1.158</td><td>0.582</td><td>0.155</td><td>0.037</td></tr><tr><td>Unrestricted Text*</td><td>0.579</td><td>0.114</td><td>0.024</td><td>0.006</td></tr><tr><td>Vector Machines*</td><td>0.004</td><td>0.593</td><td>0.473</td><td>0.122</td></tr><tr><td>Word Embeddings**</td><td>0.000</td><td>0.000</td><td>0.076</td><td>1.070</td></tr><tr><td>Word Representations**</td><td>0.000</td><td>0.000</td><td>0.367</td><td>1.065</td></tr></table>
+
+Figure 10: Bigram citation percentages of some notable terms found in the titles of cited papers across different time intervals. For example, "Neural Machine" occurred in  $3.313\%$  of the titles of cited papers in the 2016-2021 interval.
+
+![](images/227d7c33b468a5ee1786e34062ae66f2d5f076d40c2544efb0155dc72de25955.jpg)  
+(a) Papers published between 2000 and 2010.
+
+![](images/85784b0bf3052bccff3bc1059b58d6632e3e271f6037a02cf5e18a5af4f72b8a.jpg)  
+(b) Papers published between 2010 and 2016.
+
+![](images/a402db2022ccaa116a464ceb00491a3e86878574b6af6b5e8dab16dd18a02c59.jpg)  
+Figure 11: Variation of mean  $mAoC$  and Citation Age Diversity (CAD) (shown on y-axis) for papers with different citation counts (shown on x-axis).
+
+![](images/88df6e931ede7d16b167cbc6f32d2cf35b5f9a88dce14224a73117ee90b4920f.jpg)  
+(b) Language model.
+
+![](images/0706704eee1140796f5956c4431a0ae3604ef666d54a6795bfd8f66b21c695d6.jpg)  
+(a) Language inference.
+
+![](images/1e8d0abdb9c4bcbfbaa2e4a872ceeaaab6940b21147211c1a5ccfaa9c14191b2.jpg)
+
+![](images/7e7b341c7a6ef4dd1c004c0514419c59a55614d42043633884dafc6211f51546.jpg)  
+(c) Entity recognition.  
+(d) Sense disambiguation.  
+(e) Speech tagging.  
+Figure 12: Variation of mean  $mAoC$  and  $CADIndex$  (shown on y-axis) for papers with different citation counts (shown on x-axis) for papers published between 1965 and 2021 across various research topics.
+
+# Citational Amnesia
+
+Demo to predict the number of references, mean age of citation(mAoC), and comparison of mAoC with all the papers in the ACL Anthology. Kindly enter the Semantic Scholar ID(SSID) of the paper in the box and click "Generate"
+
+# Retrieving SSID
+
+For paper : https://wwwsemanticscholar.org/paper/BERT%3A-Pre-training-of-Deep-Bidirectional-for-Devlin-Chang/df2b0e26d0599ce3e70df8a9da02e51594e0e992SSID is : df2b0e26d0599ce3e70df8a9da02e51594e0e992Note: Currently we only support SSID as the input format
+
+Semantic Scholar ID
+
+df2b0e26d0599ce3e70df8a9da02e51594e0e992
+
+# Generate
+
+Number of references
+
+56
+
+Mean AoC
+
+6.142857142857143
+
+# Top 5 oldest papers cited:
+
+[1953] Title: "Cloze Procedure": A New Tool for Measuring Readability  
+[1992] Title: Class-Based n-gram Models of Natural Language  
+[2003] Title: Introduction to the CoNLL-2003 Shared Task: Language-Independent Named Entity Recognition  
+[2005] Title: A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data  
+[2005] Title: Automatically Constructing a Corpus of Sentential
+
+![](images/4d6f73679809216f9b7ff2573a077cc44112c788bf2d95c89ea9c8a710b53013.jpg)  
+Plot mAoc of your paper is at 49.45-th percentile of all the papers in our database (papers published until 2021 years)  
+Figure 13: Screenshot of the online demo to compute Age-of-Citation metrics for a paper.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work? 8  
+A2. Did you discuss any potential risks of your work? Not applicable. Left blank.  
+A3. Do the abstract and introduction summarize the paper's main claims?  
+A4. Have you used AI writing assistants when working on this paper? Left blank.
+
+B Did you use or create scientific artifacts?
+
+Not applicable. Left blank.
+
+B1. Did you cite the creators of artifacts you used? Not applicable. Left blank.  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Not applicable. Left blank.  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Not applicable. Left blank.  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Not applicable. Left blank.
+
+C Did you run computational experiments?
+
+Left blank.
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? No response.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? No response.  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? No response.  
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? No response.
+
+# D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? No response.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? No response.  
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? No response.  
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? No response.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? No response.

2023/Forgotten Knowledge_ Examining the Citational Amnesia in NLP/images.zip

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+size 772500

2023/FormNetV2_ Multimodal Graph Contrastive Learning for Form Document Information Extraction/374a8618-2dba-4970-9c92-9dbdb98b467b_origin.pdf

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2023/FormNetV2_ Multimodal Graph Contrastive Learning for Form Document Information Extraction/full.md

@@ -0,0 +1,416 @@
+# FormNetV2: Multimodal Graph Contrastive Learning for Form Document Information Extraction
+
+Chen-Yu Lee $^{1*}$ , Chun-Liang Li $^{1}$ , Hao Zhang $^{2}$ , Timothy Dozat $^{2}$ , Vincent Perot $^{2}$ , Guolong Su $^{2}$ , Xiang Zhang $^{1}$ , Kihyuk Sohn $^{2}$ , Nikolai Glushnev $^{3}$ , Renshen Wang $^{2}$ , Joshua Ainslie $^{2}$ , Shangbang Long $^{2}$ , Siyang Qin $^{2}$ , Yasuhisa Fujii $^{2}$ , Nan Hua $^{2}$ , Tomas Pfister $^{1}$ $^{1}$ Google Cloud AI Research,  $^{2}$ Google Research,  $^{3}$ Google Cloud AI
+
+# Abstract
+
+The recent advent of self-supervised pretraining techniques has led to a surge in the use of multimodal learning in form document understanding. However, existing approaches that extend the mask language modeling to other modalities require careful multitask tuning, complex reconstruction target designs, or additional pre-training data. In FormNetV2, we introduce a centralized multimodal graph contrastive learning strategy to unify self-supervised pre-training for all modalities in one loss. The graph contrastive objective maximizes the agreement of multimodal representations, providing a natural interplay for all modalities without special customization. In addition, we extract image features within the bounding box that joins a pair of tokens connected by a graph edge, capturing more targeted visual cues without loading a sophisticated and separately pre-trained image encoder. FormNetV2 establishes new state-of-the-art performance on FUNSD, CORD, SROIE and Payment benchmarks with a more compact model size.
+
+# 1 Introduction
+
+Automated information extraction is essential for many practical applications, with form-like documents posing unique challenges compared to article-like documents, which have led to an abundance of recent research in the area. In particular, form-like documents often have complex layouts that contain structured objects like tables, columns, and fillable regions. Layout-aware language modeling has been critical for many successes (Xu et al., 2020; Majumder et al., 2020; Lee et al., 2022).
+
+To further boost the performance, many recent approaches adopt multiple modalities (Xu et al.,
+
+2021; Huang et al., 2022; Appalaraju et al., 2021). Specifically, the image modality adds more structural information and visual cues to the existing layout and text modalities. They therefore extend the masked language modeling (MLM) from text to masked image modeling (MIM) for image and text-image alignment (TIA) for cross-modal learning. The alignment objective may also help to prime the layout modality, though it does not directly involve text layouts or document structures.
+
+In this work, we propose FormNetV2, a multimodal transformer model for form information extraction. Unlike existing works – which may use the whole image as one representation (Appalaraju et al., 2021), or image patches (Xu et al., 2021), or image features of token bounding boxes (Xu et al., 2020) – we propose using image features extracted from the region bounded by a pair of tokens connected in the constructed graph. This allows us to capture a richer and more targeted visual component of the intra- and inter-entity information. Furthermore, instead of using multiple self-supervised objectives for each individual modality, we introduce graph contrastive learning (Li et al., 2019; You et al., 2020; Zhu et al., 2021) to learn multimodal embeddings jointly. These two additions to FormNetV1 (Lee et al., 2022) enable the graph convolutions to produce better super-tokens, resulting in both improved performance and a smaller model size.
+
+In experiments, FormNetV2 outperforms its predecessor FormNetV1 as well as the existing multimodal approaches on four standard benchmarks. In particular, compared with FormNetV1, FormNetV2 outperforms it by a large margin on FUNSD (86.35 v.s. 84.69) and Payment (94.90 v.s. 92.19); compared with DocFormer (Appalaraju et al., 2021), FormNetV2 outperforms it on FUNSD and CORD with nearly  $2.5\mathrm{x}$  less number of parameters.
+
+# 2 Related Work
+
+Early works on form document information extraction are based on rule-based models or learning-based models with handcrafted features (Lebourgeois et al., 1992; O'Gorman, 1993; Ha et al., 1995; Simon et al., 1997; Marinai et al., 2005; Chiticariu et al., 2013). Later on, various deep neural models have been proposed, including methods based on recurrent nets (Palm et al., 2017; Aggarwal et al., 2020), convolutional nets (Katti et al., 2018; Zhao et al., 2019; Denk and Reisswig, 2019), and transformers (Majumder et al., 2020; Garncarek et al., 2020; Wang et al., 2022c).
+
+Recently, in addition to the text, researchers have explored the layout attribute in form document modeling, such as the OCR word reading order (Lee et al., 2021; Gu et al., 2022b), text coordinates (Majumder et al., 2020; Xu et al., 2020; Garncarek et al., 2020; Li et al., 2021a; Lee et al., 2022), layout grids (Lin et al., 2021), and layout graphs (Lee et al., 2022). The image attribute also provides essential visual cues such as fonts, colors, and sizes. Other visual signals can be useful as well, including logos and separating lines from form tables. Xu et al. (2020) uses Faster R-CNN (Ren et al., 2015) to extract token image features; Appalaraju et al. (2021) uses ResNet50 (He et al., 2016) to extract full document image features; Li et al. (2022) use ViT (Dosovitskiy et al., 2020) with FPN (Lin et al., 2017) to extract non-overlapping patch image features. These sophisticated image embedders require a separate pre-training step using external image datasets (e.g. ImageNet (Russakovsky et al., 2015) or PubLayNet (Zhong et al., 2019)), and sometimes depend upon a visual codebook pre-trained by a discrete variational autoencoder (dVAE).
+
+When multiple modalities come into play, different supervised or self-supervised multimodal pre-training techniques have been proposed. They include mask prediction, reconstruction, and matching for one or more modalities (Xu et al., 2020, 2021; Appalaraju et al., 2021; Li et al., 2021b; Gu et al., 2022a; Huang et al., 2022; Li et al., 2022; Pramanik et al., 2020). Next-word prediction (Kim et al., 2022) or length prediction (Li et al., 2021c) have been studied to bridge text and image modalities. Direct and relative position predictions (Cosma et al., 2020; Wei et al., 2020; Li et al., 2021a; Wang et al., 2022a; Li et al., 2021c) have been proposed to explore the underlying lay
+
+out semantics of documents. Nevertheless, these pre-training objectives require strong domain expertise, specialized designs, and multi-task tuning between involved modalities. In this work, our proposed graph contrastive learning performs multimodal pre-training in a centralized design, unifying the interplay between all involved modalities without the need for prior domain knowledge.
+
+# 3 FormNetV2
+
+We briefly review the backbone architecture FormNetV1 (Lee et al., 2022) in Sec 3.1, introduce the multimodal input design in Sec 3.2, and detail the multimodal graph contrastive learning in Sec 3.3.
+
+# 3.1 Preliminaries
+
+ETC. FormNetV1 (Lee et al., 2022) uses Extended Transformer Construction (ETC; Ainslie et al., 2020) as the backbone to work around the quadratic memory cost of attention for long form documents. ETC permits only a few special tokens to attend to every token in the sequence (global attention); all other tokens may only attend to  $k$  local neighbors within a small window, in addition to these special tokens (local attention). This reduces the computational complexity from  $O(n^{2})$  query-key pairs that need scoring to  $O(kn)$ . Eq. (2) formalizes the computation of the attention vector  $\mathbf{a}_0$  for a model with one global token at index 0, and Eq. (2) formalizes computation of the attention vector  $\mathbf{a}_{i > 0}$  for the rest of the tokens in the model.
+
+$$
+\mathbf {a} _ {0} = \operatorname {a t t e n d} \left(\mathbf {h} _ {0}, \left[ \mathbf {h} _ {0}, \mathbf {h} _ {1}, \dots , \mathbf {h} _ {n} \right]\right) \tag {1}
+$$
+
+$$
+\mathbf {a} _ {i > 0} = \operatorname {a t t e n d} \left(\mathbf {h} _ {i}, \left[ \mathbf {h} _ {0}, \mathbf {h} _ {i - k}, \dots , \mathbf {h} _ {i + k} \right]\right) \tag {2}
+$$
+
+Rich Attention. To address the distorted semantic relatedness of tokens created by imperfect OCR serialization, FormNetV1 adapts the attention mechanism to model spatial relationships between tokens by proposing Rich Attention, a mathematically sound way of conditioning attention on low-level spatial features without resorting to quantizing the document into regions associated with distinct embeddings in a lookup table. In Rich Attention, the model constructs the (pre-softmax) attention score (Eq. 10) from multiple components: the usual transformer attention score (Eq. 7); the order of tokens along the x-axis and the y-axis (Eq. 8); and the log distance (in number of pixels) between tokens, again along both axes (Eq. 9). The expression for a transformer head with Rich Attention on the x-axis is provided in Eqs. (3-10); we
+
+![](images/2959543b25ca2d9d8619b1e005ba884ccbd6e6f00084139e2025c5f109f67d14.jpg)  
+Figure 1: Graph of a sample region from a form. Token bounding boxes are identified, and from them the graph is constructed. Nodes are labeled and the graph structure is shown abstracted away from its content.
+
+![](images/d5e523bfa4d3d0113054abe73ec8c3ba09077aa6b61ca87315ba9606ede191af.jpg)  
+Figure 2: Multimodal graph representations are composed from three modalities: text at node-level; concatenation of layout and image at edge-level.
+
+refer the interested reader to Lee et al. (2022) for further details.
+
+$$
+o _ {i j} = \operatorname {i n t} \left(x _ {i} <   x _ {j}\right) \tag {3}
+$$
+
+$$
+d _ {i j} = \ln \left(1 + \left| x _ {i} - x _ {j} \right|\right) \tag {4}
+$$
+
+$$
+p _ {i j} = \operatorname {S i g m o i d} \left(\operatorname {a f f i n e} ^ {(p)} \left([ \mathbf {q} _ {i}; \mathbf {k} _ {j} ]\right)\right) \tag {5}
+$$
+
+$$
+\mu_ {i j} = \operatorname {a f f i n e} ^ {(\mu)} ([ \mathbf {q} _ {i}; \mathbf {k} _ {j} ]) \tag {6}
+$$
+
+$$
+s _ {i j} ^ {(t)} = \mathbf {q} _ {i} ^ {\top} \mathbf {k} _ {j} \tag {7}
+$$
+
+$$
+s _ {i j} ^ {(o)} = o _ {i j} \ln \left(p _ {i j}\right) + \left(1 - o _ {i j}\right) \ln \left(1 - p _ {i j}\right) \tag {8}
+$$
+
+$$
+s _ {i j} ^ {(d)} = - \frac {\theta^ {2} \left(d _ {i j} - \mu_ {i j}\right) ^ {2}}{2} \tag {9}
+$$
+
+$$
+s _ {i j} = s _ {i j} ^ {(t)} + s _ {i j} ^ {(o)} + s _ {i j} ^ {(d)} \tag {10}
+$$
+
+GCN. Finally, FormNetV1 includes a graph convolutional network (GCN) contextualization step before serializing the text to send to the ETC transformer component. The graph for the GCN locates up to  $K$  neighbors for each token - defined broadly by geographic "nearness" - before convolving their token embeddings to build up supertoken representations as shown in Figure 1. This allows the network to build a weaker but more complete picture of the layout modality than Rich Attention, which is constrained by local attention.
