Daily Papers

The flat lensless camera design reduces the camera size and weight significantly. In this design, the camera lens is replaced by another optical element that interferes with the incoming light. The image is recovered from the raw sensor measurements using a reconstruction algorithm. Yet, the quality of the reconstructed images is not satisfactory. To mitigate this, we propose utilizing a pre-trained diffusion model with a control network and a learned separable transformation for reconstruction. This allows us to build a prototype flat camera with high-quality imaging, presenting state-of-the-art results in both terms of quality and perceptuality. We demonstrate its ability to leverage also textual descriptions of the captured scene to further enhance reconstruction. Our reconstruction method which leverages the strong capabilities of a pre-trained diffusion model can be used in other imaging systems for improved reconstruction results.

Large language models can answer scientific questions, yet a correct output does not reveal whether the model represents or uses the governing physics. Here we show that materials science mechanism information in the open-weight google/gemma-4-E4B-it model has three experimentally separable forms: concepts are readable in individual hidden states, constitutive orientation is carried by controlled transformations between states, and selected internal representations causally control engineering answers. We combine matched direct and Jacobian vocabulary readouts, option-free state geometry, a 60-law counterfactual benchmark and causal interventions. In 50 held-out materials descriptions, three independently fitted Jacobian lenses reproduced concept ranks, and target-free word sets from both readouts enabled blinded identification of 9 of 10 mechanism families. A separate 72-prompt benchmark produced mechanism-specific hidden-state neighborhoods, but an exact graph audit showed that this apparent physical organization was equally explained by numerical comparison. We therefore compared otherwise identical prompts in which only the direction of the physical input was reversed, asking whether the resulting hidden-state movement followed the supplied constitutive law. These state transformations ordered direct, physically neutral and inverse laws across 60 frozen relations and correctly oriented 39 of 40 directional laws, whereas lexical controls were near chance. Bidirectional interventions shifted answer probabilities toward or away from the physically appropriate outcome across all 12 matched cases, while counterfactual state patches transferred opposing decision signals across mechanisms and answer formats. Physical relationships were therefore more visible in controlled state changes than in absolute states alone.

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture (SNA) addresses this by formalising a representational class that unifies additive, quadratic and tensor-decomposed neural models. By constraining interaction order and tensor rank, SNAs impose a structural inductive bias that factorises high-dimensional mappings into low-arity components. Separability need not be a property of the system itself: it often emerges in the coordinates or representations through which the system is expressed. Crucially, this coordinate-aware formulation reveals a structural analogy between chaotic spatiotemporal dynamics and linguistic autoregression. By treating continuous physical states as smooth, separable embeddings, SNAs enable distributional modelling of chaotic systems. This approach mitigates the nonphysical drift characteristics of deterministic operators whilst remaining applicable to discrete sequences. The compositional versatility of this approach is demonstrated across four domains: autonomous waypoint navigation via reinforcement learning, inverse generation of multifunctional microstructures, distributional modelling of turbulent flow and neural language modelling. These results establish the separable neural architecture as a domain-agnostic primitive for predictive and generative intelligence, capable of unifying both deterministic and distributional representations.

Image compression techniques typically focus on compressing rectangular images for human consumption, however, resulting in transmitting redundant content for downstream applications. To overcome this limitation, some previous works propose to semantically structure the bitstream, which can meet specific application requirements by selective transmission and reconstruction. Nevertheless, they divide the input image into multiple rectangular regions according to semantics and ignore avoiding information interaction among them, causing waste of bitrate and distorted reconstruction of region boundaries. In this paper, we propose to decouple an image into multiple groups with irregular shapes based on a customized group mask and compress them independently. Our group mask describes the image at a finer granularity, enabling significant bitrate saving by reducing the transmission of redundant content. Moreover, to ensure the fidelity of selective reconstruction, this paper proposes the concept of group-independent transform that maintain the independence among distinct groups. And we instantiate it by the proposed Group-Independent Swin-Block (GI Swin-Block). Experimental results demonstrate that our framework structures the bitstream with negligible cost, and exhibits superior performance on both visual quality and intelligent task supporting.

The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity. Indeed, knowing the separation power of a family of models is a necessary condition to obtain fine-grained universality results. In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks. We first present a complete characterization of inputs indistinguishable by models derived by a given architecture. From this results, we derive how separability is influenced by hyperparameters and architectural choices-such as activation functions, depth, hidden layer width, and representation types. Notably, all non-polynomial activations, including ReLU and sigmoid, are equivalent in expressivity and reach maximum separation power. Depth improves separation power up to a threshold, after which further increases have no effect. Adding invariant features to hidden representations does not impact separation power. Finally, block decomposition of hidden representations affects separability, with minimal components forming a hierarchy in separation power that provides a straightforward method for comparing the separation power of models.

Recurrent Neural Networks (RNNs) have long been the dominant architecture in sequence-to-sequence learning. RNNs, however, are inherently sequential models that do not allow parallelization of their computations. Transformers are emerging as a natural alternative to standard RNNs, replacing recurrent computations with a multi-head attention mechanism. In this paper, we propose the SepFormer, a novel RNN-free Transformer-based neural network for speech separation. The SepFormer learns short and long-term dependencies with a multi-scale approach that employs transformers. The proposed model achieves state-of-the-art (SOTA) performance on the standard WSJ0-2/3mix datasets. It reaches an SI-SNRi of 22.3 dB on WSJ0-2mix and an SI-SNRi of 19.5 dB on WSJ0-3mix. The SepFormer inherits the parallelization advantages of Transformers and achieves a competitive performance even when downsampling the encoded representation by a factor of 8. It is thus significantly faster and it is less memory-demanding than the latest speech separation systems with comparable performance.

We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesian and parabolic coordinates. The complementary Cartesian separation operator \[ Y=\partial_y^2-ω^2y^2+1/4-c^2{y^2} \] is of Laguerre type, while the parabolic integral \(W=L_2\) is its algebraic Heun partner. With \(Z=[Y,W]\), the defining relations are \[ [Y,Z]=16ω^2W-2bY,\qquad [W,Z]=6Y^2-4HY+2bW+8ω^2(1-c^2), \] where \(H\) is central. This gives a direct superintegrable realization of the Laguerre--Heun algebra.

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (subquadratic) algorithm. We ask to what extent hand-crafting these algorithms and implementations is necessary, what structural priors they encode, and how much knowledge is required to automatically learn a fast algorithm for a provided structured transform. Motivated by a characterization of fast matrix-vector multiplication as products of sparse matrices, we introduce a parameterization of divide-and-conquer methods that is capable of representing a large class of transforms. This generic formulation can automatically learn an efficient algorithm for many important transforms; for example, it recovers the O(N log N) Cooley-Tukey FFT algorithm to machine precision, for dimensions N up to 1024. Furthermore, our method can be incorporated as a lightweight replacement of generic matrices in machine learning pipelines to learn efficient and compressible transformations. On a standard task of compressing a single hidden-layer network, our method exceeds the classification accuracy of unconstrained matrices on CIFAR-10 by 3.9 points -- the first time a structured approach has done so -- with 4X faster inference speed and 40X fewer parameters.

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

Transformers have recently achieved state-of-the-art performance in speech separation. These models, however, are computationally-demanding and require a lot of learnable parameters. This paper explores Transformer-based speech separation with a reduced computational cost. Our main contribution is the development of the Resource-Efficient Separation Transformer (RE-SepFormer), a self-attention-based architecture that reduces the computational burden in two ways. First, it uses non-overlapping blocks in the latent space. Second, it operates on compact latent summaries calculated from each chunk. The RE-SepFormer reaches a competitive performance on the popular WSJ0-2Mix and WHAM! datasets in both causal and non-causal settings. Remarkably, it scales significantly better than the previous Transformer and RNN-based architectures in terms of memory and inference-time, making it more suitable for processing long mixtures.

Equivariant Transformers such as Equiformer have demonstrated the efficacy of applying Transformers to the domain of 3D atomistic systems. However, they are still limited to small degrees of equivariant representations due to their computational complexity. In this paper, we investigate whether these architectures can scale well to higher degrees. Starting from Equiformer, we first replace SO(3) convolutions with eSCN convolutions to efficiently incorporate higher-degree tensors. Then, to better leverage the power of higher degrees, we propose three architectural improvements -- attention re-normalization, separable S^2 activation and separable layer normalization. Putting this all together, we propose EquiformerV2, which outperforms previous state-of-the-art methods on the large-scale OC20 dataset by up to 12% on forces, 4% on energies, offers better speed-accuracy trade-offs, and 2times reduction in DFT calculations needed for computing adsorption energies.

