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+# Self-Perturbed Anomaly-Aware Graph Dynamics for Multivariate Time-Series Anomaly Detection
+
+# Jinyu Cai
+
+Institute of Data Science
+
+National University of Singapore
+
+jinyucai@nus.edu.sg
+
+# Glynnis Lim
+
+Institute of Data Science
+
+National University of Singapore
+
+glynnis@nus.edu.sg
+
+# Roger Zimmermann
+
+School of Computing
+
+National University of Singapore
+
+dcsrz@nus.edu.sg
+
+# Yuan Xie*
+
+School of Computing
+
+National University of Singapore
+
+xieyuan_sss@outlook.com
+
+# Yifang Yin
+
+Institute for Infocomm Research
+
+A*STAR, Singapore
+
+yin_yifang@i2r.a-star.edu.sg
+
+# See-Kiong Ng
+
+Institute of Data Science
+
+National University of Singapore
+
+seekiong@nus.edu.sg
+
+# Abstract
+
+Detecting anomalies in multivariate time-series data is an essential task across various domains, yet there are unresolved challenges such as (1) severe class imbalance between normal and anomalous data due to rare anomaly availability in the real world; (2) limited adaptability of the static graph-based methods to dynamically changing inter-variable correlations; and (3) neglect of subtle anomalies due to overfitting to normal patterns in reconstruction-based methods. To tackle these issues, we propose Self-Perturbed Anomaly-Aware Graph Dynamics (SPAGD), a framework for time-series anomaly detection. SPAGD employs a self-perturbation module that generates self-perturbed time series from the reconstruction process of normal ones, which provide auxiliary signals to alleviate class imbalance during training. Concurrently, an anomaly-aware graph construction module is proposed to dynamically adjust the graph structure by leveraging the reconstruction residuals of self-perturbed time series, thereby emphasizing the inter-variable disruptions induced by anomalous candidates. A unified spatio-temporal anomaly detection module then integrates both spatial and temporal convolutions to train a classifier that distinguishes normal time series from the auxiliary self-perturbed samples. Extensive experiments across multiple benchmark datasets demonstrate the effectiveness of SPAGD compared to state-of-the-art baselines.
+
+# 1 Introduction
+
+Time-series anomaly detection (TSAD) [Blázquez-García et al., 2021; Zamanzadeh Darban et al., 2024] is an essential machine learning task with significant influence in various domains, such as cybersecurity, industrial systems, healthcare, and finance [Veeravalli et al., 2017; Cook et al., 2019; Schmidl et al., 2022; Zhang et al., 2024b; Qi et al., 2025; Fang et al., 2025]. It aims to identify patterns that deviate from expected behavior over a period of time, and to alert to potential faults,
+
+![](images/146fd6393feb0af5b5c11dcd979f1c9fb9a8b7c1fe288579bdb90ca9daed01d8.jpg)  
+Figure 1: An illustration of the proposed SPAGD framework, which contains three main components: (1) Self-perturbation time-series generation; (2) Anomaly-aware graph construction; and (3) Spatiotemporal modeling for anomaly detection.
+
+intrusions, or critical events. Multivariate time-series anomaly detection, in particular, presents a significant challenge due to the complex spatial and temporal inter-variable dependencies among multiple time-series data.
+
+Over the past decades, TSAD has witnessed significant progress. Early methods are mainly based on proximity [Breunig et al., 2000; Qi and Chen, 2022], linear model [Wold et al., 1987; Scholkopf et al., 2001], clustering [Chen et al., 2022b; Liu et al., 2022; Chen et al., 2022a; Liang et al., 2025; Fu et al., 2025] or outlier ensembles [Liu et al., 2008]. These methods rely on strong assumptions and often struggle with large-scale or high-dimensional data. In recent years, deep learning has emerged as a powerful alternative [Zamanzadeh Darban et al., 2024], with various types of approaches being proposed. For example, the reconstruction-based methods [Audibert et al., 2020; Yang et al., 2023; Wang et al., 2023] employ deep neural network architectures [Baldi, 2012; Goodfellow et al., 2020] to learn latent representations of normal behavior. Anomalies are detected as instances exhibiting significant reconstruction errors, reflecting their deviation from learned norms. Concurrently, forecast-based methods [Tuli et al., 2022; Xu et al., 2022; Wu et al., 2023a] have leveraged sequence modeling techniques [Medsker et al., 2001; Vaswani et al., 2017; Fang et al., 2023] to capture temporal dependencies and predict future values, where anomalies are flagged when observed values diverge from predictions. Although these approaches exhibited effectiveness, they generally treat each variable or time stamp independently, neglecting the rich inter-variable dependencies in multivariate time series. Therefore, recent endeavors [Zhao et al., 2020; Deng and Hooi, 2021] have explored the potential of graph neural networks (GNNs) [Kipf and Welling, 2017; Liu et al., 2023; Wu et al., 2023b; Cai et al., 2024a, 2025b; Liu et al., 2025b] to explicitly model inter-variable dependencies, where variables (e.g., sensors) are represented as nodes in a graph, with edges encoding spatial relationships. Advanced methods [Zheng et al., 2023; Chen et al., 2024] further incorporate GNNs with temporal convolution to capture temporal dynamics for detecting anomalies.
+
+Although these advanced methods provide a promising solution for detecting anomalies in multivariate time-series data, several key challenges still persist:
+
+1. Time-series anomalies are rare or even unavailable in real-world scenarios. The severe imbalance between normal and anomalous time series [Zamanzadeh Darban et al., 2024] could bias the model towards normal patterns during training, thus significantly weakening its generalizability.  
+2. Existing graph-based methods [Deng and Hooi, 2021; Zheng et al., 2023] typically rely on a static graph construction strategy to model spatial dependencies of time-series data, yet these dependencies may significantly alter due to dynamic anomaly-induced distortion.
+
+3. The "anomaly reconstruction" problem [Audibert et al., 2020; Song et al., 2023] indicates that certain anomalies may inadvertently be well-reconstructed in reconstruction-based methods due to the overfit towards normal patterns, thereby overlooking anomalies with low reconstruction error.
+
+To address these challenges, we propose a new TSAD framework named Self-Perturbed Anomaly-aware Graph Dynamics (SPAGD). SPAGD introduces a self-perturbation module that leverages inherent deviations during the process of reconstructing normal time series to generate self-perturbed time series. These generated time-series data subsequently serve as the auxiliary signal for training the anomaly detection model, where the model is exposed to diverse potential anomalous patterns for alleviating the imbalance problem. Simultaneously, an anomaly-aware graph construction scheme is introduced to learn dynamic inter-variable correlations derived from the evolving reconstruction residuals of self-perturbed time series. Then, we developed a spatio-temporal anomaly detection module to distinguish the self-perturbed time series from normal ones, which effectively integrates both spatial dependencies and temporal dynamics to yield holistic representations for TSAD. SPAGD is trained in an end-to-end manner for the mutual improvement of all components during training. Extensive experiments compared to state-of-the-art TSAD baselines demonstrate the superiority of the proposed SPAGD method. We summarize the main contributions of this paper as follows:
+
+- We introduce a self-perturbation module that generates diverse auxiliary anomalous time series through the evolving reconstruction process of the normal time-series data, which alleviates the severe imbalance problem without relying on any external anomalous data.  
+- We propose an anomaly-aware graph construction module that dynamically adjusts the graph structure based on the reconstruction residuals of the self-perturbed time series, thus reflecting the changing inter-variable correlations that traditional static strategies fail to capture.  
+- We build an anomaly detection framework that trains a classifier by exploiting both spatial and temporal dependencies to distinguish normal time series from auxiliary self-perturbed ones, which jumps out of the reconstruction-based framework and mitigates the anomaly reconstruction problem.
+
+# 2 Related Works
+
+Multivariate TSAD [Blázquez-García et al., 2021; Zamanzadeh Darban et al., 2024; Zhang et al., 2024a] is a complex and challenging research area, with a variety of methods emerging in recent years. The sequence-centric models primarily leverage the temporal dynamics of time series, such as Anomaly Transformer [Xu et al., 2022] and TranAD [Tuli et al., 2022], which utilize a Transformer architecture to capture long-term dependencies, while TimesNet [Wu et al., 2023a] enhances detection accuracy through multi-scale temporal decomposition. These methods excel at modeling temporal patterns within individual channels, however, they typically process each variable channel independently, overlooking inter-variable correlations. In recent years, graph-based models have been widely explored to address this limitation, where a graph is constructed to represent the relationships between multiple variables, with GNNs [Cai et al., 2024b; Liu et al., 2024; Cai et al., 2025a] employed for anomaly detection. For instance, GDN [Deng and Hooi, 2021] pre-constructs a similarity graph to help predict anomalies, and GRELEN [Zhang et al., 2022] integrates graph relational learning to improve feature extraction. Moreover, recent approaches [Zheng et al., 2023; Ding et al., 2023] have proposed learning comprehensive representations by incorporating both spatial and temporal dependencies. However, their reliance on fixed graph structures renders them less effective in scenarios where time-series relationships evolve dynamically. Although a few studies have investigated dynamic graph learning [Jin et al., 2024], the graph construction in them is generally decoupled from the anomaly detection optimization process.
+
+The proposed SPAGD method exhibits differences from existing TSAD methods in the following aspects: (1) Rather than relying on random imposed noise [Wang et al., 2023] or traditional augmentation techniques [Yang et al., 2023], SPAGD employs a self-perturbation mechanism to generate auxiliary self-perturbed time-series data, where the perturbations are adaptive and closely tied to anomaly detection. (2) Unlike static graph-based methods [Deng and Hooi, 2021], SPAGD adapts to dynamic changes in inter-variable correlations caused by evolving anomalous candidates. (3) SPAGD leverages the generated auxiliary time series data to train a classifier, which is more flexible and does not require a hand-crafted anomaly-scoring function in reconstruction-based approaches [Song et al., 2023]. (4) SPAGD unifies all components in an end-to-end framework, so that auxiliary time series generation and anomaly detection mutually improve each other.
+
+# 3 Methodology
+
+# 3.1 Problem Formulation
+
+In multivariate time-series anomaly detection, we consider a time series  $\mathbf{X} = [\mathbf{x}_1,\mathbf{x}_2,\dots ,\mathbf{x}_T]$  collected across  $T$  discrete time steps. Each feature vector  $\mathbf{x}_t\in \mathbb{R}^d$  denotes multidimensional observations at timestamp  $t$ , where  $d > 1$  denotes the feature dimensions of the multivariate time-series data. Typically, a time-series dataset  $\mathcal{D} = \{\mathbf{X}_1,\mathbf{X}_2,\ldots ,\mathbf{X}_N\}$  with  $N$  samples is constructed by applying a sliding window of length  $T$  to sample a long time series collected from different sources, e.g., industrial sensors. The dataset  $\mathcal{D}$  serves as the training foundation for building an anomaly detection model that generalizes to an unknown test dataset  $\mathcal{D}_{\mathrm{test}}$ . Our goal is to train an anomaly detection model  $\mathcal{F}_{\Theta}:\mathbb{R}^{d\times T}\to \{0,1\}$  parameterized by  $\Theta$  based on  $\mathcal{D}$ , where the model is able to predict the anomaly state  $\hat{y}\in \{0,1\}$  for each test time sequence  $\hat{\mathbf{X}}_i\in \mathcal{D}_{\mathrm{test}}$ . Here,  $\hat{y} = 1$  and  $\hat{y} = 0$  denote anomalous and normal states, respectively.
+
+Despite the abundance of normal time-series data in the real world, current TSAD methods still face several fundamental challenges, such as the severe data imbalance, static spatio-temporal correlation modeling, and anomaly reconstruction problem (refer to Section 1). To tackle these challenges, we propose SPAGD, an end-to-end TSAD framework composed of: (i) self-perturbation time-series generation to alleviate data imbalance; (ii) graph construction to model dynamical inter-variable correlations; and (iii) a spatio-temporal anomaly detection module to mitigate the anomaly reconstruction problem. We will detail each component of SPAGD in the following subsections.
+
+# 3.2 Time-Series Generation via Self-Perturbation
+
+To alleviate the severe data imbalance inherent in multivariate time-series anomaly detection, we propose a self-perturbation mechanism that harnesses the intrinsic imperfections of reconstruction models to generate pseudo-anomalous samples. Our approach is motivated by two key observations. First, during early training stages, the reconstruction model tends to produce systematic errors when replicating the input  $\mathbf{X} \in \mathbb{R}^{d \times T}$  due to its limited representational capacity. We argue that these reconstruction errors, which manifest as deviations from the normal data, can serve as effective proxies for genuine anomalies. Second, as the reconstruction model is progressively trained, the magnitude of these errors diminishes, exposing the anomaly detection model to a continuum of deviations, i.e., from large, obvious discrepancies to subtle differences. By incorporating these generated auxiliary samples into the training process as supervised signals, the anomaly detection model is able to progressively refine its decision boundary by identifying a broader spectrum of potential anomalous patterns.
+
+Formally, given an input time series  $\mathbf{X}$ , we employ a Transformer-based model for reconstruction:
+
+$$
+\tilde {\mathbf {X}} = \operatorname {T r a n} _ {\mathrm {d}} \left(\operatorname {T r a n} _ {\mathrm {e}} (\mathbf {X}; \Theta_ {\mathrm {e}}); \Theta_ {\mathrm {d}}\right), \tag {1}
+$$
+
+where  $\tilde{\mathbf{X}}\in \mathbb{R}^{d\times T}$  denotes the reconstructed time series, and  $\mathrm{Tran_e}(\cdot)$  and  $\mathrm{Tran_d}(\cdot)$  are the encoder and decoder networks parameterized by  $\Theta_{\mathrm{e}}$  and  $\Theta_{\mathrm{d}}$ , respectively. The reconstruction model is trained on the dataset  $\mathcal{D} = \{\mathbf{X}_i\}_{i = 1}^N$  by minimizing:
+
+$$
+\mathcal {L} _ {\mathrm {s p}} = \sum_ {i = 1} ^ {N} \left\| \mathbf {X} _ {i} - \operatorname {T r a n} _ {\mathrm {d}} \left(\operatorname {T r a n} _ {\mathrm {e}} \left(\mathbf {X} _ {i}; \Theta_ {\mathrm {e}}\right); \Theta_ {\mathrm {d}}\right) \right\| _ {F} ^ {2}. \tag {2}
+$$
+
+Initially,  $\tilde{\mathbf{X}}$  deviates substantially from  $\mathbf{X}$ , and these deviations are treated as auxiliary anomalous patterns for training the subsequent anomaly detection model. As training progresses and reconstruction quality improves,  $\tilde{\mathbf{X}}$  will gradually converge towards  $\mathbf{X}$ , providing the anomaly detection model with increasingly subtle deviation signals. Particularly, this progressive refinement can dynamically update the quality of pseudo-anomalous samples throughout the training process, which ensures that the anomaly detection model does not overfit to specific types of anomalies but instead generalizes to a broader range of potential anomalies.
+
+# 3.3 Anomaly-Aware Graph Construction
+
+Existing graph-based TSAD approaches [Deng and Hooi, 2021; Zheng et al., 2023] encode each variable (e.g., sensor) as a node  $(V)$  and pairwise affinities as edges  $(E)$ , allowing GNNs to exploit
+
+cross-variable dependencies via graph  $G = (V, E)$ , which is unavailable to purely sequence-centric models. However, these methods typically rely on static similarity measures (e.g., cosine similarity) to construct the graph, and keep it fixed throughout training and inference. A static topology can accurately reflect normal correlations, yet it fails to capture dynamic disruptions induced by self-perturbed time-series data. To overcome this limitation, we propose an anomaly-aware graph construction (AAGC) mechanism, which can dynamically adjust the graph structure based on the reconstruction residuals of the self-perturbed time series, thereby ensuring that the influence of potential anomalies on the spatial relationships can be emphasized.
+
+Initial Graph Construction Given a normal time-series  $\mathbf{X} \in \mathbb{R}^{d \times T}$  from a dataset  $\mathcal{D} = \{\mathbf{X}_1, \mathbf{X}_2, \dots, \mathbf{X}_N\}$ , we first construct an adjacency matrix  $\mathbf{A}$  to capture baseline inter-variable correlations. For variables  $i$  and  $j$ , we compute pairwise cosine similarity as follows:
+
+$$
+S _ {i j} = \operatorname {S i g m o i d} \left(\frac {\langle \mathbf {X} _ {i , :} , \mathbf {X} _ {j , :} \rangle}{\| \mathbf {X} _ {i , :} \| \cdot \| \mathbf {X} _ {j , :} \|}\right), \tag {3}
+$$
+
+where  $\mathbf{X}_{i,:} \in \mathbb{R}^T$  represents the time-series for variable  $i$ , and Sigmoid  $(\cdot)$  is the Sigmoid function mapping similarity scores to  $[0,1]$ , indicating connection strength. To ensure sparsity and focus on the most informative relationships, we retain only the top- $K$  neighbors for each variable:
+
+$$
+\mathbf {A} _ {i j} = \left\{ \begin{array}{l l} S _ {i j}, & \text {i f} j \in \operatorname {t o p} - K \text {n e i g h b o r s o f} i, \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {4}
+$$
+
+This step ensures the graph remains sparse, reducing computational complexity while preserving the most relevant inter-variable correlations. The initial graph  $\mathbf{A}$  serves as a static representation of interactions between normal multivariate time series.
+
+Dynamic Adjustment with Reconstruction Residuals While static graphs are suitable for capturing inter-variable correlations between normal time-series pairs, they cannot reflect the transient changes (e.g., sensor failures or external disturbances) in dynamic time series. To adapt to dynamic anomalous patterns introduced via generated self-perturbed time series, we construct a dynamically adjusted graph  $\tilde{\mathbf{A}}$  to reflect the influence of anomalous candidates on the learned graph structure. To achieve this, we first compute the node-specific reconstruction residual score  $r_i$  for each variable:
+
+$$
+r _ {i} = \frac {1}{T} \sum_ {t = 1} ^ {T} \left| \mathbf {X} _ {i, t} - \tilde {\mathbf {X}} _ {i, t} \right|, \tag {5}
+$$
+
+where  $\mathbf{X}_{i,t}$  and  $\tilde{\mathbf{X}}_{i,t}$  are the input and reconstructed values for time series  $i$  at time  $t$ , respectively. The reconstruction residual  $r_i$  quantifies the anomalous degree of the  $i$ -th variable within the self-perturbed samples, with higher values indicating greater deviation from normal behavior. Next, we identify the top- $m\%$  variables ranked by their residual scores  $r$  as anomalous candidates. The affinity matrix for the self-perturbed time-series is then dynamically adjusted to emphasize these variables:
+
+$$
+\tilde {S} _ {i j} = S _ {i j} + \mathbb {I} (i \in \mathcal {M}) \phi \left(r _ {i}\right) + \mathbb {I} (j \in \mathcal {M}) \phi \left(r _ {j}\right), \tag {6}
+$$
+
+where  $\phi (r_i) = \frac{1}{1 + e^{-r_i}}$  normalizes the anomaly score to a bounded interval [0, 1], and  $\mathbb{I}(\cdot)$  is the indicator function. Particularly, for  $i = j$ , we add  $\phi (r_i)$  only once. Following a similar procedure in Eq. (4), we can obtain the adjusted adjacency  $\tilde{\mathbf{A}}_{ij}$ . Note that we symmetrize the dynamically enhanced similarity before sparsification to ensure numerical stability and a well-posed enhanced structure. This adjustment adaptively boosts the connection strength between any two nodes where at least one is an anomalous candidate. Essentially, compared to static graph construction, the proposed AAGC strategy leverages the node-specific reconstruction residuals  $r_i$  to dynamically emphasize connections involving anomalous candidates  $(\mathcal{M})$ , thereby adapting the graph structure to reflect anomaly-induced changes in inter-variable correlations.
+
+# 3.4 Spatio-Temporal Modeling for TSAD
+
+With the auxiliary time-series dataset  $\tilde{\mathcal{D}} = \{\tilde{\mathbf{X}}_1,\tilde{\mathbf{X}}_2,\dots ,\tilde{\mathbf{X}}_N\}$  generated via self-perturbation (Section 3.2) and learned graph structures  $\mathbf{A}$  and  $\tilde{\mathbf{A}}$  (Section 3.3), we propose a spatio-temporal anomaly detection module designed to effectively capture both instantaneous variable interactions and their temporal dynamics for TSAD. Specifically, the module leverages a unified spatio-temporal representation learning framework and trains a classifier that distinguishes between normal and self-perturbed (auxiliary anomalous) time-series data.
+
+Dual-Graph Spatial Message Propagation To effectively model spatial inter-variable dependencies, we employ a graph attention network (GAT) layer. Let  $\mathbf{H}^{(l)}$  and  $\tilde{\mathbf{H}}^{(l)}$  be the matrices containing node representations for normal and self-perturbed time series at layer  $l$ . The GAT updates these representations based on learned attention weights. For each node  $i$ , the attention coefficient  $\alpha_{ij}^{(l)}$  regarding neighbor  $j$  is computed by:
+
+$$
+\alpha_ {i j} ^ {(l)} = \frac {\exp (\text {L e a k y R e L U} (\vec {a} ^ {(l) \top} [ \mathbf {h} _ {i} ^ {(l)} \mathbf {W} ^ {(l)} | | \mathbf {h} _ {j} ^ {(l)} \mathbf {W} ^ {(l)} ] ^ {\top}))}{\sum_ {u \in \mathcal {N} (i) \cup \{i \}} \exp (\text {L e a k y R e L U} (\vec {a} ^ {(l) \top} [ \mathbf {h} _ {i} ^ {(l)} \mathbf {W} ^ {(l)} | | \mathbf {h} _ {u} ^ {(l)} \mathbf {W} ^ {(l)} ] ^ {\top}))}, \tag {7}
+$$
+
+where  $\mathbf{W}^{(l)}$  and  $\vec{a}^{(l)}$  are shared learnable parameters for layer  $l$ , || denotes concatenation, and  $\mathcal{N}(i)$  is the neighborhood of node  $i$  based on graph  $\mathbf{A}$ . Similarly,  $\tilde{\alpha}_{ij}^{(l)}$  is computed using  $\tilde{\mathbf{h}}_i^{(l)}, \tilde{\mathbf{h}}_j^{(l)}$  (rows of  $\tilde{\mathbf{H}}^{(l)}$ ) and the neighborhood  $\tilde{\mathcal{N}}(i)$  derived from  $\tilde{\mathbf{A}}$ , using the same parameters  $\mathbf{W}^{(l)}$  and  $\vec{a}^{(l)}$ . The GAT layer then aggregates neighbor information using these attention weights to produce the output matrices  $\mathbf{H}^{(l+1)}$  and  $\tilde{\mathbf{H}}^{(l+1)}$  for the next layer. This operation, applied node-wise for all nodes  $i$ , can be represented as:
+
+$$
+\mathbf {H} _ {i,:} ^ {(l + 1)} = \sigma \left(\sum_ {j \in \mathcal {N} (i) \cup \{i \}} \alpha_ {i j} ^ {(l)} \mathbf {H} _ {j,:} ^ {(l)} \mathbf {W} ^ {(l)}\right), \quad \tilde {\mathbf {H}} _ {i,:} ^ {(l + 1)} = \sigma \left(\sum_ {j \in \tilde {\mathcal {N}} (i) \cup \{i \}} \tilde {\alpha} _ {i j} ^ {(l)} \tilde {\mathbf {H}} _ {j,:} ^ {(l)} \mathbf {W} ^ {(l)}\right), \tag {8}
+$$
+
+where  $\mathbf{H}_{i,:}^{(l + 1)}$  denotes the  $i$ -th row of  $\mathbf{H}^{(l + 1)}$ , and similarly for  $\tilde{\mathbf{H}}_{i,:}^{(l + 1)}$ .  $\sigma (\cdot)$  is the activation function, such as ReLU. Particularly,  $\mathbf{H}^{(0)} = \mathbf{X}$  and  $\tilde{\mathbf{H}}^{(0)} = \tilde{\mathbf{X}}$ . This mechanism ensures the model learns stable normal spatial relationships via  $\mathbf{A}$  while adapting to dynamically changing inter-variable correlations through  $\tilde{\mathbf{A}}$ .