+
+The final system was pretrained end-to-end with a standard masked language modeling (MLM) objective. See Sec A.3 in Appendix for more details.
+
+![](images/fc85ee764f13ac82ca26353f83c58a0261e34d2e02f5122da4fdd920b2f7fbad.jpg)  
+(a) Within entity
+
+![](images/e32f3e96be20a47e69f902c116fdc40d09a4d38ac06c915763b95d014266166e.jpg)  
+(b) Cross entity  
+Figure 3: Image features are extracted from bounding boxes (red) that join pairs of tokens connected by edges to capture (a) similar patterns within an entity, or (b) dissimilar patterns or separating lines between entities.
+
+# 3.2 Multimodal Input
+
+In FormNetV2, we propose adding the image modality to the model in addition to the text and layout modalities that are already used in FormNetV1 (Sec 3.3 in Lee et al. (2022)). We expect that image features from documents contain information absent from the text or the layout, such as fonts, colors, and sizes of OCR words.
+
+To do this, we run a ConvNet to extract dense image features on the whole document image, and then use Region-of-Interest (RoI) pooling (He et al., 2017) to pool the features within the bounding box that joins a pair of tokens connected by a GCN edge. Finally, the RoI pooled features go through another small ConvNet for refinement. After the image features are extracted, they are injected into the network through concatenation with the existing layout features at edges of the GCN. Figure 2 illustrates how all three modalities are utilized in this work and Sec 4.2 details the architecture.
+
+Most of the recent approaches (Table 1) that incorporate image modality extract features from either (a) the whole image as one vector, (b) non-overlapping image patches as extra input tokens to transformers, or (c) token bounding boxes that are added to the text features for all tokens.
+
+However, form document images often contain OCR words that are relatively small individually and are densely distributed in text blocks. They also contain a large portion of the background region without any texts. Therefore, the aforementioned method (a) only generates global visual representations with large noisy background regions but not
+
+![](images/78d00cfc185ff2d5ca12cc2fcbd4f0292e0518013bafbfe72886d82d6a8a2f77.jpg)  
+Figure 4: Multimodal graph contrastive learning. Two corrupted graphs are sampled from an input graph by corruption of graph topology (edges) and attributes (multimodal features). The system is trained to identify which pair of nodes across all pairs of corrupted nodes (including within the same graph) came from the same node.
+
+targeted entity representations; method (b) tends to be sensitive to the patch size and often chops OCR words or long entities to different patches, while also increasing computational cost due to the increased token length; and method (c) only sees regions within each token's bounding box and lacks context between or outside of tokens.
+
+On the other hand, the proposed edge-level image feature representation can precisely model the relationship between two nearby, potentially related "neighbor" tokens and the surrounding region, while ignoring all irrelevant or distracting regions. Figure 3 demonstrates that the targeted RoI image feature pooling through the union bounding box can capture any similar patterns (e.g. font, color, size) within an entity (left) or dissimilar patterns or separating lines between entities (right). See Sec 4.4 for detailed discussion.
+
+# 3.3 Multimodal Graph Contrastive Learning
+
+Previous work in multimodal document understanding requires manipulating multiple supervised or self-supervised objectives to learn embeddings from one or multiple modalities during pre-training. By contrast, in FormNetV2, we propose utilizing the graph representation of a document to learn multimodal embeddings with a contrastive loss.
+
+Specifically, we first perform stochastic graph corruption to sample two corrupted graphs from the original input graph of each training instance. This step generates node embeddings based on partial contexts. Then, we apply a contrastive objective by maximizing agreement between tokens at node-level. That is, the model is asked to identify which pairs of nodes across all pairs of nodes - within the same graph and across graphs - came from the
+
+same original node. We adopt the standard normalized temperature-scaled cross entropy (NT-Xent) loss formulation (Chen et al., 2020; Wu et al., 2018; Oord et al., 2018; Sohn, 2016) with temperature 0.1 in all experiments.
+
+To build a centralized contrastive loss that unifies the interactions between multiple input modalities, we corrupt the original graph at both graph topology level and graph feature level. Topology corruption includes edge dropping by randomly removing edges in the original graph. Feature corruption includes applying dropping to all three modalities: dropping layout and image features from edges and dropping text features from nodes. Note that we only corrupt the graph in the GCN encoder and keep the ETC decoder intact to leverage the semantically meaningful graph representation of the document during graph contrastive learning.
+
+To further diversify the contexts in two corrupted graphs and reduce the risk of training the model to over-rely on certain modalities, we further design an inductive graph feature dropping mechanism by adopting imbalanced drop-rates of modalities between the two corrupted graphs. Precisely, for a given modality, we discard  $p$  percent of the features in the first corrupted graph and discard  $1 - p$  percent of the features in the second corrupted graph. Experiments in Sec 4.4 show that  $p = 0.8$  works best empirically and the inductive feature dropping mechanism provides further performance boost over the vanilla version. We stipulate that this boom-and-bust approach to regularization allows the model to learn rich, complex representations that take full advantage of the model's capacity without becoming overly dependent on specific feature interactions. Figure 4 illustrates the overall
+
+process.
+
+The proposed graph contrastive objective is also general enough in principle to adopt other corruption mechanisms (Zhu et al., 2020; Hassani and Khasahmadi, 2020; You et al., 2020; Velickovic et al., 2019). The multimodal feature dropping provides a natural playground to consume and allow interactions between multiple input modalities in one single loss design. It is straightforward to extend the framework to include more modalities without the need for hand crafting specialized loss by domain experts. To the best of our knowledge, we are the first to use graph contrastive learning during pre-training for form document understanding.
+
+# 4 Evaluation
+
+# 4.1 Datasets
+
+FUNSD. FUNSD (Jaume et al., 2019) contains a collection of research, marketing, and advertising forms that vary extensively in their structure and appearance. The dataset consists of 199 annotated forms with 9,707 entities and 31,485 word-level annotations for 4 entity types: header, question, answer, and other. We use the official 75-25 split for the training and test sets.
+
+CORD. CORD (Park et al., 2019) contains over 11,000 Indonesian receipts from shops and restaurants. The annotations are provided in 30 fine-grained semantic entities such as store name, quantity of menu, tax amount, discounted price, etc. We use the official 800-100-100 split for training, validation, and test sets.
+
+SROIE. The ICDAR 2019 Challenge on Scanned Receipts OCR and key Information Extraction (SROIE) (Huang et al., 2019) offers 1,000 whole scanned receipt images and annotations. 626 samples are for training and 347 samples are for testing. The task is to extract four predefined entities: company, date, address, or total.
+
+Payment. We use the large-scale payment data (Majumder et al., 2020) that consists of roughly 10,000 documents and 7 semantic entity labels from human annotators. We follow the same evaluation protocol and dataset splits used in Majumder et al. (2020).
+
+# 4.2 Experimental Setup
+
+We follow the FormNetV1 (Lee et al., 2022) architecture with a slight modification to incorporate multiple modalities used in the proposed method.
+
+Our backbone model consists of a 6-layer GCN encoder to generate structure-aware super-tokens, followed by a 12-layer ETC transformer decoder equipped with Rich Attention for document entity extraction. The number of hidden units is set to 768 for both GCN and ETC. The number of attention heads is set to 1 in GCN and 12 in ETC. The maximum sequence length is set to 1024. We follow Ainslie et al. (2020); Lee et al. (2022) for other hyper-parameter settings. For the image embedder architecture, see Sec A.1 in Appendix.
+
+Pre-training. We pre-train FormNetV2 using two unsupervised objectives: Masked Language Modeling (MLM) (Taylor, 1953; Devlin et al., 2019) and the proposed multimodal Graph Contrastive Learning (GCL).
+
+Different from BERT (Devlin et al., 2019), here MLM has access to layout and image modalities during pre-training similar to Appalaraju et al. (2021); Xu et al. (2021, 2020). Nevertheless, the layout and image features are constructed at edge level instead of at node level, supplementing the text features for better underlying representation learning without directly leaking the trivial information.
+
+GCL provides a natural playground for effective interactions between all three modalities from a document in a contrastive fashion. For each graph representation of a document, we generate two corrupted views by edge dropping, edge feature dropping, and node feature dropping with dropping rates  $\{0.3, 0.8, 0.8\}$ , respectively. The weight matrices in both GCN and ETC are shared across the two views.
+
+We follow Appalaraju et al. (2021); Xu et al. (2021, 2020) and use the large-scale IIT-CDIP document collection (Lewis et al., 2006) for pretraining, which contains 11 million document images. We train the models from scratch using Adam optimizer with batch size of 512. The learning rate is set to 0.0002 with a warm-up proportion of 0.01. We find that GCL generally converges faster than MLM, therefore we set the loss weightings to 1 and 0.5 for MLM and GCL, respectively.
+
+Note that we do not separately pre-train or load a pre-trained checkpoint for the image embedder as done in other recent approaches shown in Table 1. In fact, in our implementation, we find that using sophisticated image embedders or pre-training with natural images, such as ImageNet (Russakovsky et al., 2015), do not improve the final downstream
+
+<table><tr><td>Dataset</td><td>Method</td><td>P</td><td>R</td><td>F1</td><td>F1†</td><td>Modality</td><td>Image Embedder</td><td>#Params</td></tr><tr><td rowspan="11">FUNSD</td><td>SPADE (Hwang et al., 2021)</td><td>-</td><td>-</td><td>70.5</td><td>-</td><td>T+L</td><td>-</td><td>110M</td></tr><tr><td>UniLMv2 (Bao et al., 2020)</td><td>67.80</td><td>73.91</td><td>70.72</td><td>-</td><td>T</td><td>-</td><td>355M</td></tr><tr><td>LayoutLMv1 (Xu et al., 2020)</td><td>75.36</td><td>80.61</td><td>77.89</td><td>-</td><td>T+L</td><td>-</td><td>343M</td></tr><tr><td>DocFormer (Appalaraju et al., 2021)</td><td>81.33</td><td>85.44</td><td>83.33</td><td>-</td><td>T+L+I</td><td>ResNet50</td><td>502M</td></tr><tr><td>FormNetV1 (Lee et al., 2022)</td><td>85.21</td><td>84.18</td><td>84.69</td><td>-</td><td>T+L</td><td>-</td><td>217M</td></tr><tr><td>LayoutLMv1 (Xu et al., 2020)</td><td>76.77</td><td>81.95</td><td>79.27</td><td>-</td><td>T+L+I</td><td>ResNet101</td><td>160M</td></tr><tr><td>LayoutLMv2 (Xu et al., 2021)</td><td>83.24</td><td>85.19</td><td>84.20</td><td>-</td><td>T+L+I</td><td>ResNeXt101-FPN</td><td>426M</td></tr><tr><td>DocFormer (Appalaraju et al., 2021)</td><td>82.29</td><td>86.94</td><td>84.55</td><td>-</td><td>T+L+I</td><td>ResNet50</td><td>536M</td></tr><tr><td>StructuralLM (Li et al., 2021a)</td><td>-</td><td>-</td><td>-</td><td>85.14</td><td>T+L</td><td>-</td><td>355M</td></tr><tr><td>LayoutLMv3 (Huang et al., 2022)</td><td>81.35</td><td>83.75</td><td>82.53</td><td>92.08</td><td>T+L+I</td><td>Tokenization</td><td>368M</td></tr><tr><td>FormNetV2 (ours)</td><td>85.78</td><td>86.94</td><td>86.35</td><td>92.51</td><td>T+L+I</td><td>3-layer ConvNet</td><td>204M</td></tr><tr><td rowspan="10">CORD</td><td>SPADE (Hwang et al., 2021)</td><td>-</td><td>-</td><td>91.5</td><td>-</td><td>T+L</td><td>-</td><td>110M</td></tr><tr><td>UniLMv2 (Bao et al., 2020)</td><td>91.23</td><td>92.89</td><td>92.05</td><td>-</td><td>T</td><td>-</td><td>355M</td></tr><tr><td>LayoutLMv1 (Xu et al., 2021)</td><td>94.32</td><td>95.54</td><td>94.93</td><td>-</td><td>T+L</td><td>-</td><td>343M</td></tr><tr><td>DocFormer (Appalaraju et al., 2021)</td><td>96.46</td><td>96.14</td><td>96.30</td><td>-</td><td>T+L+I</td><td>ResNet50</td><td>502M</td></tr><tr><td>FormNetV1 (Lee et al., 2022)</td><td>98.02</td><td>96.55</td><td>97.28</td><td>-</td><td>T+L</td><td>-</td><td>345M</td></tr><tr><td>LayoutLMv2 (Xu et al., 2021)</td><td>95.65</td><td>96.37</td><td>96.01</td><td>-</td><td>T+L+I</td><td>ResNeXt101-FPN</td><td>426M</td></tr><tr><td>TILT (Powalski et al., 2021)</td><td>-</td><td>-</td><td>96.33</td><td>-</td><td>T+L+I</td><td>U-Net</td><td>780M</td></tr><tr><td>DocFormer (Appalaraju et al., 2021)</td><td>97.25</td><td>96.74</td><td>96.99</td><td>-</td><td>T+L+I</td><td>ResNet50</td><td>536M</td></tr><tr><td>LayoutLMv3 (Huang et al., 2022)</td><td>95.82</td><td>96.03</td><td>95.92</td><td>97.46</td><td>T+L+I</td><td>Tokenization</td><td>368M</td></tr><tr><td>FormNetV2 (ours)</td><td>97.74</td><td>97.00</td><td>97.37</td><td>97.70</td><td>T+L+I</td><td>3-layer ConvNet</td><td>204M</td></tr><tr><td rowspan="4">SROIE</td><td>UniLMv2 (Bao et al., 2020)</td><td>-</td><td>-</td><td>94.88</td><td>-</td><td>T</td><td>-</td><td>355M</td></tr><tr><td>LayoutLMv1 (Xu et al., 2021)</td><td>95.24</td><td>95.24</td><td>95.24</td><td>-</td><td>T+L</td><td>-</td><td>343M</td></tr><tr><td>LayoutLMv2 (Xu et al., 2021)</td><td>99.04</td><td>96.61</td><td>97.81</td><td>-</td><td>T+L+I</td><td>ResNeXt101-FPN</td><td>426M</td></tr><tr><td>FormNetV2 (ours)</td><td>98.56</td><td>98.05</td><td>98.31</td><td>-</td><td>T+L+I</td><td>3-layer ConvNet</td><td>204M</td></tr><tr><td rowspan="3">Payment</td><td>NeuralScoring (Majumder et al., 2020)</td><td>-</td><td>-</td><td>87.80</td><td>-</td><td>T+L</td><td>-</td><td>-</td></tr><tr><td>FormNetV1 (Lee et al., 2022)</td><td>92.70</td><td>91.69</td><td>92.19</td><td>-</td><td>T+L</td><td>-</td><td>217M</td></tr><tr><td>FormNetV2 (ours)</td><td>94.11</td><td>95.71</td><td>94.90</td><td>-</td><td>T+L+I</td><td>3-layer ConvNet</td><td>204M</td></tr></table>
+
+Table 1: Entity-level precision, recall, and F1 score comparisons on four standard benchmarks. “T/L/I” denotes “text/layout/image” modality. The proposed FormNetV2 establishes new state-of-the-art results on all four datasets. FormNetV2 significantly outperforms the most recent DocFormer (Appalaraju et al., 2021) and LayoutLMv3 (Huang et al., 2022) while using a  $38\%$  and  $55\%$  sized model, respectively. Note that LayoutLMv3 (Huang et al., 2022) and StructuralLM (Li et al., 2021a) use segment-level layout positions that incorporate ground truth entity bounding boxes, which is less practical for real-world applications. We nevertheless report our results under the same protocol in column  $\mathbf{F}1^{\dagger}$ . See Sec 4.3 and Sec A.2 in Appendix for details.