TFDWT is an open-source Python library that allows the construction of TensorFlow Layers for Fast Discrete Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT) in end-to-end backpropagation learning networks. By definition, a multiresolution signal representation using a multi-rate discrete wavelet system creates enriched joint natural-frequency representations. These layers facilitate the construction of multilevel DWT filter banks and Wavelet Packet Transform (WPT) filter banks for a spatial-frequency representation of the inputs and features in shallow or deep networks. The discrete wavelet system partitions the frequency plane into subbands using orthogonal dilated and translated lowpass scaling and highpass wavelet function. The realization of a fast discrete wavelet system is a two-band perfect reconstruction multi-rate filter bank with FIR filters corresponding to the impulse responses of the scaling and wavelet function with downsampling and upsampling operations. A filter bank for a higher dimensional input is a seamless extension by successive separable circular convolutions across each independent axis. The command `pip install TFDWT' installs the latest version of the package.

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the cost of restricting the functional forms. This poses a question on their representation power: are CF-INNs universal approximators for invertible functions? Without a universality, there could be a well-behaved invertible transformation that the CF-INN can never approximate, hence it would render the model class unreliable. We answer this question by showing a convenient criterion: a CF-INN is universal if its layers contain affine coupling and invertible linear functions as special cases. As its corollary, we can affirmatively resolve a previously unsolved problem: whether normalizing flow models based on affine coupling can be universal distributional approximators. In the course of proving the universality, we prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes, a theoretical insight that is of interest by itself.

Single-image reflection separation is fundamentally challenged by the entanglement of transmission and reflection layers under complex image formation processes. Existing approaches largely rely on simplified assumptions or independent modeling, limiting their ability to handle real-world scenarios. In this work, we revisit the problem from a unified perspective and identify a key issue of existing approaches, i.e., the widely adopted linear composition model in the sRGB domain fails to capture the nonlinear coupling introduced by real-world image signal processing pipelines. To address this, we introduce a learnable nonlinear superposition model that more faithfully characterizes layer interactions and improves decomposition fidelity. Building upon this formulation, we propose a generalized dual-stream interactive framework that explicitly models bidirectional dependencies between transmission and reflection through feature exchange. This framework unifies activation-, gating-, and attention-based interaction mechanisms, and is compatible with both CNN and Transformer backbones. Extensive experiments on diverse real-world benchmarks demonstrate that the proposed approach achieves superior performance with strong generalization capability. More importantly, our study reveals that reflection separation is not about undoing a linear mixture, but about learning nonlinear formation and interaction}, offering new insights into the design of principled image decomposition models. Code and models are publicly available at https://mingcv.github.io/DIRS-Page.

Time-domain Transformer neural networks have proven their superiority in speech separation tasks. However, these models usually have a large number of network parameters, thus often encountering the problem of GPU memory explosion. In this paper, we proposed Tiny-Sepformer, a tiny version of Transformer network for speech separation. We present two techniques to reduce the model parameters and memory consumption: (1) Convolution-Attention (CA) block, spliting the vanilla Transformer to two paths, multi-head attention and 1D depthwise separable convolution, (2) parameter sharing, sharing the layer parameters within the CA block. In our experiments, Tiny-Sepformer could greatly reduce the model size, and achieves comparable separation performance with vanilla Sepformer on WSJ0-2/3Mix datasets.

Language models trained on natural text learn to represent numbers using periodic features with dominant periods at T=2, 5, 10. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs, and classical word embeddings trained in different ways all learn features that have period-T spikes in the Fourier domain, only some learn geometrically separable features that can be used to linearly classify a number mod-T. To explain this incongruity, we prove that Fourier domain sparsity is necessary but not sufficient for mod-T geometric separability. Empirically, we investigate when model training yields geometrically separable features, finding that the data, architecture, optimizer, and tokenizer all play key roles. In particular, we identify two different routes through which models can acquire geometrically separable features: they can learn them from complementary co-occurrence signals in general language data, including text-number co-occurrence and cross-number interaction, or from multi-token (but not single-token) addition problems. Overall, our results highlight the phenomenon of convergent evolution in feature learning: A diverse range of models learn similar features from different training signals.

In recent years, many video tasks have achieved breakthroughs by utilizing the vision transformer and establishing spatial-temporal decoupling for feature extraction. Although multi-view 3D reconstruction also faces multiple images as input, it cannot immediately inherit their success due to completely ambiguous associations between unstructured views. There is not usable prior relationship, which is similar to the temporally-coherence property in a video. To solve this problem, we propose a novel transformer network for Unstructured Multiple Images (UMIFormer). It exploits transformer blocks for decoupled intra-view encoding and designed blocks for token rectification that mine the correlation between similar tokens from different views to achieve decoupled inter-view encoding. Afterward, all tokens acquired from various branches are compressed into a fixed-size compact representation while preserving rich information for reconstruction by leveraging the similarities between tokens. We empirically demonstrate on ShapeNet and confirm that our decoupled learning method is adaptable for unstructured multiple images. Meanwhile, the experiments also verify our model outperforms existing SOTA methods by a large margin. Code will be available at https://github.com/GaryZhu1996/UMIFormer.

Uniform random rotations are a useful primitive in applications such as fast Johnson-Lindenstrauss embeddings, kernel approximation, communication-efficient learning, and recent AI compression pipelines, but they are computationally expensive to generate and apply in high dimensions. A common practical replacement is repeated structured random rotations built from Walsh-Hadamard transforms and random sign diagonals. Applying the structured random rotation twice has been shown empirically to be useful, but the supporting theory is still limited. In this paper we study the approximation quality achieved when using this two-block structured Hadamard rotation. Our results are both positive and negative. On the positive side, we prove that every fixed coordinate of the two-block transform converges uniformly, over all inputs, to the corresponding coordinate of a uniformly rotated vector, with an explicit Kolmogorov-distance bound of order d^{-1/5}. On the negative side, we prove an explicit lower bound on the Wasserstein distance between the full vector distributions, showing that the two-block transform is not a globally accurate surrogate for a uniform random rotation in the worst case. For the extremal input used in the lower bound, we also prove a matching asymptotic upper bound, showing that the lower-bound scale is sharp for that input. Taken together, the results identify a clear separation between one-dimensional marginal behavior, where approximation improves with dimension, and full high-dimensional geometry, where a nonvanishing discrepancy remains. This provides a partial theoretical explanation for the empirical success of structured Hadamard rotations in some algorithms, while also clarifying the limitations of treating them as drop-in replacements for true uniform random rotations.

Shift operation is an efficient alternative over depthwise separable convolution. However, it is still bottlenecked by its implementation manner, namely memory movement. To put this direction forward, a new and novel basic component named Sparse Shift Layer (SSL) is introduced in this paper to construct efficient convolutional neural networks. In this family of architectures, the basic block is only composed by 1x1 convolutional layers with only a few shift operations applied to the intermediate feature maps. To make this idea feasible, we introduce shift operation penalty during optimization and further propose a quantization-aware shift learning method to impose the learned displacement more friendly for inference. Extensive ablation studies indicate that only a few shift operations are sufficient to provide spatial information communication. Furthermore, to maximize the role of SSL, we redesign an improved network architecture to Fully Exploit the limited capacity of neural Network (FE-Net). Equipped with SSL, this network can achieve 75.0% top-1 accuracy on ImageNet with only 563M M-Adds. It surpasses other counterparts constructed by depthwise separable convolution and the networks searched by NAS in terms of accuracy and practical speed.

Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model size compression. However, these studies often approach various lossy and lossless compression methods in isolation, leading to challenges in achieving high compression ratios efficiently. This work proposes a post-training model size compression method that combines lossy and lossless compression in a unified way. We first propose a unified parametric weight transformation, which ensures different lossy compression methods can be performed jointly in a post-training manner. Then, a dedicated differentiable counter is introduced to guide the optimization of lossy compression to arrive at a more suitable point for later lossless compression. Additionally, our method can easily control a desired global compression ratio and allocate adaptive ratios for different layers. Finally, our method can achieve a stable 10times compression ratio without sacrificing accuracy and a 20times compression ratio with minor accuracy loss in a short time. Our code is available at https://github.com/ModelTC/L2_Compression .