+
+**Chunk-Wise Temporal Dependency Aggregation** Following the spatial convolution process, we adopt a chunk-wise temporal graph convolution strategy. For the learned spatial feature  $\mathbf{H}^{(L)}$  derived from the final spatial convolutional layer, we partition the temporal axis  $T$  into  $C$  chunks, i.e.,  $\mathbf{H}^{(L)} = \{\mathbf{H}_1^{(L)}, \mathbf{H}_2^{(L)}, \ldots, \mathbf{H}_C^{(L)}\}$ . Similarly, we can apply the same operation to partition the spatial representation  $\tilde{\mathbf{H}}^{(L)} = \{\tilde{\mathbf{H}}_1^{(L)}, \tilde{\mathbf{H}}_2^{(L)}, \ldots, \tilde{\mathbf{H}}_C^{(L)}\}$  for the self-perturbed time series. Subsequently, these spatial features are separately processed via a temporal convolution network  $\mathcal{T}(\cdot)$  to capture the temporal dependencies:
+
+$$
+\mathcal {Z} _ {c} = \mathcal {T} \left(\mathbf {H} _ {c} ^ {(L)}; \Theta_ {\mathrm {T e m}}\right), \tilde {\mathcal {Z}} _ {c} = \mathcal {T} \left(\tilde {\mathbf {H}} _ {c} ^ {(L)}; \Theta_ {\mathrm {T e m}}\right), \tag {9}
+$$
+
+where  $c$  denotes the  $c$ -th chunk of spatial features,  $\Theta_{\mathrm{Tem}}$  denotes the parameters of the temporal convolution network.  $\mathcal{Z}_c$  and  $\tilde{\mathcal{Z}}_c$  are the learned temporal representations for the  $c$ -th chunk of normal time series and self-perturbed time series, respectively. We then horizontally concatenate the features learned from each chunk to form comprehensive chunk-wise temporal representations:
+
+$$
+\mathcal {Z} _ {T} = \left[ \mathcal {Z} _ {1}, \mathcal {Z} _ {2}, \dots , \mathcal {Z} _ {C} \right], \quad \tilde {\mathcal {Z}} _ {T} = \left[ \tilde {\mathcal {Z}} _ {1}, \tilde {\mathcal {Z}} _ {2}, \dots , \tilde {\mathcal {Z}} _ {C} \right]. \tag {10}
+$$
+
+End-to-End Anomaly Detection The final spatio-temporal features  $\mathcal{Z}_T$  and  $\tilde{\mathcal{Z}}_T$  are then vertically stacked as  $\mathcal{Z}_{\mathrm{stack}} = [\mathcal{Z}_T;\tilde{\mathcal{Z}}_T]$  and passed through a predictor  $\mathcal{P}(\cdot)$ , which outputs the final prediction for both normal and self-perturbed time series:
+
+$$
+\hat {\mathbf {p}} = \mathcal {P} \left(\mathcal {Z} _ {\text {s t a c k}}; \Theta_ {\mathcal {P}}\right), \tag {11}
+$$
+
+where  $\hat{\mathbf{p}}\in [0,1]^{2N}$  denotes the predicted anomaly probability for the normal and self-perturbed time series, and  $\Theta_{\mathcal{P}}$  comprises the network parameters of the predictor. Finally, we train the entire model in an end-to-end manner by jointly optimizing the self-perturbation loss  $\mathcal{L}_{\mathrm{sp}}$  (Eq. (2)) and the following anomaly detection loss:
+
+$$
+\mathcal {L} _ {\mathrm {a d}} = - \frac {1}{2 N} \sum_ {i = 1} ^ {2 N} \left[ y _ {i} \log \left(\hat {p} _ {i}\right) + \left(1 - y _ {i}\right) \log \left(1 - \hat {p} _ {i}\right) \right]. \tag {12}
+$$
+
+For training the model, we simply set the label for the normal and self-perturbed time series to 0 and 1, respectively. We summarize the overall objective function of the proposed SPAGD framework as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {s p}} + \beta \mathcal {L} _ {\mathrm {a d}}, \tag {13}
+$$
+
+where the hyperparameter  $\beta$  controls the trade-off between the reconstruction and anomaly detection losses. Particularly, the self-perturbation module is trained with randomly initialized weights, and we explicitly avoid pre-training because the evolution of the reconstruction model is crucial to our proposed learning paradigm. This end-to-end design framework ensures mutual enhancement across the auxiliary time-series generation and spatio-temporal anomaly detection. In the inference stage, we use the output of the trained anomaly detector as the anomaly scores for evaluation. We also provide a detailed algorithm description in the Appendix C.
+
+# 4 Experiment
+
+# 4.1 Experimental Configuration
+
+Datasets In this paper, we evaluate the proposed SPAGD method on three public time-series datasets collected from different real-world scenarios, including (1) Secure Water Treatment (SWaT) [Mathur and Tippenhauer, 2016], (2) Soil Moisture Active Passive (SMAP) [Hundman et al., 2018], and (3) Mars Science Laboratory (MSL) [Hundman et al., 2018]. Table 1 summarizes the main attributes of these datasets, and we also detail the information of each dataset in the Appendix A.
+
+Table 1: Statistics of the three time-series datasets. "AR" denotes anomaly-point ratio in the test split.  
+
+<table><tr><td>Dataset</td><td>Domain</td><td># Channels (Dimensions)</td><td># Train samples (Normal)</td><td># Test samples (Mixed)</td><td>AR (%)</td></tr><tr><td>SWaT</td><td>Water treatment ICS</td><td>51</td><td>496,800</td><td>449,919</td><td>11.98</td></tr><tr><td>SMAP</td><td>Spacecraft telemetry</td><td>25</td><td>135,183</td><td>427,617</td><td>13.13</td></tr><tr><td>MSL</td><td>Spacecraft telemetry</td><td>55</td><td>58,317</td><td>73,729</td><td>10.72</td></tr></table>
+
+Experimental Settings For a fair evaluation, all baseline methods were trained and tested using identical data splits for each dataset. For SPAGD, we employed a Transformer-based reconstruction model comprising 8 attention heads and 3 encoder layers for self-perturbation learning. During the spatio-temporal modeling stage, each time series sample first undergoes spatial graph convolution that contains 2 graph attention network (GAT) [Veličković et al., 2018] layers with a latent dimension of 256. The learned spatial features were subsequently partitioned into 5 equal-length segments for temporal convolution processing. Aggregated spatio-temporal features were then passed through a predictor consisting of two fully-connected layers to produce final anomaly scores. For other experimental settings and training details, please refer to the Appendix B.
+
+Baselines We compared SPAGD with extensive state-of-the-art baselines, including:  $k$ -NN [Ramaswamy et al., 2000], OCSVM [Scholkopf et al., 2001], LOF [He et al., 2003], IForest [Liu et al., 2008], Deep-SVDD [Ruff et al., 2018], COPOD [Li et al., 2020], USAD [Audibert et al., 2020], GDN [Deng and Hooi, 2021], TcnED [Garg et al., 2021], TranAD [Tuli et al., 2022], Anomaly-Trans [Xu et al., 2022], NCAD [Carmona et al., 2022], Deep IF [Xu et al., 2023], TimesNet [Wu et al., 2023a], DCdetector [Yang et al., 2023], COUTA [Xu et al., 2024]. Note that we ensured a fair comparison by reproducing the performance of each baseline using the publicly available codes under the same experiment setting and following the default settings provided in the related papers.
+
+Evaluation Metrics To comprehensively evaluate the anomaly detection performance of SPAGD and other baselines, we employ three widely recognized evaluation metrics, including Area Under the ROC Curve (AUC), Area Under the Precision-Recall Curve (AUPRC), and F1-score (F1). We want to specifically highlight that we did not use the point-adjustment strategy in our evaluation due to its overestimation of model performance [Kim et al., 2022; Liu and Paparrizos, 2024].
+
+# 4.2 Comparison with State-of-the-Art TSAD methods
+
+We comprehensively evaluated SPAGD against extensive state-of-the-art TSAD baselines. Table 2 summarizes the experimental results across multiple benchmark datasets. The key insights are: (1) We can observe that SPAGD showed competitive performance in all three metrics across all datasets. As shown in Table 2, SPAGD achieved AUCs of  $86.30\%$  (SWaT),  $62.38\%$  (SMAP), and
+
+Table 2: Anomaly detection performance of SPAGD and baseline methods in terms of AUC, AUPRC, and F1 (in %). Note that the best two results are marked in **bold** and **underline**, respectively.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">SWaT</td><td colspan="3">SMAP</td><td colspan="3">MSL</td><td rowspan="2">Avg.</td></tr><tr><td>AUC</td><td>AUPRC</td><td>F1</td><td>AUC</td><td>AUPRC</td><td>F1</td><td>AUC</td><td>AUPRC</td><td>F1</td></tr><tr><td>k-NN [Ramaswamy et al., 2000]</td><td>77.30</td><td>68.28</td><td>71.95</td><td>39.73</td><td>11.48</td><td>25.08</td><td>59.32</td><td>17.55</td><td>32.46</td><td>44.79</td></tr><tr><td>OCSVM [Scholkopf et al., 2001]</td><td>76.06</td><td>67.27</td><td>71.79</td><td>39.87</td><td>11.46</td><td>25.08</td><td>59.33</td><td>17.58</td><td>32.61</td><td>44.56</td></tr><tr><td>LOF [He et al., 2003]</td><td>73.33</td><td>45.23</td><td>53.18</td><td>42.94</td><td>12.35</td><td>25.40</td><td>56.37</td><td>20.06</td><td>27.61</td><td>39.61</td></tr><tr><td>IForest [Liu et al., 2008]</td><td>78.74</td><td>66.87</td><td>66.24</td><td>39.78</td><td>11.21</td><td>25.08</td><td>56.91</td><td>16.85</td><td>29.59</td><td>43.47</td></tr><tr><td>Deep-SVDD [Ruff et al., 2018]</td><td>82.55</td><td>73.49</td><td>74.88</td><td>52.00</td><td>13.87</td><td>25.06</td><td>56.65</td><td>12.23</td><td>21.36</td><td>45.78</td></tr><tr><td>COPOD [Li et al., 2020]</td><td>81.66</td><td>71.57</td><td>70.85</td><td>40.04</td><td>12.02</td><td>25.08</td><td>60.56</td><td>18.17</td><td>32.77</td><td>45.85</td></tr><tr><td>USAD [Audibert et al., 2020]</td><td>79.67</td><td>70.24</td><td>72.60</td><td>39.51</td><td>11.41</td><td>22.69</td><td>61.67</td><td>12.86</td><td>27.12</td><td>44.19</td></tr><tr><td>GDN [Deng and Hooi, 2021]</td><td>81.55</td><td>71.33</td><td>75.23</td><td>58.09</td><td>16.97</td><td>19.24</td><td>49.73</td><td>12.13</td><td>22.68</td><td>45.22</td></tr><tr><td>TcnED [Garg et al., 2021]</td><td>82.38</td><td>72.38</td><td>76.26</td><td>53.57</td><td>12.03</td><td>19.65</td><td>48.54</td><td>12.80</td><td>23.23</td><td>44.53</td></tr><tr><td>TranAD [Tuli et al., 2022]</td><td>81.85</td><td>71.62</td><td>76.45</td><td>56.44</td><td>15.24</td><td>26.51</td><td>42.97</td><td>10.03</td><td>19.35</td><td>44.49</td></tr><tr><td>AnomalyTrans [Xu et al., 2022]</td><td>79.77</td><td>62.28</td><td>73.03</td><td>40.03</td><td>11.39</td><td>22.78</td><td>52.19</td><td>11.33</td><td>19.25</td><td>41.33</td></tr><tr><td>NCAD [Carmona et al., 2022]</td><td>19.00</td><td>8.77</td><td>21.76</td><td>39.67</td><td>11.69</td><td>22.68</td><td>59.40</td><td>14.13</td><td>21.98</td><td>24.34</td></tr><tr><td>Deep IF [Xu et al., 2023]</td><td>80.77</td><td>70.67</td><td>72.97</td><td>60.89</td><td>17.33</td><td>28.48</td><td>55.97</td><td>10.98</td><td>23.09</td><td>46.79</td></tr><tr><td>TimesNet [Wu et al., 2023a]</td><td>32.45</td><td>14.21</td><td>21.80</td><td>39.90</td><td>11.36</td><td>22.69</td><td>55.06</td><td>11.79</td><td>21.26</td><td>25.61</td></tr><tr><td>DCdetector [Yang et al., 2023]</td><td>49.68</td><td>12.20</td><td>21.97</td><td>49.79</td><td>12.76</td><td>22.70</td><td>50.10</td><td>10.55</td><td>19.09</td><td>27.64</td></tr><tr><td>COUTA [Xu et al., 2024]</td><td>82.95</td><td>74.78</td><td>78.68</td><td>47.20</td><td>12.56</td><td>22.69</td><td>52.17</td><td>11.84</td><td>19.08</td><td>44.66</td></tr><tr><td>SPAGD</td><td>86.30</td><td>77.20</td><td>78.77</td><td>62.38</td><td>18.15</td><td>27.32</td><td>66.50</td><td>21.45</td><td>30.89</td><td>52.11</td></tr></table>
+
+$66.50\%$  (MSL), outperforming the runner-up baselines, i.e., COUTA, DeepIF, and USAD by  $3.35\%$ ,  $1.49\%$ , and  $4.83\%$ , respectively. This observation suggests that the auxiliary signals provided by the generated self-perturbed time series during training ensure the stable performance of SPAGD achieved on different datasets. (2) SPAGD also outperformed reconstruction-based approaches, such as TranAD and AnomalyTrans. This significant performance improvement can be attributed to the designed spatio-temporal anomaly detection module, which leverages the self-perturbed samples to train a classifier instead of reconstruction-based strategies, which helped address the "anomaly reconstruction" problem. (3) Compared to graph-based methods such as GDN, SPAGD demonstrated superior performance. This comparison highlights the significance of the AAGC strategy in SPAGD, which leverages reconstruction residuals induced by self-perturbed time series to dynamically adjust the graph structure, thereby enabling the model to adapt to changing inter-variable correlations that static graph-based methods cannot.
+
+# 4.3 Parameter Analysis
+
+We perform a parameter sensitivity analysis to evaluate the influence of several critical hyperparameters on the performance of SPAGD. Figure 2 illustrates the impact of window size and trade-off parameter  $\beta$  on the performance. The experimental results shown in Figure 2(a) revealed that smaller or excessively large window sizes degrade performance to a certain extent, whereas window sizes in the range of [80, 100] consistently yield optimal performance.
+
+This is due to the fact that too
+
+![](images/0d544c95738b4340210dd0e109d713499472d605d1a8c64d79b5f94f00e7278d.jpg)  
+Figure 2: Anomaly detection performance under different window sizes and  $\beta$  values on SWaT. Note that we vary the window size and  $\beta$  value in a wide range of [20, 200] and  $[10^{-4}, 10^{2}]$ , respectively.
+
+![](images/23b4e0c12a8d606d97c49d3823acb5d29367df159785deee104493de1559c3fd.jpg)
+
+short a window is not conducive to capturing temporal dependencies, while too long a window leads to difficulties in long-term dependencies learning. Additionally, Figure 2(b) presents the performance under different  $\beta$  values, which control the contributions of self-perturbation and anomaly detection losses during training. We can observe a steady performance improvement as  $\beta$  increases from  $\beta = 10^{-3}$  towards  $\beta = 10^{-2}$ . Though beyond this point, all metrics slightly decrease, the model maintains relatively stable performance under varying  $\beta$  in general. This suggests that overemphasizing anomaly detection loss can lead to overlooking the learning of informative self-perturbed samples for training, which highlights the importance of balancing informative reconstruction and discriminative anomaly detection in practice.
+
+![](images/b092761e30c058814fa10a337b671bfd3202cd74be52ba450148eb97c9002c0f.jpg)  
+(a) Ground Truth
+
+![](images/ef6a2e44d8f7b8aa313fb59a1796994676368c93fb9c26e3dfb9b26605fa67fe.jpg)  
+(b)TranAD  
+Figure 3: Anomaly score visualization on the MSL dataset. We randomly sampled data of length 500 and compared SPAGD with several baselines. The red area indicates the ground truth anomaly.
+
+![](images/7f5cf57c9b2b6a1a3dded2c151f2f0a051fe2fa742e700dad8b74de0793df731.jpg)  
+(c) AnomalyTrans
+
+![](images/602e09f0c0352a15f4ea936ac87f5472d67e93c90a074fcfc594ddddf35f585e.jpg)  
+(d) SPAGD
+
+Table 3: Ablation study results on the three datasets. The best results are marked in bold.  
+
+<table><tr><td>Dataset</td><td colspan="3">SWaT</td><td colspan="3">SMAP</td><td colspan="3">MSL</td><td rowspan="2">Avg.</td></tr><tr><td>Metric</td><td>AUC</td><td>AUPRC</td><td>F1</td><td>AUC</td><td>AUPRC</td><td>F1</td><td>AUC</td><td>AUPRC</td><td>F1</td></tr><tr><td>w/o SP</td><td>80.30</td><td>70.34</td><td>74.04</td><td>51.31</td><td>12.49</td><td>13.25</td><td>61.37</td><td>18.75</td><td>10.54</td><td>43.60</td></tr><tr><td>SP w/ Recon</td><td>76.82</td><td>61.95</td><td>62.11</td><td>46.19</td><td>11.35</td><td>22.68</td><td>51.38</td><td>14.39</td><td>19.07</td><td>40.66</td></tr><tr><td>w/o AAGC (Spatial)</td><td>81.51</td><td>70.07</td><td>74.20</td><td>57.86</td><td>15.72</td><td>15.79</td><td>62.63</td><td>18.95</td><td>15.68</td><td>45.82</td></tr><tr><td>w/o AAGC (Temporal)</td><td>83.16</td><td>72.18</td><td>75.11</td><td>60.60</td><td>17.12</td><td>16.33</td><td>59.19</td><td>13.08</td><td>14.04</td><td>45.65</td></tr><tr><td>w/o AAGC (Both)</td><td>80.54</td><td>70.59</td><td>74.28</td><td>55.34</td><td>16.01</td><td>23.84</td><td>54.74</td><td>12.27</td><td>19.78</td><td>45.27</td></tr><tr><td>w/o JT</td><td>82.97</td><td>72.01</td><td>73.83</td><td>38.60</td><td>9.98</td><td>12.79</td><td>52.09</td><td>11.45</td><td>11.21</td><td>40.55</td></tr><tr><td>SPAGD</td><td>86.30</td><td>77.20</td><td>78.77</td><td>62.38</td><td>18.15</td><td>27.32</td><td>66.50</td><td>21.45</td><td>30.89</td><td>52.11</td></tr></table>
+
+# 4.4 Anomaly Score Visualization
+
+We provide a visualization of anomaly scores for an intuitive detection capability comparison. Figure 3 presents the visualization results on MSL, where we compare SPAGD with several baseline methods such as TranAD and AnomalyTrans. We can observe that the anomaly scores of SPAGD are more distinguishable, and the predictions are closely aligned with the ground truth anomaly in Figure 3(a). Other baseline methods exhibit higher detection uncertainty, characterized by frequent false alarms or overlooked anomalies. In particular, we can observe that reconstruction-based methods, such as TranAD, exhibit low reconstruction errors in anomalous events, which further validates the aforementioned "anomaly reconstruction" problem. In contrast, SPAGD is capable of detecting anomalies at these locations. These comparisons visually demonstrate the superior practical detection capability and reliability of SPAGD in real-world scenarios.
+
+# 4.5 Ablation Study
+
+We conducted ablation experiments to evaluate the contribution of each component in the proposed SPAGD method by comparing the SPAGD model against the following variants that shared the same backbones and hyperparameter settings:
+
+1. w/o Self-Perturbed Generation (SP): This variant removes the self-perturbation module so that no auxiliary signals are available during training. In this case, the model detects anomalies by solely relying on reconstruction errors.  
+2. SP w/ Recon: This variant retains the self-perturbation module, and uses a traditional reconstruction model to reconstruct both the input and generate auxiliary time series. In the testing stage, the anomaly score is defined by the reconstruction error of a test sample.  
+3. w/o Anomaly-Aware Strategy (AAGC): This variant preserves the self-perturbation module but disables the anomaly-aware strategy in graph construction. Note that we build three variants using a static graph instead of the AAGC strategy for (1) spatial, (2) temporal, and (3) both spatial and temporal modeling, respectively.  
+4. w/o Joint Training (JT): This variant employs a two-stage pipeline where the reconstruction model is pre-trained and then generates the self-perturbed time series once to train the spatiotemporal anomaly detector.
+
+Table 3 shows the experimental results, with the following observations. (1) Removing the self-perturbation module generally leads to a performance drop across all datasets, such as AUCs dropping by  $6.00\%$  (SWaT),  $11.07\%$  (SMAP), and  $5.13\%$  (MSL). This is because the self-perturbation module
+
+provides rich auxiliary potential anomalous signals for model training, which mitigates the class imbalance problem and improves the generalizability. (2) The performance of the "SP w/ Recon" variant significantly decreases, which indicates that a purely reconstruction-based objective encourages the model to fit the self-perturbed patterns rather than distinguish them. Consequently, true anomalies receive lower reconstruction errors and are more difficult to detect in the testing stage, which is a classic example of the "anomaly reconstruction" problem. (3) The performance also decreases when we remove the spatial/temporal or both of them from the AAGC strategy. For example, on the MSL dataset, the performance of the variant that disables AAGC in spatial modeling decreases by  $3.87\%$  (AUC),  $2.50\%$  (AUPRC), and  $15.21\%$  (F1), respectively. This can be attributed to the failure of the model to capture the dynamically changing inter-variable correlations, resulting in the anomaly-induced information within self-perturbed time series being modeled inappropriately. (4) We also observed a significant performance decrease in three datasets after replacing the joint training with a two-stage training paradigm. Generated samples cannot be optimized for the anomaly detection task without joint training, and they are too similar to normal time-series data, which presents significant challenges for the model to distinguish normal time series from them. All in all, the ablation study results provided clear and strong evidence of the effectiveness of each component in SPAGD.
+
+# 4.6 More Experimental Analysis
+
+We further provide more experimental analysis in the Appendix, such as extra parameter analysis and visualization results, comparison with different backbone networks and different graph construction methods, comparison with the random-perturbation strategy, and point-adjusted results and more evaluation metrics (VUS-AUC/PR) for reference.
+
+# 5 Conclusion
+
+In this paper, we introduced SPAGD, a new TSAD framework to address several inherent challenges of multivariate time-series anomaly detection. By integrating a self-perturbation module, SPAGD generates diverse auxiliary time-series samples, effectively mitigating the class imbalance as well as providing rich auxiliary potential anomalous signals for training. An adaptive anomaly-aware graph construction method is proposed to dynamically adjust inter-variable correlations for evolving self-perturbed time series. We then train an anomaly detector to distinguish the normal time series from the self-perturbed ones by modeling both spatial and temporal dependencies. Through comprehensive experiments on several benchmark datasets compared to state-of-the-art TSAD methods, SPAGD consistently achieved competitive performance. The parameter analysis, visualization, and ablation study further justify the effectiveness of SPAGD. Despite these advances, SPAGD presumes a relatively homogeneous sensing landscape, which may not be applicable under highly heterogeneous streams [Shao et al., 2024; Jia et al., 2024; Liu et al., 2025a] with asynchronous sensors or weak inter-variable dependencies. Future work could explore heterogeneity-aware graph learning and domain-adaptive perturbation strategies to extend SPAGD to address heterogeneous problems.
+
+# Broader Impact Statement
+
+We provide the broader impact of our work from the following two aspects:
+
+- Positive social impacts: Our work has significant potential for enhancing the safety and reliability of critical cyber-physical systems. For instance, early anomaly detection can prevent catastrophic equipment failures, ensuring worker safety and preventing environmental damage. In aerospace applications, it can improve mission success and safety by flagging potential faults in spacecraft telemetry.  
+- Potential negative risks: (1) Over-reliance on the system could lead operators to dismiss their own expertise. Mitigation: We advocate for deploying SPAGD as a decision-support tool that provides interpretable outputs (e.g., highlighting anomalous sensors and their correlations) rather than as a fully autonomous system. (2) A sophisticated adversary could potentially craft inputs to either evade detection or trigger false alarms. Mitigation: This is a critical area for future work, focusing on improving the model's adversarial robustness.
+
+# Acknowledgement
+
+This research is supported by the National University of Singapore, Institute of Data Science. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of the National University of Singapore.
+
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+Bharadwaj Veeravalli, Chacko John Deepu, and DuyHoa Ngo. Real-time, personalized anomaly detection in streaming data for wearable healthcare devices. Handbook of Large-Scale Distributed Computing in Smart Healthcare, pages 403-426, 2017.
+
+Petar Velicković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. In Proceedings of the International Conference on Learning Representations, 2018.  
+Chengsen Wang, Zirui Zhuang, Qi Qi, Jingyu Wang, Xingyu Wang, Haifeng Sun, and Jianxin Liao. Drift doesn't matter: dynamic decomposition with diffusion reconstruction for unstable multivariate time series anomaly detection. Advances in Neural Information Processing Systems, 36:10758-10774, 2023.  
+Svante Wold, Kim Esbensen, and Paul Geladi. Principal component analysis. *Chemometrics and Intelligent Laboratory Systems*, 2(1-3):37-52, 1987.  
+Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. In Proceedings of the International Conference on Learning Representations, 2023.  
+Zhihao Wu, Zhao Zhang, and Jicong Fan. Graph convolutional kernel machine versus graph convolutional networks. Advances in Neural Information Processing Systems, 36:19650-19672, 2023.  
+Jiehui Xu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Anomaly transformer: Time series anomaly detection with association discrepancy. In Proceedings of the International Conference on Learning Representations, 2022.  