+
+entity extraction F1 scores, and they sometimes even degrade the performance. This might be because the visual patterns presented in form documents are drastically different from natural images that have multiple real objects. The best practice for conventional vision tasks (classification, detection, segmentation) might not be optimal for form document understanding.
+
+Fine-tuning. We fine-tune all models for the downstream entity extraction tasks in the experiments using Adam optimizer with batch size of 8. The learning rate is set to 0.0001 without warm-up. The fine-tuning is conducted on Tesla V100 GPUs for approximately 10 hours on the largest corpus. Other hyper-parameters follow the settings in Lee et al. (2022).
+
+# 4.3 Benchmark Results
+
+Table 1 lists the results that are based on the same evaluation protocol<sup>1</sup>.
+
+![](images/c2534929582f2662c1eb3fad66358125268ee48d20317cc3d4655becb21f7035.jpg)  
+Figure 5: Model Size vs. Entity Extraction F1 Score on FUNSD benchmark. The FormNetV2 family significantly outperforms other recent approaches – FormNetV2 achieves highest F1 score (86.35%) while using a 2.6x smaller model than DocFormer (84.55%; Appalaraju et al., 2021). FormNetV2 also outperforms FormNetV1 (Lee et al., 2022) by a large margin (1.66 F1) while using fewer parameters.
+
+As the field is actively growing, researchers have started to explore incorporating additional
+
+information into the system. For example, LayoutLMv3 (Huang et al., 2022) and StructuralLM (Li et al., 2021a) use segment-level layout positions derived from ground truth entity bounding boxes - the {Begin, Inside, Outside, End, Single} schema information (Ratinov and Roth, 2009) that determine the spans of entities are given to the model, which is less practical for real-world applications. We nevertheless report our results under the same protocol in column  $\mathbf{F1}^{\dagger}$  in Table 1. We also report LayoutLMv3 results without ground-truth entity segments for comparisons.
+
+Furthermore, UDoc (Gu et al., 2022a) uses additional paragraph-level supervision returned by a third-party OCR engine EasyOCR $^2$ . Additional PubLayNet (Zhong et al., 2019) dataset is used to pre-train the vision backbone. UDoc also uses different training/test splits (626/247) on CORD instead of the official one (800/100) adopted by other works. ERNIE-mmLayout (Wang et al., 2022b) utilizes a third-party library  $\mathrm{spaCy}^3$  to provide external knowledge for the Common Sense Enhancement module in the system. The F1 scores on FUNSD and CORD are  $85.74\%$  and  $96.31\%$  without the external knowledge. We hope the above discussion can help clarify the standard evaluation protocol and decouple the performance improvement from modeling design vs. additional information.
+
+Figure 5 shows model size vs. F1 score for the recent approaches that are directly comparable. The proposed method significantly outperforms other approaches in both F1 score and parameter efficiency: FormNetV2 achieves highest F1 score (86.35%) while using a 38% sized model than DocFormer (84.55%; Appalaraju et al., 2021). FormNetV2 also outperforms FormNetV1 (Lee et al., 2022) by a large margin (1.66 F1) while using fewer parameters. Table 1 shows that FormNetV2 outperforms LayoutLMv3 (Huang et al., 2022) and StructuralLM (Li et al., 2021a) with a considerable performance leap while using a 55% and 57% sized model, respectively. From Table 1 we also observe that using all three modalities (text+layout+image) generally outperforms using two modalities (text+layout), and using two modalities (text+layout) outperforms using one modality (text) only across different approaches.
+
+# 4.4 Ablation Studies
+
+We perform studies over the effect of image modality, graph contrastive learning, and decoupled graph corruption. The backbone for these studies is a 4-layer 1-attention-head GCN encoder followed by a 4-layer 8-attention-head ETC transformers decoder with 512 hidden units. The model is pre-trained on the 1M IIT-CDIP subset. All other hyperparameters follow Sec 4.2.
+
+Effect of Image Modality and Image Embedder. Table 2 lists results of FormNetV1 (a) backbone only, (b) with additional tokens constructed from image patches $^4$ , and (c) with the proposed image feature extracted from edges of a graph. The networks are pre-trained with MLM only to showcase the impact of input with image modality.
+
+We observe that while (b) provides slight F1 score improvement, it requires  $32\%$  additional parameters over baseline (a). The proposed (c) approach achieves a significant F1 boost with less than  $1\%$  additional parameters over baseline (a). Secondly, we find the performance of more advanced image embedders (He et al., 2016) is inferior to the 3-layer ConvNet used here, which suggests that these methods may be ineffective in utilizing image modality. Nevertheless, the results demonstrate the importance of image modality as part of the multimodal input. Next we will validate the importance of an effective multimodal pre-training mechanism through graph contrastive learning.
+
+<table><tr><td>Method</td><td>FUNSD</td><td>CORD</td><td>#Params</td></tr><tr><td>FormNetV1</td><td>82.53</td><td>95.16</td><td>81.7M</td></tr><tr><td>FormNetV1+Image Patch</td><td>82.65</td><td>95.43</td><td>107.0M</td></tr><tr><td>FormNetV1+Edge Image (ours)</td><td>83.13</td><td>95.85</td><td>82.3M</td></tr></table>
+
+Table 2: F1 with different image modality setups.
+
+Effect of Graph Contrastive Learning. The graph corruption step (Figure 4) in the proposed multimodal graph contrastive learning requires corruption of the original graph at both topology and feature levels. Considering the corruption happens in multiple places: edges, edge features, and node features, a naive graph corruption implementation would be to use the same drop-rate value everywhere. In Figure 6(a)(b), we show the downstream entity extraction F1 scores on FUNSD and CORD datasets by varying the dropping rate value during the graph contrastive pre-training. The selected
+
+![](images/13b2acedc1d3a925d926c9280e04cbe0a8972fcdc739a0b121f3089b38feaf06.jpg)  
+(a) FUNSD
+
+![](images/31cfc298e7bc3e3d0a22c2bf72219597b119da3503a21a6ef95c84715dee7ed5.jpg)  
+(b) CORD
+
+![](images/0d88ba19efff44452280f96a78c2463b14bd2145cadf9be0aa9a838f4da0cb0a.jpg)  
+(c) FUNSD  
+Figure 6: Entity Extraction F1 Score vs. Graph Corruption Mechanism on FUNSD and CORD benchmarks. (a)(b) show results using the same drop-rate across modalities. The proposed multimodal graph contrastive learning improves MLM pretraining at almost all drop-rates; (c)(d) show results using different drop-rates across modalities. The decoupled dropping mechanism permits further boosts to the F1 scores over non-decoupled counterparts. See Sec 4.4 for discussion.
+
+![](images/2862028fb508681976750300346b8f334c2147fdd71bfa5ad597115730e47b62.jpg)  
+(d) CORD
+
+dropping rate is shared across all aforementioned places.
+
+Results show that the proposed multimodal graph contrastive learning works out of the box across a wide range of dropping rates. It demonstrates the necessity of multimodal corruption at both topology level and feature level - it brings up to  $0.66\%$  and  $0.64\%$  F1 boost on FUNSD and CORD respectively, when the model is pre-trained on MLM plus the proposed graph contrastive learning over MLM only. Our method is also stable to perturbation of different drop-rates.
+
+We observe less or no performance improvement when extreme drop-rates are used; for example, dropping  $10\%$  edges and features or dropping  $90\%$  edges and features. Intuitively, dropping too few or too much information provides either no node context changes or too few remaining node contexts in different corrupted graphs for effective contrastive learning.
+
+Effect of Decoupled Graph Corruption. In this study, we investigate whether decoupling the drop-rate in different places of graph corruption can learn better representations during pre-training and bring further improvement to the downstream entity extraction tasks. Specifically, we select different dropping rates for all four different places: edge, layout and image features at edge level, and text features at node level. At feature level (layout, image, text), when one of the corrupted graphs selects dropping rate  $p$  for a certain feature, the other corrupted graph will use the complement of the selected dropping rate  $1 - p$  for the same feature as introduced in Sec 3.3. This inductive multimodal contrastive design creates stochastically imbalanced information access to the features between two cor
+
+rupted views. It provides more diverse contexts at node level in different views and makes the optimization of the contrastive objective harder, ideally generating more semantically meaningful representations between the three modalities.
+
+Figure 6(c)(d) show the downstream entity extraction F1 scores on FUNSD and CORD datasets by pre-training with three different edge dropping rates and three different feature dropping rates. We observe that decoupling the dropping rate at various levels further boosts the performance on both datasets - it brings another  $0.34\%$  and  $0.07\%$  F1 boost on FUNSD and CORD respectively, when decoupled dropping rates are used over the non-decoupled ones.
+
+We also observe nonlinear interactions between different dropping rates at edge level and feature level. The best performing feature dropping rate might be sub-optimal when a different edge dropping rate is applied. This is noteworthy but not surprising behavior, since different edge dropping rates would drastically change the graph topology (and therefore the node embeddings). We expect the amount of information needed for maximizing the agreement of node contexts between two corrupted graphs to be different when the graph topology is altered. Nevertheless, we find that low edge dropping rates (e.g. 0.3) generally perform better than high edge dropping rates, and therefore select a low edge dropping rate in our final design.
+
+Visualization. We visualize (Vig, 2019) the local-to-local attention scores of a CORD example for model pre-trained with MLM only and MLM+GCL but before fine-tuning in Figure 7(a). We observe that with GCL, the model can identify more meaningful token clusterings, leveraging
+
+![](images/2b42fe7e19da9353665780497d37d7d063f707af22d5361903320748e895e2b8.jpg)  
+(a) Attention scores w/ and w/o GCL
+
+![](images/b6e6b21ab8a6120c7423c3480106b013febd520f1707427132f45782b2da34c9.jpg)  
+Figure 7: (a) The attention scores for MLM and MLM+GCL(Graph Contrastive Learning) models on CORD before fine-tuning. When pre-trained with the proposed GCL, the model can identify more meaningful token clusterings, leveraging multimodal input effectively; (b) Difficult cases where the model predictions do not match the human-annotated ground truth. In this visualization we highlight disagreements only.
+
+![](images/74800da2d6acb266cf122b3b5a9cfeb695c983d5b961212bf10c15a40755ce91.jpg)
+
+![](images/fe85684f28b08c1556f0d41b933ffe3970418ff4fa6dbcc71dac05854d4deb03.jpg)  
+(b) Model outputs for difficult cases.
+
+![](images/52c2a6200dc13b1f97ee6eca785568617c2f16d59ce2dd93b7cb2b3e2e9d08ea.jpg)
+
+multimodal input more effectively.
+
+We also show sample model outputs that do not match the human-annotated ground truth in Figure 7(b). The model confuses between 'header' and 'other' on the top of the form and between 'question' and 'answer' for the multiple choice questions on the bottom half of the form. More visualization can be found in Figure 9 in Appendix.
+
+# 5 Conclusion
+
+FormNetV2 augments an existing strong FormNetV1 backbone with image features bounded by pairs of neighboring tokens and the graph contrastive objective that learns to differentiate between the multimodal token representations of two corrupted versions of an input graph. The centralized design sheds new light to the understanding of multimodal form understanding.
+
+# 6 Limitations
+
+Our work follows the general assumption that the training and test set contain the same list of predefined entities. Without additional or necessary modifications, the few-shot or zero-shot capability of the model is expected to be limited. Future work includes exploring prompt-based architectures to unify pre-training and fine-tuning into the same query-based procedure.
+
+# 7 Ethics Consideration
+
+We have read and compiled with the ACL Code of Ethics. The proposed FormNetV2 follows the prevailing large-scale pre-training then fine-tuning framework. Although we use the standard IIT-
+
+CDIP dataset for pre-training in all experiments, the proposed method is not limited to using specific datasets for pre-training. Therefore, it shares the same potential concerns of existing large language models, such as biases from the pre-training data and privacy considerations. We suggest following a rigorous and careful protocol when preparing the pre-training data for public-facing applications.
+
+# References
+
+Milan Aggarwal, Hiresh Gupta, Mausoom Sarkar, and Balaji Krishnamurthy. 2020. Form2seq: A framework for higher-order form structure extraction. In EMNLP.  
+Joshua Ainslie, Santiago Ontañón, Chris Alberti, Vaclav Cvicek, Zachary Fisher, Philip Pham, Anirudh Ravula, Sumit Sanghai, Qifan Wang, and Li Yang. 2020. Etc: Encoding long and structured data in transformers. In EMNLP.  
+Srikar Appalaraju, Bhavan Jasani, Bhargava Urala Kota, Yusheng Xie, and R Manmatha. 2021. Docformer: End-to-end transformer for document understanding. In ICCV.  
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+
+# A Appendix
+
+# A.1 Image Embedder Architecture
+
+Our image embedder is a 3-layer ConvNet with filter sizes \{32, 64, 128\} and kernel size 3 throughout. Stride 2 is used in the middle layer and stride 1 is used everywhere else. We resize the input document image to  $512 \times 512$  with aspect ratio fixed and zero padding for the background region. After extracting the dense features of the whole input image, we perform feature RoI pooling (He et al., 2017) within the bounding box that joins a pair of tokens connected by a GCN edge. The height and width of the pooled region are set to 3 and 16, respectively. Finally, the pooled features go through another 3-layer ConvNet with filter size \{64, 32, 16\} and kernel size 3 throughout. Stride 2 is used in the first 2 layers horizontally and stride 1 is used everywhere else. To consume image modality in our backbone model, we simply concatenate the pooled image features with the existing layout features at edge level of GCN as shown in Figure 2.
+
+# A.2 More Implementation Details
+
+We conduct additional experiments on FUNSD and CORD using base and large versions of LayoutLMv3 (Huang et al., 2022). Instead of using entity segment indexes inferred from ground truth, we use word boxes provided by OCR. We observe considerable performance degradation when the model has access to word-level box information instead of segment-level. The results are shown in Table 3.
+
+<table><tr><td>Method</td><td>Setting</td><td>FUNSD</td><td>CORD</td></tr><tr><td rowspan="3">LayoutLMv3-base</td><td>Reported</td><td>90.29</td><td>96.56</td></tr><tr><td>Reproduced</td><td>90.59</td><td>95.85</td></tr><tr><td>Word box</td><td>78.35</td><td>95.81</td></tr><tr><td rowspan="3">LayoutLMv3-large</td><td>Reported</td><td>92.08</td><td>97.46</td></tr><tr><td>Reproduced</td><td>92.14</td><td>96.78</td></tr><tr><td>Word box</td><td>82.53</td><td>95.92</td></tr></table>
+
+Table 3: LayoutLMv3 results with entity segment indexes (reproduced) or word level indexes (word box). We observe considerable performance degradation when the model has access to word-level box information instead of segment-level.
+
+# A.3 Preliminaries
+
+FormNetV1 (Lee et al., 2022) simplifies the task of document entity extraction by framing it as fundamentally text-centric, and then seeks to solve the
+
+problems that immediately arise from this. Serialized forms can be very long, so FormNetV1 uses a transformer architecture with a local attention window (ETC) as the backbone to work around the quadratic memory cost of attention. This component of the system effectively captures the text modality.