Deep neural networks are susceptible to adversarial attacks due to the accumulation of perturbations in the feature level, and numerous works have boosted model robustness by deactivating the non-robust feature activations that cause model mispredictions. However, we claim that these malicious activations still contain discriminative cues and that with recalibration, they can capture additional useful information for correct model predictions. To this end, we propose a novel, easy-to-plugin approach named Feature Separation and Recalibration (FSR) that recalibrates the malicious, non-robust activations for more robust feature maps through Separation and Recalibration. The Separation part disentangles the input feature map into the robust feature with activations that help the model make correct predictions and the non-robust feature with activations that are responsible for model mispredictions upon adversarial attack. The Recalibration part then adjusts the non-robust activations to restore the potentially useful cues for model predictions. Extensive experiments verify the superiority of FSR compared to traditional deactivation techniques and demonstrate that it improves the robustness of existing adversarial training methods by up to 8.57% with small computational overhead. Codes are available at https://github.com/wkim97/FSR.

We introduce UniGraspTransformer, a universal Transformer-based network for dexterous robotic grasping that simplifies training while enhancing scalability and performance. Unlike prior methods such as UniDexGrasp++, which require complex, multi-step training pipelines, UniGraspTransformer follows a streamlined process: first, dedicated policy networks are trained for individual objects using reinforcement learning to generate successful grasp trajectories; then, these trajectories are distilled into a single, universal network. Our approach enables UniGraspTransformer to scale effectively, incorporating up to 12 self-attention blocks for handling thousands of objects with diverse poses. Additionally, it generalizes well to both idealized and real-world inputs, evaluated in state-based and vision-based settings. Notably, UniGraspTransformer generates a broader range of grasping poses for objects in various shapes and orientations, resulting in more diverse grasp strategies. Experimental results demonstrate significant improvements over state-of-the-art, UniDexGrasp++, across various object categories, achieving success rate gains of 3.5%, 7.7%, and 10.1% on seen objects, unseen objects within seen categories, and completely unseen objects, respectively, in the vision-based setting. Project page: https://dexhand.github.io/UniGraspTransformer.

Although deep learning has substantially advanced speech separation in recent years, most existing studies continue to prioritize separation quality while overlooking computational efficiency, an essential factor for low-latency speech processing in real-time applications. In this paper, we propose SepPrune, the first structured pruning framework specifically designed to compress deep speech separation models and reduce their computational cost. SepPrune begins by analyzing the computational structure of a given model to identify layers with the highest computational burden. It then introduces a differentiable masking strategy to enable gradient-driven channel selection. Based on the learned masks, SepPrune prunes redundant channels and fine-tunes the remaining parameters to recover performance. Extensive experiments demonstrate that this learnable pruning paradigm yields substantial advantages for channel pruning in speech separation models, outperforming existing methods. Notably, a model pruned with SepPrune can recover 85% of the performance of a pre-trained model (trained over hundreds of epochs) with only one epoch of fine-tuning, and achieves convergence 36times faster than training from scratch. Code is available at https://github.com/itsnotacie/SepPrune.

Modern retrieval system often requires recomputing the representation of every piece of data in the gallery when updating to a better representation model. This process is known as backfilling and can be especially costly in the real world where the gallery often contains billions of samples. Recently, researchers have proposed the idea of Backward Compatible Training (BCT) where the new representation model can be trained with an auxiliary loss to make it backward compatible with the old representation. In this way, the new representation can be directly compared with the old representation, in principle avoiding the need for any backfilling. However, followup work shows that there is an inherent tradeoff where a backward compatible representation model cannot simultaneously maintain the performance of the new model itself. This paper reports our ``not-so-surprising'' finding that adding extra dimensions to the representation can help here. However, we also found that naively increasing the dimension of the representation did not work. To deal with this, we propose Backward-compatible Training with a novel Basis Transformation (BT^2). A basis transformation (BT) is basically a learnable set of parameters that applies an orthonormal transformation. Such a transformation possesses an important property whereby the original information contained in its input is retained in its output. We show in this paper how a BT can be utilized to add only the necessary amount of additional dimensions. We empirically verify the advantage of BT^2 over other state-of-the-art methods in a wide range of settings. We then further extend BT^2 to other challenging yet more practical settings, including significant change in model architecture (CNN to Transformers), modality change, and even a series of updates in the model architecture mimicking the evolution of deep learning models.

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides exact translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods.

We present Three-Phase Transformer (3PT), a residual-stream structural prior for decoder-only Transformers on a standard SwiGLU + RMSNorm + RoPE + GQA backbone. The hidden vector is partitioned into N equally-sized cyclic channels, each maintained by phase-respecting ops: a per-channel RMSNorm, a 2D Givens rotation between attention and FFN that rotates each channel by theta + i*(2*pi/N), and a head-count constraint aligning GQA heads with the partition. The architecture is a self-stabilizing equilibrium between scrambling and re-imposition, not a bolted-on module. The partition carves out a one-dimensional DC subspace orthogonal to the channels, into which we inject a fixed Gabriel's horn profile r(p) = 1/(p+1) as an absolute-position side-channel composing orthogonally with RoPE's relative-position rotation. The canonical N=3 borrows its metaphor from balanced three-phase AC, where three sinusoids 120 degrees apart sum to zero with no anti-correlated pair. At 123M parameters on WikiText-103, 3PT achieves -7.20% perplexity (-2.62% bits-per-byte) over a matched RoPE-Only baseline at +1,536 parameters (0.00124% of total), with 1.93x step-count convergence speedup (1.64x wall-clock). N behaves as a parameter-sharing knob rather than a unique optimum: at 5.5M an N-sweep over {1,2,3,4,6,8,12} is near-monotone with N=1 winning; at 123M a three-seed sweep finds N=3 and N=1 statistically indistinguishable. The load-bearing mechanism is the channel-partitioned residual stream, per-block rotation, per-phase normalization, and horn DC injection. We characterize (a) self-stabilization of the geometry without explicit enforcement, a novel instance of the conservation-law framework for neural networks; (b) a U-shaped depth profile of rotation-angle drift at 12 layers; (c) orthogonal composition with RoPE, attention, and FFN.

We tackle the task of geometric image editing, where an object within an image is repositioned, reoriented, or reshaped while preserving overall scene coherence. Previous diffusion-based editing methods often attempt to handle all relevant subtasks in a single step, proving difficult when transformations become large or structurally complex. We address this by proposing a decoupled pipeline that separates object transformation, source region inpainting, and target region refinement. Both inpainting and refinement are implemented using a training-free diffusion approach, FreeFine. In experiments on our new GeoBench benchmark, which contains both 2D and 3D editing scenarios, FreeFine outperforms state-of-the-art alternatives in image fidelity, and edit precision, especially under demanding transformations. Code and benchmark are available at: https://github.com/CIawevy/FreeFine

We investigate how pair-wise data augmentation techniques like Mixup affect the sample complexity of finding optimal decision boundaries in a binary linear classification problem. For a family of data distributions with a separability constant kappa, we analyze how well the optimal classifier in terms of training loss aligns with the optimal one in test accuracy (i.e., Bayes optimal classifier). For vanilla training without augmentation, we uncover an interesting phenomenon named the curse of separability. As we increase kappa to make the data distribution more separable, the sample complexity of vanilla training increases exponentially in kappa; perhaps surprisingly, the task of finding optimal decision boundaries becomes harder for more separable distributions. For Mixup training, we show that Mixup mitigates this problem by significantly reducing the sample complexity. To this end, we develop new concentration results applicable to n^2 pair-wise augmented data points constructed from n independent data, by carefully dealing with dependencies between overlapping pairs. Lastly, we study other masking-based Mixup-style techniques and show that they can distort the training loss and make its minimizer converge to a suboptimal classifier in terms of test accuracy.

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at generating independent configurations. We show that, using a carefully constructed network architecture, our approach can be easily scaled to large lattice volumes with minimal retraining effort. The source code for our implementation is publicly available online at https://github.com/nftqcd/fthmc.

Recently, diffusion transformers have gained wide attention with its excellent performance in text-to-image and text-to-vidoe models, emphasizing the need for transformers as backbone for diffusion models. Transformer-based models have shown better generalization capability compared to CNN-based models for general vision tasks. However, much less has been explored in the existing literature regarding the capabilities of transformer-based diffusion backbones and expanding their generative prowess to other datasets. This paper focuses on enabling a single pre-trained diffusion transformer model to scale across multiple datasets swiftly, allowing for the completion of diverse generative tasks using just one model. To this end, we propose DiffScaler, an efficient scaling strategy for diffusion models where we train a minimal amount of parameters to adapt to different tasks. In particular, we learn task-specific transformations at each layer by incorporating the ability to utilize the learned subspaces of the pre-trained model, as well as the ability to learn additional task-specific subspaces, which may be absent in the pre-training dataset. As these parameters are independent, a single diffusion model with these task-specific parameters can be used to perform multiple tasks simultaneously. Moreover, we find that transformer-based diffusion models significantly outperform CNN-based diffusion models methods while performing fine-tuning over smaller datasets. We perform experiments on four unconditional image generation datasets. We show that using our proposed method, a single pre-trained model can scale up to perform these conditional and unconditional tasks, respectively, with minimal parameter tuning while performing as close as fine-tuning an entire diffusion model for that particular task.