+Hongzuo Xu, Guansong Pang, Yijie Wang, and Yongjun Wang. Deep isolation forest for anomaly detection. IEEE Transactions on Knowledge and Data Engineering, 35(12):12591-12604, 2023.  
+Hongzuo Xu, Yijie Wang, Songlei Jian, Qing Liao, Yongjun Wang, and Guansong Pang. Calibrated one-class classification for unsupervised time series anomaly detection. IEEE Transactions on Knowledge and Data Engineering, 2024.  
+Yiyuan Yang, Chaoli Zhang, Tian Zhou, Qingsong Wen, and Liang Sun. Dcdetector: Dual attention contrastive representation learning for time series anomaly detection. In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pages 3033-3045, 2023.  
+Zahra Zamanzadeh Darban, Geoffrey I Webb, Shirui Pan, Charu Aggarwal, and Mahsa Salehi. Deep learning for time series anomaly detection: A survey. ACM Computing Surveys (CSUR), 57(1):1-42, 2024.  
+Weiqi Zhang, Chen Zhang, and Fugee Tsung. Grelen: Multivariate time series anomaly detection from the perspective of graph relational learning. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 2390-2397, 2022.  
+Kexin Zhang, Qingsong Wen, Chaoli Zhang, Rongyao Cai, Ming Jin, Yong Liu, James Y Zhang, Yuxuan Liang, Guansong Pang, Dongjin Song, et al. Self-supervised learning for time series analysis: Taxonomy, progress, and prospects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(10):6775-6794, 2024.  
+Yunhe Zhang, Yan Sun, Jinyu Cai, and Jicong Fan. Deep orthogonal hypersphere compression for anomaly detection. In Proceedings of the International Conference on Learning Representations, 2024.  
+Hang Zhao, Yujing Wang, Juanyong Duan, Congrui Huang, Defu Cao, Yunhai Tong, Bixiong Xu, Jing Bai, Jie Tong, and Qi Zhang. Multivariate time-series anomaly detection via graph attention network. In Proceedings of the IEEE International Conference on Data Mining, pages 841-850. IEEE, 2020.  
+Yu Zheng, Huan Yee Koh, Ming Jin, Lianhua Chi, Khoa T Phan, Shirui Pan, Yi-Ping Phoebe Chen, and Wei Xiang. Correlation-aware spatial-temporal graph learning for multivariate time-series anomaly detection. IEEE Transactions on Neural Networks and Learning Systems, 35(9):11802-11816, 2023.
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
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+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
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+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: The limitations of the work have been discussed in the conclusion.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
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+
+# 3. Theory assumptions and proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+Answer: [Yes]
+
+Justification: We have provided the relevant theoretical analysis of the proposed method in the Appendix.
+
+# Guidelines:
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+
+# 4. Experimental result reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+# Answer: [Yes]
+
+Justification: The paper has fully disclosed all the information needed to reproduce the main experimental results.
+
+# Guidelines:
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+- The answer NA means that the paper does not include experiments.  
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+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
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+
+# 6. Experimental setting/details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
+Justification: The paper has specified all the training and test details.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
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+
+# 7. Experiment statistical significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [Yes]
+
+Justification: This paper has conducted Student's t-test to demonstrate the statistical significance of the experiments.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
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+
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+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: The paper has provided sufficient information on the computer resources for each experiment.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code of ethics
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+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
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+
+# 10. Broader impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [Yes]
+
+Justification: We have properly discussed the societal impact of our work.
+
+Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.  
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
+
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+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: The paper poses no such risks.
+
+# Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
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+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
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+Answer: [Yes]
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+Justification: The creators or original owners of assets (e.g., code, data, models), used in the paper, are properly credited and the license and terms of use explicitly are mentioned and properly respected.
+
+# Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
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+
+# 13. New assets
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+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
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+Guidelines:
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+# 14. Crowdsourcing and research with human subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
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+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
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+
+# 15. Institutional review board (IRB) approvals or equivalent for research with human subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The paper does not involve crowdsourcing nor research with human subjects.
+
+Guidelines:
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+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
+
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+# 16. Declaration of LLM usage
+
+Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
+
+Answer: [NA]
+
+Justification: The core method development in this research does not involve LLMs as any important, original, or non-standard components.
+
+Guidelines:
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+- The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.  
+- Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) for what should or should not be described.

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+        "text": "Self-Supervised Direct Preference Optimization for Text-to-Image Diffusion Models",
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+        "text": "Liang Peng $^{1*}$  Boxi Wu $^{2*‡}$  Haoran Cheng $^{2*}$  Yibo Zhao $^{1,2}$  Xiaofei He $^{1,2}$",
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+        "text": "$^{1}$ FABU Inc.  $^{2}$ Zhejiang University",
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+        "text": "{pengliang, wuboxi, chenghaoran}@zju.edu.cn",
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+        "text": "Direct preference optimization (DPO) is an effective method for aligning generative models with human preferences and has been successfully applied to fine-tune text-to-image diffusion models. Its practical adoption, however, is hindered by a labor-intensive pipeline that first produces a large set of candidate images and then requires humans to rank them pairwise. We address this bottleneck with self-supervised direct preference optimization, a new paradigm that removes the need for any pre-generated images or manual ranking. During training, we create preference pairs on the fly through self-supervised image transformations, allowing the model to learn from fresh and diverse comparisons at every iteration. This online strategy eliminates costly data collection and annotation while remaining plug-and-play for any text-to-image diffusion method. Surprisingly, the on-the-fly pairs produced by the proposed method not only match but exceed the effectiveness of conventional DPO, which we attribute to the greater diversity of preferences sampled during training. Extensive experiments with Stable Diffusion 1.5 and Stable Diffusion XL confirm that our method delivers substantial gains.",
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+        "text": "1 Introduction",
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+        "text": "Text-to-image diffusion models [1, 2, 3, 4, 5, 6, 7, 8] have emerged as a dominant paradigm for high-quality image generation conditioned on natural language prompts. They have demonstrated the ability to synthesize diverse and visually appealing images across a wide range of prompts and styles. However, while these models are typically pretrained on large-scale datasets, they can fail to align with human preferences, especially in applications requiring text-image alignment or subjective aesthetic quality. To bridge this gap, recent works have explored preference-based post-training strategies that adjust the model's outputs based on human feedback.",
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+        "text": "One prominent method in this direction is Direct Preference Optimization (DPO) [9, 10], which trains generative models using pairwise human preference data. DPO has shown strong results in aligning text-to-image models with user intent. Nevertheless, its practical adoption is hindered by a costly and rigid training pipeline: it first requires the offline generation of a large set of image candidates, followed by extensive human annotation in the form of pairwise ranking. This process is not only time-consuming and expensive but also inflexible—once the ranking data is collected, it cannot easily adapt to new prompts or domains. Furthermore, the fixed nature of the dataset may limit the diversity of learning signals, potentially affecting generalization.",
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+        "text": "In this work, we present Self-Supervised Direct Preference Optimization (Self-DPO), a novel framework that eliminates the reliance on pre-generated images and manual rankings. Instead of requiring",
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+        "text": "*Equal contribution",
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+        "text": "$\\dagger$  Work was done at FABU Inc.",
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+        "type": "page_footnote",
+        "text": "$\\ddagger$  Corresponding author",
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+    {
+        "type": "footer",
+        "text": "39th Conference on Neural Information Processing Systems (NeurIPS 2025).",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/92cc8d046adc26c19241aaf21c8cee2da79d689a05d1c73045afc64ac4cc8c91.jpg",
+        "image_caption": [
+            "Figure 1: We propose Self-DPO, incorporating direct preference optimization in a self-supervised manner. We provide the comparisons on SDXL base model with the same seed. Our method requires less data, yet generate more visually appealing results. Best viewed in color with zoom in."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "img_path": "images/c0e6ef0f9d7fa64c4a9b0d224b52410c58cf1b77911adaa0c87eef415c384095.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "external preference data, our method constructs training pairs dynamically using self-supervised image transformations. During each training iteration, the model first identifies a \"winning image\" that satisfies human-aligned quality criteria. We then generate a corresponding \"losing image\" by intentionally degrading the winner, either through visual-quality reductions or text-image misalignment. The resulting win-lose pair supplies an immediate preference signal, allowing the model to perform online direct preference optimization. By learning from this continuous stream of synthetically generated preference pairs, Self-DPO achieves effective human alignment.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This self-supervised, on-the-fly approach brings several key advantages. It removes the need for costly pre-generated images and human ranking efforts, enables scalable and dynamic training, and introduces greater diversity into the preference supervision signal. We summarize the data requirements in Table 1. Remarkably, we find that Self-DPO not only matches but surpasses conventional DPO in both qualitative and quantitative metrics (e.g., boosting ImageReward win rate from 61 to 85). We provide some visualiza",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "tion results in Figure 1. Experiments on Stable Diffusion 1.5 [1] and XL [2] demonstrate consistent improvements in visual quality and text-image alignment. Our method is plug-and-play, generalizable across architectures, and easily integrable into existing diffusion model training pipelines.",
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+    {
+        "type": "table",
+        "img_path": "images/10123d480f5086041c5854b14d38ee78ba4e329eb4527a3462005b84bba2982c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Data requirements</td><td>SFT</td><td>Self-DPO</td><td>DPO</td></tr><tr><td>Text Caption</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Image</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Extra Preference Image</td><td>-</td><td>-</td><td>✓</td></tr></table>",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Post-training data requirements. Self-DPO shares the same data requirements as SFT [11]. DPO [10] requires extra preference images that are collected and annotated by humans, which is highly time-consuming and expensive.",
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+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "2.1 Text-to-Image Diffusion Models",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Text-to-image diffusion models have recently attracted significant attention in generative modeling due to their ability to produce high-quality and diverse images from textual descriptions. The introduction",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "text",
+        "text": "of Denoising Diffusion Probabilistic Models (DDPMs) [12, 13] marked a major breakthrough in this field, establishing diffusion models as a powerful generative approach. Diffusion models [12, 14, 15] operate by reversing a gradual diffusion process, where noise is incrementally added to the clean latent and then learned to be removed, ultimately synthesizing a coherent and realistic image/video. Building upon this foundation, diffusion models have become a representative paradigm in text-to-image generation, leading to models like GLIDE [16] for text-guided image editing, Imagen [17] with cascaded diffusion for high-resolution synthesis, and Stable Diffusion [1] using latent diffusion for efficient generation. To enhance image generation quality, researchers typically focus on two main directions. One approach involves architectural improvements, with the Diffusion Transformer (DiT) [3] gaining attention for its improved image fidelity, performance, and diversity. Notable advancements include PixArt-  $\\alpha$  [18], Hunyuan-DiT [19], and SD3 [4]. Another approach leverages supervised fine-tuning to refine text-to-image diffusion models. These methods curate datasets by integrating various strategies, such as preference models [2], pre-trained image models [20, 21, 22, 23, 24] (e.g., image captioning models), and expert-assisted data filtering [11].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 Preference-Based Optimization Methods",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In recent years, preference-based optimization has gained traction, refining models through user feedback or ranked preference pairs. In Large Language Models, Reinforcement Learning from Human Feedback (RLHF) leverages human comparisons to train a reward model that guides policy learning [25, 26]. Alternatively, direct preference optimization (DPO) fine-tunes models directly on preference data, bypassing the need for an explicit reward model while achieving comparable performance [9]. Subsequently, preference-based optimization has been applied to image generation. Some methods enhance image quality by increasing rewards for preferred outputs [27, 28, 29], while others use reinforcement learning [29, 30]. However, training reliable reward models remains challenging and computationally expensive, with over-optimization potentially leading to mode collapse, reducing diversity [31, 28]. Similarly, Direct Preference Optimization has been introduced in text-to-image generation, with Diffusion-DPO [10] demonstrating the effectiveness of optimizing on human comparison data to enhance both visual appeal and text alignment. Additionally, direct score preference optimization [32] refines diffusion models through score matching, providing a novel approach to preference learning. Several recent studies have further explored adapting preference learning techniques from large language models to fine-tune diffusion models [33, 34? , 35], highlighting the growing interest in aligning generative models with human preferences.",
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+    },
+    {
+        "type": "text",
+        "text": "2.3 Self-Supervised Learning",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Self-supervised learning has emerged as a pivotal paradigm in machine learning. Among its most widely used approaches are contrastive self-supervised learning and generative self-supervised learning. Contrastive self-supervised learning distinguishes representations by pulling similar instances closer while pushing dissimilar ones apart. MoCo [36] enhances training efficiency through a momentum encoder, while SimCLR [37] simplifies the process with strong data augmentations. CLIP [38] extends contrastive learning to vision-language tasks, aligning images and text in a shared latent space, enabling zero-shot transfer. Generative approaches inherently follow unsupervised or self-supervised learning principles, training without labeled data to model the underlying distributions of the input. GANs [39] utilize adversarial training to generate realistic data, while VAEs [40] encode data into a structured latent space for controlled synthesis. VQ-VAE [41] introduces discrete latent representations for high-quality generation. MAE [42] leverages masked image modeling to learn rich visual features. More recently, denoising diffusion models [13] have demonstrated impressive results by iteratively adding and removing noise, learning robust representations in a self-supervised manner. Self-supervised learning enables training without manually labeled data, laying the foundation for future advancements in representation learning, generative modeling, and multimodal understanding.",
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+    {
+        "type": "text",
+        "text": "3 Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 Preliminary",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Diffusion Models. Denoising Diffusion Probabilistic Models [13] represent the image generation process as a Markovian process. Let  $\\pmb{x}_0 \\in \\mathbb{R}^d$  be the data point and  $q(\\pmb{x}_t | \\pmb{x}_{t-1})$  denote the forward",
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+    {
+        "type": "page_number",
+        "text": "3",
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+    {
+        "type": "text",
+        "text": "process, where noise is added to the data at each timestep  $t$ . The forward process is defined as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1}, \\beta_ {t} \\mathbb {I}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\beta_{t}$  is a schedule that controls the variance of noise added at each timestep, and  $\\mathcal{N}(\\cdot)$  denotes the normal distribution. The forward process gradually adds noise, with  $x_{T}$  being pure noise after  $T$  timesteps. The reverse process aims to learn the distribution  $p_{\\theta}(\\boldsymbol{x}_{t-1}|\\boldsymbol{x}_t)$ , which represents the process of denoising and generating data from pure noise. The reverse process can be parameterized as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} \\mid \\boldsymbol {x} _ {t}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right), \\Sigma_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right)\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "where  $\\mu_{\\theta}(\\pmb{x}_t,t)$  and  $\\Sigma_{\\theta}(\\pmb{x}_t,t)$  are the mean and covariance learned by the model at each timestep  $t$ . The model is trained by minimizing the following objective:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {t, \\boldsymbol {x} _ {0}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} \\right], \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\epsilon$  is the noise added at each timestep, and  $\\epsilon_{\\theta}(\\boldsymbol{x}_t,t)$  is the model's predicted noise. The model is trained to predict this noise accurately at each step, enabling it to reverse the diffusion process and generate high-quality data.",
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+    {
+        "type": "text",
+        "text": "Reinforcement Learning from Human Feedback. For diffusion models, human preferences at each diffusion step are modeled using a Bradley-Terry formulation [43], where the probability of preferring a \"winning\" sample  $\\boldsymbol{x}_t^w$  over a \"losing\" sample  $\\boldsymbol{x}_t^l$  for a given prompt  $c$  is defined as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\mathrm {B T}} \\left(\\boldsymbol {x} _ {t} ^ {w} \\succ \\boldsymbol {x} _ {t} ^ {l} \\mid \\boldsymbol {c}\\right) = \\sigma \\left(r \\left(\\boldsymbol {c}, \\boldsymbol {x} _ {t} ^ {w}\\right) - r \\left(\\boldsymbol {c}, \\boldsymbol {x} _ {t} ^ {l}\\right)\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with  $\\sigma, r, c$  representing the sigmoid function, reward model, and prompt, respectively. Subsequently, by conceptualizing the diffusion denoising process as a multi-step Markov Decision Process, the generative model is fine-tuned via reinforcement learning. The training objective [10, 44] is formulated as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r l h f}} = \\mathbb {E} _ {\\boldsymbol {c} \\sim D} \\mathbb {E} _ {p _ {\\theta} (\\boldsymbol {x} _ {0: T} | \\boldsymbol {c})} \\sum_ {t = 0} ^ {T - 1} r (\\boldsymbol {c}, \\boldsymbol {x} _ {t}) - \\lambda \\mathbb {D} _ {\\mathrm {K L}} \\left(p _ {\\theta} (\\boldsymbol {x} _ {0: T} | \\boldsymbol {c}) \\| p _ {\\text {r e f}} (\\boldsymbol {x} _ {0: T} | \\boldsymbol {c})\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $p_{\\mathrm{ref}}(\\pmb{x}_{0:T}|\\pmb{c})$  is the distribution from the pretrained diffusion model and  $\\lambda$  controls the influence of the KL divergence regularization term.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Direct Preference Optimization (DPO). DPO streamlines RLHF by using the learning policy's log likelihood to implicitly encode the reward. In text-to-image diffusion models, this leads to a step-wise reward defined as:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr (\\boldsymbol {c}, \\boldsymbol {x} _ {t}) = \\lambda \\log \\frac {p _ {\\theta} \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t + 1} , \\boldsymbol {c}\\right)}{p _ {\\text {r e f}} \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t + 1} , \\boldsymbol {c}\\right)}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Recent works [10, 32] follow this line and adapt it to diffusion models. They optimize the model  $p_{\\theta}$  based on the Bradley-Terry model [43], leading to an objective function:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {D i f f u s i o n - D P O}} = - \\mathbb {E} \\left[ \\log \\sigma \\left(\\lambda \\log \\frac {p _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {w} \\mid \\boldsymbol {x} _ {t + 1} ^ {w} , \\boldsymbol {c}\\right)}{p _ {\\text {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {w} \\mid \\boldsymbol {x} _ {t + 1} ^ {w} , \\boldsymbol {c}\\right)} - \\lambda \\log \\frac {p _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {l} \\mid \\boldsymbol {x} _ {t + 1} ^ {l} , \\boldsymbol {c}\\right)}{p _ {\\text {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {l} \\mid \\boldsymbol {x} _ {t + 1} ^ {l} , \\boldsymbol {c}\\right)}\\right) \\right], \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the winning and losing samples  $(\\pmb{x}_t^w, \\pmb{x}_t^l)$  and the prompt  $\\pmb{c}$  are drawn from the dataset, and timestep  $t$  is uniformly sampled from the diffusion process. This formulation effectively aligns the learning policy with human preference signals embedded in the reference model.",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 Self-DPO for Text-to-image Diffusion Models",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Inspired by DPO's effective alignment with human preferences at the image level [10], our work aims to extend this formulation into the standard post-training process for diffusion models (e.g., SFT). Unfortunately, a direct application of DPO is not feasible because it requires collecting image pairs (typically generated by different models with the same prompt or by using different seeds with the same model—along with their associated manual rankings). This approach does not align with the conventional fine-tuning pipeline and incurs significant additional costs. To overcome this limitation, we propose Self-DPO, which generates preference image pairs in a self-supervised manner.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In each training iteration, we denote the text-image pair as  $(c, x)$ , where the image component is regarded as the wining image  $x^w$ . Traditional DPO methods [10, 9] require generating image pairs corresponding to the same prompt, followed by manual selection of the preferred (winning) and less preferred (losing) images, denoted as  $x^w$  and  $x^l$ , respectively. Our method removes such cumbersome",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4693b2bc53110e83e66a8b4e00d5c481e6e2505ba47508081e0958244249d937.jpg",
+        "image_caption": [
+            "Figure 2: Different post-training processes. We generate the \"losing\" images self-supervisedly, enabling direct preference optimization without extra collecting and ranking steps. This lightweight procedure eliminates the substantial overhead of conventional DPO while retaining the same data requirements as standard SFT. Best viewed in color with zoom in."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/17435a36b6a3914a873757a29f882fef78dd42c958e1fee64b5480146822bbcf.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            333,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/44892986196040f9b73dc47af0629d5ad226251946a2cda27f7884859269d48c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "steps. Because every image in the curated high-quality dataset already satisfies human preference, each can be regarded as a winner  $\\pmb{x}^w$ . We obtain a corresponding self-supervised losing sample by deliberately degrading the winner:  $\\pmb{x}^{sl} = \\mathbf{Downgrade}(\\pmb{x}^w)$ . Inspired by [10], the self-supervised direct preference loss is:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {S e l f - D P O}} = - \\log \\sigma \\left(C \\left(\\left\\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) - \\boldsymbol {\\epsilon} ^ {w} \\right\\| _ {2} ^ {2} - \\left\\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {s l}, t\\right) - \\boldsymbol {\\epsilon} ^ {s l} \\right\\| _ {2} ^ {2}\\right) \\right. \\\\ \\left. - \\left(\\| \\boldsymbol {\\epsilon} _ {\\mathrm {r e f}} (\\boldsymbol {x} _ {t} ^ {w}, t) - \\boldsymbol {\\epsilon} ^ {w} \\| _ {2} ^ {2} - \\| \\boldsymbol {\\epsilon} _ {\\mathrm {r e f}} (\\boldsymbol {x} _ {t} ^ {s l}, t) - \\boldsymbol {\\epsilon} ^ {s l} \\| _ {2} ^ {2}\\right)\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw h e r e \\quad \\boldsymbol {x} ^ {s l} = \\text {D o w n g r a d e} (\\boldsymbol {x} ^ {w}) \\tag {8}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $C$  and  $\\epsilon^{sl}$  refer to a scale factor and the noise corresponding to losing images, and  $\\epsilon_{\\mathrm{ref}}$  is the reference model. In our experiments, the Downgrade operation can be simply performed by randomly selecting images from the training dataset. For each self-generated image pair, the winning sample closely aligns with the prompt, whereas the losing sample fails to correspond to the description. Surprisingly, this simple manner brings significant improvements to the model. We also compare different degradation strategies in the experiments. The training process overview is shown in Figure 2. The final loss is as follows:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\mathrm {M S E}} + \\lambda_ {2} \\mathcal {L} _ {\\text {S e l f - D P O}} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We empirically set  $\\lambda_{1}$  and  $\\lambda_{2}$  to 0.5, 0.5, respectively.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Setup",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Implement Details: Following Diffusion-DPO [10], for the SD1.5 [1] experiments, AdamW [47] is utilized, while SDXL [2] training is conducted with Adafactor [48] to conserve memory. Following the official implementation in Diffusion-DPO [10],  $C$  in Equation 8 is set to  $-2500$ . For SD 1.5, a batch size of 2048 pairs (resolution:  $512*512$ ) is maintained by training across 4 NVIDIA A100 GPU. Each GPU handles 8 pairs locally with gradient accumulation",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/54544e0c741186cadd96f508e61833ef677539959116bc9a59121c9092085e8a.jpg",
+        "image_caption": [
+            "Figure 5: Implicit accuracy during the training stage."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/b9ed0b5c07523ab21b529ce39ade470715cd1270a7680daf36c78c3bb0a268d7.jpg",
+        "image_caption": [