+
+OCR serialization also distorts strong cues of semantic relatedness - a word that is just above another word may be related to it, but if there are many tokens to the right of the upper word or to the left of the lower word, they will intervene between the two after serialization, and the model will be unable to take advantage of the heuristic that nearby tokens tend to be related. To address this, FormNetV1 adapts the attention mechanism to model spatial relationships between tokens using Rich Attention, a mathematically sound way of conditioning attention on low-level spatial features without resorting to quantizing the document into regions associated with distinct embeddings in a lookup table. This allows the system to build powerful representations from the layout modality for tokens that fall within the local attention window.
+
+Finally, while Rich Attention maximizes the potential of local attention, there remains the problem of what to do when there are so many interveners between two related tokens that they do not fall within the local attention window and cannot attend to each other at all. To this end FormNetV1 includes a graph convolutional network (GCN) contextualization step before serializing the text to send to the transformer component. The graph for the GCN locates up to  $K$  potentially related neighbors for each token before convolving to build up the token representations that will be fed to the transformer after OCR serialization. Unlike with Rich Attention, which directly learns concepts like "above", "below", and infinitely many degrees of "nearness", the graph at this stage does not consider spatial relationships beyond "is a neighbor" and "is not a neighbor" - see Figure 1. This allows the network to build a weaker but more complete picture of the layout modality than Rich Attention, which is constrained by local attention. A similar architecture is also found to be useful in graph learning tasks by Wu et al. (2021).
+
+Thus the three main components of FormNetV1 cover each other's weaknesses, strategically trading off representational power and computational efficiency in order to allow the system to construct
+
+![](images/4ad3cead071b9940bd2c961ec3d72f5a2a0186982d491380885ccef4058effbc.jpg)  
+Figure 8: (a) During multimodal graph contrastive pre-training, two corrupted graphs are sampled from an input graph by corruption of graph topology (edges) and attributes (multimodal features). (b) During task-specific fine-tuning, only the original input graph is used.
+
+![](images/4413d2ccd4e6c9e94556cf9a38345ad24b0748544bbb8410b321d4fe7a83a088.jpg)
+
+![](images/7dc4496c6e2c79f36c117f862385d68f04a7627e68fd82844b8d7862af96be49.jpg)  
+Figure 9: The ambiguous cases where the model predictions do not match the human-annotated ground truth. In this visualization we only showcase mismatched entities.
+
+useful representations while simplifying the problem to be fundamentally textual rather than visual. The final system was pretrained end-to-end on large scale unlabeled form documents with a standard masked language modeling (MLM) objective.
+
+ing footnotes.
+
+# A.4 Output Visualization
+
+Figure 9 shows additional FormNetV2 model outputs on FUNSD.
+
+# A.5 License or Terms
+
+Please see the license or terms for IIT-CDIP $^{6}$ , FUNSD $^{7}$ , CORD $^{8}$ , and SROIE $^{9}$  in the correspond
+
+$^{6}$ ir.nist.gov/cdip/README.txt  
+<sup>7</sup>guillaumejaume.github.io/FUNSD/work/  
+$^{8}$ github.com/clovaai/cord/blob/master/License-CC-BY  
+9rrc.cvc.uab.es/?ch=13
+
+A For every submission:
+
+A1. Did you describe the limitations of your work? Sec 6  
+A2. Did you discuss any potential risks of your work? Sec 7  
+A3. Do the abstract and introduction summarize the paper's main claims? Main claims are in Sec 3 with experimental validation in Sec 4.  
+A4. Have you used AI writing assistants when working on this paper? Left blank.
+
+B Did you use or create scientific artifacts?
+
+Sec 4
+
+B1. Did you cite the creators of artifacts you used? Sec 4.2  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Sec A5  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Sec 7  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Sec A5  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Sec 4.1
+
+C Did you run computational experiments?
+
+Sec 4
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Sec 4
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? Sec 4  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?  
+Sec 4  
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Sec 4
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? No response.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? No response.  
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? No response.  
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? No response.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? No response.

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+[
+    {
+        "type": "text",
+        "text": "Free Lunch for Efficient Textual Commonsense Integration in Language Models",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Wanyun Cui",
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+    {
+        "type": "text",
+        "text": "Shanghai University of Finance and Economics",
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+    {
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+        "text": "cui.wanyun@shufe.edu.cn",
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+    {
+        "type": "text",
+        "text": "Xingran Chen",
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "University of Michigan",
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+    {
+        "type": "text",
+        "text": "chenxran@umich.edu",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Recent years have witnessed the emergence of textual commonsense knowledge bases, aimed at providing more nuanced and context-rich knowledge. The integration of external commonsense into language models has been shown to be a key enabler in advancing the state-of-the-art for a wide range of NLP tasks. However, incorporating textual commonsense descriptions is computationally expensive, as compared to encoding conventional symbolic knowledge. In this paper, we propose a method to improve its efficiency without modifying the model. We group training samples with similar commonsense descriptions into a single batch, thus reusing the encoded description across multiple samples. One key observation is that the upper bound of batch partitioning can be reduced to the classic graph  $k$ -cut problem. Consequently, we propose a spectral clustering-based algorithm to solve this problem. Extensive experiments illustrate that the proposed batch partitioning approach effectively reduces the computational cost while preserving performance. The efficiency improvement is more pronounced on larger datasets and on devices with more memory capacity, attesting to its practical utility for large-scale applications.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "While pre-trained language models have made substantial progress in natural language processing, they still lack certain knowledge. Thus it is critical to incorporate external knowledge sources (Peters et al., 2019; Zhang et al., 2019; Logan et al., 2019). Previous research has primarily focused on incorporating symbolic knowledge from structured knowledge graphs. Recently, realizing the lack of expressiveness and contextualization of symbolic knowledge, many forms of commonsense knowledge bases are constructed, such as if-then knowledge (Sap et al., 2019) and discourse knowledge (Fang et al., 2021). The integration of such textual commonsense knowledge into language",
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+    },
+    {
+        "type": "text",
+        "text": "models has been shown to improve the state of the art for various tasks, such as named entity recognition (Wu et al., 2020) and commonsense knowledge base completion (Malaviya et al., 2020).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "However, integrating such commonsense knowledge are computationally expensive. Commonsense knowledge in text form requires more complex encoders (e.g. Transformer (Vaswani et al., 2017)), as opposed to the simple lookup operation for discrete symbolic knowledge. The feedforward and back-propagation process for the text encoder is significantly more computationally expensive than the standalone symbolic knowledge embeddings. Therefore, it is essential to reduce the computational cost for efficient integration of textual commonsense knowledge, particularly for large-scale applications.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a method to accelerate the process of incorporating textual commonsense knowledge into language models. Our approach is based on the observation that if multiple training samples in a mini-batch share the same commonsense description, the encoding for that description can be reused across those samples. In other words, we only need to encode each distinct description in a mini-batch once. For example, consider the training samples  $x_{1\\dots 4}$  and the associated commonsense  $t_{1\\dots 4}$  in Fig. 1. In the batch partitioning in Fig. 1a, the samples in one batch have no shared descriptions, requiring seven times of commonsense encoding for  $t_i$ . However, in the batch partitioning shown in Fig. 1b, each description will be encoded only once, resulting in only four times of encoding for  $t_i$ . The cost of encoding the commonsense is significantly reduced by effective partitioning of the training samples. Therefore, our goal is to group the training samples in such a way as to minimize the total number of distinct commonsense descriptions per mini-batch.",
+        "bbox": [
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+        "type": "text",
+        "text": "To optimize the batch partitioning, we begin by theoretically analyzing the objective (§2.1). Our",
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+        "text": "3759",
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+    {
+        "type": "footer",
+        "text": "Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics",
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+    {
+        "type": "footer",
+        "text": "Volume 1: Long Papers, pages 3759-3770",
+        "bbox": [
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+    },
+    {
+        "type": "footer",
+        "text": "July 9-14, 2023 ©2023 Association for Computational Linguistics",
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+        "img_path": "images/c35b5b81f8681f5b5e8aa3e40211045bd0b81af122f065d8d982b4f08f5e3e5c.jpg",
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+        "image_caption": [
+            "(a) If samples are divided randomly into batches, a total of 7 times of encoding for  $t_i$  is required.",
+            "Figure 1: Idea of batch partitioning."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
+        "type": "image",
+        "img_path": "images/84faf0256f9a788c89ba90d160196ec7a64a373964f9b537701c4da0fa65b807.jpg",
+        "image_caption": [
+            "(b) If samples are divided delicately, only a total of 4 times of encoding for  $t_i$  is required."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "key observation is that the upper bound of the cost can be reduced to the well-studied graph  $k$ -cut problem (Rangapuram et al., 2014) ( $\\S 3.1$ $\\S 3.2$ ). As a result, we minimize the upper bound instead by adapting the classic spectral clustering algorithm ( $\\S 3.3$ ). The average distinct commonsense descriptions per batch are approximated by the distance to the cluster centroid, and is optimized by spectral clustering. This is also empirically verified ( $\\S 5.4$ ).",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main contributions of this paper are as follows: (1) We propose the use of batch partitioning for improving the efficiency of textual commonsense integration for language models. (2) We theoretically demonstrate that the batch partitioning problem can be reduced to the classic graph  $k$ -cut problem, and we use the well-studied spectral clustering to optimize it. (3) We empirically show that the efficiency of integrating commonsense descriptions can be significantly improved without sacrificing effectiveness. The acceleration is even more pronounced for large-scale training.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 The Batch Partitioning Problem",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we analyze the training efficiency w.r.t. batch partitioning. We first show in § 2.1 that the complexity of the model depends on the number of corresponding knowledge descriptions per sample. Then, in § 2.2, we formally define this batch partitioning problem.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 Model Setup and Complexity Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we use the OK-Transformer (Cui and Chen, 2022) as the backbone. OK-Transformer is a recently proposed model that effectively introduces commonsense knowledge into language",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "models. Traditional approaches for such introduction required pre-training language models on a large corpus along with external commonsense, which was time-consuming (Peters et al., 2019; Zhang et al., 2019). The OK-Transformer model, on the other hand, is able to directly incorporate extra knowledge without pre-training. This model utilizes commonsense tokens and attention mechanisms to effectively integrate textual commonsense. Our proposed batch partitioning method is also applicable to other models that encode target sentences and associated commonsense descriptions.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To analyze the computational complexity of encoding commonsense knowledge and formulate the problem, we briefly describe how the original OK-Transformer works. It consists of three Transformers, where  $\\mathrm{Transformer}^{(1)}$  is used to represent the target sentence,  $\\mathrm{Transformer}^{(2)}$  is used to represent each textual commonsense description, and  $\\mathrm{Transformer}^{(3)}$  is used to incorporate commonsense embeddings from  $\\mathrm{Transformer}^{(2)}$  into  $\\mathrm{Transformer}^{(1)}$ .",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We now concretely analyze the complexity of integrating external textual commonsense. When encoding a sample with associated commonsense descriptions, the complexity consists of three modules:",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- For encoding the target sentence via  $\\mathrm{Transformer}^{(1)}$ , the complexity of encoding a sentence of length  $L$  into dimension  $D$  is  $O(L^2 D)$ .",
+            "- For encoding textual commonsense descriptions via Transformer $^{(2)}$ , the complexity of encoding  $C$  knowledge descriptions of length  $L$  is  $O(CL^2 D)$ .",
+            "- For integrating the knowledge embeddings into the target sentence via Transformer $^{(3)}$ , the complexity is  $O(C^2 D)$ ."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "table",
+        "img_path": "images/72bd3f13af46e5e2d15c52d9042a892510893234aad91c8b84f9f56096ec6acb.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Module</td><td>Complexity</td></tr><tr><td>Target sentence encoding</td><td>O(L2D)</td></tr><tr><td>External knowledge encoding</td><td>O(CL2D)</td></tr><tr><td>Knowledge integration</td><td>O(C2D)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Module complexities.",
+        "bbox": [
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+            840
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We summarize the complexity in Table 1. Since in practice we usually have  $L^2 \\gg C$ , the key is to reduce the complexity of encoding for textual commonsense descriptions, i.e., reduce  $O(CL^2 D)$ .",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "3760",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Relation to retrieval-based knowledge incorporation Integrating text commonsense is related to learning dense retrievers for efficiently retrieving and introducing external textual commonsense, such as REALM (Guu et al., 2020). In commonsense incorporation, each sample only retrieves a small number of knowledge descriptions based on trigger words. So the key of our problem is to efficiently and effectively incorporate certain knowledge descriptions, rather than the information retrieval in dense retrievers. Specifically, dense retrievers typically consist of a retriever and a knowledge-augmented encoder. Our work can be analogous to reducing the cost of the knowledge-augmented encoder.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We now formulate the problem of batch partitioning. As stated in the introduction, different samples may correspond to the same textual commonsense description. We only need to encode the distinct commonsense descriptions once for a batch of samples. Therefore, the goal of batch partitioning is to minimize the number of distinct commonsense descriptions per batch.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "More formally, suppose the training data is  $\\mathcal{D}_{train} = \\{x_i,T(x_i),y_i\\}_{i = 1}^N$  , where  $x_{i}$  is the original sample,  $y_{i}$  is the corresponding label, and  $T(x_{i}) = \\{t_{i1},\\dots ,t_{ic_{i}}\\}$  is a collection of external knowledge descriptions for  $x_{i}$  . For a batch with  $s$  samples  $x_{1},\\dots ,x_{s}$  , the number of knowledge descriptions we need to encode is  $|\\bigcup_{i = 1}^{s}T(x_{i})|$",
+        "bbox": [
+            112,
+            487,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For convenience, we assume that  $N$  is divisible by batch size  $s$ . To reduce the time complexity, we need to partition  $\\mathcal{D}_{train}$  into  $k = N / s$  batches  $B_{1},\\dots ,B_{k}$  such that each batch contains  $s$  samples and the total number of distinct textual commonsense descriptions in each batch is minimized:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  \\sum_ {i = 1} ^ {k} | \\bigcup_ {x \\in B _ {i}} T (x) |\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "s.t.  $|B_i| = s$  (size constraint for each batch) (1)",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Solving the Batch Partitioning Problem",
+        "text_level": 1,
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To solve the batch partitioning problem, we first approximate the upper bound of Eq. (1) in § 3.1. We minimize its upper bound instead of directly minimizing Eq. (1). In § 3.2, we show that optimizing the upper bound can be reduced to the classic",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "minimum graph  $k$ -cut problem, so that some well-studied algorithms can be applied. We show how we adapt the classical spectral clustering to this problem in  $\\S 3.3$ , and how to scale it up in  $\\S 3.4$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Upper Bound Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We analyze the upper bound of Eq. (1) in Theorem 1.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Theorem 1 (Upper bound).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\sum_ {i = 1} ^ {k} \\left| \\bigcup_ {x \\in B _ {i}} T (x) \\right| \\\\ \\leq \\sum_ {i = 1} ^ {k} \\left[ \\sum_ {x \\in B _ {i}} | T (x) | - s \\mathbb {E} _ {x _ {a}, x _ {b} \\in B _ {i}, x _ {a} \\neq x _ {b}} | T (x _ {a}) \\cap T (x _ {b}) | \\right] \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Proof. For a batch  $B$  with  $s$  samples  $\\{x_{1},\\dots ,x_{s}\\}$  we have:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\left| \\bigcup_ {i = 1} ^ {s} T (x _ {i}) \\right| = \\sum_ {i = 1} ^ {s} \\left| T (x _ {i}) - \\bigcup_ {j = 1} ^ {i - 1} T (x _ {j}) \\right| \\\\ = \\sum_ {i = 1} ^ {s} | T (x _ {i}) - \\bigcup_ {j = 1} ^ {i - 1} T (x _ {j}) \\cap T (x _ {i}) | \\tag {3} \\\\ = \\sum_ {i = 1} ^ {s} | T (x _ {i}) | - \\sum_ {i = 1} ^ {s} \\left| \\bigcup_ {j = 1} ^ {i - 1} T (x _ {j}) \\cap T (x _ {i}) \\right| \\\\ \\leq \\sum_ {i = 1} ^ {s} | T (x _ {i}) | - \\sum_ {i = 1} ^ {s} \\max  _ {1 \\leq j \\leq i - 1} | T (x _ {j}) \\cap T (x _ {i}) | \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The upper bound in Eq. (3) after relaxation is related to the sample order of that batch, while our original objective in Eq. (1) is actually order-independent. To introduce order-independence, let  $\\pi$  be an arrangement of  $1\\cdots s$  that  $\\pi_i \\in \\{1, \\cdots, s\\}$ . Noticing that  $\\sum_{i=1}^{s}|T(x_i)|$  is a constant, based on the order-independence, we transform Eq. (3) into the expectation under different  $\\pi$ s:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\pi} \\sum_ {i = 1} ^ {s} \\max _ {1 \\leq j \\leq i - 1} | T (x _ {\\pi_ {j}}) \\cap T (x _ {\\pi_ {i}}) | \\\\ = \\sum_ {i = 1} ^ {s} \\mathbb {E} _ {\\pi} \\max  _ {1 \\leq j \\leq i - 1} | T \\left(x _ {\\pi_ {j}}\\right) \\cap T \\left(x _ {\\pi_ {i}}\\right) | \\tag {4} \\\\ \\geq \\sum_ {i = 1} ^ {s} \\max  _ {1 \\leq j \\leq i - 1} \\mathbb {E} _ {\\pi} | T (x _ {\\pi_ {j}}) \\cap T (x _ {\\pi_ {i}}) | \\\\ = s \\mathbb {E} _ {x _ {a}, x _ {b} \\in B _ {i}, x _ {a} \\neq x _ {b}} | T (x _ {a}) \\cap T (x _ {b}) | \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Therefore Theorem 1 holds.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/bffd5dc32c5e08715f73edb9171483e670d37c7257156076b14537714679565f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It is worth highlighting that the relaxation in the last inequality of Eq. (3) is valid due to the nonrandom distribution of words in samples. Specifically, samples with similar meanings tend to have similar word distributions. By grouping similar",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3761",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "samples into the same batch, each sample pair within a batch will possess similar textual commonsense knowledge descriptions. This allows us to use the maximal common descriptions between  $T(x_{i})$  and  $T(x_{j})$  as an approximation for the common descriptions between  $T(x_{i})$  and  $\\bigcup_{j = 1}^{i - 1}T(x_j)$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "According to Theorem 1, since  $\\sum_{i=1}^{s} \\sum_{x \\in B_i} |T(x)| = \\sum_{x \\in D_{train}} |T(x)|$  is a constant, minimizing Eq. (1) is equivalent to maximizing:",
+        "bbox": [
+            112,
+            181,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sum_ {i = 1} ^ {k} \\mathbb {E} _ {x _ {a}, x _ {b} \\in B _ {i}, x _ {a} \\neq x _ {b}} | T (x _ {a}) \\cap T (x _ {b}) | \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            159,
+            256,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We will show that this is a balanced graph  $k$ -cut problem in § 3.2.",
+        "bbox": [
+            112,
+            310,
+            487,
+            342
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Connection to the Graph  $k$ -Cut Problem",
+        "text_level": 1,
+        "bbox": [
+            112,
+            353,
+            478,
+            369
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We now illustrate the relationship between Eq. (5) and the graph  $k$ -cut problem. We demonstrate that, with proper transformation, maximizing Eq. (5) can be reduced to the graph  $k$ -cut problem. Additionally, in § 3.3, we explain how to incorporate the constraint of the size of each mini-batch using the balanced graph  $k$ -cut.",
+        "bbox": [
+            112,
+            373,
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+            485
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Consider constructing a weighted graph  $G(V,E)$  as follows:",
+        "bbox": [
+            112,
+            486,
+            487,
+            517
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- For each sample  $x_{i}$  in the training data, create a vertex  $v_{i}$ .",
+            "- For each pair of distinct vertices  $(v_{i}, v_{j})$ , create an edge between them with a weight of  $|T(x_{i}) \\cap T(x_{j})|$ ."