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

In this work, we study the task of multi-singer separation in a cappella music, where the number of active singers varies across mixtures. To address this, we use a power set-based data augmentation strategy that expands limited multi-singer datasets into exponentially more training samples. To separate singers, we introduce SepACap, an adaptation of SepReformer, a state-of-the-art speaker separation model architecture. We adapt the model with periodic activations and a composite loss function that remains effective when stems are silent, enabling robust detection and separation. Experiments on the JaCappella dataset demonstrate that our approach achieves state-of-the-art performance in both full-ensemble and subset singer separation scenarios, outperforming spectrogram-based baselines while generalizing to realistic mixtures with varying numbers of singers.

We present an interpretation of Inception modules in convolutional neural networks as being an intermediate step in-between regular convolution and the depthwise separable convolution operation (a depthwise convolution followed by a pointwise convolution). In this light, a depthwise separable convolution can be understood as an Inception module with a maximally large number of towers. This observation leads us to propose a novel deep convolutional neural network architecture inspired by Inception, where Inception modules have been replaced with depthwise separable convolutions. We show that this architecture, dubbed Xception, slightly outperforms Inception V3 on the ImageNet dataset (which Inception V3 was designed for), and significantly outperforms Inception V3 on a larger image classification dataset comprising 350 million images and 17,000 classes. Since the Xception architecture has the same number of parameters as Inception V3, the performance gains are not due to increased capacity but rather to a more efficient use of model parameters.

Flow-based propagation and spatiotemporal Transformer are two mainstream mechanisms in video inpainting (VI). Despite the effectiveness of these components, they still suffer from some limitations that affect their performance. Previous propagation-based approaches are performed separately either in the image or feature domain. Global image propagation isolated from learning may cause spatial misalignment due to inaccurate optical flow. Moreover, memory or computational constraints limit the temporal range of feature propagation and video Transformer, preventing exploration of correspondence information from distant frames. To address these issues, we propose an improved framework, called ProPainter, which involves enhanced ProPagation and an efficient Transformer. Specifically, we introduce dual-domain propagation that combines the advantages of image and feature warping, exploiting global correspondences reliably. We also propose a mask-guided sparse video Transformer, which achieves high efficiency by discarding unnecessary and redundant tokens. With these components, ProPainter outperforms prior arts by a large margin of 1.46 dB in PSNR while maintaining appealing efficiency.

Deep learning techniques for separating audio into different sound sources face several challenges. Standard architectures require training separate models for different types of audio sources. Although some universal separators employ a single model to target multiple sources, they have difficulty generalizing to unseen sources. In this paper, we propose a three-component pipeline to train a universal audio source separator from a large, but weakly-labeled dataset: AudioSet. First, we propose a transformer-based sound event detection system for processing weakly-labeled training data. Second, we devise a query-based audio separation model that leverages this data for model training. Third, we design a latent embedding processor to encode queries that specify audio targets for separation, allowing for zero-shot generalization. Our approach uses a single model for source separation of multiple sound types, and relies solely on weakly-labeled data for training. In addition, the proposed audio separator can be used in a zero-shot setting, learning to separate types of audio sources that were never seen in training. To evaluate the separation performance, we test our model on MUSDB18, while training on the disjoint AudioSet. We further verify the zero-shot performance by conducting another experiment on audio source types that are held-out from training. The model achieves comparable Source-to-Distortion Ratio (SDR) performance to current supervised models in both cases.

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

Power transforms, such as the Box-Cox transform and Tukey's ladder of powers, are a fundamental tool in mathematics and statistics. These transforms are primarily used for normalizing and standardizing datasets, effectively by raising values to a power. In this work I present a novel power transform, and I show that it serves as a unifying framework for wide family of loss functions, kernel functions, probability distributions, bump functions, and neural network activation functions.

We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix) to optimize non-paraxial specifications (e.g., optical aberrations). In this study, we propose two kinds of three-matrix decomposition of ABCD matrices by focusing on the fact that the ABCD matrices have three real-number degrees of freedom. In addition, we formulate a transformation between the two kinds of decomposition for a single matrix, which can increase or decrease the number of refraction surfaces in the optical configuration while keeping the paraxial specifications fixed. This nature is useful for the optical design of multi-component systems with optimized non-paraxial characteristics.

Transformer-based models, capable of learning better global dependencies, have recently demonstrated exceptional representation learning capabilities in computer vision and medical image analysis. Transformer reformats the image into separate patches and realizes global communication via the self-attention mechanism. However, positional information between patches is hard to preserve in such 1D sequences, and loss of it can lead to sub-optimal performance when dealing with large amounts of heterogeneous tissues of various sizes in 3D medical image segmentation. Additionally, current methods are not robust and efficient for heavy-duty medical segmentation tasks such as predicting a large number of tissue classes or modeling globally inter-connected tissue structures. To address such challenges and inspired by the nested hierarchical structures in vision transformer, we proposed a novel 3D medical image segmentation method (UNesT), employing a simplified and faster-converging transformer encoder design that achieves local communication among spatially adjacent patch sequences by aggregating them hierarchically. We extensively validate our method on multiple challenging datasets, consisting of multiple modalities, anatomies, and a wide range of tissue classes, including 133 structures in the brain, 14 organs in the abdomen, 4 hierarchical components in the kidneys, inter-connected kidney tumors and brain tumors. We show that UNesT consistently achieves state-of-the-art performance and evaluate its generalizability and data efficiency. Particularly, the model achieves whole brain segmentation task complete ROI with 133 tissue classes in a single network, outperforming prior state-of-the-art method SLANT27 ensembled with 27 networks.

The objective of this paper is to be able to separate a video into its natural layers, and to control which of the separated layers to attend to. For example, to be able to separate reflections, transparency or object motion. We make the following three contributions: (i) we introduce a new structured neural network architecture that explicitly incorporates layers (as spatial masks) into its design. This improves separation performance over previous general purpose networks for this task; (ii) we demonstrate that we can augment the architecture to leverage external cues such as audio for controllability and to help disambiguation; and (iii) we experimentally demonstrate the effectiveness of our approach and training procedure with controlled experiments while also showing that the proposed model can be successfully applied to real-word applications such as reflection removal and action recognition in cluttered scenes.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Detection Transformer (DETR) directly transforms queries to unique objects by using one-to-one bipartite matching during training and enables end-to-end object detection. Recently, these models have surpassed traditional detectors on COCO with undeniable elegance. However, they differ from traditional detectors in multiple designs, including model architecture and training schedules, and thus the effectiveness of one-to-one matching is not fully understood. In this work, we conduct a strict comparison between the one-to-one Hungarian matching in DETRs and the one-to-many label assignments in traditional detectors with non-maximum supervision (NMS). Surprisingly, we observe one-to-many assignments with NMS consistently outperform standard one-to-one matching under the same setting, with a significant gain of up to 2.5 mAP. Our detector that trains Deformable-DETR with traditional IoU-based label assignment achieved 50.2 COCO mAP within 12 epochs (1x schedule) with ResNet50 backbone, outperforming all existing traditional or transformer-based detectors in this setting. On multiple datasets, schedules, and architectures, we consistently show bipartite matching is unnecessary for performant detection transformers. Furthermore, we attribute the success of detection transformers to their expressive transformer architecture. Code is available at https://github.com/jozhang97/DETA.

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For n axis-aligned rectangles inside an axis-aligned bounding box B, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches B and the density k is minimized, where k is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box B. REP is NP-hard for k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 2-approximation algorithm for SEP with kgeq2 with time complexity O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for kgeq 3 is 3/2 which is tight. We also give a 8-approximation algorithm for REP with time complexity O(nlog n+nk) and give a MPC version of this algorithm for k=O(1) which is the first parallel algorithm for this problem.