+            "Figure 3: Qualitative comparisons with the SD1.5 base model. All results are generated with the same random seed. Comparing with SFT and DPO [10], the model trained by Self-DPO demonstrates superior text prompt alignment. It also shows more appealing visual quality, especially in layout, colors, and details. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "over 64 steps. For SDXL, considering the resource limitation, we use the total batch size of 96 pairs (resolution:  $1024 \\times 1024$ ). Training is performed at fixed square resolutions. We use a learning rate of 1e-6 coupled with a  $25\\%$  linear warmup.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Training Dataset: Our training data is sourced from the Pick-a-Pic V2 dataset[45], which keeps the same to Diffusion-DPO [10]. It contains pairwise preference annotations for images generated by Dreamlike (a fine-tuned variant of SD1.5), SD2.1, and SDXL. These prompts and preferences were collected from users of the Pick-a-Pic web application. Please note that Self-DPO only uses the preference image and associated text in the dataset, instead of using the whole manually annotated image pairs.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation: We conduct evaluation on three datasets: Pick-a-Pic V2 [45] validation set (contains 500 prompts), PartiPrompts [46] (contains 1632 prompts, including diverse categories and challenge aspects), and HPDv2 [24] (contains 3200 prompts, including anime, concept art, paintings and photo). We compare Self-DPO with three different type baselines, i.e., base models (Stable Diffusion 1.5 (SD1.5) and Stable Diffusion XL (SDXL)), SFT models, DPO models, where DPO models are the",
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+    },
+    {
+        "type": "page_number",
+        "text": "6",
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+    },
+    {
+        "type": "text",
+        "text": "a marine iguana on a surfboard",
+        "bbox": [
+            192,
+            419,
+            334,
+            429
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c3c26484fb23bf2b4a15dd62c1834aeda4400fdea43b007052db0dd55edb9668.jpg",
+        "image_caption": [
+            "Prints, Ink, Paper, Relief prints, Woodblock prints, Printing books, Wood blocks, Asia, Japan, ca. 1853, Japan, Polyhrome woodblock print; ink and color on paper, Metropolitan Museum of Art",
+            "Harry potter as a cat, pixar style, octane render, HD, high-detail",
+            "Cadillac EIDorado de style Badass Steampunk dans une vieille rue pavée, trending on artstation, sharp focus, studio photo, intricate details, highly detailed, by greg rutkowski",
+            "character sheet, The little girl riding an electric scooter bike, in a beautiful anime scene by Hayao Miyazaki: a snowy Tokyo city with massive Miyazaki clouds floating in the blue sky, enchanting snowscapes of the city with bright sunlight. Miyazaki's landscape imagery, Japanese art, 16:9",
+            "Figure 4: Qualitative comparisons with the SDXL base model. All results are generated using the same random seed. Please note that the training dataset (Pick-a-Pic V2 [45]) used for fine-tuning is obtained from a SD1.5 variant, SD2.1, and SDXL models. Consequently, directly fine-tuning (SFT) on this dataset does not lead to improvements—and may even result in degraded performance (e.g., as shown in the second row). In contrast, DPO [10] optimizes the model by leveraging preference relationships with pre-ranked pairs, thereby avoiding this issue. Self-DPO uses the same data requirements as SFT but yields significant improvements in both text prompt alignment and visual quality, demonstrating its effectiveness. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            339,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "publicly released from Diffusion-DPO [10]. For evaluation metrics, we employ the popular PickScore [45], Aesthetics [49], CLIP [38], HPS V2 [24], and ImageAward [50] scores. For convenience of comparison, we scale the scores to fit a similar range ( $\\times 100$  for PickScore, CLIP, HPS, and ImageAward,  $\\times 10$  for Aesthetics). PickScore is a caption-sensitive scoring model, originally trained on Pick-a-Pic (v1), that estimates the perceived image quality by humans. Aesthetics assesses the visual appeal of an image, considering factors such as lighting, color harmony, composition, and overall artistic quality. CLIP measures the semantic alignment between an image and a corresponding text prompt. By computing the cosine similarity between the image and text embeddings, this score evaluates how well the image content matches the provided textual description. Human Preference Score (HPS V2) is a metric designed to align with human judgments of image quality, particularly in the context of text-to-image synthesis. ImageAward quantifies the quality, aesthetic appeal, or alignment of a generated image with respect to desired attributes. It is typically derived from a reward model trained on human preference data.",
+        "bbox": [
+            169,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/6ec50fbaa2df1c678f51c29712ab16ba1192a03c47850244f59ebab18b2faebc.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 2: Quantitative comparisons. We compare different fine-tuning methods (SFT, DPO [10], and Self-DPO) on SD 1.5 and SDXL base models over three datasets (Pick-a-Pic V2 [45], PartiPrompts [46], and HPDv2 [24]). \"P.S.\" refers to PickScore, \"Aes.\" is Aesthetics, and \"I.R.\" denotes ImageAward. For the SD1.5 base model, our method achieves the best performance across most metrics. In contrast, for the SDXL base model, we observe that SFT clearly degrades performance. This is likely due to the fact that the training dataset (Pick-a-pic V2 [45]) used for fine-tuning is derived from SD1.5 variant, SD2.1, and SDXL models. Interestingly, our method still achieves competitive results compared to DPO, which utilizes the full dataset and optimizes the model by leveraging preference relationships with pre-ranked pairs. These results underscore the effectiveness and robustness of our approach."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Datasets</td><td rowspan=\"2\" colspan=\"2\">Methods</td><td colspan=\"5\">SD1.5</td><td colspan=\"5\">SDXL</td></tr><tr><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td rowspan=\"7\">Pick-a-Pic V2</td><td>Base</td><td rowspan=\"4\">Avg score</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td><td>22.10</td><td>60.01</td><td>35.86</td><td>26.83</td><td>50.62</td></tr><tr><td>SFT</td><td>21.10</td><td>56.35</td><td>33.75</td><td>27.03</td><td>45.03</td><td>21.48</td><td>57.84</td><td>35.67</td><td>26.67</td><td>30.89</td></tr><tr><td>DPO</td><td>20.91</td><td>54.07</td><td>33.19</td><td>26.46</td><td>4.13</td><td>22.57</td><td>59.93</td><td>37.30</td><td>27.30</td><td>81.14</td></tr><tr><td>Self-DPO</td><td>21.23</td><td>56.35</td><td>34.79</td><td>27.33</td><td>71.00</td><td>22.34</td><td>59.97</td><td>37.53</td><td>27.89</td><td>103.96</td></tr><tr><td>SFT</td><td rowspan=\"3\">Win rate</td><td>75.00</td><td>77.20</td><td>60.40</td><td>90.20</td><td>80.00</td><td>19.40</td><td>31.80</td><td>47.00</td><td>44.60</td><td>42.4</td></tr><tr><td>DPO</td><td>73.80</td><td>60.00</td><td>60.00</td><td>71.80</td><td>61.00</td><td>72.60</td><td>47.20</td><td>63.00</td><td>79.80</td><td>69.8</td></tr><tr><td>Self-DPO</td><td>78.60</td><td>77.80</td><td>68.40</td><td>94.20</td><td>85.20</td><td>60.80</td><td>50.80</td><td>62.40</td><td>93.80</td><td>79.2</td></tr><tr><td rowspan=\"7\">PartiPrompts</td><td>Base</td><td rowspan=\"4\">Avg score</td><td>21.39</td><td>53.13</td><td>33.21</td><td>26.79</td><td>1.48</td><td>22.63</td><td>57.69</td><td>35.77</td><td>27.33</td><td>69.78</td></tr><tr><td>SFT</td><td>21.75</td><td>55.31</td><td>33.93</td><td>27.57</td><td>50.75</td><td>22.02</td><td>56.41</td><td>35.31</td><td>27.13</td><td>47.29</td></tr><tr><td>DPO</td><td>21.61</td><td>53.58</td><td>33.88</td><td>26.98</td><td>21.43</td><td>22.90</td><td>57.85</td><td>36.95</td><td>27.73</td><td>103.36</td></tr><tr><td>Self-DPO</td><td>21.84</td><td>55.09</td><td>35.11</td><td>27.84</td><td>75.66</td><td>22.79</td><td>58.69</td><td>37.00</td><td>28.30</td><td>117.50</td></tr><tr><td>SFT</td><td rowspan=\"3\">Win rate</td><td>67.28</td><td>70.89</td><td>53.43</td><td>85.42</td><td>73.35</td><td>21.38</td><td>38.11</td><td>45.10</td><td>43.75</td><td>40.93</td></tr><tr><td>DPO</td><td>67.10</td><td>57.17</td><td>56.74</td><td>61.83</td><td>63.05</td><td>63.42</td><td>53.62</td><td>62.32</td><td>73.10</td><td>68.44</td></tr><tr><td>Self-DPO</td><td>69.85</td><td>68.50</td><td>63.24</td><td>89.40</td><td>81.00</td><td>56.19</td><td>60.48</td><td>60.17</td><td>92.16</td><td>76.84</td></tr><tr><td rowspan=\"7\">HPD V2</td><td>Base</td><td rowspan=\"4\">Avg score</td><td>20.84</td><td>54.32</td><td>33.96</td><td>26.84</td><td>-11.79</td><td>22.78</td><td>61.34</td><td>37.68</td><td>27.68</td><td>78.27</td></tr><tr><td>SFT</td><td>21.57</td><td>57.41</td><td>35.26</td><td>27.89</td><td>57.74</td><td>22.24</td><td>60.08</td><td>37.39</td><td>27.76</td><td>66.62</td></tr><tr><td>DPO</td><td>21.30</td><td>55.80</td><td>34.68</td><td>27.22</td><td>13.24</td><td>23.18</td><td>61.35</td><td>38.45</td><td>28.14</td><td>102.74</td></tr><tr><td>Self-DPO</td><td>21.58</td><td>57.10</td><td>36.30</td><td>28.11</td><td>76.13</td><td>22.98</td><td>61.30</td><td>38.35</td><td>28.77</td><td>110.67</td></tr><tr><td>SFT</td><td rowspan=\"3\">Win rate</td><td>79.53</td><td>75.31</td><td>59.34</td><td>90.10</td><td>81.16</td><td>23.47</td><td>37.28</td><td>46.63</td><td>58.22</td><td>45.81</td></tr><tr><td>DPO</td><td>75.72</td><td>66.28</td><td>57.56</td><td>72.43</td><td>64.69</td><td>72.66</td><td>50.28</td><td>58.69</td><td>80.56</td><td>69.78</td></tr><tr><td>Self-DPO</td><td>79.53</td><td>74.03</td><td>68.47</td><td>92.49</td><td>85.19</td><td>58.78</td><td>48.06</td><td>55.65</td><td>94.97</td><td>72.50</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 Quantitative Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We provide quantitative comparisons in Table 2. We compare our method with SFT and DPO [10]. For the SD1.5 base model, our method significantly outperforms the alternatives. For example, Self-DPO achieves a CLIP score of 34.79 on the Pick-a-Pic V2 dataset—an improvement of +2.21 over the base model—whereas SFT and DPO yield improvements of +1.17 and +0.61, respectively. In terms of overall human preference metrics, Self-DPO delivers substantially higher gains, improving the base model from -14.81 to 71.00 on the ImageReward metric, which far exceeds the improvements observed with SFT (45.03) and DPO (4.13).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Notably, the win rate of Self-DPO reaches 94.20 on the HPS metric. Results on other datasets (PartiPrompts and HPD v2) further confirm these improvements. In contrast, results on the SDXL base model show a slightly different scenario, particularly with SFT. We observe that SFT substantially degrades the performance of the base model. This degradation is likely due to the",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/28e0277d4c052705c457dcd3c456a5e4dd78c549c4c8114c5ee842ea1c785a0b.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3: Ablation on different downgrade manners. The \"Random image\" row achieves most significant improvements, implying that degrading the image quality can be detrimental."
+        ],
+        "table_body": "<table><tr><td>Methods</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td>Base model</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td></tr><tr><td>DPO</td><td>20.91</td><td>54.07</td><td>33.19</td><td>26.46</td><td>4.13</td></tr><tr><td>w/ Blur</td><td>20.80</td><td>55.16</td><td>33.22</td><td>26.57</td><td>4.26</td></tr><tr><td>w/ Random grid</td><td>20.85</td><td>55.86</td><td>32.71</td><td>26.64</td><td>24.21</td></tr><tr><td>w/ Random image</td><td>21.23</td><td>56.35</td><td>34.79</td><td>27.33</td><td>71.00</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "fact that, while the training dataset (comprising generations from an SD1.5 variant, SD2.1, and SDXL) is of much higher quality than that used for SD1.5, it does not exhibit clear superiority for SDXL. Nevertheless, the model trained by Self-DPO still demonstrates significantly better performance compared to both SFT and the base model. On the PickScore, Aesthetics, and CLIP metrics, Self-DPO achieves results comparable to DPO, and it attains superior scores on the HPS and ImageRe",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ward metrics. These findings validate our hypothesis that image-level learning benefits text-to-image diffusion models and highlight the superiority of Self-DPO. We also employ UnifiedReward [51] as the VLM evaluation metric, a state-of-the-art reward model designed for multimodal understanding and generation tasks. Built upon strong VLM models [52, 53, 54, 55], it supports pointwise scoring to align model outputs with human preferences. The results are shown in Table 4.4. We further validate our method's effectiveness by using a new real-world T2I evaluation setting. Specifically, we conduct experiments on a subset of the LAION-COCO dataset containing  $400\\mathrm{k}$  text-image pairs. Unlike carefully curated datasets, we do not manually design the data distribution or employ re-captioning techniques to refine prompts. The results are shown in Table 4.4. While naive SFT degrades performance, our Self-DPO method achieves consistent improvements. Please note that we cannot provide a DPO baseline as it requires additional paired images and annotations for the same prompts, which are not available in regular text-image dataset.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3 Qualitative Results",
+        "text_level": 1,
+        "bbox": [
+            171,
+            273,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We provide qualitative comparisons in Figure 3 and Figure 4 for SD1.5 and SDXL, respectively. All quantitative and qualitative results are generated using the same random seed. We observe that Self-DPO consistently improves over other models, particularly in terms of producing more vivid colors and better adherence to text prompts. For example, in the third row of Figure 3, only Self-DPO successfully reveals the concept \"cyberpunk\". In the fourth row of Figure 4, both DPO and Self-DPO capture the intended meaning of the prompt, but Self-DPO exhibits a more appealing visual quality. These quantitative and qualitative results confirm the effectiveness of our approach. We show the implicit win rate to measure the optimization process in Figure 5. Specifically, the implicit win rate during training refers to the probability that the model prefers the winning image over the losing image. In other words, a higher implicit win rate indicates a stronger preference for the winning image. As training progresses, it steadily increases and eventually reaches around 0.85. This demonstrates that the model gradually learns to distinguish between the winning and losing images, and prefers to generate the winning image.",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4 Ablation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We conduct ablation studies on various downgrade approaches, as shown in Table 3. In particular, we examine two additional methods—namely, blur (which involves downsampling and upsampling the image by a factor of 4) and random grid (which divides the image into an  $8 \\times 8$  grid and randomly swaps two grids). We observe that these two down",
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+        "table_footnote": [
+            "Table 4: Ablation on MSE loss. When removing MSE loss, Self-DPO still shows comparable performance and demonstrates the superiority to DPO."
+        ],
+        "table_body": "<table><tr><td>Methods</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td>Base model</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td></tr><tr><td>DPO</td><td>20.91</td><td>54.07</td><td>33.19</td><td>26.46</td><td>4.13</td></tr><tr><td>Self-DPO w/o MSE</td><td>21.26</td><td>56.22</td><td>35.00</td><td>27.31</td><td>67.78</td></tr><tr><td>Self-DPO</td><td>21.23</td><td>56.35</td><td>34.79</td><td>27.33</td><td>71.00</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "grade methods lead to worse performance, indicating that significantly degraded image quality can be harmful. Additionally, we remove the MSE loss and report the results in Table 4. Interestingly, the performance does not drop noticeably and consistently perform better than DPO, further confirming the effectiveness of Self-DPO.",
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+        "table_body": "<table><tr><td>Methods</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td>Base</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td></tr><tr><td>SFT</td><td>20.49</td><td>52.63</td><td>31.83</td><td>26.13</td><td>-23.95</td></tr><tr><td>Self-DPO</td><td>20.68</td><td>52.87</td><td>34.31</td><td>26.52</td><td>17.11</td></tr></table>",
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+        "table_caption": [
+            "Table 5: Results on a real-world image-text dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Base model</td><td>Base</td><td>SFT</td><td>DPO</td><td>Self-DPO</td></tr><tr><td>SD1.5</td><td>2.44</td><td>2.62</td><td>2.53</td><td>2.72</td></tr><tr><td>SDXL</td><td>2.96</td><td>2.73</td><td>3.10</td><td>3.07</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 6: Comparisons on UnifiedReward.",
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+    {
+        "type": "text",
+        "text": "5 Limitation and Future Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In the present implementation, we construct losing samples by randomly sampling images from the training set. This manner can become unreliable when the dataset is small, as the resulting",
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+    {
+        "type": "page_number",
+        "text": "9",
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+    {
+        "type": "text",
+        "text": "losers may fail to provide sufficiently informative preference signals. Future work therefore can explore more sophisticated self-supervised strategies for synthesizing losing images, such as more content-aware perturbations or adversarial degradations that better challenge the model. Furthermore, our approach is built on direct preference optimization, which is an offline reinforcement-learning paradigm. Extending the self-supervised pairing concept to online policy-gradient or actor-critic frameworks represents another promising direction.",
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+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose Self-Supervised Direct Preference Optimization (Self-DPO), a fully self-supervised framework that aligns generative models with human preferences without requiring pre-generated image pools or manual rankings. By synthesizing win-lose pairs on the fly, Self-DPO not only removes costly data-collection steps but also exposes the model to a broader and more diverse set of preference signals. At every training iteration, it constructs its own preference pairs through controlled degradations of high-quality images and immediately updates the model via preference learning. Extensive experiments across multiple datasets and base architectures demonstrate that Self-DPO consistently delivers superior performance, validating its effectiveness and versatility.",
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+    {
+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This research was supported by The National Nature Science Foundation of China (Grant Nos: 62402417, 62273302, 62036009, 61936006), in part by the Key R&D Program of Ningbo (Grant Nos: 2024Z115, 2025Z035), in part by Yongjiang Talent Introduction Programme (Grant No: 2023A-197-G).",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            173,
+            460,
+            267,
+            474
+        ],
+        "page_idx": 9
+    },
+    {
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+        "sub_type": "ref_text",
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+        ],
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+        "type": "page_number",
+        "text": "13",
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+    {
+        "type": "text",
+        "text": "NeurIPS Paper Checklist",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "1. Claims",
+        "text_level": 1,
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?",
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+    {
+        "type": "text",
+        "text": "Answer: [Yes]",
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+    {
+        "type": "text",
+        "text": "2. Limitations",
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+    {
+        "type": "text",
+        "text": "Question: Does the paper discuss the limitations of the work performed by the authors?",
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+    {
+        "type": "text",
+        "text": "Answer: [Yes]",
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+    {
+        "type": "text",
+        "text": "3. Theory assumptions and proofs",
+        "text_level": 1,
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?",
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+        "type": "text",
+        "text": "Answer: [Yes]",
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+    {
+        "type": "text",
+        "text": "4. Experimental result reproducibility",
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2025/Self-Supervised Direct Preference Optimization for Text-to-Image Diffusion Models/25616841-9137-4baa-b910-a3a7e0f6a858_origin.pdf

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2025/Self-Supervised Direct Preference Optimization for Text-to-Image Diffusion Models/full.md

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+# Self-Supervised Direct Preference Optimization for Text-to-Image Diffusion Models
+
+Liang Peng $^{1*}$  Boxi Wu $^{2*‡}$  Haoran Cheng $^{2*}$  Yibo Zhao $^{1,2}$  Xiaofei He $^{1,2}$
+
+$^{1}$ FABU Inc.  $^{2}$ Zhejiang University
+
+{pengliang, wuboxi, chenghaoran}@zju.edu.cn
+
+# Abstract
+
+Direct preference optimization (DPO) is an effective method for aligning generative models with human preferences and has been successfully applied to fine-tune text-to-image diffusion models. Its practical adoption, however, is hindered by a labor-intensive pipeline that first produces a large set of candidate images and then requires humans to rank them pairwise. We address this bottleneck with self-supervised direct preference optimization, a new paradigm that removes the need for any pre-generated images or manual ranking. During training, we create preference pairs on the fly through self-supervised image transformations, allowing the model to learn from fresh and diverse comparisons at every iteration. This online strategy eliminates costly data collection and annotation while remaining plug-and-play for any text-to-image diffusion method. Surprisingly, the on-the-fly pairs produced by the proposed method not only match but exceed the effectiveness of conventional DPO, which we attribute to the greater diversity of preferences sampled during training. Extensive experiments with Stable Diffusion 1.5 and Stable Diffusion XL confirm that our method delivers substantial gains.
+
+# 1 Introduction
+
+Text-to-image diffusion models [1, 2, 3, 4, 5, 6, 7, 8] have emerged as a dominant paradigm for high-quality image generation conditioned on natural language prompts. They have demonstrated the ability to synthesize diverse and visually appealing images across a wide range of prompts and styles. However, while these models are typically pretrained on large-scale datasets, they can fail to align with human preferences, especially in applications requiring text-image alignment or subjective aesthetic quality. To bridge this gap, recent works have explored preference-based post-training strategies that adjust the model's outputs based on human feedback.
+
+One prominent method in this direction is Direct Preference Optimization (DPO) [9, 10], which trains generative models using pairwise human preference data. DPO has shown strong results in aligning text-to-image models with user intent. Nevertheless, its practical adoption is hindered by a costly and rigid training pipeline: it first requires the offline generation of a large set of image candidates, followed by extensive human annotation in the form of pairwise ranking. This process is not only time-consuming and expensive but also inflexible—once the ranking data is collected, it cannot easily adapt to new prompts or domains. Furthermore, the fixed nature of the dataset may limit the diversity of learning signals, potentially affecting generalization.
+
+In this work, we present Self-Supervised Direct Preference Optimization (Self-DPO), a novel framework that eliminates the reliance on pre-generated images and manual rankings. Instead of requiring
+
+![](images/92cc8d046adc26c19241aaf21c8cee2da79d689a05d1c73045afc64ac4cc8c91.jpg)  
+Figure 1: We propose Self-DPO, incorporating direct preference optimization in a self-supervised manner. We provide the comparisons on SDXL base model with the same seed. Our method requires less data, yet generate more visually appealing results. Best viewed in color with zoom in.
+
+![](images/c0e6ef0f9d7fa64c4a9b0d224b52410c58cf1b77911adaa0c87eef415c384095.jpg)
+
+external preference data, our method constructs training pairs dynamically using self-supervised image transformations. During each training iteration, the model first identifies a "winning image" that satisfies human-aligned quality criteria. We then generate a corresponding "losing image" by intentionally degrading the winner, either through visual-quality reductions or text-image misalignment. The resulting win-lose pair supplies an immediate preference signal, allowing the model to perform online direct preference optimization. By learning from this continuous stream of synthetically generated preference pairs, Self-DPO achieves effective human alignment.
+
+This self-supervised, on-the-fly approach brings several key advantages. It removes the need for costly pre-generated images and human ranking efforts, enables scalable and dynamic training, and introduces greater diversity into the preference supervision signal. We summarize the data requirements in Table 1. Remarkably, we find that Self-DPO not only matches but surpasses conventional DPO in both qualitative and quantitative metrics (e.g., boosting ImageReward win rate from 61 to 85). We provide some visualiza
+
+tion results in Figure 1. Experiments on Stable Diffusion 1.5 [1] and XL [2] demonstrate consistent improvements in visual quality and text-image alignment. Our method is plug-and-play, generalizable across architectures, and easily integrable into existing diffusion model training pipelines.
+
+<table><tr><td>Data requirements</td><td>SFT</td><td>Self-DPO</td><td>DPO</td></tr><tr><td>Text Caption</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Image</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Extra Preference Image</td><td>-</td><td>-</td><td>✓</td></tr></table>
+
+Table 1: Post-training data requirements. Self-DPO shares the same data requirements as SFT [11]. DPO [10] requires extra preference images that are collected and annotated by humans, which is highly time-consuming and expensive.
+
+# 2 Related Work
+
+# 2.1 Text-to-Image Diffusion Models
+
+Text-to-image diffusion models have recently attracted significant attention in generative modeling due to their ability to produce high-quality and diverse images from textual descriptions. The introduction
+
+of Denoising Diffusion Probabilistic Models (DDPMs) [12, 13] marked a major breakthrough in this field, establishing diffusion models as a powerful generative approach. Diffusion models [12, 14, 15] operate by reversing a gradual diffusion process, where noise is incrementally added to the clean latent and then learned to be removed, ultimately synthesizing a coherent and realistic image/video. Building upon this foundation, diffusion models have become a representative paradigm in text-to-image generation, leading to models like GLIDE [16] for text-guided image editing, Imagen [17] with cascaded diffusion for high-resolution synthesis, and Stable Diffusion [1] using latent diffusion for efficient generation. To enhance image generation quality, researchers typically focus on two main directions. One approach involves architectural improvements, with the Diffusion Transformer (DiT) [3] gaining attention for its improved image fidelity, performance, and diversity. Notable advancements include PixArt-  $\alpha$  [18], Hunyuan-DiT [19], and SD3 [4]. Another approach leverages supervised fine-tuning to refine text-to-image diffusion models. These methods curate datasets by integrating various strategies, such as preference models [2], pre-trained image models [20, 21, 22, 23, 24] (e.g., image captioning models), and expert-assisted data filtering [11].
+
+# 2.2 Preference-Based Optimization Methods
+
+In recent years, preference-based optimization has gained traction, refining models through user feedback or ranked preference pairs. In Large Language Models, Reinforcement Learning from Human Feedback (RLHF) leverages human comparisons to train a reward model that guides policy learning [25, 26]. Alternatively, direct preference optimization (DPO) fine-tunes models directly on preference data, bypassing the need for an explicit reward model while achieving comparable performance [9]. Subsequently, preference-based optimization has been applied to image generation. Some methods enhance image quality by increasing rewards for preferred outputs [27, 28, 29], while others use reinforcement learning [29, 30]. However, training reliable reward models remains challenging and computationally expensive, with over-optimization potentially leading to mode collapse, reducing diversity [31, 28]. Similarly, Direct Preference Optimization has been introduced in text-to-image generation, with Diffusion-DPO [10] demonstrating the effectiveness of optimizing on human comparison data to enhance both visual appeal and text alignment. Additionally, direct score preference optimization [32] refines diffusion models through score matching, providing a novel approach to preference learning. Several recent studies have further explored adapting preference learning techniques from large language models to fine-tune diffusion models [33, 34? , 35], highlighting the growing interest in aligning generative models with human preferences.