+        ],
+        "bbox": [
+            134,
+            529,
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+            621
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The graph  $k$ -cut for  $G(V,E)$  partitions  $G(V,E)$  into  $k$  non-empty components:  $V_{1},\\dots ,V_{k}$  such that the sum weight of cross-component edges is minimized. According to the construction of  $G(V,E)$ , maximizing Eq. (5) is equivalent to minimizing the sum weight of the cut. This is formalized in Theorem 2.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Theorem 2 (Relation to minimum  $k$ -cut problem). Suppose the weight of the  $k$ -cut for  $G(V,E)$  is  $w$ , then we have:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nE q. (5) = \\frac {2}{s (s - 1)} \\sum_ {i = 1} ^ {n - 1} \\sum_ {j = i} ^ {n} | T (x _ {i}) \\cap T (x _ {j}) | - w \\tag {6}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Proof. A k-cut of  $G(V, E)$  consists of  $k$  components. These  $k$  components correspond to  $k$  batches in the  $k$ -partition. Therefore, the sum weight of",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "inner-component edges of the  $k$ -cut is equal to Eq. (5)  $\\frac{s(s - 1)}{2}$ . Since the total weight of edges in  $G(V,E)$  is equal to the sum weight of inner-component edges plus the sum weight of the cut, Theorem 2 holds.",
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+    },
+    {
+        "type": "text",
+        "text": "As  $\\sum_{i=1}^{n-1} \\sum_{j=i}^{n} |T(x_i) \\cap T(x_j)|$  is a constant for the given training data, Theorem 2 shows that maximizing Eq. (5) is equivalent to minimizing the  $k$ -cut for  $G(V, E)$ . Thus, we convert the problem of maximizing Eq. (5) into the classic minimum  $k$ -cut problem.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.3 Spectral Clustering for the Balanced  $k$ -Cut",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Based on the analysis in § 3.2, we propose to use spectral clustering, a widely used approach for solving the minimum graph  $k$ -cut problem, as our batch partition algorithm. Spectral clustering employs spectral relaxation of the ratio/normalized cut and uses  $k$ -means in the embedding of the vertices found by the first  $k$  eigenvectors of the graph Laplacian in order to obtain the clustering. In addition to the classic minimum graph  $k$ -cut problem, we need to incorporate the constraint that each cut/batch must have a size of  $s$ .",
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+    {
+        "type": "text",
+        "text": "To incorporate the batch size constraint, we make a simple modification to the k-means step in spectral clustering. In the traditional k-means, each node is assigned to the nearest cluster center. In our algorithm, if the nearest cluster center has already been assigned  $s$  nodes, the node will be assigned to the nearest center that has fewer than  $s$  assigned nodes. The specific spectral clustering algorithm is presented as follows.",
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+        "type": "list",
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+        "list_items": [
+            "1. Compute the spectral embedding  $Y\\in \\mathbb{R}^{n\\times k}$  by stacking the normalized first  $k$  eigenvectors of  $G(V,E)$  in columns as described in (Ng et al., 2002).",
+            "2. Treat the  $i$ -th row of  $Y$  as the feature of the  $i$ -th training point  $e_i \\in \\mathbb{R}^k$ .",
+            "3. Given an initial set of  $k$  means  $m_{1},\\dots ,m_{k}$  by randomly selecting  $k$  nodes as centers, repeat the following two steps until convergence:"
+        ],
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+    {
+        "type": "text",
+        "text": "(a) Assignment step Assign nodes to centers:",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "i. Compute distances to centers  $dis_{i,j} = \\text{distance}(e_i, m_j)$ , where the Euclidean distance is used.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "3762",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ii. Sort  $i,j$  in ascending order of  $dis_{i,j}$  for all  $1\\leq i\\leq n,1\\leq j\\leq k$",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "iii. Iterate through all  $i, j$ . If node  $i$  is not assigned in this round and center  $j$  has less than  $s$  assigned nodes, assign node  $i$  to center  $j$ .",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "(b) Update step Compute new centers by taking the mean of their assigned nodes.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 Spectral Clustering at Scale",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The above algorithm consists of computation of the eigenvectors, and the use of k-means. K-means is efficient even for large-scale data. However, when  $n$  and  $k$  are large, the graph construction and eigenvectors computation become computationally expensive.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To compute the spectral embeddings at scale, high-performance optimization techniques are available such as (Liu et al., 2013; Kolev and Mehlhorn, 2016; Boutsidis et al., 2015; Tremblay et al., 2016). Also, in our experiments, a simple trick was found that yields meaningful results: only calculate  $k'$ -dimensional feature vectors ( $k' < k$ ) and perform k-means with the  $k'$  dimensions. We found that  $k' = 8$  is a good practice in our experiments.",
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+    {
+        "type": "text",
+        "text": "4 Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Integrating knowledge into language models has been one of the focuses of language modeling research in recent years. The main integration methods currently include using pre-trained entity embeddings, and constructing knowledge-aware corpora. ERNIE (Zhang et al., 2019), KnowBERT (Peters et al., 2019), and KGLM (Logan et al., 2019) are typical methods using pre-trained entity embeddings. ERNIE uses Wikidata (Vrandečić and Krötzsch, 2014) as the knowledge base and uses TransE (Bordes et al., 2013) to encode knowledge. KnowBERT, on the other hand, uses skip-gram like objective (Mikolov et al., 2013) based on Wikipedia descriptions as the pre-trained entity embeddings. In addition, KnowBERT adds a loss on entity linking to the pre-trained objective. KGLM (Logan et al., 2019) allows modification/updating of knowledge by building a local knowledge graph for the target sentence. WKLM (Xiong et al., 2019) constructs a corpus of incorrect knowledge descriptions by replacing Wikipedia's entities with different entities of the same type. It trains the model to identify incorrect and correct knowl",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "edge descriptions. Recently, models that integrate textual knowledge have also been proposed. In this paper, we adopt the model structure in OK-Transformer (Cui and Chen, 2022).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Textual knowledge bases Noting the deficiencies of symbolic knowledge in terms of expressiveness and contextual information representation, some work has started to use text as a form of knowledge. ATOMIC (Sap et al., 2019; Hwang et al., 2021) is a large-scale manually annotated common-sense textual knowledge base that includes social interaction, event-centered, physical entity. ATOMIC contains knowledge like (PersonX reaches PersonX's home, Before, PersonX needs to park the car). ASER (Zhang et al., 2020) is an eventuality knowledge graph of activities, states, events, and their relations. Its knowledge atoms are in natural language form, e.g. (I do not have lunch, succession, I am hungry). COMET (Bosselut et al., 2019) is an extension of ATOMIC based on the generative language model. It mainly solves the problem of insufficient coverage of ATOMIC. Some primitive research (Guan et al., 2020; Shwartz et al., 2020) has started to apply these textual knowledge bases in some specific tasks. OK-Transformer (Cui and Chen, 2022) is proposed to integrate textual knowledge for general purposes. However, in our experimental tests, it takes too much time in encoding the commonsense. To our knowledge, there is still a lack of research on how to integrate textual knowledge into general text understanding tasks efficiently.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Comparison with dense textual knowledge retriever When introducing external texts, another style is to use a retriever that returns only top  $k$  candidate texts in terms of similarity (Chen et al., 2017; Karpukhin et al., 2020; Wang et al., 2019). However, this method requires a heavy pre-training process to learn the retriever. On the other hand, for the textual knowledge base we use in this paper, we can directly use the manually labeled trigger words for each knowledge description to retrieve knowledge. Therefore, in this paper, we focus on how to efficiently and effectively integrate knowledge from a textual knowledge base.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "High-performance language models More general techniques for high-performance language models have also received extensive studies. The main approaches of previous studies include (1) model compression and quantization (Sanh et al., 2019; Jacob et al., 2018), and (2) efficient repre",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "3763",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "sensation of long texts (Kitaev et al., 2019; Peng et al., 2020). However, the model compression approaches require heavy pre-training before they can be adapted to language models. Moreover, the techniques for optimizing the efficiency for long text do not have significant effects on short texts (Peng et al., 2020). Besides, each commonsense description we considered in this paper tends to be short. In addition, these works have not considered the characteristics of the knowledge integration problem in this paper, i.e., a training sample corresponds to multiple candidate textual knowledge from the knowledge base.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conducted extensive experiments to evaluate batch partitioning. We aim to address the following key questions:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. ( $\\S 5.2$ ) How much is the efficiency improvement of batch partitioning? Can it improve efficiency without sacrificing effectiveness?",
+            "2. ( $\\S 5.3$ ) What is the scalability of batch partitioning as an acceleration method, and can it be applied to large-scale training?",
+            "3. (§ 5.4) Is the main theoretical contribution of this paper, i.e., solving the balanced graph- $k$  cut by spectral clustering, consistent with the real datasets?"
+        ],
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+    {
+        "type": "text",
+        "text": "5.1 Implementation Details and Setup",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Textual knowledge base We follow (Cui and Chen, 2022) to use ATOMIC2020 (Hwang et al., 2021) as the textual knowledge base. Each atom in ATOMIC2020 is commonsense in text form. For each sentence in the downstream task, we retrieve the knowledge associated with it from the textual knowledge base. Note that, unlike retrieving knowledge from free text (Guu et al., 2020), the textual knowledge base ATOMIC2020 is constructed manually, and each knowledge description has corresponding trigger words. These trigger words are usually verbs or verb phrases. We retrieve related textual commonsense descriptions by keyword-matching of these trigger words.",
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+    {
+        "type": "text",
+        "text": "Model architecture We use OK-Transformer (Cui and Chen, 2022) as the backbone of our model. It directly incorporates extra knowledge without pre-training. OK-Transformer is based on either BERT or RoBERTa. We use OK-Transformer based on BERT by",
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+    {
+        "type": "text",
+        "text": "default. We also follow the hyperparameter settings of OK-Transformer. All experiments were run on 8 Nvidia RTX 3090Ti GPUs.",
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+    {
+        "type": "text",
+        "text": "Datasets We evaluate batch partitioning via commonsense reasoning and sentence classification. Since the textual knowledge introduced in this paper is commonsense descriptions, we first verify whether the proposed method in this paper could be applied to the commonsense reasoning tasks. To this end, we choose a wide range of commonsense reasoning tasks to conduct the experiments: CommonsenseQA (Talmor et al., 2019), PhysicalQA (Bisk et al., 2020), as well as several Winograd Schema Challenge (WSC) datasets including WSC273 (Levesque et al., 2012), PDP (Morgenstern et al., 2016), WinoGrande (Sakaguchi et al., 2019), WinoGender (Rudinger et al., 2018). Furthermore, for a comprehensive comparison, we also evaluate the efficiency and effectiveness of the proposed batch partitioning method on the text classification benchmark GLUE (Wang et al., 2018).",
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+    {
+        "type": "text",
+        "text": "5.2 Effectiveness and Efficiency",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Baselines To verify the efficiency and effectiveness of batch partitioning, we used the following baselines:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Vanilla BERT/RoBERTa without external knowledge.",
+            "- OK-Transformer To show the efficiency gains of the batch partitioning proposed in this paper, we compare it with the original OK-Transformer. The baseline randomly partitions samples into batches. We consider this baseline as the lower upper bound of effectiveness of commonsense integration.",
+            "- Frozen knowledge encodings For a comprehensive comparison, we propose to freeze the encoding of commonsense descriptions during fine-tuning. This approach allows us to introduce external textual commonsense descriptions via embedding lookup with minimal time cost. We consider this baseline as the upper bound on the efficiency of commonsense integration."