We introduce ReplaceMe, a generalized training-free depth pruning method that effectively replaces transformer blocks with a linear operation, while maintaining high performance for low compression ratios. In contrast to conventional pruning approaches that require additional training or fine-tuning, our approach requires only a small calibration dataset that is used to estimate a linear transformation, which approximates the pruned blocks. The estimated linear mapping can be seamlessly merged with the remaining transformer blocks, eliminating the need for any additional network parameters. Our experiments show that ReplaceMe consistently outperforms other training-free approaches and remains highly competitive with state-of-the-art pruning methods that involve extensive retraining/fine-tuning and architectural modifications. Applied to several large language models (LLMs), ReplaceMe achieves up to 25\% pruning while retaining approximately 90\% of the original model's performance on open benchmarks - without any training or healing steps, resulting in minimal computational overhead. We provide an open-source library implementing ReplaceMe alongside several state-of-the-art depth pruning techniques, available at https://github.com/mts-ai/ReplaceMe

This paper proposes an unsupervised method that leverages topological characteristics of data manifolds to estimate class separability of the data without requiring labels. Experiments conducted in this paper on several datasets demonstrate a clear correlation and consistency between the class separability estimated by the proposed method with supervised metrics like Fisher Discriminant Ratio~(FDR) and cross-validation of a classifier, which both require labels. This can enable implementing learning paradigms aimed at learning from both labeled and unlabeled data, like semi-supervised and transductive learning. This would be particularly useful when we have limited labeled data and a relatively large unlabeled dataset that can be used to enhance the learning process. The proposed method is implemented for language model fine-tuning with automated stopping criterion by monitoring class separability of the embedding-space manifold in an unsupervised setting. The proposed methodology has been first validated on synthetic data, where the results show a clear consistency between class separability estimated by the proposed method and class separability computed by FDR. The method has been also implemented on both public and internal data. The results show that the proposed method can effectively aid -- without the need for labels -- a decision on when to stop or continue the fine-tuning of a language model and which fine-tuning iteration is expected to achieve a maximum classification performance through quantification of the class separability of the embedding manifold.

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-isomorphic geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks. Our code is available at https://github.com/yonatansverdlov/E-GenNet.

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between representations and ensuring compatibility across independently trained neural networks. In the literature, two primary approaches are commonly used to adapt different learned representations: affine transformations, which adapt well to specific distributions but can significantly alter the original representation, and orthogonal transformations, which preserve the original structure with strict geometric constraints but limit adaptability. A key challenge is adapting the latent spaces of updated models to align with those of previous models on downstream distributions while preserving the newly learned representation spaces. In this paper, we impose a relaxed orthogonality constraint, namely λ-Orthogonality regularization, while learning an affine transformation, to obtain distribution-specific adaptation while retaining the original learned representations. Extensive experiments across various architectures and datasets validate our approach, demonstrating that it preserves the model's zero-shot performance and ensures compatibility across model updates. Code available at: https://github.com/miccunifi/lambda_orthogonality.git{https://github.com/miccunifi/lambda\_orthogonality}.

The Transformer architecture has revolutionized various regions since it was proposed, and its effectiveness largely depends on the ability to encode positional information. Traditional position encoding methods exhibit significant limitations due to lack of robustness and flexibility of position. Therefore, Rotary Positional Encoding (RoPE) was proposed to alleviate these issues, which integrates positional information by rotating the embeddings in the attention mechanism. However, RoPE requires manually defined rotation matrices with limited transformation space, constraining the model's capacity. In this work, we propose ComRoPE, which generalizes RoPE by defining it in terms of trainable commuting angle matrices. Specifically, we demonstrate that pairwise commutativity of these matrices is essential for RoPE to achieve scalability and positional robustness. We formally define the RoPE Equation, which is an essential condition that ensures consistent performance with position offsets. Based on the theoretical analysis, we present two types of trainable commuting angle matrices as sufficient solutions to the RoPE equation, which significantly improve performance, surpassing the current state-of-the-art method by 1.6% at training resolution and 2.9% at higher resolution on the ImageNet-1K dataset. Furthermore, our framework shows versatility in generalizing to existing RoPE formulations and offering new insights for future positional encoding research. To ensure reproducibility, the source code and instructions are available at https://github.com/Longin-Yu/ComRoPE

The Transformer model has revolutionized Natural Language Processing tasks such as Neural Machine Translation, and many efforts have been made to study the Transformer architecture, which increased its efficiency and accuracy. One potential area for improvement is to address the computation of empty tokens that the Transformer computes only to discard them later, leading to an unnecessary computational burden. To tackle this, we propose an algorithm that sorts translation sentence pairs based on their length before batching, minimizing the waste of computing power. Since the amount of sorting could violate the independent and identically distributed (i.i.d) data assumption, we sort the data partially. In experiments, we apply the proposed method to English-Korean and English-Luganda language pairs for machine translation and show that there are gains in computational time while maintaining the performance. Our method is independent of architectures, so that it can be easily integrated into any training process with flexible data lengths.

Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object. Yet every weight matrix carries two distinct quantities -- a magnitude and a direction -- and all optimizers stepping in the matrix as a whole couple their dynamics: the directional change from an update depends on the current magnitude, while the magnitude drifts as a byproduct of learning the direction, so neither is governed directly by the learning rate. Typical training therefore leans on surrounding recipes such as weight decay and warmup to keep learning stable at scale, though these regulate the coupling only indirectly; other recent methods instead constrain the weight to a fixed-norm sphere, but add no learnable magnitude, leaving scale control to normalization layers alone. We propose Magnitude--Direction (MD) Decoupling, an optimizer modification that factorizes each weight into a fixed-norm direction on a hypersphere and learnable per-row and per-column magnitude gains, updated at separate learning rates, all while the model still sees a single fused weight tensor. The method is agnostic to the base optimizer and removes the need for weight decay and warmup. Across both Adam and Muon, MD Decoupling improves on well-tuned baselines, transfers the optimal LR across model width without retuning, and continues to help at scale on large Mixture-of-Experts (MoE) models. Treating magnitude and direction as separately controlled quantities thus yields more predictable training dynamics and a simple, broadly applicable improvement to modern optimizers.

Model merging aims to combine multiple fine-tuned models into a single set of weights that performs well across all source tasks. While prior work has shown that merging can approximate the performance of individual fine-tuned models for each task, it largely overlooks scenarios where models are compressed into low-rank representations, either through low-rank adaptation (LoRA) or post-training singular value decomposition (SVD). We first demonstrate that applying conventional merging methods to low-rank weights leads to severe performance degradation in the merged model. Motivated by this phenomenon, we propose a fundamentally different approach: instead of collapsing all adapters into one set of weights, we construct a compact basis (e.g., an equivalent of holding two or more models) from which original task-specific models can be recovered via linear combination. This reframes merging as generating a reconstruction-capable model space rather than producing a single merged model. Crucially, this allows us to ``revert'' to each individual model when needed, recognizing that no merged model can consistently outperform one specialized for its task. Building on this insight, we introduce our method, Reversible Model Merging (RMM), an efficient, data-free, and flexible method that provides a closed-form solution for selecting the optimal basis of model weights and task-specific coefficients for linear combination. Extensive experiments across diverse datasets and model scales demonstrate that RMM consistently outperforms existing merging approaches, preserving the performance of low-rank compressed models by a significant margin.

We present a neat yet effective recursive operation on vision transformers that can improve parameter utilization without involving additional parameters. This is achieved by sharing weights across the depth of transformer networks. The proposed method can obtain a substantial gain (~2%) simply using naive recursive operation, requires no special or sophisticated knowledge for designing principles of networks, and introduces minimal computational overhead to the training procedure. To reduce the additional computation caused by recursive operation while maintaining the superior accuracy, we propose an approximating method through multiple sliced group self-attentions across recursive layers which can reduce the cost consumption by 10~30% with minimal performance loss. We call our model Sliced Recursive Transformer (SReT), a novel and parameter-efficient vision transformer design that is compatible with a broad range of other designs for efficient ViT architectures. Our best model establishes significant improvement on ImageNet-1K over state-of-the-art methods while containing fewer parameters. The proposed weight sharing mechanism by sliced recursion structure allows us to build a transformer with more than 100 or even 1000 shared layers with ease while keeping a compact size (13~15M), to avoid optimization difficulties when the model is too large. The flexible scalability has shown great potential for scaling up models and constructing extremely deep vision transformers. Code is available at https://github.com/szq0214/SReT.

Differentiable architecture search (DARTS) is successfully applied in many vision tasks. However, directly using DARTS for Transformers is memory-intensive, which renders the search process infeasible. To this end, we propose a multi-split reversible network and combine it with DARTS. Specifically, we devise a backpropagation-with-reconstruction algorithm so that we only need to store the last layer's outputs. By relieving the memory burden for DARTS, it allows us to search with larger hidden size and more candidate operations. We evaluate the searched architecture on three sequence-to-sequence datasets, i.e., WMT'14 English-German, WMT'14 English-French, and WMT'14 English-Czech. Experimental results show that our network consistently outperforms standard Transformers across the tasks. Moreover, our method compares favorably with big-size Evolved Transformers, reducing search computation by an order of magnitude.