+
+# 2.3 Self-Supervised Learning
+
+Self-supervised learning has emerged as a pivotal paradigm in machine learning. Among its most widely used approaches are contrastive self-supervised learning and generative self-supervised learning. Contrastive self-supervised learning distinguishes representations by pulling similar instances closer while pushing dissimilar ones apart. MoCo [36] enhances training efficiency through a momentum encoder, while SimCLR [37] simplifies the process with strong data augmentations. CLIP [38] extends contrastive learning to vision-language tasks, aligning images and text in a shared latent space, enabling zero-shot transfer. Generative approaches inherently follow unsupervised or self-supervised learning principles, training without labeled data to model the underlying distributions of the input. GANs [39] utilize adversarial training to generate realistic data, while VAEs [40] encode data into a structured latent space for controlled synthesis. VQ-VAE [41] introduces discrete latent representations for high-quality generation. MAE [42] leverages masked image modeling to learn rich visual features. More recently, denoising diffusion models [13] have demonstrated impressive results by iteratively adding and removing noise, learning robust representations in a self-supervised manner. Self-supervised learning enables training without manually labeled data, laying the foundation for future advancements in representation learning, generative modeling, and multimodal understanding.
+
+# 3 Methods
+
+# 3.1 Preliminary
+
+Diffusion Models. Denoising Diffusion Probabilistic Models [13] represent the image generation process as a Markovian process. Let  $\pmb{x}_0 \in \mathbb{R}^d$  be the data point and  $q(\pmb{x}_t | \pmb{x}_{t-1})$  denote the forward
+
+process, where noise is added to the data at each timestep  $t$ . The forward process is defined as:
+
+$$
+q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t - 1}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t}; \sqrt {1 - \beta_ {t}} \boldsymbol {x} _ {t - 1}, \beta_ {t} \mathbb {I}\right), \tag {1}
+$$
+
+where  $\beta_{t}$  is a schedule that controls the variance of noise added at each timestep, and  $\mathcal{N}(\cdot)$  denotes the normal distribution. The forward process gradually adds noise, with  $x_{T}$  being pure noise after  $T$  timesteps. The reverse process aims to learn the distribution  $p_{\theta}(\boldsymbol{x}_{t-1}|\boldsymbol{x}_t)$ , which represents the process of denoising and generating data from pure noise. The reverse process can be parameterized as:
+
+$$
+p _ {\theta} \left(\boldsymbol {x} _ {t - 1} \mid \boldsymbol {x} _ {t}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t - 1}; \mu_ {\theta} \left(\boldsymbol {x} _ {t}, t\right), \Sigma_ {\theta} \left(\boldsymbol {x} _ {t}, t\right)\right), \tag {2}
+$$
+
+where  $\mu_{\theta}(\pmb{x}_t,t)$  and  $\Sigma_{\theta}(\pmb{x}_t,t)$  are the mean and covariance learned by the model at each timestep  $t$ . The model is trained by minimizing the following objective:
+
+$$
+\mathcal {L} _ {\text {d i f f u s i o n}} = \mathbb {E} _ {t, \boldsymbol {x} _ {0}, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} (\boldsymbol {x} _ {t}, t) \| ^ {2} \right], \tag {3}
+$$
+
+where  $\epsilon$  is the noise added at each timestep, and  $\epsilon_{\theta}(\boldsymbol{x}_t,t)$  is the model's predicted noise. The model is trained to predict this noise accurately at each step, enabling it to reverse the diffusion process and generate high-quality data.
+
+Reinforcement Learning from Human Feedback. For diffusion models, human preferences at each diffusion step are modeled using a Bradley-Terry formulation [43], where the probability of preferring a "winning" sample  $\boldsymbol{x}_t^w$  over a "losing" sample  $\boldsymbol{x}_t^l$  for a given prompt  $c$  is defined as:
+
+$$
+p _ {\mathrm {B T}} \left(\boldsymbol {x} _ {t} ^ {w} \succ \boldsymbol {x} _ {t} ^ {l} \mid \boldsymbol {c}\right) = \sigma \left(r \left(\boldsymbol {c}, \boldsymbol {x} _ {t} ^ {w}\right) - r \left(\boldsymbol {c}, \boldsymbol {x} _ {t} ^ {l}\right)\right), \tag {4}
+$$
+
+with  $\sigma, r, c$  representing the sigmoid function, reward model, and prompt, respectively. Subsequently, by conceptualizing the diffusion denoising process as a multi-step Markov Decision Process, the generative model is fine-tuned via reinforcement learning. The training objective [10, 44] is formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {r l h f}} = \mathbb {E} _ {\boldsymbol {c} \sim D} \mathbb {E} _ {p _ {\theta} (\boldsymbol {x} _ {0: T} | \boldsymbol {c})} \sum_ {t = 0} ^ {T - 1} r (\boldsymbol {c}, \boldsymbol {x} _ {t}) - \lambda \mathbb {D} _ {\mathrm {K L}} \left(p _ {\theta} (\boldsymbol {x} _ {0: T} | \boldsymbol {c}) \| p _ {\text {r e f}} (\boldsymbol {x} _ {0: T} | \boldsymbol {c})\right), \tag {5}
+$$
+
+where  $p_{\mathrm{ref}}(\pmb{x}_{0:T}|\pmb{c})$  is the distribution from the pretrained diffusion model and  $\lambda$  controls the influence of the KL divergence regularization term.
+
+Direct Preference Optimization (DPO). DPO streamlines RLHF by using the learning policy's log likelihood to implicitly encode the reward. In text-to-image diffusion models, this leads to a step-wise reward defined as:
+
+$$
+r (\boldsymbol {c}, \boldsymbol {x} _ {t}) = \lambda \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t + 1} , \boldsymbol {c}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t + 1} , \boldsymbol {c}\right)}. \tag {6}
+$$
+
+Recent works [10, 32] follow this line and adapt it to diffusion models. They optimize the model  $p_{\theta}$  based on the Bradley-Terry model [43], leading to an objective function:
+
+$$
+\mathcal {L} _ {\text {D i f f u s i o n - D P O}} = - \mathbb {E} \left[ \log \sigma \left(\lambda \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t} ^ {w} \mid \boldsymbol {x} _ {t + 1} ^ {w} , \boldsymbol {c}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t} ^ {w} \mid \boldsymbol {x} _ {t + 1} ^ {w} , \boldsymbol {c}\right)} - \lambda \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t} ^ {l} \mid \boldsymbol {x} _ {t + 1} ^ {l} , \boldsymbol {c}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t} ^ {l} \mid \boldsymbol {x} _ {t + 1} ^ {l} , \boldsymbol {c}\right)}\right) \right], \tag {7}
+$$
+
+where the winning and losing samples  $(\pmb{x}_t^w, \pmb{x}_t^l)$  and the prompt  $\pmb{c}$  are drawn from the dataset, and timestep  $t$  is uniformly sampled from the diffusion process. This formulation effectively aligns the learning policy with human preference signals embedded in the reference model.
+
+# 3.2 Self-DPO for Text-to-image Diffusion Models
+
+Inspired by DPO's effective alignment with human preferences at the image level [10], our work aims to extend this formulation into the standard post-training process for diffusion models (e.g., SFT). Unfortunately, a direct application of DPO is not feasible because it requires collecting image pairs (typically generated by different models with the same prompt or by using different seeds with the same model—along with their associated manual rankings). This approach does not align with the conventional fine-tuning pipeline and incurs significant additional costs. To overcome this limitation, we propose Self-DPO, which generates preference image pairs in a self-supervised manner.
+
+In each training iteration, we denote the text-image pair as  $(c, x)$ , where the image component is regarded as the wining image  $x^w$ . Traditional DPO methods [10, 9] require generating image pairs corresponding to the same prompt, followed by manual selection of the preferred (winning) and less preferred (losing) images, denoted as  $x^w$  and  $x^l$ , respectively. Our method removes such cumbersome
+
+![](images/4693b2bc53110e83e66a8b4e00d5c481e6e2505ba47508081e0958244249d937.jpg)  
+Figure 2: Different post-training processes. We generate the "losing" images self-supervisedly, enabling direct preference optimization without extra collecting and ranking steps. This lightweight procedure eliminates the substantial overhead of conventional DPO while retaining the same data requirements as standard SFT. Best viewed in color with zoom in.
+
+![](images/17435a36b6a3914a873757a29f882fef78dd42c958e1fee64b5480146822bbcf.jpg)
+
+![](images/44892986196040f9b73dc47af0629d5ad226251946a2cda27f7884859269d48c.jpg)
+
+steps. Because every image in the curated high-quality dataset already satisfies human preference, each can be regarded as a winner  $\pmb{x}^w$ . We obtain a corresponding self-supervised losing sample by deliberately degrading the winner:  $\pmb{x}^{sl} = \mathbf{Downgrade}(\pmb{x}^w)$ . Inspired by [10], the self-supervised direct preference loss is:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {S e l f - D P O}} = - \log \sigma \left(C \left(\left\| \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t} ^ {w}, t\right) - \boldsymbol {\epsilon} ^ {w} \right\| _ {2} ^ {2} - \left\| \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t} ^ {s l}, t\right) - \boldsymbol {\epsilon} ^ {s l} \right\| _ {2} ^ {2}\right) \right. \\ \left. - \left(\| \boldsymbol {\epsilon} _ {\mathrm {r e f}} (\boldsymbol {x} _ {t} ^ {w}, t) - \boldsymbol {\epsilon} ^ {w} \| _ {2} ^ {2} - \| \boldsymbol {\epsilon} _ {\mathrm {r e f}} (\boldsymbol {x} _ {t} ^ {s l}, t) - \boldsymbol {\epsilon} ^ {s l} \| _ {2} ^ {2}\right)\right), \\ \end{array}
+$$
+
+$$
+w h e r e \quad \boldsymbol {x} ^ {s l} = \text {D o w n g r a d e} (\boldsymbol {x} ^ {w}) \tag {8}
+$$
+
+where  $C$  and  $\epsilon^{sl}$  refer to a scale factor and the noise corresponding to losing images, and  $\epsilon_{\mathrm{ref}}$  is the reference model. In our experiments, the Downgrade operation can be simply performed by randomly selecting images from the training dataset. For each self-generated image pair, the winning sample closely aligns with the prompt, whereas the losing sample fails to correspond to the description. Surprisingly, this simple manner brings significant improvements to the model. We also compare different degradation strategies in the experiments. The training process overview is shown in Figure 2. The final loss is as follows:
+
+$$
+\mathcal {L} = \lambda_ {1} \mathcal {L} _ {\mathrm {M S E}} + \lambda_ {2} \mathcal {L} _ {\text {S e l f - D P O}} \tag {9}
+$$
+
+We empirically set  $\lambda_{1}$  and  $\lambda_{2}$  to 0.5, 0.5, respectively.
+
+# 4 Experiments
+
+# 4.1 Setup
+
+Implement Details: Following Diffusion-DPO [10], for the SD1.5 [1] experiments, AdamW [47] is utilized, while SDXL [2] training is conducted with Adafactor [48] to conserve memory. Following the official implementation in Diffusion-DPO [10],  $C$  in Equation 8 is set to  $-2500$ . For SD 1.5, a batch size of 2048 pairs (resolution:  $512*512$ ) is maintained by training across 4 NVIDIA A100 GPU. Each GPU handles 8 pairs locally with gradient accumulation
+
+![](images/54544e0c741186cadd96f508e61833ef677539959116bc9a59121c9092085e8a.jpg)  
+Figure 5: Implicit accuracy during the training stage.
+
+![](images/b9ed0b5c07523ab21b529ce39ade470715cd1270a7680daf36c78c3bb0a268d7.jpg)  
+Figure 3: Qualitative comparisons with the SD1.5 base model. All results are generated with the same random seed. Comparing with SFT and DPO [10], the model trained by Self-DPO demonstrates superior text prompt alignment. It also shows more appealing visual quality, especially in layout, colors, and details. Best viewed in color.
+
+over 64 steps. For SDXL, considering the resource limitation, we use the total batch size of 96 pairs (resolution:  $1024 \times 1024$ ). Training is performed at fixed square resolutions. We use a learning rate of 1e-6 coupled with a  $25\%$  linear warmup.
+
+Training Dataset: Our training data is sourced from the Pick-a-Pic V2 dataset[45], which keeps the same to Diffusion-DPO [10]. It contains pairwise preference annotations for images generated by Dreamlike (a fine-tuned variant of SD1.5), SD2.1, and SDXL. These prompts and preferences were collected from users of the Pick-a-Pic web application. Please note that Self-DPO only uses the preference image and associated text in the dataset, instead of using the whole manually annotated image pairs.
+
+Evaluation: We conduct evaluation on three datasets: Pick-a-Pic V2 [45] validation set (contains 500 prompts), PartiPrompts [46] (contains 1632 prompts, including diverse categories and challenge aspects), and HPDv2 [24] (contains 3200 prompts, including anime, concept art, paintings and photo). We compare Self-DPO with three different type baselines, i.e., base models (Stable Diffusion 1.5 (SD1.5) and Stable Diffusion XL (SDXL)), SFT models, DPO models, where DPO models are the
+
+a marine iguana on a surfboard
+
+![](images/c3c26484fb23bf2b4a15dd62c1834aeda4400fdea43b007052db0dd55edb9668.jpg)  
+Prints, Ink, Paper, Relief prints, Woodblock prints, Printing books, Wood blocks, Asia, Japan, ca. 1853, Japan, Polyhrome woodblock print; ink and color on paper, Metropolitan Museum of Art  
+Harry potter as a cat, pixar style, octane render, HD, high-detail  
+Cadillac EIDorado de style Badass Steampunk dans une vieille rue pavée, trending on artstation, sharp focus, studio photo, intricate details, highly detailed, by greg rutkowski  
+character sheet, The little girl riding an electric scooter bike, in a beautiful anime scene by Hayao Miyazaki: a snowy Tokyo city with massive Miyazaki clouds floating in the blue sky, enchanting snowscapes of the city with bright sunlight. Miyazaki's landscape imagery, Japanese art, 16:9  
+Figure 4: Qualitative comparisons with the SDXL base model. All results are generated using the same random seed. Please note that the training dataset (Pick-a-Pic V2 [45]) used for fine-tuning is obtained from a SD1.5 variant, SD2.1, and SDXL models. Consequently, directly fine-tuning (SFT) on this dataset does not lead to improvements—and may even result in degraded performance (e.g., as shown in the second row). In contrast, DPO [10] optimizes the model by leveraging preference relationships with pre-ranked pairs, thereby avoiding this issue. Self-DPO uses the same data requirements as SFT but yields significant improvements in both text prompt alignment and visual quality, demonstrating its effectiveness. Best viewed in color.
+
+publicly released from Diffusion-DPO [10]. For evaluation metrics, we employ the popular PickScore [45], Aesthetics [49], CLIP [38], HPS V2 [24], and ImageAward [50] scores. For convenience of comparison, we scale the scores to fit a similar range ( $\times 100$  for PickScore, CLIP, HPS, and ImageAward,  $\times 10$  for Aesthetics). PickScore is a caption-sensitive scoring model, originally trained on Pick-a-Pic (v1), that estimates the perceived image quality by humans. Aesthetics assesses the visual appeal of an image, considering factors such as lighting, color harmony, composition, and overall artistic quality. CLIP measures the semantic alignment between an image and a corresponding text prompt. By computing the cosine similarity between the image and text embeddings, this score evaluates how well the image content matches the provided textual description. Human Preference Score (HPS V2) is a metric designed to align with human judgments of image quality, particularly in the context of text-to-image synthesis. ImageAward quantifies the quality, aesthetic appeal, or alignment of a generated image with respect to desired attributes. It is typically derived from a reward model trained on human preference data.
+
+<table><tr><td rowspan="2">Datasets</td><td rowspan="2" colspan="2">Methods</td><td colspan="5">SD1.5</td><td colspan="5">SDXL</td></tr><tr><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td rowspan="7">Pick-a-Pic V2</td><td>Base</td><td rowspan="4">Avg score</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td><td>22.10</td><td>60.01</td><td>35.86</td><td>26.83</td><td>50.62</td></tr><tr><td>SFT</td><td>21.10</td><td>56.35</td><td>33.75</td><td>27.03</td><td>45.03</td><td>21.48</td><td>57.84</td><td>35.67</td><td>26.67</td><td>30.89</td></tr><tr><td>DPO</td><td>20.91</td><td>54.07</td><td>33.19</td><td>26.46</td><td>4.13</td><td>22.57</td><td>59.93</td><td>37.30</td><td>27.30</td><td>81.14</td></tr><tr><td>Self-DPO</td><td>21.23</td><td>56.35</td><td>34.79</td><td>27.33</td><td>71.00</td><td>22.34</td><td>59.97</td><td>37.53</td><td>27.89</td><td>103.96</td></tr><tr><td>SFT</td><td rowspan="3">Win rate</td><td>75.00</td><td>77.20</td><td>60.40</td><td>90.20</td><td>80.00</td><td>19.40</td><td>31.80</td><td>47.00</td><td>44.60</td><td>42.4</td></tr><tr><td>DPO</td><td>73.80</td><td>60.00</td><td>60.00</td><td>71.80</td><td>61.00</td><td>72.60</td><td>47.20</td><td>63.00</td><td>79.80</td><td>69.8</td></tr><tr><td>Self-DPO</td><td>78.60</td><td>77.80</td><td>68.40</td><td>94.20</td><td>85.20</td><td>60.80</td><td>50.80</td><td>62.40</td><td>93.80</td><td>79.2</td></tr><tr><td rowspan="7">PartiPrompts</td><td>Base</td><td rowspan="4">Avg score</td><td>21.39</td><td>53.13</td><td>33.21</td><td>26.79</td><td>1.48</td><td>22.63</td><td>57.69</td><td>35.77</td><td>27.33</td><td>69.78</td></tr><tr><td>SFT</td><td>21.75</td><td>55.31</td><td>33.93</td><td>27.57</td><td>50.75</td><td>22.02</td><td>56.41</td><td>35.31</td><td>27.13</td><td>47.29</td></tr><tr><td>DPO</td><td>21.61</td><td>53.58</td><td>33.88</td><td>26.98</td><td>21.43</td><td>22.90</td><td>57.85</td><td>36.95</td><td>27.73</td><td>103.36</td></tr><tr><td>Self-DPO</td><td>21.84</td><td>55.09</td><td>35.11</td><td>27.84</td><td>75.66</td><td>22.79</td><td>58.69</td><td>37.00</td><td>28.30</td><td>117.50</td></tr><tr><td>SFT</td><td rowspan="3">Win rate</td><td>67.28</td><td>70.89</td><td>53.43</td><td>85.42</td><td>73.35</td><td>21.38</td><td>38.11</td><td>45.10</td><td>43.75</td><td>40.93</td></tr><tr><td>DPO</td><td>67.10</td><td>57.17</td><td>56.74</td><td>61.83</td><td>63.05</td><td>63.42</td><td>53.62</td><td>62.32</td><td>73.10</td><td>68.44</td></tr><tr><td>Self-DPO</td><td>69.85</td><td>68.50</td><td>63.24</td><td>89.40</td><td>81.00</td><td>56.19</td><td>60.48</td><td>60.17</td><td>92.16</td><td>76.84</td></tr><tr><td rowspan="7">HPD V2</td><td>Base</td><td rowspan="4">Avg score</td><td>20.84</td><td>54.32</td><td>33.96</td><td>26.84</td><td>-11.79</td><td>22.78</td><td>61.34</td><td>37.68</td><td>27.68</td><td>78.27</td></tr><tr><td>SFT</td><td>21.57</td><td>57.41</td><td>35.26</td><td>27.89</td><td>57.74</td><td>22.24</td><td>60.08</td><td>37.39</td><td>27.76</td><td>66.62</td></tr><tr><td>DPO</td><td>21.30</td><td>55.80</td><td>34.68</td><td>27.22</td><td>13.24</td><td>23.18</td><td>61.35</td><td>38.45</td><td>28.14</td><td>102.74</td></tr><tr><td>Self-DPO</td><td>21.58</td><td>57.10</td><td>36.30</td><td>28.11</td><td>76.13</td><td>22.98</td><td>61.30</td><td>38.35</td><td>28.77</td><td>110.67</td></tr><tr><td>SFT</td><td rowspan="3">Win rate</td><td>79.53</td><td>75.31</td><td>59.34</td><td>90.10</td><td>81.16</td><td>23.47</td><td>37.28</td><td>46.63</td><td>58.22</td><td>45.81</td></tr><tr><td>DPO</td><td>75.72</td><td>66.28</td><td>57.56</td><td>72.43</td><td>64.69</td><td>72.66</td><td>50.28</td><td>58.69</td><td>80.56</td><td>69.78</td></tr><tr><td>Self-DPO</td><td>79.53</td><td>74.03</td><td>68.47</td><td>92.49</td><td>85.19</td><td>58.78</td><td>48.06</td><td>55.65</td><td>94.97</td><td>72.50</td></tr></table>
+
+Table 2: Quantitative comparisons. We compare different fine-tuning methods (SFT, DPO [10], and Self-DPO) on SD 1.5 and SDXL base models over three datasets (Pick-a-Pic V2 [45], PartiPrompts [46], and HPDv2 [24]). "P.S." refers to PickScore, "Aes." is Aesthetics, and "I.R." denotes ImageAward. For the SD1.5 base model, our method achieves the best performance across most metrics. In contrast, for the SDXL base model, we observe that SFT clearly degrades performance. This is likely due to the fact that the training dataset (Pick-a-pic V2 [45]) used for fine-tuning is derived from SD1.5 variant, SD2.1, and SDXL models. Interestingly, our method still achieves competitive results compared to DPO, which utilizes the full dataset and optimizes the model by leveraging preference relationships with pre-ranked pairs. These results underscore the effectiveness and robustness of our approach.
+
+# 4.2 Quantitative Results
+
+We provide quantitative comparisons in Table 2. We compare our method with SFT and DPO [10]. For the SD1.5 base model, our method significantly outperforms the alternatives. For example, Self-DPO achieves a CLIP score of 34.79 on the Pick-a-Pic V2 dataset—an improvement of +2.21 over the base model—whereas SFT and DPO yield improvements of +1.17 and +0.61, respectively. In terms of overall human preference metrics, Self-DPO delivers substantially higher gains, improving the base model from -14.81 to 71.00 on the ImageReward metric, which far exceeds the improvements observed with SFT (45.03) and DPO (4.13).
+
+Notably, the win rate of Self-DPO reaches 94.20 on the HPS metric. Results on other datasets (PartiPrompts and HPD v2) further confirm these improvements. In contrast, results on the SDXL base model show a slightly different scenario, particularly with SFT. We observe that SFT substantially degrades the performance of the base model. This degradation is likely due to the
+
+<table><tr><td>Methods</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td>Base model</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td></tr><tr><td>DPO</td><td>20.91</td><td>54.07</td><td>33.19</td><td>26.46</td><td>4.13</td></tr><tr><td>w/ Blur</td><td>20.80</td><td>55.16</td><td>33.22</td><td>26.57</td><td>4.26</td></tr><tr><td>w/ Random grid</td><td>20.85</td><td>55.86</td><td>32.71</td><td>26.64</td><td>24.21</td></tr><tr><td>w/ Random image</td><td>21.23</td><td>56.35</td><td>34.79</td><td>27.33</td><td>71.00</td></tr></table>
+
+Table 3: Ablation on different downgrade manners. The "Random image" row achieves most significant improvements, implying that degrading the image quality can be detrimental.
+
+fact that, while the training dataset (comprising generations from an SD1.5 variant, SD2.1, and SDXL) is of much higher quality than that used for SD1.5, it does not exhibit clear superiority for SDXL. Nevertheless, the model trained by Self-DPO still demonstrates significantly better performance compared to both SFT and the base model. On the PickScore, Aesthetics, and CLIP metrics, Self-DPO achieves results comparable to DPO, and it attains superior scores on the HPS and ImageRe
+
+ward metrics. These findings validate our hypothesis that image-level learning benefits text-to-image diffusion models and highlight the superiority of Self-DPO. We also employ UnifiedReward [51] as the VLM evaluation metric, a state-of-the-art reward model designed for multimodal understanding and generation tasks. Built upon strong VLM models [52, 53, 54, 55], it supports pointwise scoring to align model outputs with human preferences. The results are shown in Table 4.4. We further validate our method's effectiveness by using a new real-world T2I evaluation setting. Specifically, we conduct experiments on a subset of the LAION-COCO dataset containing  $400\mathrm{k}$  text-image pairs. Unlike carefully curated datasets, we do not manually design the data distribution or employ re-captioning techniques to refine prompts. The results are shown in Table 4.4. While naive SFT degrades performance, our Self-DPO method achieves consistent improvements. Please note that we cannot provide a DPO baseline as it requires additional paired images and annotations for the same prompts, which are not available in regular text-image dataset.