+        ],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The results of commonsense reasoning and text classification are presented in Table 2 and Table 3, respectively. The effectiveness of our batch partitioning approach is demonstrated by its improvement over vanilla language models on both commonsense reasoning and text classification tasks.",
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+    {
+        "type": "page_number",
+        "text": "3764",
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+    {
+        "type": "table",
+        "img_path": "images/9732fa5924c0e0d2b64c99092fe4a51de6010bf00f3e9ca3e95a977903d8757f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>LM</td><td>Comm.QA</td><td>PhysicalQA</td><td>WSC273</td><td>PDP</td><td>WinoGrande</td><td>WinoGender</td><td>Avg.</td><td>Speed-up ↑</td></tr><tr><td>BERT</td><td>BERT</td><td>55.86</td><td>68.71</td><td>66.30</td><td>85.00</td><td>51.38</td><td>68.19</td><td>65.44</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>BERT</td><td>56.43</td><td>68.06</td><td>65.93</td><td>83.33</td><td>51.30</td><td>68.47</td><td>65.59</td><td>1.4×</td></tr><tr><td>OK-Transformer</td><td>BERT</td><td>56.27</td><td>69.09</td><td>67.40</td><td>86.67</td><td>52.64</td><td>71.53</td><td>66.56</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>BERT</td><td>56.59</td><td>69.53</td><td>66.67</td><td>86.67</td><td>52.17</td><td>72.78</td><td>67.40</td><td>1.4×</td></tr><tr><td>RoBERTa</td><td>RoB.</td><td>73.55</td><td>79.76</td><td>90.10</td><td>90.00</td><td>-</td><td>94.60</td><td>83.95</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>RoB.</td><td>75.02</td><td>52.77</td><td>90.48</td><td>88.33</td><td>-</td><td>96.81</td><td>80.01</td><td>1.5×</td></tr><tr><td>OK-Transformer</td><td>RoB.</td><td>75.92</td><td>80.09</td><td>91.58</td><td>90.00</td><td>-</td><td>95.00</td><td>84.75</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>RoB.</td><td>75.59</td><td>80.20</td><td>90.48</td><td>91.66</td><td>-</td><td>96.25</td><td>85.14</td><td>1.4×</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e5c1bdde97afc51c02061c6b61c92ffdee4500ef585970332b92c0d873bc95f3.jpg",
+        "table_caption": [
+            "Table 2: Results on commonsense reasoning tasks. The effectiveness of batch partitioning surpasses the vanilla BERT/RoBERTa, and is competitive with its upper bound (OK-Transformer). In terms of efficiency, the speed-up of batch partitioning is also competitive to its upper bound (frozen knowledge). RoB. denotes RoBERTa."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>LM</td><td>MRPC</td><td>CoLA</td><td>RTE</td><td>QNLI</td><td>STS-B</td><td>SST-2</td><td>Avg.</td><td>Speed-up</td></tr><tr><td>BERT</td><td>BERT</td><td>86.52/90.66</td><td>59.50</td><td>71.43</td><td>91.20</td><td>89.35/88.93</td><td>91.97</td><td>82.28</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>BERT</td><td>87.50/91.28</td><td>57.31</td><td>70.76</td><td>91.71</td><td>87.31/87.20</td><td>92.43</td><td>81.78</td><td>2.3×</td></tr><tr><td>OK-Transformer</td><td>BERT</td><td>87.50/91.04</td><td>58.29</td><td>72.20</td><td>91.58</td><td>89.82/89.46</td><td>92.66</td><td>82.54</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>BERT</td><td>87.99/91.45</td><td>61.41</td><td>71.48</td><td>91.32</td><td>89.64/89.19</td><td>93.69</td><td>83.09</td><td>2.1×</td></tr><tr><td>RoBERTa</td><td>RoB.</td><td>90.49/93.07</td><td>66.84</td><td>86.28</td><td>93.37</td><td>91.83/91.95</td><td>95.64</td><td>87.86</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>RoB.</td><td>89.71/92.61</td><td>68.22</td><td>87.36</td><td>94.39</td><td>90.74/90.47</td><td>96.10</td><td>88.19</td><td>2.4×</td></tr><tr><td>OK-Transformer</td><td>RoB.</td><td>91.91/94.24</td><td>66.89</td><td>86.28</td><td>94.71</td><td>92.19/92.36</td><td>96.44</td><td>88.49</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>RoB.</td><td>90.69/93.44</td><td>67.75</td><td>85.92</td><td>94.07</td><td>92.41/92.20</td><td>96.22</td><td>88.27</td><td>2.1×</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Results on text classification tasks. Both the effectiveness and the efficiency of batch partitioning are competitive to their upper bounds (OK-Transformer and frozen knowledge).",
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+        "image_caption": [
+            "Figure 2: The effect of the scale of extra commonsense. We control the scale by limiting the upper number of commonsense descriptions per sample in SST-2."
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+        "text": "The effectiveness is comparable or slightly superior to that of OK-Transformer, which serves as the upper bound for effectiveness. In terms of efficiency, our approach significantly accelerates knowledge integration models across a range of tasks. On average, it reduces the time cost for knowledge encoding by  $40\\%$  for commonsense reasoning tasks, and  $110\\%$  for text classification tasks. This acceleration is close to the frozen knowledge, and serves as the upper bound for efficiency. Overall, our approach is close to its efficiency upper bound without losing effectiveness.",
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+        "text": "5.3 Scalability for Dataset Sizes, Device Capacities, and Knowledge Sizes",
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+        "text": "In this subsection, we investigate the scalability of batch partitioning with different batch sizes, as well as the different dataset sizes. Larger dataset sizes usually mean devices with larger memory. In particular, we calculated the speedups of knowledge encoding for different batch sizes and different tasks. The results are shown in Fig. 4. The datasets are sorted by size in descending order.",
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+        "text": "It can be clearly seen that as the size of the dataset rises or the memory of the device rises (larger batch size), the speedup of batch partitioning becomes more significant. This is because, for data-intensive tasks, the knowledge overlapping among different samples is more significant, which increases the feasibility of using batch partitioning. This result verifies the scalability of batch partitioning.",
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+        "text": "We also investigate the scalability of batch partitioning over different scales of integrated commonsense. To control the scale, we set the upper number of commonsense descriptions for each sample to 16/32/64, respectively, and study the efficiency. Intuitively, richer commonsense descriptions lead to higher effectiveness but more computation cost. The results are shown in Fig. 2.",
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+        "text": "As commonsense knowledge becomes richer, the",
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+            "(a) MRPC"
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+            "(b) CoLA",
+            "Figure 3: Strong correlation between the distinct commonsense descriptions per batch and the average distance to the centroid during clustering."
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+            "(d) STS-B"
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+        "image_caption": [
+            "Figure 4: Speed-up of proposed batch partitioning method over different training batch size and dataset size. Note that the datasets are arranged in descending order according to dataset size."
+        ],
+        "image_footnote": [],
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+    {
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+        "text": "effectiveness and the acceleration both increase. This is because the knowledge overlapping among samples also becomes more significant. The result verifies that batch partitioning is applicable for incorporating large-scale commonsense knowledge bases.",
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+        "text": "5.4 Effect of Spectral Clustering Theory",
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+        "text": "In this paper, we propose the use of spectral clustering to solve the batch partitioning problem. We approximate and optimize the distinct number of descriptions per batch in Eq. (1) by minimizing the distance of each node to the centroid of the cluster in spectral clustering. In this subsection, we demonstrate the rationale behind this approximation by highlighting the strong correlation between the objective of Eq. (1) and the distance minimization in spectral embeddings.",
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+        "text": "To this end, we plot how the centroid distance and the distinct descriptions per batch vary at each iteration of the spectral clustering algorithm in Fig. 3. The results show a strong correlation between the value we directly optimize (i.e., the cen",
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+        "type": "text",
+        "text": "troid distance) and the target of the batch partitioning (i.e., distinct descriptions per batch). This supports the feasibility of using spectral clustering to convert the batch partitioning problem into a balanced graph  $k$ -cut problem and solve it efficiently.",
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+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we study how to improve the efficiency of incorporating commonsense knowledge in language models. Due to the high encoding costs of commonsense descriptions, it is crucial to reduce their encoding complexity. Our idea is that by carefully dividing samples with similar descriptions into the same batch, the knowledge encoding utilization can be improved.",
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+        "type": "text",
+        "text": "With such an idea, we theoretically analyze the optimization objective of this batch partitioning. We found that the upper bound of this problem can be reduced to the classical graph  $k$ -cut problem. We propose to use the well-studied spectral clustering algorithm to optimize the batch partitioning. By experimenting with a variety of tasks, we show that the proposed batch partitioning approaches its upper bound in terms of both effectiveness and efficiency. And the method is more applicable for larger datasets and on devices with more capabilities.",
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+    {
+        "type": "text",
+        "text": "7 Limitations",
+        "text_level": 1,
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+        "text": "The theoretical results and the algorithm should be applicable for other knowledge integration models which encode target sentences and associated textual knowledge descriptions in mini-batches. However, this paper does not extensively apply the proposed method to various knowledge integration models to explore its efficiency and effectiveness.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+        "text": "A For every submission:",
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+            "A1. Did you describe the limitations of your work? Sec 5",
+            "A2. Did you discuss any potential risks of your work? Not applicable. Left blank.",
+            "A3. Do the abstract and introduction summarize the paper's main claims? Left blank.",
+            "A4. Have you used AI writing assistants when working on this paper? Left blank."
+        ],
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+    {
+        "type": "text",
+        "text": "B Did you use or create scientific artifacts?",
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+    },
+    {
+        "type": "text",
+        "text": "Left blank.",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "B1. Did you cite the creators of artifacts you used? Not applicable. Left blank.",
+            "B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Not applicable. Left blank.",
+            "B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Not applicable. Left blank.",
+            "B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.",
+            "B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.",
+            "B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Left blank."
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+    {
+        "type": "text",
+        "text": "C Did you run computational experiments?",
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+    {
+        "type": "text",
+        "text": "we discuss the experiments in sec5",
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+        "type": "text",
+        "text": "C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? parameters same as BERT/RoBERTa.",
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+    {
+        "type": "header",
+        "text": "ACL 2023 Responsible NLP Checklist",
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+    {
+        "type": "page_footnote",
+        "text": "The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.",
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+            "C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? in sec5",
+            "C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Fig. 2",
+            "C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? We follow the implementation and experiments setting of OK-Transformer as we mentioned in sec 5."
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+    {
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+        "text": "D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.",
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+            "D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? Not applicable. Left blank.",
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2023/Free Lunch for Efficient Textual Commonsense Integration in Language Models/a325db9e-aab0-4f36-8d85-9ab6ad31543b_origin.pdf

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2023/Free Lunch for Efficient Textual Commonsense Integration in Language Models/full.md

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+# Free Lunch for Efficient Textual Commonsense Integration in Language Models
+
+Wanyun Cui
+
+Shanghai University of Finance and Economics
+
+cui.wanyun@shufe.edu.cn
+
+Xingran Chen
+
+University of Michigan
+
+chenxran@umich.edu
+
+# Abstract
+
+Recent years have witnessed the emergence of textual commonsense knowledge bases, aimed at providing more nuanced and context-rich knowledge. The integration of external commonsense into language models has been shown to be a key enabler in advancing the state-of-the-art for a wide range of NLP tasks. However, incorporating textual commonsense descriptions is computationally expensive, as compared to encoding conventional symbolic knowledge. In this paper, we propose a method to improve its efficiency without modifying the model. We group training samples with similar commonsense descriptions into a single batch, thus reusing the encoded description across multiple samples. One key observation is that the upper bound of batch partitioning can be reduced to the classic graph  $k$ -cut problem. Consequently, we propose a spectral clustering-based algorithm to solve this problem. Extensive experiments illustrate that the proposed batch partitioning approach effectively reduces the computational cost while preserving performance. The efficiency improvement is more pronounced on larger datasets and on devices with more memory capacity, attesting to its practical utility for large-scale applications.
+
+# 1 Introduction
+
+While pre-trained language models have made substantial progress in natural language processing, they still lack certain knowledge. Thus it is critical to incorporate external knowledge sources (Peters et al., 2019; Zhang et al., 2019; Logan et al., 2019). Previous research has primarily focused on incorporating symbolic knowledge from structured knowledge graphs. Recently, realizing the lack of expressiveness and contextualization of symbolic knowledge, many forms of commonsense knowledge bases are constructed, such as if-then knowledge (Sap et al., 2019) and discourse knowledge (Fang et al., 2021). The integration of such textual commonsense knowledge into language
+
+models has been shown to improve the state of the art for various tasks, such as named entity recognition (Wu et al., 2020) and commonsense knowledge base completion (Malaviya et al., 2020).
+
+However, integrating such commonsense knowledge are computationally expensive. Commonsense knowledge in text form requires more complex encoders (e.g. Transformer (Vaswani et al., 2017)), as opposed to the simple lookup operation for discrete symbolic knowledge. The feedforward and back-propagation process for the text encoder is significantly more computationally expensive than the standalone symbolic knowledge embeddings. Therefore, it is essential to reduce the computational cost for efficient integration of textual commonsense knowledge, particularly for large-scale applications.
+
+In this paper, we propose a method to accelerate the process of incorporating textual commonsense knowledge into language models. Our approach is based on the observation that if multiple training samples in a mini-batch share the same commonsense description, the encoding for that description can be reused across those samples. In other words, we only need to encode each distinct description in a mini-batch once. For example, consider the training samples  $x_{1\dots 4}$  and the associated commonsense  $t_{1\dots 4}$  in Fig. 1. In the batch partitioning in Fig. 1a, the samples in one batch have no shared descriptions, requiring seven times of commonsense encoding for  $t_i$ . However, in the batch partitioning shown in Fig. 1b, each description will be encoded only once, resulting in only four times of encoding for  $t_i$ . The cost of encoding the commonsense is significantly reduced by effective partitioning of the training samples. Therefore, our goal is to group the training samples in such a way as to minimize the total number of distinct commonsense descriptions per mini-batch.
+
+To optimize the batch partitioning, we begin by theoretically analyzing the objective (§2.1). Our
+
+![](images/c35b5b81f8681f5b5e8aa3e40211045bd0b81af122f065d8d982b4f08f5e3e5c.jpg)
+
+![](images/56a3b649cda9e075cfa5532338baf0f4fd6c64a07c3ba4ba1bb2aa17ac598a4a.jpg)
+
+![](images/933a5d86ed8bc186c324d784281d08659a2dd6161b5b176f4e16b36a53cf7f36.jpg)  
+(a) If samples are divided randomly into batches, a total of 7 times of encoding for  $t_i$  is required.  
+Figure 1: Idea of batch partitioning.
+
+![](images/84faf0256f9a788c89ba90d160196ec7a64a373964f9b537701c4da0fa65b807.jpg)  
+(b) If samples are divided delicately, only a total of 4 times of encoding for  $t_i$  is required.
+
+key observation is that the upper bound of the cost can be reduced to the well-studied graph  $k$ -cut problem (Rangapuram et al., 2014) ( $\S 3.1$ $\S 3.2$ ). As a result, we minimize the upper bound instead by adapting the classic spectral clustering algorithm ( $\S 3.3$ ). The average distinct commonsense descriptions per batch are approximated by the distance to the cluster centroid, and is optimized by spectral clustering. This is also empirically verified ( $\S 5.4$ ).
+
+The main contributions of this paper are as follows: (1) We propose the use of batch partitioning for improving the efficiency of textual commonsense integration for language models. (2) We theoretically demonstrate that the batch partitioning problem can be reduced to the classic graph  $k$ -cut problem, and we use the well-studied spectral clustering to optimize it. (3) We empirically show that the efficiency of integrating commonsense descriptions can be significantly improved without sacrificing effectiveness. The acceleration is even more pronounced for large-scale training.
+
+# 2 The Batch Partitioning Problem
+
+In this section, we analyze the training efficiency w.r.t. batch partitioning. We first show in § 2.1 that the complexity of the model depends on the number of corresponding knowledge descriptions per sample. Then, in § 2.2, we formally define this batch partitioning problem.