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

The growing size of datasets and deep learning models has made faster and memory-efficient training crucial. Reversible transformers have recently been introduced as an exciting new method for extremely memory-efficient training, but they come with an additional computation overhead of activation re-computation in the backpropagation phase. We present PaReprop, a fast Parallelized Reversible Backpropagation algorithm that parallelizes the additional activation re-computation overhead in reversible training with the gradient computation itself in backpropagation phase. We demonstrate the effectiveness of the proposed PaReprop algorithm through extensive benchmarking across model families (ViT, MViT, Swin and RoBERTa), data modalities (Vision & NLP), model sizes (from small to giant), and training batch sizes. Our empirical results show that PaReprop achieves up to 20% higher training throughput than vanilla reversible training, largely mitigating the theoretical overhead of 25% lower throughput from activation recomputation in reversible training. Project page: https://tylerzhu.com/pareprop.

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling evolved from recurrent neural networks to attention-based models, culminating in the Transformer architecture. Transformers have achieved state-of-the-art performance in natural language processing (for example, BERT and GPT-3) and have been applied in computer vision and computational biology. However, theoretical understanding of these models remains limited. In this paper, we examine the mathematical foundations of deep learning and Transformers and present a novel theoretical result. We review key concepts from linear algebra, probability, and optimization that underpin deep learning, and we analyze the multi-head self-attention mechanism and the backpropagation algorithm in detail. Our main contribution is a universal approximation theorem for Transformers: we prove that a single-layer Transformer, comprising one self-attention layer followed by a position-wise feed-forward network with ReLU activation, can approximate any continuous sequence-to-sequence mapping on a compact domain to arbitrary precision. We provide a formal statement and a complete proof. Finally, we present case studies that demonstrate the practical implications of this result. Our findings advance the theoretical understanding of Transformer models and help bridge the gap between theory and practice.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

We compare two strategies for compressing the KV cache in transformer inference: rank reduction (discard dimensions) and quantization (keep all dimensions, reduce precision). At matched storage budgets across five models (124M-14B, MHA and GQA), we find that quantization consistently outperforms rank reduction by 4-364 PPL depending on model and compression level. The gap persists even when rank reduction is combined with quantization in hybrid baselines, and it grows with GQA aggressiveness. On LAMBADA, INT4 matches FP16 accuracy (+0.23 PPL on Mistral 7B, +0.58 on GPT-2) while rank-32 at identical storage collapses to 0.4%. We trace this gap to a structural asymmetry: under softmax attention routing, removing a dimension can flip which token is attended (a discrete failure), while quantization noise is bounded and typically preserves score ordering. We formalize this via a perturbation result showing projection damage exceeds quantization damage by 3 x 2^(2b) per direction under the softmax Fisher metric. A basis ablation confirms the finding is basis-independent (spread <0.4 PPL), establishing that the advantage comes from preserving dimensions, not from a better coordinate system. Joint K+V INT4 quantization achieves 75% total KV reduction at only +0.18 PPL on Mistral 7B.

Unstructured pruning produces sparse weight tensors, but the standard implementation keeps tensor shapes unchanged so the deployed model is no smaller than before pruning. We present an exact structural rewrite, which we call minimization, that converts a masked network into a smaller dense network with the same forward function up to floating-point rounding. The Squeeze-Release cycle iterates pruning and minimization with an intermediate release step that re-enables the exact-zero positions inside the compacted tensors as small calibrated noise, turning otherwise wasted capacity back into trainable parameters. Successive cycles use that capacity to find structural redundancy a single pass cannot reach. We additionally introduce CompensatedLayerNorm, a function-preserving replacement for LayerNorm that extends minimization to channel reduction across LayerNorm-equipped residual streams. Squeeze-Release compresses the deployable network to 39x smaller than the unpruned model on a fully-connected model network and 14.8x smaller on modern CNN (ConvNeXt-Tiny), at comparable accuracy. In addition we prove that the rewrite can be extended to transformer architectures.

Speech separation, the task of isolating multiple speech sources from a mixed audio signal, remains challenging in noisy environments. In this paper, we propose a generative correction method to enhance the output of a discriminative separator. By leveraging a generative corrector based on a diffusion model, we refine the separation process for single-channel mixture speech by removing noises and perceptually unnatural distortions. Furthermore, we optimize the generative model using a predictive loss to streamline the diffusion model's reverse process into a single step and rectify any associated errors by the reverse process. Our method achieves state-of-the-art performance on the in-domain Libri2Mix noisy dataset, and out-of-domain WSJ with a variety of noises, improving SI-SNR by 22-35% relative to SepFormer, demonstrating robustness and strong generalization capabilities.

We develop a theory of pseudo-differential operators associated with the gyrator transform on modulation spaces. The gyrator transform is a two-dimensional linear canonical transform which can be viewed as a rotation in the time-frequency plane and is closely related to the fractional Fourier transform. Motivated by the global structure of the gyrator kernel, we work with Shubin global symbol classes on R^4. We first recall basic properties of modulation spaces and establish continuity and invertibility of the gyrator transform on these spaces, using its representation as a metaplectic operator. Then we introduce pseudo-differential operators defined via the gyrator transform and a Shubin symbol, and we prove boundedness results on modulation spaces and on gyrator-based modulation-Sobolev spaces. Our work extends and generalises earlier results of Mahato, Arya and Prasad on Schwartz and Sobolev spaces MahatoGyrator to the more flexible framework of modulation spaces.

Representational similarity analysis and related methods compare the internal geometries of neural networks, but they measure only alignment between spaces, leaving a blind spot -- whether a representation's structure is reliably recoverable, not merely similar. We introduce geometric stability, a distinct axis, and Shesha, a metric that quantifies it from a single representation by correlating dissimilarity matrices built from complementary random halves of the feature dimensions. Unlike CKA and Procrustes distance, Shesha is provably non-invariant to orthogonal rotations of the feature basis. This is by design: the basis is privileged for learned models, since probes, patching, and steering act on coordinates, and a rotation-invariant metric cannot see whether the targeted structure survives them. A double dissociation isolates the mechanism -- removing the top principal component collapses CKA while Shesha holds, whereas rotating a representation into its eigenbasis, which preserves the spectrum and CKA exactly, collapses Shesha. Across 2,463 encoder configurations in seven domains, the metrics are redundant under geometry-preserving transforms and anti-correlate under compression (ρ=-0.47). Across 170 vision models spanning 6 clean and 38 corruption-shifted datasets, DINOv2 ranks first or second in transferability on three of six clean datasets yet bottom-quartile in stability on five, an isolated dissociation rather than a trade-off.

Contrastive Analysis is a sub-field of Representation Learning that aims at separating common factors of variation between two datasets, a background (i.e., healthy subjects) and a target (i.e., diseased subjects), from the salient factors of variation, only present in the target dataset. Despite their relevance, current models based on Variational Auto-Encoders have shown poor performance in learning semantically-expressive representations. On the other hand, Contrastive Representation Learning has shown tremendous performance leaps in various applications (classification, clustering, etc.). In this work, we propose to leverage the ability of Contrastive Learning to learn semantically expressive representations well adapted for Contrastive Analysis. We reformulate it under the lens of the InfoMax Principle and identify two Mutual Information terms to maximize and one to minimize. We decompose the first two terms into an Alignment and a Uniformity term, as commonly done in Contrastive Learning. Then, we motivate a novel Mutual Information minimization strategy to prevent information leakage between common and salient distributions. We validate our method, called SepCLR, on three visual datasets and three medical datasets, specifically conceived to assess the pattern separation capability in Contrastive Analysis. Code available at https://github.com/neurospin-projects/2024_rlouiset_sep_clr.

Transformers have been the most successful architecture for various speech modeling tasks, including speech separation. However, the self-attention mechanism in transformers with quadratic complexity is inefficient in computation and memory. Recent models incorporate new layers and modules along with transformers for better performance but also introduce extra model complexity. In this work, we replace transformers with Mamba, a selective state space model, for speech separation. We propose dual-path Mamba, which models short-term and long-term forward and backward dependency of speech signals using selective state spaces. Our experimental results on the WSJ0-2mix data show that our dual-path Mamba models of comparably smaller sizes outperform state-of-the-art RNN model DPRNN, CNN model WaveSplit, and transformer model Sepformer. Code: https://github.com/xi-j/Mamba-TasNet

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general solution to a longstanding open problem relevant to a wide variety of applications in robotics, tracking, and control systems. The new inverse complements the Drazin inverse (which is consistent with respect to similarity transformations) and the Moore-Penrose inverse (which is consistent with respect to unitary/orthonormal transformations) to complete a trilogy of generalized matrix inverses that exhausts the standard family of analytically-important linear system transformations. Results are generalized to obtain unit-consistent and unit-invariant matrix decompositions and examples of their use are described.