+
+# 4.3 Qualitative Results
+
+We provide qualitative comparisons in Figure 3 and Figure 4 for SD1.5 and SDXL, respectively. All quantitative and qualitative results are generated using the same random seed. We observe that Self-DPO consistently improves over other models, particularly in terms of producing more vivid colors and better adherence to text prompts. For example, in the third row of Figure 3, only Self-DPO successfully reveals the concept "cyberpunk". In the fourth row of Figure 4, both DPO and Self-DPO capture the intended meaning of the prompt, but Self-DPO exhibits a more appealing visual quality. These quantitative and qualitative results confirm the effectiveness of our approach. We show the implicit win rate to measure the optimization process in Figure 5. Specifically, the implicit win rate during training refers to the probability that the model prefers the winning image over the losing image. In other words, a higher implicit win rate indicates a stronger preference for the winning image. As training progresses, it steadily increases and eventually reaches around 0.85. This demonstrates that the model gradually learns to distinguish between the winning and losing images, and prefers to generate the winning image.
+
+# 4.4 Ablation
+
+We conduct ablation studies on various downgrade approaches, as shown in Table 3. In particular, we examine two additional methods—namely, blur (which involves downsampling and upsampling the image by a factor of 4) and random grid (which divides the image into an  $8 \times 8$  grid and randomly swaps two grids). We observe that these two down
+
+<table><tr><td>Methods</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td>Base model</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td></tr><tr><td>DPO</td><td>20.91</td><td>54.07</td><td>33.19</td><td>26.46</td><td>4.13</td></tr><tr><td>Self-DPO w/o MSE</td><td>21.26</td><td>56.22</td><td>35.00</td><td>27.31</td><td>67.78</td></tr><tr><td>Self-DPO</td><td>21.23</td><td>56.35</td><td>34.79</td><td>27.33</td><td>71.00</td></tr></table>
+
+Table 4: Ablation on MSE loss. When removing MSE loss, Self-DPO still shows comparable performance and demonstrates the superiority to DPO.
+
+grade methods lead to worse performance, indicating that significantly degraded image quality can be harmful. Additionally, we remove the MSE loss and report the results in Table 4. Interestingly, the performance does not drop noticeably and consistently perform better than DPO, further confirming the effectiveness of Self-DPO.
+
+<table><tr><td>Methods</td><td>P.S.</td><td>Aes.</td><td>CLIP</td><td>HPS</td><td>I.R.</td></tr><tr><td>Base</td><td>20.57</td><td>53.15</td><td>32.58</td><td>26.17</td><td>-14.81</td></tr><tr><td>SFT</td><td>20.49</td><td>52.63</td><td>31.83</td><td>26.13</td><td>-23.95</td></tr><tr><td>Self-DPO</td><td>20.68</td><td>52.87</td><td>34.31</td><td>26.52</td><td>17.11</td></tr></table>
+
+Table 5: Results on a real-world image-text dataset.  
+
+<table><tr><td>Base model</td><td>Base</td><td>SFT</td><td>DPO</td><td>Self-DPO</td></tr><tr><td>SD1.5</td><td>2.44</td><td>2.62</td><td>2.53</td><td>2.72</td></tr><tr><td>SDXL</td><td>2.96</td><td>2.73</td><td>3.10</td><td>3.07</td></tr></table>
+
+Table 6: Comparisons on UnifiedReward.
+
+# 5 Limitation and Future Work
+
+In the present implementation, we construct losing samples by randomly sampling images from the training set. This manner can become unreliable when the dataset is small, as the resulting
+
+losers may fail to provide sufficiently informative preference signals. Future work therefore can explore more sophisticated self-supervised strategies for synthesizing losing images, such as more content-aware perturbations or adversarial degradations that better challenge the model. Furthermore, our approach is built on direct preference optimization, which is an offline reinforcement-learning paradigm. Extending the self-supervised pairing concept to online policy-gradient or actor-critic frameworks represents another promising direction.
+
+# 6 Conclusion
+
+In this paper, we propose Self-Supervised Direct Preference Optimization (Self-DPO), a fully self-supervised framework that aligns generative models with human preferences without requiring pre-generated image pools or manual rankings. By synthesizing win-lose pairs on the fly, Self-DPO not only removes costly data-collection steps but also exposes the model to a broader and more diverse set of preference signals. At every training iteration, it constructs its own preference pairs through controlled degradations of high-quality images and immediately updates the model via preference learning. Extensive experiments across multiple datasets and base architectures demonstrate that Self-DPO consistently delivers superior performance, validating its effectiveness and versatility.
+
+# Acknowledgments
+
+This research was supported by The National Nature Science Foundation of China (Grant Nos: 62402417, 62273302, 62036009, 61936006), in part by the Key R&D Program of Ningbo (Grant Nos: 2024Z115, 2025Z035), in part by Yongjiang Talent Introduction Programme (Grant No: 2023A-197-G).
+
+# References
+
+[1] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684-10695, 2022.  
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+[3] William Peebles and Saining Xie. Scalable diffusion models with transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pages 4195-4205, 2023.  
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+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
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+
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+
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+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+# 3. Theory assumptions and proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
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+
+# 4. Experimental result reproducibility
+
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+
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+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
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+
+# 6. Experimental setting/details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
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+
+# 7. Experiment statistical significance
+
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+
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+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
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+
+# 9. Code of ethics
+
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+
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+# 10. Broader impacts
+
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+# 11. Safeguards
+
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+
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+# 12. Licenses for existing assets
+
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+
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+
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+
+# 16. Declaration of LLM usage
+
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+
+Answer: [NA]
+
+Justification: The core method development in this research does not involve LLMs as any important, original, or non-standard components.

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+# Self-Supervised Learning of Graph Representations for Network Intrusion Detection
+
+Lorenzo Guerra $^{1,2}$  Thomas Chapuis $^{2}$  Guillaume Duc $^{1}$
+
+Pavlo Mozharovskyi<sup>1</sup> Van-Tam Nguyen<sup>1</sup>
+
+<sup>1</sup>LTCI, Télecom Paris, Institut Polytechnique de Paris, Palaiseau, France {name.surname}@telecom-paris.fr
+
+<sup>2</sup>Ampere Software Technology, Guyancourt, France {name.surname}@ampere.cars
+
+# Abstract
+
+Detecting intrusions in network traffic is a challenging task, particularly under limited supervision and constantly evolving attack patterns. While recent works have leveraged graph neural networks for network intrusion detection, they often decouple representation learning from anomaly detection, limiting the utility of the embeddings for identifying attacks. We propose GraphIDS, a self-supervised intrusion detection model that unifies these two stages by learning local graph representations of normal communication patterns through a masked autoencoder. An inductive graph neural network embeds each flow with its local topological context to capture typical network behavior, while a Transformer-based encoder-decoder reconstructs these embeddings, implicitly learning global co-occurrence patterns via self-attention without requiring explicit positional information. During inference, flows with unusually high reconstruction errors are flagged as potential intrusions. This end-to-end framework ensures that embeddings are directly optimized for the downstream task, facilitating the recognition of malicious traffic. On diverse NetFlow benchmarks, GraphIDS achieves up to  $99.98\%$  PR-AUC and  $99.61\%$  macro F1-score, outperforming baselines by 5–25 percentage points. $^{1}$
+
+# 1 Introduction
+
+As more devices are connected to the internet, the frequency and sophistication of cyberattacks continue to rise, exposing vulnerabilities across diverse network environments, from enterprise infrastructures to embedded devices. These threats are difficult to anticipate, as they evolve rapidly and exploit previously unknown weaknesses, making timely and accurate detection essential for protecting critical services. Although numerous network intrusion detection methods have been proposed, most rely on supervised learning and depend on large volumes of labeled data, which are expensive and labor-intensive to obtain. Additionally, supervised models are typically trained on known patterns, limiting their ability to detect novel threats and requiring frequent retraining to remain effective. Unsupervised methods have also been explored, but they often struggle to capture the complexity of network traffic, reducing their effectiveness against subtle or sophisticated attack patterns [1].
+
+Self-supervised learning has emerged as a promising alternative by enabling the extraction of rich representations from data without the need for explicit labels. In the context of network intrusion detection, recent studies have leveraged network topology through graph-based methods [2], achieving substantial improvements over traditional techniques. As computer networks can be naturally
+
+![](images/bd9625dfc2d85a6b22a6585632fc48450d2e00331f920be61daf81bc63c79cf3.jpg)  
+Figure 1: Overview of GraphIDS: the model detects network intrusions by evaluating the reconstruction error of graph-based flow embeddings. Flows representing attacks (highlighted in red) typically yield higher reconstruction errors, as they deviate from normal communication patterns.
+
+represented as graphs, where nodes represent hosts and edges represent communication flows, we can employ Graph Neural Networks (GNNs) to learn meaningful representations that facilitate modeling the normal network behavior. However, unlike typical GNN applications, where the relevant information is encoded in node features and their connections, network intrusion detection primarily encodes critical information within the edges, which reflect either normal host interactions or malicious activities.
+
+Nevertheless, most existing approaches decouple graph representation learning from the anomaly detection task, which limits their ability to learn meaningful embeddings that are directly useful for detecting intrusions. Moreover, the self-supervised pretext tasks frequently rely on the availability of negative samples or prior knowledge to construct them—assumptions that often do not hold in practical intrusion detection scenarios, where labeled anomalies or well-defined negative examples are scarce or entirely unavailable.
+
+To address these limitations, we propose GraphIDS, a self-supervised model jointly trained to reconstruct local graph representations of benign network traffic, using reconstruction error to identify potential intrusions (Figure 1). In network intrusion detection, anomalous behavior often manifests through irregular communication patterns and deviations from typical structural or statistical relationships. The GNN encoder captures local topological context by modeling the immediate neighborhood of each flow, integrating both structural and edge-level features that characterize the underlying structure of benign traffic.
+
+The autoencoding objective, applied to batches of flow embeddings, enables the Transformer to learn broader contextual dependencies and co-occurrence patterns across the network. During training, we apply attention masking as a structured regularizer, randomly disabling a subset of attention links while keeping all input embeddings visible. This encourages the model to infer from partial context and learn a stable distribution of normal behavior. At inference time, flows that significantly deviate from this learned distribution exhibit high reconstruction errors and are flagged as potential intrusions. This end-to-end framework enables the model to generalize effectively to unseen attack types and dynamic network environments without relying on supervision or negative samples.
+
+We evaluate our model on multiple NetFlow-based datasets for Network Intrusion Detection Systems (NIDS), including NF-UNSW-NB15 and NF-CSE-CIC-IDS2018. We use both their second version (v2), which includes 43 NetFlow features, and their third version (v3), which extends these with 10 additional temporal features, resulting in a total of 53 features [3][4].
+
+This work makes the following key contributions:
+
+1. We present GraphIDS, a novel self-supervised framework that jointly trains a GNN encoder and a Transformer-based masked autoencoder to reconstruct local representations of benign network traffic. By leveraging both topological and contextual information in an end-to-end manner, GraphIDS directly optimizes flow embeddings for anomaly detection, without
+
+relying on labeled data or prior knowledge of attack patterns. To the best of our knowledge, this is the first application of a jointly trained GNN-Transformer architecture for network intrusion detection (Section 3).
+
+2. We conduct extensive experiments on NIDS datasets, covering diverse network environments and a wide range of attack types. GraphIDS achieves state-of-the-art performance, outperforming existing methods by  $5\%$  to over  $25\%$  in both macro F1 and PR-AUC. These results demonstrate its strong generalization to previously unseen attacks, highlighting its practical effectiveness for real-world intrusion detection (Section 4).
+
+# 2 Related Work
+
+Self-supervised Masked Modeling: Masked modeling has emerged as a fundamental technique for self-supervised learning across various data modalities. In natural language processing, BERT is trained to reconstruct randomly masked tokens through a bidirectional Transformer, thereby learning to generate word embeddings that are transferable to a wide range of downstream tasks [5]. Similarly, in computer vision, masked autoencoders are trained to reconstruct randomly masked patches of an image by employing an asymmetric encoder-decoder architecture, compelling the model to extract rich contextual representations from the input data [6]. GraphMAE [7] extended this concept to the graph domain by training a graph masked autoencoder to reconstruct masked node features in order to learn meaningful graph representations.
+
+All of these models share a common objective: learning the normal structure or contextual dependencies of the data through a reconstruction-based task. This paradigm is particularly well-suited for anomaly and intrusion detection, as anomalies, such as attacks, typically lead to poor reconstruction, and can thus be effectively identified by quantifying the reconstruction error relative to the original data. For example, Georgescu [8] applied MAE to medical imaging, training the model exclusively on healthy samples to identify abnormal scans based on reconstruction discrepancies. Similarly, BERT-like models have also been adapted to textual anomaly detection, enabling the identification of system malfunctions or malicious activity in log data by capturing deviations from learned normal patterns [9].
+
+Graph Neural Networks for Supervised Intrusion Detection: GNNs provide a principled framework for integrating graph topology with node/edge attributes into learned embeddings. Foundational models such as Graph Convolutional Networks (GCN) formulate spectral convolutions on graphs and learn node embeddings by aggregating information from local neighborhoods [10]. GraphSAGE [11] introduces an inductive approach that learns to aggregate and transform features from a node's neighbors to embed unseen nodes or graphs. These architectures propagate node features through edges to encode local topology and features simultaneously. More advanced variants, including Graph Attention and Graph Transformers, enhance expressivity, but the fundamental principle remains the same: summarizing each node's local structure into its embedding.
+
+While standard GNNs primarily focus on node embeddings, edge-level representations can also be learned by various techniques, such as employing the line graph, or combining end-point embeddings. For example, E-GraphSAGE [12] explicitly incorporates edge features into GraphSAGE by performing message passing that aggregates edge attributes and node attributes together. With network flow data represented as a graph of endpoints connected by edges (flows), E-GraphSAGE becomes crucial for capturing edge features (e.g., flow statistics) along with network topology. Alternatively, Friji et al. [13] propose a novel graph construction in which each network flow is represented as a node within a directed "flow graph". This formulation allows complex behaviors such as multi-step attacks and spoofing to emerge as recognizable graph patterns. In another example, Zhou et al. [14] introduces a NIDS that exclusively leverages topology information to detect botnet activity, such as the hierarchical organization of centralized botnets or the fast-mixing structure of decentralized ones. Collectively, these studies highlight the inherent capability of GNNs to model rich structural properties in network data. However, they rely on labeled traffic, which constrains their deployment in practical, large-scale environments where annotated data is scarce or unavailable.
+
+Graph Neural Networks for Self-Supervised Intrusion Detection: To address the limitations imposed by the need for labeled data, Caville et al. [2] recently introduced Anomal-E, a self-supervised framework designed to detect attack patterns without relying on flow labels. The approach begins
+
+![](images/140732140b2bf8f4577126ba05c19e88f4747408f78d3a2d5508c29c7563dc94.jpg)  
+Figure 2: Illustration of the graph construction process. Network flows are transformed into a directed graph, where nodes represent hosts (IP addresses) and edges correspond to communication flows between them. Edge features capture flow statistics such as packet count, byte count, and protocol information.
+
+with the pretraining of a GNN-based encoder using a contrastive pretext task, which is then used to generate representative flow embeddings. Afterwards, a separate unsupervised algorithm is applied to identify the anomalous embeddings.
+
+In contrast to Anomal-E, our method adopts an end-to-end training paradigm that jointly optimizes a GNN with the Transformer encoder-decoder within a masked reconstruction framework. This design enables the GNN to learn representations that are intrinsically aligned with the intrusion detection objective. Moreover, our approach eliminates its reliance on contrastive learning and negative samples, thereby removing the necessity for prior knowledge of attack patterns. Instead, the model is trained exclusively on benign traffic, which is generally more accessible and easier to obtain in real-world environments. This design choice allows the system to robustly capture the normal behavior of network traffic, making it particularly suitable for practical deployment in dynamic and evolving threat landscapes, where the nature of attacks can change significantly over time.
+
+# 3 Method
+
+# 3.1 Graph Construction and Framework Introduction
+
+We define a network flow as a unidirectional sequence of packets that share at least five attributes [15]: ingress interface, source IP address, destination IP address, IP protocol number, and IP Type of Service. When UDP or TCP protocols are used, source and destination ports are also included, providing additional granularity to uniquely identify individual flows.
+
+Using the collected network flows, we construct a graph representation of the computer network, where nodes correspond to hosts (identified by IP addresses) and edges represent communication flows. Each flow defines a directed edge from a source node (source IP address) to a destination node (destination IP address), with edge features derived from flow statistics that provide a high-level summary of the communication. The overall graph construction process is illustrated in Figure 2.
+
+Assuming the ability to monitor communications among network hosts to be protected from malicious activity, we begin by collecting and aggregating network flows to obtain a comprehensive view of network activity over time. These flows are then used to construct the graph, on which we apply a GNN to compute flow-level embeddings that include neighborhood context, integrating information about recent local communications. To learn the normal behavior of the network, we train the model to reconstruct these local graph representations, enabling it to detect anomalies based on reconstruction errors.
+
+# 3.2 Graph Representation Learning
+
+To incorporate local graph context into flow embeddings, we employ E-GraphSAGE [12], an extension of the original GraphSAGE [11] which includes edge features during the embedding process. As edges are the most informative elements in our graphs, this approach allows GraphIDS to integrate local topological patterns into each flow representation, improving its ability to distinguish between benign and malicious activity.
+
+Unlike early GNN models such as the original GCN [10], which are mainly transductive (i.e., they can only make predictions on nodes seen during training), E-GraphSAGE is designed for inductive learning. It can generalize to unseen edges and graphs at inference time by learning aggregation functions over neighborhoods rather than depending on a fixed adjacency matrix.
+
+To ensure scalability, we use neighborhood sampling, which makes the method efficient in both memory and computation and enables training on large graphs using mini-batches. In addition, by not relying on a fixed graph structure, E-GraphSAGE is well-suited for network intrusion detection, where the underlying graph is dynamic and affected by noise.
+
+Although in principle deeper GNN architectures could be employed, we restrict our GNN to a 1-hop neighborhood to efficiently capture informative local context, a design choice validated by our ablation study in Appendix C.5. In network intrusion detection, the immediate neighborhood of a flow often reveals meaningful patterns that are indicative of malicious behavior, such as unusual connections or bursty communications. Global co-occurrence patterns, which may span multiple flows or hosts, are instead captured by the Transformer operating over batches of flow embeddings. This separation of roles allows GraphIDS to jointly model both local and global dependencies without incurring the computational overhead of deeper GNN layers.
+
+To further reduce memory usage when processing graphs with a very large number of edges relative to the number of nodes, we impose a configurable limit on each node's fanout during sampling. This fanout is treated as a tunable hyperparameter.
+
+# 3.3 Masked Autoencoder
+
+To learn global co-occurrence patterns, our model employs a Transformer-based masked autoencoder designed to reconstruct benign graph representations. This component operates on batches of flow embeddings,  $\mathbf{H} = \{h_1,\dots ,h_n\}$ , produced by the GNN layer, where each  $h_i\in \mathbb{R}^{d_{\mathrm{gnn}}}$ . We construct each batch by concatenating 64 flow windows of 512 flows each, resulting in a sequence of  $n = 32,768$  embeddings. Before being passed to the Transformer, these embeddings are projected to a lower-dimensional space  $\mathbb{R}^{d_{\mathrm{model}}}$  through a linear layer, encouraging the model to learn more compact representations and reducing computational cost.
+
+The Transformer consists of an encoder and a decoder, each built from a stack of identical blocks. Each block contains a multi-head self-attention module followed by a position-wise feed-forward network. Both sub-layers are wrapped with residual connections and layer normalization. During training, we apply a symmetric binary attention mask that disables attention between a randomly sampled subset of positions. Unlike conventional masked autoencoders that remove input tokens, our approach applies a mask directly to the attention mechanism, functioning as a form of structured dropout on the attention weights to improve generalization. This process encourages the model to build more robust and distributed representations by preventing over-reliance on specific contextual links. Random masking is disabled at inference.
+
+The encoder processes the projected embeddings to produce contextual representations. The decoder then takes the same projected sequence as reconstruction queries and attends to the encoder outputs via cross-attention to compute per-position reconstructions. Finally, an output projection layer maps these reconstructed embeddings,  $\hat{\mathbf{H}}^{\prime}$ , back to the original GNN embedding space to produce the final output,  $\hat{\mathbf{H}} = \{\hat{h}_1,\dots ,\hat{h}_n\}$ . The anomaly score for each flow is its squared reconstruction error, computed in the original GNN embedding space:
+
+$$
+s _ {i} = \left\| h _ {i} - \hat {h} _ {i} \right\| ^ {2} \tag {1}
+$$
+
+During inference, higher anomaly scores identify potential attacks.
+
+Let  $n_{\mathrm{valid}}$  be the number of non-padded embeddings in a batch. The model is trained end-to-end by minimizing the Mean Squared Error (MSE) over these embeddings:
+
+$$
+\mathcal {L} _ {\mathrm {M S E}} = \frac {1}{n _ {\text {v a l i d}}} \sum_ {i = 1} ^ {n _ {\text {v a l i d}}} s _ {i} = \frac {1}{n _ {\text {v a l i d}}} \sum_ {i = 1} ^ {n _ {\text {v a l i d}}} \| h _ {i} - \hat {h} _ {i} \| ^ {2} \tag {2}
+$$
+
+The gradient of the MSE loss is backpropagated through both the Transformer and the GNN, jointly updating their parameters. This aligns the training objectives of the two components, allowing the model to capture both local structural context and global co-occurrence patterns without requiring labeled attack data.
+
+![](images/b08cf4d1a193d02eff3c0fcad5c4f38d521a2f759199f52838e66f2c8b25b85b.jpg)  
+Figure 3: Overview of the full training pipeline. During inference, attention masking is omitted. The reconstruction errors  $s_1, s_2, \ldots, s_n$  serve as anomaly scores for each network flow.
+
+# 3.4 Summary of the Pipeline
+
+The full training pipeline is illustrated in Figure 3. Network flows are first collected and processed into a graph, where edges represent communications between hosts. Using neighborhood sampling, E-GraphSAGE integrates local context into edge embeddings  $h_1, h_2, \ldots, h_n$ . These embeddings are then batched, projected, and passed to the masked autoencoder. The model's parameters are optimized end-to-end by backpropagating the gradient of the MSE loss. This gradient flows from the output of the decoder back through both the Transformer and the GNN, allowing for the joint update of all model parameters. This ensures that the GNN learns to produce representations that are not only structurally informative but also optimized for the reconstruction task performed by the Transformer.
+
+At inference time, the model processes batches of flow embeddings without masking. Attacks are detected by applying a threshold to the reconstruction error, calculated as the squared L2 norm between the original GNN embeddings and their final reconstructions. Flows with higher reconstruction errors are flagged as potential intrusions, as they deviate from the learned patterns of normal network traffic.
+
+# 4 Experimental Evaluation
+
+# 4.1 Datasets
+
+For our experiments, we selected two widely used datasets for evaluating NIDS: UNSW-NB15 [16], captured in a smaller-scale network environment, and CSE-CIC-IDS2018 [17], which captures traffic from a significantly larger infrastructure. Specifically, we used their NetFlow-based versions, which correct flow extraction errors introduced by CICFlowMeter [18] and provide a standard feature set including IP addresses, allowing us to construct the graphs and fairly evaluate the models across datasets. We conduct our experiments both on their second version [4], which includes 43 NetFlow features, and their recently released third version [3], which adds 10 additional temporal features $^{2}$ .
+
+Table 1 summarizes the main characteristics of the datasets. By selecting two datasets collected from different network environments and with different attack scenarios, we can verify if our approach is able to generalize across different settings. The datasets feature extensive encrypted traffic (e.g., HTTPS, SSH) and diverse communication patterns, representing realistic, modern network environments. We note that the differences in statistics between the second and third versions of each dataset are due to variations in the NetFlow aggregation process during feature extraction, although the details are not documented by the original authors.
+
+# 4.2 Data Preprocessing
+
+Before training, we replace missing or invalid values with zeros and split the dataset into  $80\%$  for the training set,  $10\%$  for the validation set, and  $10\%$  for the test set, preserving the class distribution of attack types. We normalize all NetFlow features to the interval [0, 1] using Min-Max scaling. The scalar is fitted on the training set, which contains only benign flows, and then applied to transform
+
+Table 1: Statistics of the NetFlow-based datasets, varying in scale and anomaly prevalence.  
+
+<table><tr><td>Dataset</td><td>Number of Flows</td><td>Number of Hosts</td><td>Anomaly Ratio</td></tr><tr><td>NF-UNSW-NB15-v2</td><td>2,390,275</td><td>44</td><td>3.98%</td></tr><tr><td>NF-UNSW-NB15-v3</td><td>2,365,424</td><td>44</td><td>5.40%</td></tr><tr><td>NF-CSE-CIC-IDS2018-v2</td><td>18,893,708</td><td>255,042</td><td>11.95%</td></tr><tr><td>NF-CSE-CIC-IDS2018-v3</td><td>20,115,529</td><td>205,801</td><td>12.93%</td></tr></table>
+
+both the validation and test sets. To avoid extreme input values, any scaled value falling outside the original training range is clipped to the  $[-10, 10]$  range. For v3 datasets, timestamps are discarded, as our experiments showed that these features introduced unnecessary noise, with no performance improvement (Appendix C).