+
+# 2.1 Model Setup and Complexity Analysis
+
+In this paper, we use the OK-Transformer (Cui and Chen, 2022) as the backbone. OK-Transformer is a recently proposed model that effectively introduces commonsense knowledge into language
+
+models. Traditional approaches for such introduction required pre-training language models on a large corpus along with external commonsense, which was time-consuming (Peters et al., 2019; Zhang et al., 2019). The OK-Transformer model, on the other hand, is able to directly incorporate extra knowledge without pre-training. This model utilizes commonsense tokens and attention mechanisms to effectively integrate textual commonsense. Our proposed batch partitioning method is also applicable to other models that encode target sentences and associated commonsense descriptions.
+
+To analyze the computational complexity of encoding commonsense knowledge and formulate the problem, we briefly describe how the original OK-Transformer works. It consists of three Transformers, where  $\mathrm{Transformer}^{(1)}$  is used to represent the target sentence,  $\mathrm{Transformer}^{(2)}$  is used to represent each textual commonsense description, and  $\mathrm{Transformer}^{(3)}$  is used to incorporate commonsense embeddings from  $\mathrm{Transformer}^{(2)}$  into  $\mathrm{Transformer}^{(1)}$ .
+
+We now concretely analyze the complexity of integrating external textual commonsense. When encoding a sample with associated commonsense descriptions, the complexity consists of three modules:
+
+- For encoding the target sentence via  $\mathrm{Transformer}^{(1)}$ , the complexity of encoding a sentence of length  $L$  into dimension  $D$  is  $O(L^2 D)$ .  
+- For encoding textual commonsense descriptions via Transformer $^{(2)}$ , the complexity of encoding  $C$  knowledge descriptions of length  $L$  is  $O(CL^2 D)$ .  
+- For integrating the knowledge embeddings into the target sentence via Transformer $^{(3)}$ , the complexity is  $O(C^2 D)$ .
+
+<table><tr><td>Module</td><td>Complexity</td></tr><tr><td>Target sentence encoding</td><td>O(L2D)</td></tr><tr><td>External knowledge encoding</td><td>O(CL2D)</td></tr><tr><td>Knowledge integration</td><td>O(C2D)</td></tr></table>
+
+Table 1: Module complexities.
+
+We summarize the complexity in Table 1. Since in practice we usually have  $L^2 \gg C$ , the key is to reduce the complexity of encoding for textual commonsense descriptions, i.e., reduce  $O(CL^2 D)$ .
+
+Relation to retrieval-based knowledge incorporation Integrating text commonsense is related to learning dense retrievers for efficiently retrieving and introducing external textual commonsense, such as REALM (Guu et al., 2020). In commonsense incorporation, each sample only retrieves a small number of knowledge descriptions based on trigger words. So the key of our problem is to efficiently and effectively incorporate certain knowledge descriptions, rather than the information retrieval in dense retrievers. Specifically, dense retrievers typically consist of a retriever and a knowledge-augmented encoder. Our work can be analogous to reducing the cost of the knowledge-augmented encoder.
+
+# 2.2 Problem Formulation
+
+We now formulate the problem of batch partitioning. As stated in the introduction, different samples may correspond to the same textual commonsense description. We only need to encode the distinct commonsense descriptions once for a batch of samples. Therefore, the goal of batch partitioning is to minimize the number of distinct commonsense descriptions per batch.
+
+More formally, suppose the training data is  $\mathcal{D}_{train} = \{x_i,T(x_i),y_i\}_{i = 1}^N$  , where  $x_{i}$  is the original sample,  $y_{i}$  is the corresponding label, and  $T(x_{i}) = \{t_{i1},\dots ,t_{ic_{i}}\}$  is a collection of external knowledge descriptions for  $x_{i}$  . For a batch with  $s$  samples  $x_{1},\dots ,x_{s}$  , the number of knowledge descriptions we need to encode is  $|\bigcup_{i = 1}^{s}T(x_{i})|$
+
+For convenience, we assume that  $N$  is divisible by batch size  $s$ . To reduce the time complexity, we need to partition  $\mathcal{D}_{train}$  into  $k = N / s$  batches  $B_{1},\dots ,B_{k}$  such that each batch contains  $s$  samples and the total number of distinct textual commonsense descriptions in each batch is minimized:
+
+$$
+\min  \sum_ {i = 1} ^ {k} | \bigcup_ {x \in B _ {i}} T (x) |
+$$
+
+s.t.  $|B_i| = s$  (size constraint for each batch) (1)
+
+# 3 Solving the Batch Partitioning Problem
+
+To solve the batch partitioning problem, we first approximate the upper bound of Eq. (1) in § 3.1. We minimize its upper bound instead of directly minimizing Eq. (1). In § 3.2, we show that optimizing the upper bound can be reduced to the classic
+
+minimum graph  $k$ -cut problem, so that some well-studied algorithms can be applied. We show how we adapt the classical spectral clustering to this problem in  $\S 3.3$ , and how to scale it up in  $\S 3.4$ .
+
+# 3.1 Upper Bound Analysis
+
+We analyze the upper bound of Eq. (1) in Theorem 1.
+
+Theorem 1 (Upper bound).
+
+$$
+\begin{array}{l} \sum_ {i = 1} ^ {k} \left| \bigcup_ {x \in B _ {i}} T (x) \right| \\ \leq \sum_ {i = 1} ^ {k} \left[ \sum_ {x \in B _ {i}} | T (x) | - s \mathbb {E} _ {x _ {a}, x _ {b} \in B _ {i}, x _ {a} \neq x _ {b}} | T (x _ {a}) \cap T (x _ {b}) | \right] \tag {2} \\ \end{array}
+$$
+
+Proof. For a batch  $B$  with  $s$  samples  $\{x_{1},\dots ,x_{s}\}$  we have:
+
+$$
+\begin{array}{l} \left| \bigcup_ {i = 1} ^ {s} T (x _ {i}) \right| = \sum_ {i = 1} ^ {s} \left| T (x _ {i}) - \bigcup_ {j = 1} ^ {i - 1} T (x _ {j}) \right| \\ = \sum_ {i = 1} ^ {s} | T (x _ {i}) - \bigcup_ {j = 1} ^ {i - 1} T (x _ {j}) \cap T (x _ {i}) | \tag {3} \\ = \sum_ {i = 1} ^ {s} | T (x _ {i}) | - \sum_ {i = 1} ^ {s} \left| \bigcup_ {j = 1} ^ {i - 1} T (x _ {j}) \cap T (x _ {i}) \right| \\ \leq \sum_ {i = 1} ^ {s} | T (x _ {i}) | - \sum_ {i = 1} ^ {s} \max  _ {1 \leq j \leq i - 1} | T (x _ {j}) \cap T (x _ {i}) | \\ \end{array}
+$$
+
+The upper bound in Eq. (3) after relaxation is related to the sample order of that batch, while our original objective in Eq. (1) is actually order-independent. To introduce order-independence, let  $\pi$  be an arrangement of  $1\cdots s$  that  $\pi_i \in \{1, \cdots, s\}$ . Noticing that  $\sum_{i=1}^{s}|T(x_i)|$  is a constant, based on the order-independence, we transform Eq. (3) into the expectation under different  $\pi$ s:
+
+$$
+\begin{array}{l} \mathbb {E} _ {\pi} \sum_ {i = 1} ^ {s} \max _ {1 \leq j \leq i - 1} | T (x _ {\pi_ {j}}) \cap T (x _ {\pi_ {i}}) | \\ = \sum_ {i = 1} ^ {s} \mathbb {E} _ {\pi} \max  _ {1 \leq j \leq i - 1} | T \left(x _ {\pi_ {j}}\right) \cap T \left(x _ {\pi_ {i}}\right) | \tag {4} \\ \geq \sum_ {i = 1} ^ {s} \max  _ {1 \leq j \leq i - 1} \mathbb {E} _ {\pi} | T (x _ {\pi_ {j}}) \cap T (x _ {\pi_ {i}}) | \\ = s \mathbb {E} _ {x _ {a}, x _ {b} \in B _ {i}, x _ {a} \neq x _ {b}} | T (x _ {a}) \cap T (x _ {b}) | \\ \end{array}
+$$
+
+Therefore Theorem 1 holds.
+
+![](images/bffd5dc32c5e08715f73edb9171483e670d37c7257156076b14537714679565f.jpg)
+
+It is worth highlighting that the relaxation in the last inequality of Eq. (3) is valid due to the nonrandom distribution of words in samples. Specifically, samples with similar meanings tend to have similar word distributions. By grouping similar
+
+samples into the same batch, each sample pair within a batch will possess similar textual commonsense knowledge descriptions. This allows us to use the maximal common descriptions between  $T(x_{i})$  and  $T(x_{j})$  as an approximation for the common descriptions between  $T(x_{i})$  and  $\bigcup_{j = 1}^{i - 1}T(x_j)$ .
+
+According to Theorem 1, since  $\sum_{i=1}^{s} \sum_{x \in B_i} |T(x)| = \sum_{x \in D_{train}} |T(x)|$  is a constant, minimizing Eq. (1) is equivalent to maximizing:
+
+$$
+\sum_ {i = 1} ^ {k} \mathbb {E} _ {x _ {a}, x _ {b} \in B _ {i}, x _ {a} \neq x _ {b}} | T (x _ {a}) \cap T (x _ {b}) | \tag {5}
+$$
+
+We will show that this is a balanced graph  $k$ -cut problem in § 3.2.
+
+# 3.2 Connection to the Graph  $k$ -Cut Problem
+
+We now illustrate the relationship between Eq. (5) and the graph  $k$ -cut problem. We demonstrate that, with proper transformation, maximizing Eq. (5) can be reduced to the graph  $k$ -cut problem. Additionally, in § 3.3, we explain how to incorporate the constraint of the size of each mini-batch using the balanced graph  $k$ -cut.
+
+Consider constructing a weighted graph  $G(V,E)$  as follows:
+
+- For each sample  $x_{i}$  in the training data, create a vertex  $v_{i}$ .  
+- For each pair of distinct vertices  $(v_{i}, v_{j})$ , create an edge between them with a weight of  $|T(x_{i}) \cap T(x_{j})|$ .
+
+The graph  $k$ -cut for  $G(V,E)$  partitions  $G(V,E)$  into  $k$  non-empty components:  $V_{1},\dots ,V_{k}$  such that the sum weight of cross-component edges is minimized. According to the construction of  $G(V,E)$ , maximizing Eq. (5) is equivalent to minimizing the sum weight of the cut. This is formalized in Theorem 2.
+
+Theorem 2 (Relation to minimum  $k$ -cut problem). Suppose the weight of the  $k$ -cut for  $G(V,E)$  is  $w$ , then we have:
+
+$$
+E q. (5) = \frac {2}{s (s - 1)} \sum_ {i = 1} ^ {n - 1} \sum_ {j = i} ^ {n} | T (x _ {i}) \cap T (x _ {j}) | - w \tag {6}
+$$
+
+Proof. A k-cut of  $G(V, E)$  consists of  $k$  components. These  $k$  components correspond to  $k$  batches in the  $k$ -partition. Therefore, the sum weight of
+
+inner-component edges of the  $k$ -cut is equal to Eq. (5)  $\frac{s(s - 1)}{2}$ . Since the total weight of edges in  $G(V,E)$  is equal to the sum weight of inner-component edges plus the sum weight of the cut, Theorem 2 holds.
+
+As  $\sum_{i=1}^{n-1} \sum_{j=i}^{n} |T(x_i) \cap T(x_j)|$  is a constant for the given training data, Theorem 2 shows that maximizing Eq. (5) is equivalent to minimizing the  $k$ -cut for  $G(V, E)$ . Thus, we convert the problem of maximizing Eq. (5) into the classic minimum  $k$ -cut problem.
+
+# 3.3 Spectral Clustering for the Balanced  $k$ -Cut
+
+Based on the analysis in § 3.2, we propose to use spectral clustering, a widely used approach for solving the minimum graph  $k$ -cut problem, as our batch partition algorithm. Spectral clustering employs spectral relaxation of the ratio/normalized cut and uses  $k$ -means in the embedding of the vertices found by the first  $k$  eigenvectors of the graph Laplacian in order to obtain the clustering. In addition to the classic minimum graph  $k$ -cut problem, we need to incorporate the constraint that each cut/batch must have a size of  $s$ .
+
+To incorporate the batch size constraint, we make a simple modification to the k-means step in spectral clustering. In the traditional k-means, each node is assigned to the nearest cluster center. In our algorithm, if the nearest cluster center has already been assigned  $s$  nodes, the node will be assigned to the nearest center that has fewer than  $s$  assigned nodes. The specific spectral clustering algorithm is presented as follows.
+
+1. Compute the spectral embedding  $Y\in \mathbb{R}^{n\times k}$  by stacking the normalized first  $k$  eigenvectors of  $G(V,E)$  in columns as described in (Ng et al., 2002).  
+2. Treat the  $i$ -th row of  $Y$  as the feature of the  $i$ -th training point  $e_i \in \mathbb{R}^k$ .  
+3. Given an initial set of  $k$  means  $m_{1},\dots ,m_{k}$  by randomly selecting  $k$  nodes as centers, repeat the following two steps until convergence:
+
+(a) Assignment step Assign nodes to centers:
+
+i. Compute distances to centers  $dis_{i,j} = \text{distance}(e_i, m_j)$ , where the Euclidean distance is used.
+
+ii. Sort  $i,j$  in ascending order of  $dis_{i,j}$  for all  $1\leq i\leq n,1\leq j\leq k$
+
+iii. Iterate through all  $i, j$ . If node  $i$  is not assigned in this round and center  $j$  has less than  $s$  assigned nodes, assign node  $i$  to center  $j$ .
+
+(b) Update step Compute new centers by taking the mean of their assigned nodes.
+
+# 3.4 Spectral Clustering at Scale
+
+The above algorithm consists of computation of the eigenvectors, and the use of k-means. K-means is efficient even for large-scale data. However, when  $n$  and  $k$  are large, the graph construction and eigenvectors computation become computationally expensive.
+
+To compute the spectral embeddings at scale, high-performance optimization techniques are available such as (Liu et al., 2013; Kolev and Mehlhorn, 2016; Boutsidis et al., 2015; Tremblay et al., 2016). Also, in our experiments, a simple trick was found that yields meaningful results: only calculate  $k'$ -dimensional feature vectors ( $k' < k$ ) and perform k-means with the  $k'$  dimensions. We found that  $k' = 8$  is a good practice in our experiments.
+
+# 4 Related Work
+
+Integrating knowledge into language models has been one of the focuses of language modeling research in recent years. The main integration methods currently include using pre-trained entity embeddings, and constructing knowledge-aware corpora. ERNIE (Zhang et al., 2019), KnowBERT (Peters et al., 2019), and KGLM (Logan et al., 2019) are typical methods using pre-trained entity embeddings. ERNIE uses Wikidata (Vrandečić and Krötzsch, 2014) as the knowledge base and uses TransE (Bordes et al., 2013) to encode knowledge. KnowBERT, on the other hand, uses skip-gram like objective (Mikolov et al., 2013) based on Wikipedia descriptions as the pre-trained entity embeddings. In addition, KnowBERT adds a loss on entity linking to the pre-trained objective. KGLM (Logan et al., 2019) allows modification/updating of knowledge by building a local knowledge graph for the target sentence. WKLM (Xiong et al., 2019) constructs a corpus of incorrect knowledge descriptions by replacing Wikipedia's entities with different entities of the same type. It trains the model to identify incorrect and correct knowl
+
+edge descriptions. Recently, models that integrate textual knowledge have also been proposed. In this paper, we adopt the model structure in OK-Transformer (Cui and Chen, 2022).