Single Image Reflection Separation (SIRS) disentangles mixed images into transmission and reflection layers. Existing methods suffer from transmission-reflection confusion under nonlinear mixing, particularly in deep decoder layers, due to implicit fusion mechanisms and inadequate multi-scale coordination. We propose ReflexSplit, a dual-stream framework with three key innovations. (1) Cross-scale Gated Fusion (CrGF) adaptively aggregates semantic priors, texture details, and decoder context across hierarchical depths, stabilizing gradient flow and maintaining feature consistency. (2) Layer Fusion-Separation Blocks (LFSB) alternate between fusion for shared structure extraction and differential separation for layer-specific disentanglement. Inspired by Differential Transformer, we extend attention cancellation to dual-stream separation via cross-stream subtraction. (3) Curriculum training progressively strengthens differential separation through depth-dependent initialization and epoch-wise warmup. Extensive experiments on synthetic and real-world benchmarks demonstrate state-of-the-art performance with superior perceptual quality and robust generalization. Our code is available at https://github.com/wuw2135/ReflexSplit.

Model merging enables powerful capabilities in neural networks without requiring additional training. In this paper, we introduce a novel perspective on model merging by leveraging the fundamental mechanisms of neural network representation. Our approach is motivated by the linear representation hypothesis, which states that neural networks encode information through linear combinations of feature vectors. We propose a method that superposes task-specific features from individual models into a merged model. Our approach specifically targets linear transformation matrices, which are crucial for feature activation and extraction in deep networks. By formulating the merging process as a linear system, we can preserve task-specific features from individual models and create merged models that effectively maintain multi-task capabilities compared to existing methods. Extensive experiments across diverse benchmarks and models demonstrate that our method outperforms existing techniques. Code is available at https://github.com/LARS-research/STF.

Motivated by the factorization inherent in the original fast multipole method and the improved fast Gauss transform we introduce a factorable form of attention that operates efficiently in high dimensions. This approach reduces the computational and memory complexity of the attention mechanism in transformers from O(N^2) to O(N). In comparison to previous attempts, our work presents a linearly scaled attention mechanism that maintains the full representation of the attention matrix without compromising on sparsification and incorporates the all-to-all relationship between tokens. We explore the properties of our new attention metric and conduct tests in various standard settings. Results indicate that our attention mechanism has a robust performance and holds significant promise for diverse applications where self-attention is used.

Transformers have achieved the state-of-the-art performance on solving the inverse problem of Snapshot Compressive Imaging (SCI) for video, whose ill-posedness is rooted in the mixed degradation of spatial masking and temporal aliasing. However, previous Transformers lack an insight into the degradation and thus have limited performance and efficiency. In this work, we tailor an efficient reconstruction architecture without temporal aggregation in early layers and Hierarchical Separable Video Transformer (HiSViT) as building block. HiSViT is built by multiple groups of Cross-Scale Separable Multi-head Self-Attention (CSS-MSA) and Gated Self-Modulated Feed-Forward Network (GSM-FFN) with dense connections, each of which is conducted within a separate channel portions at a different scale, for multi-scale interactions and long-range modeling. By separating spatial operations from temporal ones, CSS-MSA introduces an inductive bias of paying more attention within frames instead of between frames while saving computational overheads. GSM-FFN further enhances the locality via gated mechanism and factorized spatial-temporal convolutions. Extensive experiments demonstrate that our method outperforms previous methods by !>!0.5 dB with comparable or fewer parameters and complexity. The source codes and pretrained models are released at https://github.com/pwangcs/HiSViT.

By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called muP, for *widthwise hyperparameter transfer*, i.e., predicting optimal hyperparameters of wide neural networks from narrow ones. Here we investigate the analogous classification for *depthwise parametrizations* of deep residual networks (resnets). We classify depthwise parametrizations of block multiplier and learning rate by their infinite-width-then-depth limits. In resnets where each block has only one layer, we identify a unique optimal parametrization, called Depth-muP that extends muP and show empirically it admits depthwise hyperparameter transfer. We identify *feature diversity* as a crucial factor in deep networks, and Depth-muP can be characterized as maximizing both feature learning and feature diversity. Exploiting this, we find that absolute value, among all homogeneous nonlinearities, maximizes feature diversity and indeed empirically leads to significantly better performance. However, if each block is deeper (such as modern transformers), then we find fundamental limitations in all possible infinite-depth limits of such parametrizations, which we illustrate both theoretically and empirically on simple networks as well as Megatron transformer trained on Common Crawl.

In the era of large-scale training, model merging has evolved into a tool for creating multitasking models efficiently. It enables the knowledge of models to be fused, without the need for heavy computation as required in traditional multitask learning. Existing merging methods often assume that entries at identical positions in weight matrices serve the same function, enabling straightforward entry-wise comparison and merging. However, this assumption overlooks the complexity of finetuned neural networks, where neurons may develop distinct feature compositions, making direct entry-wise merging problematic. We present Decom-Renorm-Merge (DRM), a simple yet effective approach that leverages Singular Value Decomposition to decompose and coordinate weight matrices into an aligned joint space, where entry-wise merging becomes possible. We showcase the effectiveness of DRM across various settings ranging from smaller encoder-based such as ViT and DeBERTa, encoder-decoder-based such as T5, and larger decoder-based such as Llama3.1-8B. Our experimental results show that DRM outperforms several state-of-the-art merging techniques across full finetuning and low-rank adaptation settings. Moreover, our analysis reveals renormalization as the crucial component for creating a robust and even joint space for merging, significantly contributing to the method's performance.

Normalizing flows are an essential alternative to GANs for generative modelling, which can be optimized directly on the maximum likelihood of the dataset. They also allow computation of the exact latent vector corresponding to an image since they are composed of invertible transformations. However, the requirement of invertibility of the transformation prevents standard and expressive neural network models such as CNNs from being directly used. Emergent convolutions were proposed to construct an invertible 3times3 CNN layer using a pair of masked CNN layers, making them inefficient. We study conditions such that 3times3 CNNs are invertible, allowing them to construct expressive normalizing flows. We derive necessary and sufficient conditions on a padded CNN for it to be invertible. Our conditions for invertibility are simple, can easily be maintained during the training process. Since we require only a single CNN layer for every effective invertible CNN layer, our approach is more efficient than emerging convolutions. We also proposed a coupling method, Quad-coupling. We benchmark our approach and show similar performance results to emergent convolutions while improving the model's efficiency.

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is hindered by representation entanglement (e.g., superposition), where entangled features encoded in overlapping directions obstruct the recovery of symbolic expressions. We propose the Discrete Transformer, an architecture explicitly designed to bridge the gap between continuous representations and discrete symbolic logic. By injecting discreteness through temperature-annealed sampling, our framework effectively leverages hypothesis testing and symbolic regression to extract human-readable programs. Empirically, the Discrete Transformer achieves performance comparable to RNN-based methods while extending interpretability to continuous variable domains, and the annealing dynamics exhibit a clear exploration-to-exploitation transition. Finally, we show that architectural inductive biases provide fine-grained control over synthesized programs, establishing the Discrete Transformer as a robust framework for demonstration-free algorithm discovery and Transformer interpretability.

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.

Scaling multi-dimensional transformers to long sequences is indispensable across various domains. However, the challenges of large memory requirements and slow speeds of such sequences necessitate sequence parallelism. All existing approaches fall under the category of embedded sequence parallelism, which are limited to shard along a single sequence dimension, thereby introducing significant communication overhead. However, the nature of multi-dimensional transformers involves independent calculations across multiple sequence dimensions. To this end, we propose Dynamic Sequence Parallelism (DSP) as a novel abstraction of sequence parallelism. DSP dynamically switches the parallel dimension among all sequences according to the computation stage with efficient resharding strategy. DSP offers significant reductions in communication costs, adaptability across modules, and ease of implementation with minimal constraints. Experimental evaluations demonstrate DSP's superiority over state-of-the-art embedded sequence parallelism methods by remarkable throughput improvements ranging from 32.2% to 10x, with less than 25% communication volume.