+
+The graph is then constructed, as specified in Section 3.1, by using IP addresses to identify hosts, while the remaining flow features are assigned to each edge. Since attack behaviors are directional, we use a directed graph to preserve this information, allowing us to easily correlate the classification results with the network flows. We also note that one of the baseline models considered, Anomal-E, based on its original implementation and specification, is unable to efficiently process the full graph of NF-CSE-CIC-IDS2018 on our hardware. Therefore, in this case, we downsample the dataset to  $20\%$  of its original size, maintaining the proportions of the attack types.
+
+# 4.3 Training and Anomaly Detection Procedure
+
+Mini-Batch Strategies. After preprocessing, training proceeds with different mini-batch strategies for each component of our architecture. For E-GraphSAGE, we employ neighborhood sampling to manage the computational demands of graph processing. First, we divide the full set of edges into mini-batches (with batch sizes ranging from 16,384 to 32,768 depending on the dataset). For each edge in a mini-batch, we sample edges from its 1-hop neighborhood up to a dataset-specific fan-out limit.
+
+For the Transformer encoder-decoder, we process the graph embeddings in fixed-size batches of 64, where each batch contains 512 graph-based flow representations. The separate batching mechanisms reflect the fundamentally different ways the GNN and Transformer components process information: neighborhood-based for the former and context-based for the latter.
+
+Since our approach computes embeddings using batched processing and randomly sampled neighboring edges, it does not require a fixed adjacency matrix. This makes its application practical for evolving network environments, where connections to new hosts are constantly established. In realistic deployments, memory usage can be controlled by applying a graph-level time window that discards outdated edges when new ones are added.
+
+Implementation and Optimization Details. We train GraphIDS for a maximum of 100 epochs using the AdamW optimizer on a machine with an NVIDIA A100 GPU, 32 GB of RAM, and 8 CPU cores of an AMD EPYC 7302 processor. We implemented our model using PyTorch 2.3.1 and DGL 2.3.0. Random seeds were fixed to ensure reproducibility. Table 2 reports the training time for each dataset, which varies depending on early stopping. Across all experiments, including hyperparameter optimization and baselines, the total compute time was roughly 976 GPU hours.
+
+As this architecture requires careful tuning, we thoroughly optimize several hyperparameters for each dataset, including learning rate, weight decay coefficients, edge embedding dimension, autoencoder latent dimension, number of transformer layers, dropout rate and the parameters related to the batching strategies. We initially explored coarse configurations through grid search, followed by Bayesian optimization to tune the hyperparameters based on validation Precision-Recall Area Under Curve (PR-AUC).
+
+Our experiments showed that the model reaches optimal performance when stronger regularization is applied to the GNN encoder compared to the masked autoencoder. The GNN encoder typically benefits from higher weight decay coefficients (up to 0.6) and dropout rates (up to 0.7), while the masked autoencoder performs better with more moderate regularization (weight decay from 0.01 to 0.05 and dropout rate from 0 to 0.2). We also observe that an attention mask ratio of 0.15 provides a
+
+Table 2: Total number of parameters, training time and inference time of GraphIDS across all datasets. Inference is performed in batches; the reported time refers to the forward pass and excludes any preprocessing.  
+
+<table><tr><td>Dataset</td><td># Params</td><td>Training Time (h)</td><td>Inference Time (μs/sample)</td></tr><tr><td>NF-UNSW-NB15-v2</td><td>0.867M</td><td>0.39 ± 0.27</td><td>2.27 ± 0.92</td></tr><tr><td>NF-UNSW-NB15-v3</td><td>0.874M</td><td>0.63 ± 0.32</td><td>3.04 ± 1.25</td></tr><tr><td>NF-CSE-CIC-IDS2018-v2</td><td>0.570M</td><td>1.00 ± 0.55</td><td>4.89 ± 0.50</td></tr><tr><td>NF-CSE-CIC-IDS2018-v3</td><td>0.572M</td><td>1.46 ± 0.59</td><td>5.09 ± 1.09</td></tr></table>
+
+good balance between regularization and reconstruction quality across datasets (see Appendix C.4). All code and configurations used for the experiments have been publicly released to ensure full reproducibility.
+
+Early Stopping. We use early stopping based on the PR-AUC achieved on the validation set with a patience of 20 epochs. We selected PR-AUC because it provides a fair, threshold-independent evaluation of the model performance. The model checkpoint achieving the highest validation PR-AUC is saved for final evaluation and deployment. Although this procedure assumes access to a small amount of labeled data for validation and threshold tuning, it avoids the scalability and generalization issues of fully supervised models. In practice, a small amount of labeled data can reasonably be collected during deployment to support this step and it may even provide a more reliable and robust thresholding solution for practical applications. Nevertheless, exploring fully unsupervised thresholding strategies remains an interesting direction for future research.
+
+# 4.4Baselines
+
+To isolate the contribution of each component in GraphIDS, we evaluate the following targeted ablations:
+
+1. T-MAE: A Transformer-based masked autoencoder with attention masking trained directly on raw NetFlow features, without any graph-based representation learning. This ablation isolates the contribution of the GNN by evaluating performance without local topological context.  
+2. SimpleAE: A lightweight fully connected autoencoder that replaces the Transformer with a two-layer MLP encoder and a two-layer MLP decoder (ReLU activations). It is trained end-to-end together with E-GraphSAGE on the same reconstruction objective and with the same batching scheme as GraphIDS, isolating the role of self-attention and sequence modeling.
+
+We also compare GraphIDS against anomaly detection baselines:
+
+- Anomal-E [2]: A state-of-the-art method using a pre-trained E-GraphSAGE encoder to generate edge embeddings, followed by anomaly detection on those embeddings. Unlike GraphIDS, it lacks joint training and self-attention, isolating the impact of the Transformer reconstruction.  
+- CBLOF [19]: A clustering-based local outlier factor algorithm, representative of traditional unsupervised detection techniques.  
+- SAFE [20]: A recent self-supervised method that transforms tabular network traffic data into image-like representations for masked autoencoder reconstruction, followed by a lightweight novelty detector.
+
+# 4.5 Evaluation Metrics
+
+To fairly evaluate and compare models on NIDS datasets, we use two complementary metrics that are resistant to high class imbalance: a threshold-dependent macro-averaged F1-score and a threshold-independent PR-AUC. The macro F1-score gives equal weight to both classes, preventing the dominant benign class from overshadowing the minority attack class, and provides a balanced
+
+Table 3: Model performance on NetFlow datasets. Multiple values are bolded when differences are not statistically significant.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Metric</td><td colspan="2">v3 Datasets (w/ temporal features)</td><td colspan="2">v2 Datasets (w/o temporal features)</td></tr><tr><td>UNSW-NB15</td><td>CSE-CIC-IDS2018</td><td>UNSW-NB15</td><td>CSE-CIC-IDS2018</td></tr><tr><td colspan="6">External baselines</td></tr><tr><td rowspan="2">CBLOF</td><td>PR-AUC</td><td>0.3658 ± 0.0634</td><td>0.2638 ± 0.0263</td><td>0.2102 ± 0.0157</td><td>0.7822 ± 0.0198</td></tr><tr><td>Macro F1</td><td>0.7319 ± 0.0225</td><td>0.6599 ± 0.0130</td><td>0.7046 ± 0.0140</td><td>0.8889 ± 0.0068</td></tr><tr><td rowspan="2">SAFE</td><td>PR-AUC</td><td>0.8946 ± 0.0279</td><td>0.6294 ± 0.0923</td><td>0.2044 ± 0.0267</td><td>0.5222 ± 0.1896</td></tr><tr><td>Macro F1</td><td>0.9236 ± 0.0086</td><td>0.4662 ± 0.0016</td><td>0.5815 ± 0.0164</td><td>0.4684 ± 0.0001</td></tr><tr><td rowspan="2">Anomal-E</td><td>PR-AUC</td><td>0.9032 ± 0.0041</td><td>0.2555 ± 0.0383</td><td>0.7489 ± 0.0074</td><td>0.9287 ± 0.0265</td></tr><tr><td>Macro F1</td><td>0.9459 ± 0.0009</td><td>0.6709 ± 0.0394</td><td>0.9156 ± 0.0217</td><td>0.9410 ± 0.0161</td></tr><tr><td colspan="6">Ablations</td></tr><tr><td rowspan="2">T-MAE</td><td>PR-AUC</td><td>0.9914 ± 0.0022</td><td>0.7398 ± 0.0777</td><td>0.5995 ± 0.0155</td><td>0.7375 ± 0.0035</td></tr><tr><td>Macro F1</td><td>0.9933 ± 0.0017</td><td>0.4707 ± 0.0049</td><td>0.8039 ± 0.0447</td><td>0.8453 ± 0.0317</td></tr><tr><td rowspan="2">SimpleAE</td><td>PR-AUC</td><td>0.9996 ± 0.0007</td><td>0.8458 ± 0.0498</td><td>0.7864 ± 0.0608</td><td>0.9310 ± 0.0126</td></tr><tr><td>Macro F1</td><td>0.9838 ± 0.0321</td><td>0.9223 ± 0.0201</td><td>0.8680 ± 0.1579</td><td>0.9450 ± 0.0092</td></tr><tr><td colspan="6">Ours</td></tr><tr><td rowspan="2">GraphIDS</td><td>PR-AUC</td><td>0.9998 ± 0.0007</td><td>0.8819 ± 0.0347</td><td>0.8116 ± 0.0367</td><td>0.9201 ± 0.0238</td></tr><tr><td>Macro F1</td><td>0.9961 ± 0.0084</td><td>0.9447 ± 0.0213</td><td>0.9264 ± 0.0217</td><td>0.9431 ± 0.0131</td></tr></table>
+
+view of false positives and false negatives. Unlike ROC-AUC, PR-AUC is well-suited for imbalanced datasets as it focuses on the positive class without being influenced by the large number of true negatives [21]. PR-AUC is computed using scikit-learn's implementation with linear interpolation.
+
+To select the optimal threshold for the final classification, we maximize the macro F1-score on a labeled validation set and then apply the same threshold to the test set. This approach ensures a fair comparison across all models while avoiding threshold optimization bias on the test data.
+
+# 4.6 Results
+
+Table 3 presents averaged metrics across multiple random seeds, along with standard deviations. Since Anomal-E combines several anomaly detectors, we report only its best-performing variant (based on PR-AUC) for each dataset. A complete breakdown of Anomal-E's performance across all detectors is available in Appendix B.2.
+
+On the third version of the NetFlow-based datasets, GraphIDS demonstrates a strong performance, effectively leveraging both local topological context and global co-occurrence patterns to improve detection by identifying complex attack behaviors. In the smaller network environment of NF-UNSW-NB15-v3, our ablated T-MAE model, which relies solely on contextual information, performs comparably to GraphIDS. However, on the larger and more diverse NF-CSE-CIC-IDS2018-v3 dataset, T-MAE shows a substantial drop in performance, highlighting the importance of structural information in large-scale settings.
+
+On the second version of the datasets, GraphIDS achieves comparable results to Anomal-E, while clearly outperforming it on NF-UNSW-NB15-v2 in terms of PR-AUC. Although direct comparisons between dataset versions are not possible due to differing flow aggregation and feature sets, we notice that the v3 configuration made intrusion detection more challenging for NF-CSE-CIC-IDS2018 but improved it for NF-UNSW-NB15. These results suggest that both aggregation parameters and NetFlow feature selection should be carefully tuned before deployment, as they can significantly impact detection performance.
+
+Finally, the SimpleAE ablation confirms that the autoencoding objective itself is a strong driver of performance: it performs competitively across datasets and, in some cases, matches PR-AUC achieved with the Transformer. Nevertheless, GraphIDS typically attains higher macro F1 and more stable results, especially on the larger NF-CSE-CIC-IDS2018-v3, which supports the benefit of self-attention for modeling global co-occurrence patterns among flows.
+
+# 5 Conclusion
+
+We introduced GraphIDS, a novel self-supervised framework that jointly trains a graph neural network and a Transformer-based masked autoencoder to learn normal network behavior and detect complex intrusion patterns. To the best of our knowledge, this is the first end-to-end architecture that combines GNNs and masked autoencoding for network intrusion detection. Experimental results demonstrate that GraphIDS achieves state-of-the-art performance across both small-scale and large-scale scenarios, outperforming existing baselines by 5-25 percentage points. With an average inference time of 3.83  $\mu$ s per sample, the model is also well-suited for real-time deployment, where rapid response is essential.
+
+Like other unsupervised models, GraphIDS assumes a relatively stable network topology, and its performance may degrade under abrupt behavioral shifts, potentially leading to increased false positives or missed detections. Online learning techniques offer a promising avenue to mitigate this limitation by enabling continuous adaptation without requiring full retraining. Furthermore, similarly to other GNN-based approaches, GraphIDS is less effective in single host monitoring scenarios, where limited topological context constrains its representational capacity. Future work could address this by incorporating multimodal data, such as combining network flows with logs or system calls, to improve the detection of intrusions that leave minimal footprints in network traffic alone. Finally, accurately assessing real-world detection latency requires a holistic evaluation of the entire processing pipeline, including data collection, aggregation, preprocessing, and inference.
+
+Overall, our findings underscore the effectiveness of jointly modeling local topological context and global co-occurrence patterns for network intrusion detection. By unifying GNNs and Transformers under a shared reconstruction objective, GraphIDS captures normal network behavior without relying on labeled data or prior knowledge of attack signatures, offering a practical and scalable solution for real-world deployment.
+
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+[20] Elvin Li, Zhengli Shang, Onat Gungor, and Tajana Rosing. Safe: Self-supervised anomaly detection framework for intrusion detection, 2025. URL https://arxiv.org/abs/2502.07119.  
+[21] Takaya Saito and Marc Rehmsmeier. The precision-recall plot is more informative than the roc plot when evaluating binary classifiers on imbalanced datasets. PLOS ONE, 10(3):1-21, 03 2015. doi: 10.1371/journal.pone.0118432. URL https://doi.org/10.1371/journal.pone.0118432.  
+[22] Petar Velickovic, William Fedus, William L. Hamilton, Pietro Liò, Yoshua Bengio, and R. Devon Hjelm. Deep graph infomax. In 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019. OpenReview.net, 2019. URL https://openreview.net/forum?id=rklz9iAcKQ.  
+[23] Mei-Ling Shyu, Shu-Ching Chen, Kanoksri Sarinnapakorn, and LiWu Chang. A novel anomaly detection scheme based on principal component classifier. In Proceedings of the IEEE Foundations and New Directions of Data Mining Workshop, Melbourne, Florida, USA, 2003. IEEE.  
+[24] Fei Tony Liu, Kai Ming Ting, and Zhi-Hua Zhou. Isolation forest. In 2008 Eighth IEEE International Conference on Data Mining, pages 413-422, 2008. doi: 10.1109/ICDM.2008.17.  
+[25] Markus Goldstein and Andreas Dengel. Histogram-based outlier score (hbos): A fast unsupervised anomaly detection algorithm. In KI-2012: poster and demo track, 09 2012.  
+[26] Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, and Jörg Sander. Lof: identifying density-based local outliers. In Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, SIGMOD '00, page 93-104, New York, NY, USA, 2000. Association for Computing Machinery. ISBN 1581132174. doi: 10.1145/342009.335388. URL https://doi.org/10.1145/342009.335388.  
+[27] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In I. Guyon,
+
+U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017. URL https://proceedings.neurips.cc/paper_files/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf.
+
+# NeurIPS Paper Checklist
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+# 2. Limitations
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+# 3. Theory assumptions and proofs
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+
+# 5. Open access to data and code
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+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
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+# 6. Experimental setting/details
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+
+# 7. Experiment statistical significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [Yes]
+
+Justification: We report the standard deviation across several runs with different random seeds for all main metrics in all tables, as stated in Section 4.6. This reflects the statistical reliability of the results by accounting for stochastic factors like random initialization, data shuffling and train-test splitting.
+
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+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
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+# Answer: [Yes]
+
+Justification: Section 4.3 reports the compute resources used in our experiments, including GPU and CPU type, memory, and the typical runtime range per run. It also includes the total compute cost, covering all experiments conducted, including hyperparameter tuning and internal model selection.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
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+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code of ethics
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+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
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+Justification: The research conducted in this paper is in compliance with the NeurIPS Code of Ethics.
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+
+# 10. Broader impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [Yes]
+
+Justification: The paper discusses the potential positive societal impacts of our work, particularly in enhancing network security and safeguarding critical services and infrastructures from attacks. At the same time, it highlights the model's sensitivity to abrupt changes in normal network behavior, which could result in undetected attacks if the network's behavior deviates significantly.
+
+Guidelines:
+
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+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: We do not believe our model has a high risk of misuse, as its deployment to monitor a network environment requires significant resources, effort and careful analysis from security experts.
+
+Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
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+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+# Answer: [Yes]
+
+Justification: The code for GraphIDS and T-MAE was produced by the authors. All other assets (code, data, and models) are either original or properly cited, mentioning their respective licenses. Notably, the implementation of SAFE has no formal license, but we have reached out to the authors, who have granted us permission to use the code for research purposes. We do not publicly redistribute the code, but we explain the changes we made to the original implementation to allow reproducibility.
+
+# Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
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+
+# 13. New assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
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+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and research with human subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+# Answer: [NA]
+
+Justification: This paper does not involve crowdsourcing nor research with human subjects.
+
+# Guidelines:
+
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+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.
+
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+
+# 15. Institutional review board (IRB) approvals or equivalent for research with human subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The current paper does not require IRB approval as it does not contain research with human or animal subjects.
+
+# Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
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+
+# 16. Declaration of LLM usage
+
+Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
+
+Answer: [NA]
+
+Justification: LLMs have not been used for any important, original, or non-standard component of the core methods in this research. Their use was limited to editing or formatting and their output was thoroughly reviewed.
+
+# Guidelines:
+
+- The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.  
+- Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) for what should or should not be described.
+
+# A Additional Details on GraphIDS and Baseline Models
+
+CBLOF [19]. CBLOF is an unsupervised anomaly detection method which identifies outliers based on a clustering algorithm. In this case we use K-means for clustering and we compute the anomaly scores based on the distance to the closest large cluster. As we do for other models, once the anomaly scores are computed, we search for the best threshold on the validation set and we apply it to the test set for the final classification.
+
+Anomal-E [2]. Anomal-E is the first model to apply self-supervised GNNs to network intrusion detection, demonstrating significant performance gains when applying anomaly detection methods to local graph representations compared to raw NetFlow features. The model uses an E-GraphSAGE encoder trained via a modified version of Deep Graph Infomax [22], and generates embeddings that are subsequently processed by traditional unsupervised anomaly detection algorithms, including PCA-based anomaly detection [23], Isolation Forest [24], CBLOF [19], and histogram-based outlier score [25]. For our evaluation, we retained the original GNN encoder configuration, which was already tuned for these datasets, as our attempts at further tuning did not yield performance gains. We did, however, explore and adjust the hyperparameters of the downstream anomaly detection components using the same ranges as in the original work, selecting the best-performing one for each dataset to be included in the main table.
+
+During the preprocessing phase, the original authors report using target encoding for categorical features. Although the specific target used for encoding is not clarified in the paper, their public implementation<sup>3</sup> shows that attack labels are directly used as the target variable—introducing label leakage. This ground-truth information encoded in the input features allows downstream models to learn to identify attacks based on those statistics, undermining the validity of the unsupervised learning setting. To ensure a fair comparison and preserve the integrity of the evaluation, we removed the target encoding step in our implementation.
+
+SAFE [20]. SAFE is an anomaly detection framework that processes tabular network traffic data by first applying feature selection to discard irrelevant columns. The remaining features are then mapped into a 2D grid to create image-like embeddings, which a lightweight CNN-based masked autoencoder is trained to reconstruct, learning meaningful representations in the process. For novelty detection, the latent embeddings produced by the encoder are passed to a local outlier factor detector [26] to identify anomalies. In our evaluation, we tuned the hyperparameters of the LOF anomaly detection component. However, a brief exploration of alternative hyperparameters for the MAE module yielded no performance improvements. Given the high computational cost of tuning and the MAE's limited discrimination ability, as observed in the original codebase, we concluded that further tuning would offer marginal gains and not meaningfully affect the conclusions.
+
+In our experiments, we adopt different evaluation metrics, as the original implementation computes the F1-score for the normal class, effectively measuring the model's ability to recognize benign traffic rather than attacks<sup>4</sup>. While this choice may be acceptable for balanced classes, it masks the model's real performance on the highly imbalanced datasets we consider.
+
+T-MAE. T-MAE refers to our Transformer-based masked autoencoder component, similar to the one used in GraphIDS but applied directly to raw NetFlow features. We use the same batching strategy (batch size of 64 with 512 flow embeddings per batch) and tune its learning rate, weight decay, and dropout. We found that a higher learning rate proved to be especially beneficial for the performance on the NF-UNSW-NB15-v3. However, despite this adjustment, T-MAE exhibits slower convergence, resulting in significantly longer training times. On average, it requires 2.21 hours per run, compared to just 0.87 hours for GraphIDS.
+
+SimpleAE. The SimpleAE ablation replaces the Transformer with a fully connected autoencoder consisting of a two-layer MLP encoder and a two-layer MLP decoder with ReLU activations. It is trained end-to-end jointly with E-GraphSAGE on the same reconstruction objective, isolating the
+
+architectural benefit on top of our end-to-end reconstruction framework. To ensure a fair comparison, we explored different bottleneck dimensions and hyperparameters.
+
+# B Extended Results and Comparative Analysis
+
+# B.1 Qualitative Analysis of Detection Behavior
+
+Figure 4 summarizes model performance across datasets through precision-recall curves. These plots illustrate that GraphIDS consistently matches or outperforms the baselines across a variety of settings.
+
+To better understand GraphIDS's behavior on specific attack types, we plot the distribution of anomaly scores (by density) for each dataset, as shown in Figures 5, 6, 7, and 8. To maintain clarity, we present representative examples without error bars. Each plot includes the classification threshold, allowing us to visualize which attack types were correctly detected and which ones were missed. In particular, GraphIDS's lower performance on NF-UNSW-NB15-v2 is due to a higher rate of false positives, as also demonstrated by the t-SNE visualizations of the GNN and reconstructed embeddings in Figure 10. For the NF-CSE-CIC-IDS2018 datasets (both v2 and v3), the performance drop is primarily caused by misclassifications of Infiltration attacks. These involve delivering a malicious payload via email, which then attempts to exploit internal vulnerabilities by scanning the network. Because this behavior closely resembles normal traffic, GraphIDS struggles to reliably classify it as anomalous without prior knowledge of its specific signature, as illustrated in Figures 11 and 12. In contrast, the strong performance on NF-UNSW-NB15-v3 is reflected in the clear separation between benign and attack clusters in Figure 9.
+
+![](images/12a2b08485f1890a6e1d834fd1a5d55c528f0992a7e06d242dd798a3ce4d7b2f.jpg)  
+Figure 4: Precision-recall curves for all models on each dataset.
+
+![](images/5553e48f6d6d2b11cd7f6675dd20a9daa6c4e7b57c061591cde4af40a2ed605b.jpg)  
+Figure 5: Anomaly score by attack type in NF-UNSW-NB15-v3.
+
+![](images/49d1f4f0e2395235a90a21d95d6311b55ac559ae5d69388de7c9df07c8f69013.jpg)  
+Figure 6: Anomaly score by attack type in NF-UNSW-NB15-v2.
+
+![](images/d8b9830f40f2fbc6fca7fe8f67fa6c944b8c39d7cdb13df5b1e8c9cf853c4865.jpg)  
+Figure 7: Anomaly score by attack type in NF-CSE-CIC-IDS2018-v3.
+
+![](images/8083428d1ad050cdce4533563934c944d96dbcb0cb58d208a2f55c4f3b58a2e7.jpg)  
+Figure 8: Anomaly score by attack type in NF-CSE-CIC-IDS2018-v2.
+
+![](images/3e840111bd4fad2f6afcbd079f33472f677522e86fe6117577bb9d1823ad9b7f.jpg)
+
+![](images/a9f610d2b05f47d5d0f8a5d6b4ac53b3883fa0b9985b8c701c601ea4863cf9b2.jpg)
+
+![](images/575875fdc2962c43b4735c6022686c3c3dbb49fe51c9f712a964acf49cc9fb01.jpg)
+
+![](images/a317af1e9b302575282a923c426c14079b278c0024115e6dc80b526e40b5cf2c.jpg)  
+Figure 9: t-SNE visualization of embeddings by attack type in NF-UNSW-NB15-v3, with density contours illustrating the concentration of benign samples.