+
+Textual knowledge bases Noting the deficiencies of symbolic knowledge in terms of expressiveness and contextual information representation, some work has started to use text as a form of knowledge. ATOMIC (Sap et al., 2019; Hwang et al., 2021) is a large-scale manually annotated common-sense textual knowledge base that includes social interaction, event-centered, physical entity. ATOMIC contains knowledge like (PersonX reaches PersonX's home, Before, PersonX needs to park the car). ASER (Zhang et al., 2020) is an eventuality knowledge graph of activities, states, events, and their relations. Its knowledge atoms are in natural language form, e.g. (I do not have lunch, succession, I am hungry). COMET (Bosselut et al., 2019) is an extension of ATOMIC based on the generative language model. It mainly solves the problem of insufficient coverage of ATOMIC. Some primitive research (Guan et al., 2020; Shwartz et al., 2020) has started to apply these textual knowledge bases in some specific tasks. OK-Transformer (Cui and Chen, 2022) is proposed to integrate textual knowledge for general purposes. However, in our experimental tests, it takes too much time in encoding the commonsense. To our knowledge, there is still a lack of research on how to integrate textual knowledge into general text understanding tasks efficiently.
+
+Comparison with dense textual knowledge retriever When introducing external texts, another style is to use a retriever that returns only top  $k$  candidate texts in terms of similarity (Chen et al., 2017; Karpukhin et al., 2020; Wang et al., 2019). However, this method requires a heavy pre-training process to learn the retriever. On the other hand, for the textual knowledge base we use in this paper, we can directly use the manually labeled trigger words for each knowledge description to retrieve knowledge. Therefore, in this paper, we focus on how to efficiently and effectively integrate knowledge from a textual knowledge base.
+
+High-performance language models More general techniques for high-performance language models have also received extensive studies. The main approaches of previous studies include (1) model compression and quantization (Sanh et al., 2019; Jacob et al., 2018), and (2) efficient repre
+
+sensation of long texts (Kitaev et al., 2019; Peng et al., 2020). However, the model compression approaches require heavy pre-training before they can be adapted to language models. Moreover, the techniques for optimizing the efficiency for long text do not have significant effects on short texts (Peng et al., 2020). Besides, each commonsense description we considered in this paper tends to be short. In addition, these works have not considered the characteristics of the knowledge integration problem in this paper, i.e., a training sample corresponds to multiple candidate textual knowledge from the knowledge base.
+
+# 5 Experiments
+
+In this section, we conducted extensive experiments to evaluate batch partitioning. We aim to address the following key questions:
+
+1. ( $\S 5.2$ ) How much is the efficiency improvement of batch partitioning? Can it improve efficiency without sacrificing effectiveness?  
+2. ( $\S 5.3$ ) What is the scalability of batch partitioning as an acceleration method, and can it be applied to large-scale training?  
+3. (§ 5.4) Is the main theoretical contribution of this paper, i.e., solving the balanced graph- $k$  cut by spectral clustering, consistent with the real datasets?
+
+# 5.1 Implementation Details and Setup
+
+Textual knowledge base We follow (Cui and Chen, 2022) to use ATOMIC2020 (Hwang et al., 2021) as the textual knowledge base. Each atom in ATOMIC2020 is commonsense in text form. For each sentence in the downstream task, we retrieve the knowledge associated with it from the textual knowledge base. Note that, unlike retrieving knowledge from free text (Guu et al., 2020), the textual knowledge base ATOMIC2020 is constructed manually, and each knowledge description has corresponding trigger words. These trigger words are usually verbs or verb phrases. We retrieve related textual commonsense descriptions by keyword-matching of these trigger words.
+
+Model architecture We use OK-Transformer (Cui and Chen, 2022) as the backbone of our model. It directly incorporates extra knowledge without pre-training. OK-Transformer is based on either BERT or RoBERTa. We use OK-Transformer based on BERT by
+
+default. We also follow the hyperparameter settings of OK-Transformer. All experiments were run on 8 Nvidia RTX 3090Ti GPUs.
+
+Datasets We evaluate batch partitioning via commonsense reasoning and sentence classification. Since the textual knowledge introduced in this paper is commonsense descriptions, we first verify whether the proposed method in this paper could be applied to the commonsense reasoning tasks. To this end, we choose a wide range of commonsense reasoning tasks to conduct the experiments: CommonsenseQA (Talmor et al., 2019), PhysicalQA (Bisk et al., 2020), as well as several Winograd Schema Challenge (WSC) datasets including WSC273 (Levesque et al., 2012), PDP (Morgenstern et al., 2016), WinoGrande (Sakaguchi et al., 2019), WinoGender (Rudinger et al., 2018). Furthermore, for a comprehensive comparison, we also evaluate the efficiency and effectiveness of the proposed batch partitioning method on the text classification benchmark GLUE (Wang et al., 2018).
+
+# 5.2 Effectiveness and Efficiency
+
+Baselines To verify the efficiency and effectiveness of batch partitioning, we used the following baselines:
+
+- Vanilla BERT/RoBERTa without external knowledge.  
+- OK-Transformer To show the efficiency gains of the batch partitioning proposed in this paper, we compare it with the original OK-Transformer. The baseline randomly partitions samples into batches. We consider this baseline as the lower upper bound of effectiveness of commonsense integration.  
+- Frozen knowledge encodings For a comprehensive comparison, we propose to freeze the encoding of commonsense descriptions during fine-tuning. This approach allows us to introduce external textual commonsense descriptions via embedding lookup with minimal time cost. We consider this baseline as the upper bound on the efficiency of commonsense integration.
+
+The results of commonsense reasoning and text classification are presented in Table 2 and Table 3, respectively. The effectiveness of our batch partitioning approach is demonstrated by its improvement over vanilla language models on both commonsense reasoning and text classification tasks.
+
+<table><tr><td></td><td>LM</td><td>Comm.QA</td><td>PhysicalQA</td><td>WSC273</td><td>PDP</td><td>WinoGrande</td><td>WinoGender</td><td>Avg.</td><td>Speed-up ↑</td></tr><tr><td>BERT</td><td>BERT</td><td>55.86</td><td>68.71</td><td>66.30</td><td>85.00</td><td>51.38</td><td>68.19</td><td>65.44</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>BERT</td><td>56.43</td><td>68.06</td><td>65.93</td><td>83.33</td><td>51.30</td><td>68.47</td><td>65.59</td><td>1.4×</td></tr><tr><td>OK-Transformer</td><td>BERT</td><td>56.27</td><td>69.09</td><td>67.40</td><td>86.67</td><td>52.64</td><td>71.53</td><td>66.56</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>BERT</td><td>56.59</td><td>69.53</td><td>66.67</td><td>86.67</td><td>52.17</td><td>72.78</td><td>67.40</td><td>1.4×</td></tr><tr><td>RoBERTa</td><td>RoB.</td><td>73.55</td><td>79.76</td><td>90.10</td><td>90.00</td><td>-</td><td>94.60</td><td>83.95</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>RoB.</td><td>75.02</td><td>52.77</td><td>90.48</td><td>88.33</td><td>-</td><td>96.81</td><td>80.01</td><td>1.5×</td></tr><tr><td>OK-Transformer</td><td>RoB.</td><td>75.92</td><td>80.09</td><td>91.58</td><td>90.00</td><td>-</td><td>95.00</td><td>84.75</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>RoB.</td><td>75.59</td><td>80.20</td><td>90.48</td><td>91.66</td><td>-</td><td>96.25</td><td>85.14</td><td>1.4×</td></tr></table>
+
+Table 2: Results on commonsense reasoning tasks. The effectiveness of batch partitioning surpasses the vanilla BERT/RoBERTa, and is competitive with its upper bound (OK-Transformer). In terms of efficiency, the speed-up of batch partitioning is also competitive to its upper bound (frozen knowledge). RoB. denotes RoBERTa.  
+
+<table><tr><td></td><td>LM</td><td>MRPC</td><td>CoLA</td><td>RTE</td><td>QNLI</td><td>STS-B</td><td>SST-2</td><td>Avg.</td><td>Speed-up</td></tr><tr><td>BERT</td><td>BERT</td><td>86.52/90.66</td><td>59.50</td><td>71.43</td><td>91.20</td><td>89.35/88.93</td><td>91.97</td><td>82.28</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>BERT</td><td>87.50/91.28</td><td>57.31</td><td>70.76</td><td>91.71</td><td>87.31/87.20</td><td>92.43</td><td>81.78</td><td>2.3×</td></tr><tr><td>OK-Transformer</td><td>BERT</td><td>87.50/91.04</td><td>58.29</td><td>72.20</td><td>91.58</td><td>89.82/89.46</td><td>92.66</td><td>82.54</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>BERT</td><td>87.99/91.45</td><td>61.41</td><td>71.48</td><td>91.32</td><td>89.64/89.19</td><td>93.69</td><td>83.09</td><td>2.1×</td></tr><tr><td>RoBERTa</td><td>RoB.</td><td>90.49/93.07</td><td>66.84</td><td>86.28</td><td>93.37</td><td>91.83/91.95</td><td>95.64</td><td>87.86</td><td>-</td></tr><tr><td>Frozen knowledge</td><td>RoB.</td><td>89.71/92.61</td><td>68.22</td><td>87.36</td><td>94.39</td><td>90.74/90.47</td><td>96.10</td><td>88.19</td><td>2.4×</td></tr><tr><td>OK-Transformer</td><td>RoB.</td><td>91.91/94.24</td><td>66.89</td><td>86.28</td><td>94.71</td><td>92.19/92.36</td><td>96.44</td><td>88.49</td><td>1.0×</td></tr><tr><td>Batch Partitioning</td><td>RoB.</td><td>90.69/93.44</td><td>67.75</td><td>85.92</td><td>94.07</td><td>92.41/92.20</td><td>96.22</td><td>88.27</td><td>2.1×</td></tr></table>
+
+Table 3: Results on text classification tasks. Both the effectiveness and the efficiency of batch partitioning are competitive to their upper bounds (OK-Transformer and frozen knowledge).
+
+![](images/2b84a00213ca9264976d97800cd6418a4691e3d5279678013e3ca95bd4d39dbe.jpg)  
+Figure 2: The effect of the scale of extra commonsense. We control the scale by limiting the upper number of commonsense descriptions per sample in SST-2.
+
+The effectiveness is comparable or slightly superior to that of OK-Transformer, which serves as the upper bound for effectiveness. In terms of efficiency, our approach significantly accelerates knowledge integration models across a range of tasks. On average, it reduces the time cost for knowledge encoding by  $40\%$  for commonsense reasoning tasks, and  $110\%$  for text classification tasks. This acceleration is close to the frozen knowledge, and serves as the upper bound for efficiency. Overall, our approach is close to its efficiency upper bound without losing effectiveness.
+
+# 5.3 Scalability for Dataset Sizes, Device Capacities, and Knowledge Sizes
+
+In this subsection, we investigate the scalability of batch partitioning with different batch sizes, as well as the different dataset sizes. Larger dataset sizes usually mean devices with larger memory. In particular, we calculated the speedups of knowledge encoding for different batch sizes and different tasks. The results are shown in Fig. 4. The datasets are sorted by size in descending order.
+
+It can be clearly seen that as the size of the dataset rises or the memory of the device rises (larger batch size), the speedup of batch partitioning becomes more significant. This is because, for data-intensive tasks, the knowledge overlapping among different samples is more significant, which increases the feasibility of using batch partitioning. This result verifies the scalability of batch partitioning.
+
+We also investigate the scalability of batch partitioning over different scales of integrated commonsense. To control the scale, we set the upper number of commonsense descriptions for each sample to 16/32/64, respectively, and study the efficiency. Intuitively, richer commonsense descriptions lead to higher effectiveness but more computation cost. The results are shown in Fig. 2.
+
+As commonsense knowledge becomes richer, the
+
+![](images/8d1a9452fc02a40f4b0244a059b736350110a565bc1ad139471c1e3ea1ba0062.jpg)  
+(a) MRPC
+
+![](images/5066d569d43d450f479e7f435d24e869a41a877df5e839e063ee4b91e172d923.jpg)  
+(b) CoLA  
+Figure 3: Strong correlation between the distinct commonsense descriptions per batch and the average distance to the centroid during clustering.
+
+![](images/65abbb33676dfb3e6a8d644ffe711a19cec5ecd9bb0d7c19d513bddf95067c00.jpg)  
+(c) RTE
+
+![](images/2717bd99cdb36ae3036299b9159deff06406a683a9f7d37abe0c978f182d85b8.jpg)  
+(d) STS-B
+
+![](images/1594c7c7a6069f48db4954328bb329e516bb706105c6f90148c45a85be5ab1b5.jpg)  
+Figure 4: Speed-up of proposed batch partitioning method over different training batch size and dataset size. Note that the datasets are arranged in descending order according to dataset size.
+
+effectiveness and the acceleration both increase. This is because the knowledge overlapping among samples also becomes more significant. The result verifies that batch partitioning is applicable for incorporating large-scale commonsense knowledge bases.
+
+# 5.4 Effect of Spectral Clustering Theory
+
+In this paper, we propose the use of spectral clustering to solve the batch partitioning problem. We approximate and optimize the distinct number of descriptions per batch in Eq. (1) by minimizing the distance of each node to the centroid of the cluster in spectral clustering. In this subsection, we demonstrate the rationale behind this approximation by highlighting the strong correlation between the objective of Eq. (1) and the distance minimization in spectral embeddings.
+
+To this end, we plot how the centroid distance and the distinct descriptions per batch vary at each iteration of the spectral clustering algorithm in Fig. 3. The results show a strong correlation between the value we directly optimize (i.e., the cen
+
+troid distance) and the target of the batch partitioning (i.e., distinct descriptions per batch). This supports the feasibility of using spectral clustering to convert the batch partitioning problem into a balanced graph  $k$ -cut problem and solve it efficiently.
+
+# 6 Conclusion
+
+In this paper, we study how to improve the efficiency of incorporating commonsense knowledge in language models. Due to the high encoding costs of commonsense descriptions, it is crucial to reduce their encoding complexity. Our idea is that by carefully dividing samples with similar descriptions into the same batch, the knowledge encoding utilization can be improved.
+
+With such an idea, we theoretically analyze the optimization objective of this batch partitioning. We found that the upper bound of this problem can be reduced to the classical graph  $k$ -cut problem. We propose to use the well-studied spectral clustering algorithm to optimize the batch partitioning. By experimenting with a variety of tasks, we show that the proposed batch partitioning approaches its upper bound in terms of both effectiveness and efficiency. And the method is more applicable for larger datasets and on devices with more capabilities.
+
+# 7 Limitations
+
+The theoretical results and the algorithm should be applicable for other knowledge integration models which encode target sentences and associated textual knowledge descriptions in mini-batches. However, this paper does not extensively apply the proposed method to various knowledge integration models to explore its efficiency and effectiveness.
+
+# References
+
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+Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. 2013. Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems, pages 3111-3119.  
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+
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+
+A For every submission:
+
+A1. Did you describe the limitations of your work? Sec 5  
+A2. Did you discuss any potential risks of your work? Not applicable. Left blank.  
+A3. Do the abstract and introduction summarize the paper's main claims? Left blank.  
+A4. Have you used AI writing assistants when working on this paper? Left blank.
+
+B Did you use or create scientific artifacts?
+
+Left blank.
+
+B1. Did you cite the creators of artifacts you used? Not applicable. Left blank.  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Not applicable. Left blank.  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Not applicable. Left blank.  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Left blank.
+
+C Did you run computational experiments?
+
+we discuss the experiments in sec5
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? parameters same as BERT/RoBERTa.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? in sec5  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Fig. 2  
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? We follow the implementation and experiments setting of OK-Transformer as we mentioned in sec 5.
+
+# D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? Not applicable. Left blank.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? Not applicable. Left blank.  
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? Not applicable. Left blank.  
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? Not applicable. Left blank.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? Not applicable. Left blank.

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