+
+![](images/20c49c24237583c67e274d3f9635ee7750503759c005de5c396d91299c55cb45.jpg)
+
+![](images/006efbe49ccc71ab9bfe3d685ceeaf2f07d9eca9d7750619e72ea58c32cd416e.jpg)
+
+![](images/12d03e0acb51b827316492fe0ba07fda98032f02154f37828eddb41ea8b19e1b.jpg)  
+Figure 10: t-SNE visualization of embeddings by attack type in NF-UNSW-NB15-v2.
+
+![](images/439f335109c3774e9305c221808cd9730cb74e0b9160493f898800e78e0ce838.jpg)
+
+![](images/14e0f562ef535023795054a8eb776e487e083f62f63353c1de8ec08c09f2e0bf.jpg)
+
+![](images/522d8366f7d7afd19e72b58537e3c3095775b2cdb3d85eba37ce0be1aafdaa1d.jpg)  
+Figure 11: t-SNE visualization of embeddings by attack type in NF-CSE-CIC-IDS2018-v3.
+
+![](images/d06f7e589bb011ece5afc478800457d59b8a7c20ae79f08c0c06133981f81539.jpg)  
+Figure 12: t-SNE visualization of embeddings by attack type in NF-CSE-CIC-IDS2018-v2.
+
+![](images/9a3c6c6014efadaeaecd66fdc35d38fe7bcdb3db3509bbeeebf9a4bd5ded4b7b.jpg)
+
+<table><tr><td colspan="5">Attack Types</td></tr><tr><td>Benign</td><td>DDOS_attack-HOIC</td><td>DoS Attacks-Hulk</td><td>FTP-BruteForce</td><td></td></tr><tr><td>Bot</td><td>DDoS Attacks-LOIC-HTTP</td><td>DoS Attacks-SlowHTTPTest</td><td>Infiltration</td><td></td></tr><tr><td>Brute_Force_XSS</td><td>DoS Attacks-GoldenEye</td><td>DoS Attacks-Slowloris</td><td>SSH-Bruteforce</td><td></td></tr></table>
+
+# B.2 Extended Baseline Comparison: Anomal-E and Traditional Methods
+
+In Table 4, we compare the training time and peak GPU memory usage of the evaluated models across datasets. Traditional methods such as CBLOF are excluded from this comparison, as they do not leverage GPU resources.
+
+The results highlight the trade-offs between memory usage, training time, and performance across models. SAFE requires very little GPU memory thanks to its shallow architecture, low input dimensionality, and feature selection, but this comes at the cost of longer training times and substantially lower performance, as shown in Figure 4 and in Table 3. In contrast, Anomal-E's original design, which relies on batch gradient descent and aggregates over the full neighborhood, leads to a considerable memory footprint of up to  $30\mathrm{GB}$ , making it impractical for large graphs. GraphIDS offers a balanced compromise between efficiency and accuracy, using about  $1.37\mathrm{GB}$  of GPU memory and training in 0.87 hours on average. SimpleAE further reduces compute, training in about 0.76 hours with a peak of roughly  $428\mathrm{MB}$  of GPU memory, while remaining competitive in accuracy in the main tables. Finally, GraphIDS's mini-batch strategy allows it to learn normal network behavior from the full graphs of the NF-CSE-CIC-IDS2018 datasets without downsampling, which in our experiments led to improved performance and stability.
+
+Tables 5 and 6 summarize the performance of Anomal-E against the set of anomaly detection algorithms introduced in the original paper. These results show that none of these methods, unlike GraphIDS, is able to maintain a consistent performance across all datasets.
+
+In addition, Tables 7 and 8 report results for traditional anomaly detection algorithms applied directly to raw NetFlow features. All these models show substantially lower performance compared to GraphIDS. Among them, CBLOF achieves the most competitive results on average and is used in the main paper as a representative baseline for traditional methods.
+
+Table 4: Comparison of training time and peak GPU memory usage across models.  
+
+<table><tr><td>Model</td><td>Training Time (h)</td><td>Peak Memory (MB)</td></tr><tr><td>SAFE</td><td>3.59 ± 1.34</td><td>66</td></tr><tr><td>Anomal-E</td><td>2.51 ± 1.39</td><td>29,775</td></tr><tr><td>T-MAE</td><td>2.21 ± 2.87</td><td>9,063</td></tr><tr><td>SimpleAE</td><td>0.76 ± 0.65</td><td>428</td></tr><tr><td>GraphIDS</td><td>0.87 ± 0.40</td><td>1,366</td></tr></table>
+
+Table 5: Performance comparison of different anomaly detection algorithms applied to Anomal-E embeddings on the v3 datasets. Results for GraphIDS are included as reference. Bold values indicate statistically significant improvements.  
+
+<table><tr><td>Model</td><td>Metric</td><td>NF-UNSW-NB15-v3</td><td>NF-CSE-CIC-IDS2018-v3</td></tr><tr><td rowspan="2">Anomal-E-CBLOF</td><td>PR-AUC</td><td>0.7827 ± 0.0840</td><td>0.2555 ± 0.0383</td></tr><tr><td>Macro F1</td><td>0.8891 ± 0.1127</td><td>0.6709 ± 0.0394</td></tr><tr><td rowspan="2">Anomal-E-HBOS</td><td>PR-AUC</td><td>0.8735 ± 0.0126</td><td>0.1663 ± 0.0241</td></tr><tr><td>Macro F1</td><td>0.9458 ± 0.0007</td><td>0.5329 ± 0.0487</td></tr><tr><td rowspan="2">Anomal-E-IF</td><td>PR-AUC</td><td>0.7613 ± 0.0530</td><td>0.1812 ± 0.0218</td></tr><tr><td>Macro F1</td><td>0.9166 ± 0.0345</td><td>0.5514 ± 0.0195</td></tr><tr><td rowspan="2">Anomal-E-PCA</td><td>PR-AUC</td><td>0.9032 ± 0.0041</td><td>0.1098 ± 0.0165</td></tr><tr><td>Macro F1</td><td>0.9459 ± 0.0009</td><td>0.4898 ± 0.0347</td></tr><tr><td rowspan="2">GraphIDS (Ours)</td><td>PR-AUC</td><td>0.9998 ± 0.0007</td><td>0.8819 ± 0.0347</td></tr><tr><td>Macro F1</td><td>0.9961 ± 0.0084</td><td>0.9447 ± 0.0213</td></tr></table>
+
+Table 6: Performance comparison of different anomaly detection algorithms applied to Anomal-E embeddings on the v2 datasets.  
+
+<table><tr><td>Model</td><td>Metric</td><td>NF-UNSW-NB15-v2</td><td>NF-CSE-CIC-IDS2018-v2</td></tr><tr><td rowspan="2">Anomal-E-CBLOF</td><td>PR-AUC</td><td>0.7175 ± 0.0041</td><td>0.9287 ± 0.0265</td></tr><tr><td>Macro F1</td><td>0.9262 ± 0.0008</td><td>0.9410 ± 0.0161</td></tr><tr><td rowspan="2">Anomal-E-HBOS</td><td>PR-AUC</td><td>0.7489 ± 0.0074</td><td>0.9154 ± 0.0181</td></tr><tr><td>Macro F1</td><td>0.9156 ± 0.0217</td><td>0.9415 ± 0.0131</td></tr><tr><td rowspan="2">Anomal-E-IF</td><td>PR-AUC</td><td>0.7438 ± 0.0162</td><td>0.8847 ± 0.0789</td></tr><tr><td>Macro F1</td><td>0.9153 ± 0.0216</td><td>0.9332 ± 0.0302</td></tr><tr><td rowspan="2">Anomal-E-PCA</td><td>PR-AUC</td><td>0.7133 ± 0.0034</td><td>0.9178 ± 0.0078</td></tr><tr><td>Macro F1</td><td>0.9262 ± 0.0008</td><td>0.9436 ± 0.0076</td></tr><tr><td rowspan="2">GraphIDS (Ours)</td><td>PR-AUC</td><td>0.8116 ± 0.0367</td><td>0.9201 ± 0.0238</td></tr><tr><td>Macro F1</td><td>0.9264 ± 0.0217</td><td>0.9431 ± 0.0131</td></tr></table>
+
+Table 7: Evaluation of traditional anomaly detection algorithms on the v3 datasets.  
+
+<table><tr><td>Model</td><td>Metric</td><td>NF-UNSW-NB15-v3</td><td>NF-CSE-CIC-IDS2018-v3</td></tr><tr><td rowspan="2">CBLOF</td><td>PR-AUC</td><td>0.3658 ± 0.0634</td><td>0.2638 ± 0.0263</td></tr><tr><td>Macro F1</td><td>0.7319 ± 0.0225</td><td>0.6599 ± 0.0130</td></tr><tr><td rowspan="2">HBOS</td><td>PR-AUC</td><td>0.2604 ± 0.0021</td><td>0.1822 ± 0.0011</td></tr><tr><td>Macro F1</td><td>0.7171 ± 0.0007</td><td>0.5365 ± 0.0070</td></tr><tr><td rowspan="2">IF</td><td>PR-AUC</td><td>0.2537 ± 0.0205</td><td>0.1630 ± 0.0139</td></tr><tr><td>Macro F1</td><td>0.6822 ± 0.0152</td><td>0.5330 ± 0.0160</td></tr><tr><td rowspan="2">PCA</td><td>PR-AUC</td><td>0.4380 ± 0.0038</td><td>0.1200 ± 0.0003</td></tr><tr><td>Macro F1</td><td>0.7554 ± 0.0018</td><td>0.5306 ± 0.0004</td></tr><tr><td rowspan="2">GraphIDS (Ours)</td><td>PR-AUC</td><td>0.9998 ± 0.0007</td><td>0.8819 ± 0.0347</td></tr><tr><td>Macro F1</td><td>0.9961 ± 0.0084</td><td>0.9447 ± 0.0213</td></tr></table>
+
+Table 8: Evaluation of traditional anomaly detection algorithms on the v2 datasets.  
+
+<table><tr><td>Model</td><td>Metric</td><td>NF-UNSW-NB15-v2</td><td>NF-CSE-CIC-IDS2018-v2</td></tr><tr><td rowspan="2">CBLOF</td><td>PR-AUC</td><td>0.2102 ± 0.0157</td><td>0.7822 ± 0.0198</td></tr><tr><td>Macro F1</td><td>0.7046 ± 0.0140</td><td>0.8889 ± 0.0068</td></tr><tr><td rowspan="2">HBOS</td><td>PR-AUC</td><td>0.3197 ± 0.0036</td><td>0.6662 ± 0.0205</td></tr><tr><td>Macro F1</td><td>0.7032 ± 0.0012</td><td>0.8578 ± 0.0034</td></tr><tr><td rowspan="2">IF</td><td>PR-AUC</td><td>0.1914 ± 0.0075</td><td>0.6124 ± 0.0269</td></tr><tr><td>Macro F1</td><td>0.6844 ± 0.0071</td><td>0.8321 ± 0.0099</td></tr><tr><td rowspan="2">PCA</td><td>PR-AUC</td><td>0.2840 ± 0.0039</td><td>0.5911 ± 0.0014</td></tr><tr><td>Macro F1</td><td>0.6975 ± 0.0023</td><td>0.6128 ± 0.0076</td></tr><tr><td rowspan="2">GraphIDS (Ours)</td><td>PR-AUC</td><td>0.8116 ± 0.0367</td><td>0.9201 ± 0.0238</td></tr><tr><td>Macro F1</td><td>0.9264 ± 0.0217</td><td>0.9431 ± 0.0131</td></tr></table>
+
+# C Ablation Studies
+
+In this section, we aim to isolate the individual contributions of specific design choices in GraphIDS. To reduce the computational cost of the ablation study, we conducted experiments over fewer random seeds than those used for the main results. Nevertheless, the setup was sufficient to clearly identify the impact of each component.
+
+# C.1 Effect of Timestamp Features
+
+In this ablation study, we evaluate the impact of including timestamps (FLOW_START_MILLISECONDS and FLOW_END_MILLISECONDS) among the input features. Our goal is to determine whether they provide useful temporal information or only introduce noise. As shown in Table 9, their inclusion has negligible impact on NF-UNSW-NB15-v3, but clearly degrades the performance on NF-CSE-CICIDS2018-v3. This suggests that, overall, excluding timestamps leads to more efficient representations.
+
+Table 9: Effect of including timestamp features on model performance across v3 datasets.  
+
+<table><tr><td>Model</td><td>Metric</td><td>NF-UNSW-NB15-v3</td><td>NF-CSE-CIC-IDS2018-v3</td></tr><tr><td rowspan="2">w/ TS</td><td>PR-AUC</td><td>0.9991 ± 0.0011</td><td>0.7909 ± 0.0151</td></tr><tr><td>Macro F1</td><td>0.9957 ± 0.0091</td><td>0.9088 ± 0.0110</td></tr><tr><td rowspan="2">w/o TS</td><td>PR-AUC</td><td>0.9989 ± 0.0017</td><td>0.8523 ± 0.0283</td></tr><tr><td>Macro F1</td><td>0.9982 ± 0.0029</td><td>0.9385 ± 0.0122</td></tr></table>
+
+# C.2 Effect of Positional Encoding
+
+To investigate whether our model can benefit from sequence modeling, beyond co-occurrence patterns, we temporally ordered the flows in the v3 datasets and added positional encodings to each input window before passing it to the Transformer. We evaluated two variants: sinusoidal and learnable encodings.
+
+For sinusoidal positional encoding, we used the formulation from [27], where the encoding at position  $pos$  and dimension  $i$  is given by:
+
+$$
+\mathrm {P E} _ {(p o s, 2 i)} = \sin \left(\frac {p o s}{1 0 0 0 0 ^ {2 i / d}}\right), \quad \mathrm {P E} _ {(p o s, 2 i + 1)} = \cos \left(\frac {p o s}{1 0 0 0 0 ^ {2 i / d}}\right) \tag {3}
+$$
+
+For learnable positional encoding, we used a parameter matrix  $\mathbf{P} \in \mathbb{R}^{L \times d}$ , with  $L$  as the maximum sequence length and  $d$  the embedding dimension. This matrix is optimized along with the rest of the model during training.
+
+The results in Table 10 indicate that positional encodings have little impact on GraphIDS's performance, suggesting that the model primarily learns global co-occurrence patterns rather than temporal dependencies. To reflect this, we omit positional encodings in the main experiments and shuffle the flow order.
+
+Table 10: Effect of positional encoding across datasets.  
+
+<table><tr><td>Model</td><td>Metric</td><td>NF-UNSW-NB15-v3</td><td>NF-CSE-CIC-IDS2018-v3</td></tr><tr><td rowspan="2">w/ Learnable Encoding</td><td>PR-AUC</td><td>0.9939 ± 0.0126</td><td>0.8572 ± 0.0284</td></tr><tr><td>Macro F1</td><td>0.9873 ± 0.0263</td><td>0.9480 ± 0.0153</td></tr><tr><td rowspan="2">w/ Sinusoidal Encoding</td><td>PR-AUC</td><td>0.9955 ± 0.0110</td><td>0.8537 ± 0.0421</td></tr><tr><td>Macro F1</td><td>0.9904 ± 0.0214</td><td>0.9446 ± 0.0171</td></tr><tr><td rowspan="2">w/o Positional Encoding</td><td>PR-AUC</td><td>0.9955 ± 0.0126</td><td>0.8661 ± 0.0411</td></tr><tr><td>Macro F1</td><td>0.9821 ± 0.0256</td><td>0.9546 ± 0.0099</td></tr></table>
+
+# C.3 Effect of GNN Dropout Rate
+
+As shown in Table 11, the dropout rate in E-GraphSAGE has a relevant impact on GraphIDS's overall performance. Higher dropout rates achieved better results on the NF-UNSW-NB15 datasets, suggesting that the GNN is prone to overfitting in smaller network environments. In these cases, stronger regularization helps the model generalize to unseen data. On the NF-CSE-CIC-IDS2018 datasets, introducing a non-zero dropout rate also helped stabilize the learning process, although its impact on final performance was less pronounced.
+
+Table 11: Effect of the GNN dropout rate across datasets.  
+
+<table><tr><td>Dataset</td><td>Metric</td><td>0.0</td><td>0.25</td><td>0.5</td><td>0.6</td><td>0.7</td></tr><tr><td rowspan="2">NF-UNSW-NB15-v3</td><td>PR-AUC</td><td>0.9773</td><td>0.9619</td><td>0.9845</td><td>0.9998</td><td>0.9790</td></tr><tr><td>Macro F1</td><td>1.0000</td><td>0.9999</td><td>1.0000</td><td>1.0000</td><td>1.0000</td></tr><tr><td rowspan="2">NF-CSE-CIC-IDS2018-v3</td><td>PR-AUC</td><td>0.8758</td><td>0.8645</td><td>0.8630</td><td>0.8461</td><td>0.8621</td></tr><tr><td>Macro F1</td><td>0.9466</td><td>0.9270</td><td>0.9450</td><td>0.9160</td><td>0.9219</td></tr><tr><td rowspan="2">NF-UNSW-NB15-v2</td><td>PR-AUC</td><td>0.8117</td><td>0.8154</td><td>0.8129</td><td>0.8094</td><td>0.8301</td></tr><tr><td>Macro F1</td><td>0.9342</td><td>0.9303</td><td>0.9140</td><td>0.9241</td><td>0.9285</td></tr><tr><td rowspan="2">NF-CSE-CIC-IDS2018-v2</td><td>PR-AUC</td><td>0.8952</td><td>0.8964</td><td>0.9005</td><td>0.8886</td><td>0.8925</td></tr><tr><td>Macro F1</td><td>0.9322</td><td>0.9429</td><td>0.9411</td><td>0.9402</td><td>0.9396</td></tr></table>
+
+# C.4 Effect of Masking Ratio
+
+We found that the masking ratio had a noticeable impact on the model's performance for NF-CSE-CIC-IDS2018-v3. In this case, a masking ratio of 0.15 made the reconstruction task sufficiently challenging for GraphIDS to learn more complex relationships within the flow embeddings. We also noticed that ratios of 0.7 or higher led to gradient explosions and training instability across all datasets.
+
+Table 12: Effect of the attention mask ratio across datasets.  
+
+<table><tr><td>Dataset</td><td>Metric</td><td>0.0</td><td>0.15</td><td>0.3</td><td>0.5</td><td>0.7</td></tr><tr><td rowspan="2">NF-UNSW-NB15-v3</td><td>PR-AUC</td><td>0.9992</td><td>1.0000</td><td>1.0000</td><td>1.0000</td><td>1.0000</td></tr><tr><td>Macro F1</td><td>0.9998</td><td>0.9999</td><td>0.9793</td><td>0.9998</td><td>0.9998</td></tr><tr><td rowspan="2">NF-CSE-CIC-IDS2018-v3</td><td>PR-AUC</td><td>0.8659</td><td>0.8772</td><td>0.8691</td><td>0.8391</td><td>0.8216</td></tr><tr><td>Macro F1</td><td>0.9445</td><td>0.9472</td><td>0.9485</td><td>0.9051</td><td>0.9308</td></tr><tr><td rowspan="2">NF-UNSW-NB15-v2</td><td>PR-AUC</td><td>0.8373</td><td>0.8384</td><td>0.8384</td><td>0.8261</td><td>0.8289</td></tr><tr><td>Macro F1</td><td>0.9344</td><td>0.9342</td><td>0.9344</td><td>0.9299</td><td>0.8756</td></tr><tr><td rowspan="2">NF-CSE-CIC-IDS2018-v2</td><td>PR-AUC</td><td>0.9115</td><td>0.9133</td><td>0.9132</td><td>0.9132</td><td>0.9155</td></tr><tr><td>Macro F1</td><td>0.9390</td><td>0.9419</td><td>0.9419</td><td>0.9398</td><td>0.9414</td></tr></table>
+
+# C.5 Effect of Neighborhood Size
+
+We explored various neighborhood sizes during the initial development phase, as this choice directly impacts both model performance and computational cost. To rigorously validate our design, we conducted an ablation study comparing 1-hop, 2-hop, and 3-hop variants of GraphIDS under identical experimental conditions.
+
+As shown in Table 13, the 1-hop configuration delivers the most consistent performance. On both NF-UNSW-NB15-v3 and NF-CSE-CIC-IDS2018-v3, the 1-hop baseline outperforms deeper configurations in both PR-AUC and Macro F1. While increasing the receptive field to 2 or 3 hops yields marginal improvements on the v2 versions of these datasets, it does not provide a universal benefit and actually degrades performance on the v3 benchmarks.
+
+Crucially, expanding the neighborhood substantially increases training and inference runtime by up to  $3 \times$  and, on average, consumes  $29\%$  more memory. Although the multi-hop configurations
+
+demonstrate that our architecture can effectively aggregate distant information without suffering from severe over-smoothing, the mixed performance gains are insufficient to justify the added latency. Consequently, we maintain the 1-hop neighborhood as the most effective and efficient default for real-time intrusion detection.
+
+Table 13: Effect of neighborhood size (number of GNN hops) across datasets. Mean (std) over seeds.  
+
+<table><tr><td>Dataset</td><td>Metric</td><td>1-hop</td><td>2-hop</td><td>3-hop</td></tr><tr><td rowspan="2">NF-UNSW-NB15-v3</td><td>PR-AUC</td><td>0.9998 ± 0.0007</td><td>0.9994 ± 0.0011</td><td>0.9977 ± 0.0031</td></tr><tr><td>Macro F1</td><td>0.9961 ± 0.0084</td><td>0.9910 ± 0.0164</td><td>0.9839 ± 0.0302</td></tr><tr><td rowspan="2">NF-CSE-CIC-IDS2018-v3</td><td>PR-AUC</td><td>0.8819 ± 0.0347</td><td>0.8556 ± 0.0305</td><td>0.8683 ± 0.0686</td></tr><tr><td>Macro F1</td><td>0.9447 ± 0.0213</td><td>0.9352 ± 0.0094</td><td>0.9362 ± 0.0286</td></tr><tr><td rowspan="2">NF-UNSW-NB15-v2</td><td>PR-AUC</td><td>0.8116 ± 0.0367</td><td>0.8367 ± 0.0109</td><td>0.7766 ± 0.0814</td></tr><tr><td>Macro F1</td><td>0.9264 ± 0.0217</td><td>0.9334 ± 0.0185</td><td>0.9329 ± 0.0128</td></tr><tr><td rowspan="2">NF-CSE-CIC-IDS2018-v2</td><td>PR-AUC</td><td>0.9201 ± 0.0238</td><td>0.9288 ± 0.0269</td><td>0.9308 ± 0.0094</td></tr><tr><td>Macro F1</td><td>0.9431 ± 0.0131</td><td>0.9475 ± 0.0211</td><td>0.9517 ± 0.0148</td></tr></table>
+
+# D Hyperparameters
+
+Table 14 reports the complete set of optimized hyperparameters used for the GraphIDS model. While these were selected to maximize PR-AUC performance, memory usage can be reduced by decreasing the Transformer's window size, while the GNN remains efficient by randomly sampling subsets of neighboring edges.
+
+Table 14: Hyperparameters for the GraphIDS model across datasets. Dataset names are shortened for formatting.  
+
+<table><tr><td>Parameter</td><td>UNSW-NB15-v3</td><td>NF-CSE-CIC-IDS2018-v3</td><td>UNSW-NB15-v2</td><td>NF-CSE-CIC-IDS2018-v2</td></tr><tr><td colspan="5">GNN Parameters</td></tr><tr><td>edim_out</td><td>96</td><td>64</td><td>72</td><td>64</td></tr><tr><td>nhops</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>fanout</td><td>32,768</td><td>32,768</td><td>32,768</td><td>32,768</td></tr><tr><td>agg_type</td><td>mean</td><td>mean</td><td>mean</td><td>mean</td></tr><tr><td>dropout</td><td>0.6</td><td>0.5</td><td>0.75</td><td>0.5</td></tr><tr><td colspan="5">Transformer Parameters</td></tr><tr><td>num_layers</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>num_heads</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td>embed_dim</td><td>48</td><td>32</td><td>48</td><td>32</td></tr><tr><td>window_size</td><td>512</td><td>512</td><td>512</td><td>512</td></tr><tr><td>mask_ratio</td><td>0.15</td><td>0.15</td><td>0.15</td><td>0.15</td></tr><tr><td>dropout</td><td>0.0</td><td>0.2</td><td>0.0</td><td>0.2</td></tr><tr><td colspan="5">Training Parameters</td></tr><tr><td>learning_rate</td><td>\( 1 \times 10^{-4} \)</td><td>\( 1 \times 10^{-4} \)</td><td>\( 1.1 \times 10^{-5} \)</td><td>\( 7.4 \times 10^{-5} \)</td></tr><tr><td>gnn_weight Decay</td><td>0.6</td><td>0.6</td><td>0.6</td><td>0.6</td></tr><tr><td>ae_weight Decay</td><td>0.04</td><td>0.04</td><td>0.046</td><td>0.011</td></tr><tr><td>gnn_batch_size</td><td>16,384</td><td>16,384</td><td>32,768</td><td>16,384</td></tr><tr><td>ae_batch_size</td><td>64</td><td>64</td><td>64</td><td>64</td></tr></table>

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