Neural networks unintentionally memorize training data, creating privacy risks in federated learning (FL) systems, such as inference and reconstruction attacks on sensitive data. To mitigate these risks and to comply with privacy regulations, Federated Unlearning (FU) has been introduced to enable participants in FL systems to remove their data's influence from the global model. However, current FU methods primarily act post-hoc, struggling to efficiently erase information deeply memorized by neural networks. We argue that effective unlearning necessitates a paradigm shift: designing FL systems inherently amenable to forgetting. To this end, we propose a learning-to-unlearn Transformation-guided Federated Unlearning (ToFU) framework that incorporates transformations during the learning process to reduce memorization of specific instances. Our theoretical analysis reveals how transformation composition provably bounds instance-specific information, directly simplifying subsequent unlearning. Crucially, ToFU can work as a plug-and-play framework that improves the performance of existing FU methods. Experiments on CIFAR-10, CIFAR-100, and the MUFAC benchmark show that ToFU outperforms existing FU baselines, enhances performance when integrated with current methods, and reduces unlearning time.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Structured State-Space Duality (SSD) [Dao & Gu, ICML 2024] is an equivalence between a simple Structured State-Space Model (SSM) and a masked attention mechanism. In particular, a state-space model with a scalar-times-identity state matrix is equivalent to a masked self-attention with a 1-semiseparable causal mask. Consequently, the same sequence transformation (model) has two algorithmic realizations: as a linear-time O(T) recurrence or as a quadratic-time O(T^2) attention. In this note, we formalize and generalize this duality: (i) we extend SSD from the scalar-identity case to general diagonal SSMs (diagonal state matrices); (ii) we show that these diagonal SSMs match the scalar case's training complexity lower bounds while supporting richer dynamics; (iii) we establish a necessary and sufficient condition under which an SSM is equivalent to 1-semiseparable masked attention; and (iv) we show that such duality fails to extend to standard softmax attention due to rank explosion. Together, these results tighten bridge between recurrent SSMs and Transformers, and widen the design space for expressive yet efficient sequence models.

State Space Models (SSMs) are inherently recurrent along the sequence dimension, yet depth-recurrence - reusing the same block repeatedly across layers, as recently applied in looped transformers - has not been explored in this model family. We show that a looped SSM with k parameters iterated L times consistently closely matches or outperforms a standard SSM with k cdot L independent parameters across four architectures (LRU, S5, LinOSS, LrcSSM) and six time series classification benchmarks, despite operating within a strictly smaller hypothesis space, as we formally establish. Since the larger model contains the looped model as a special case, this dominance cannot be explained by expressivity and instead points to parameter sharing across depth as a beneficial inductive bias that simplifies optimization. These results demonstrate that depth-recurrence is orthogonal to sequence-recurrence and independently beneficial. We further show that input reshaping is an equally neglected design axis: concatenating timesteps for low-dimensional inputs, or flattening and rechunking the joint feature-time dimension for high-dimensional ones, yields accuracy gains of 1-6% across all models, confirmed over 5 random seeds. Both techniques provide standalone improvements that compound when combined, suggesting that depth and input reshaping are two independent and underexplored design axes for SSMs on time series.

In this work, we propose an approach to music source separation that uses a generative diffusion model as a last-stage refinement on top of a deterministic separator, progressively enhancing the separated sources through iterative denoising. While the diffusion refinement yields measurable quality gains, it requires iterative steps at inference, increasing computational cost. To speed up the inference process, we apply consistency distillation, reducing inference to a single step while maintaining quality; with two or more steps, the distilled model even surpasses the diffusion-based approach. Crucially, our method is architecture-agnostic: we demonstrate state-of-the-art results when applied to both a custom U-Net-based separator on Slakh2100 and the state-of-the-art BS-RoFormer model on MUSDB18, showing that the refinement generalizes across backbone architectures. Sound examples are available at: https://consistency-separation.github.io/.

Vision transformers have gained significant attention and achieved state-of-the-art performance in various computer vision tasks, including image classification, instance segmentation, and object detection. However, challenges remain in addressing attention complexity and effectively capturing fine-grained information within images. Existing solutions often resort to down-sampling operations, such as pooling, to reduce computational cost. Unfortunately, such operations are non-invertible and can result in information loss. In this paper, we present a novel approach called Scattering Vision Transformer (SVT) to tackle these challenges. SVT incorporates a spectrally scattering network that enables the capture of intricate image details. SVT overcomes the invertibility issue associated with down-sampling operations by separating low-frequency and high-frequency components. Furthermore, SVT introduces a unique spectral gating network utilizing Einstein multiplication for token and channel mixing, effectively reducing complexity. We show that SVT achieves state-of-the-art performance on the ImageNet dataset with a significant reduction in a number of parameters and FLOPS. SVT shows 2\% improvement over LiTv2 and iFormer. SVT-H-S reaches 84.2\% top-1 accuracy, while SVT-H-B reaches 85.2\% (state-of-art for base versions) and SVT-H-L reaches 85.7\% (again state-of-art for large versions). SVT also shows comparable results in other vision tasks such as instance segmentation. SVT also outperforms other transformers in transfer learning on standard datasets such as CIFAR10, CIFAR100, Oxford Flower, and Stanford Car datasets. The project page is available on this webpage.https://badripatro.github.io/svt/.

The wide-angle lens shows appealing applications in VR technologies, but it introduces severe radial distortion into its captured image. To recover the realistic scene, previous works devote to rectifying the content of the wide-angle image. However, such a rectification solution inevitably distorts the image boundary, which potentially changes related geometric distributions and misleads the current vision perception models. In this work, we explore constructing a win-win representation on both content and boundary by contributing a new learning model, i.e., Rectangling Rectification Network (RecRecNet). In particular, we propose a thin-plate spline (TPS) module to formulate the non-linear and non-rigid transformation for rectangling images. By learning the control points on the rectified image, our model can flexibly warp the source structure to the target domain and achieves an end-to-end unsupervised deformation. To relieve the complexity of structure approximation, we then inspire our RecRecNet to learn the gradual deformation rules with a DoF (Degree of Freedom)-based curriculum learning. By increasing the DoF in each curriculum stage, namely, from similarity transformation (4-DoF) to homography transformation (8-DoF), the network is capable of investigating more detailed deformations, offering fast convergence on the final rectangling task. Experiments show the superiority of our solution over the compared methods on both quantitative and qualitative evaluations. The code and dataset will be made available.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

There is a growing interest in designing models that can deal with images from different visual domains. If there exists a universal structure in different visual domains that can be captured via a common parameterization, then we can use a single model for all domains rather than one model per domain. A model aware of the relationships between different domains can also be trained to work on new domains with less resources. However, to identify the reusable structure in a model is not easy. In this paper, we propose a multi-domain learning architecture based on depthwise separable convolution. The proposed approach is based on the assumption that images from different domains share cross-channel correlations but have domain-specific spatial correlations. The proposed model is compact and has minimal overhead when being applied to new domains. Additionally, we introduce a gating mechanism to promote soft sharing between different domains. We evaluate our approach on Visual Decathlon Challenge, a benchmark for testing the ability of multi-domain models. The experiments show that our approach can achieve the highest score while only requiring 50% of the parameters compared with the state-of-the-art approaches.

Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer's classification decisions become less and less confident (that is, with cross-entropy approaching 1 bit per string) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of overcoming the limitation suggested by Hahn's lemma. First, we settle an open question by constructing a transformer that recognizes PARITY with perfect accuracy, and similarly for FIRST. Second, we use layer normalization to bring the cross-entropy of both models arbitrarily close to zero. Third, when transformers need to focus on a single position, as for FIRST, we find that they can fail to generalize to longer strings; we offer a simple remedy to this problem that also improves length generalization in machine translation.

As models and data scale, independently trained networks often induce analogous notions of similarity. But, matching similarities is weaker than establishing an explicit correspondence between the representation spaces, especially for multimodal models, where consistency must hold not only within each modality, but also for the learned image-text coupling. We therefore ask: given two independently trained multimodal contrastive models (with encoders (f, g) and (f,g)) -- trained on different distributions and with different architectures -- does a systematic geometric relationship exist between their embedding spaces? If so, what form does it take, and does it hold uniformly across modalities? In this work, we show that across model families such as CLIP, SigLIP, and FLAVA, this geometric relationship is well approximated by an orthogonal map (up to a global mean shift), i.e., there exists an orthogonal map Q where Q^top Q = I such that f(x)approx Q f(x) for paired images x. Strikingly, the same Q simultaneously aligns the text encoders i.e., g(y)approx Q g(y) for texts y. Theoretically, we prove that if the multimodal kernel agrees across models on a small anchor set i.e. langle f(x), g(y)rangle approx langle f(x), g(y)rangle, then the two models must be related by a single orthogonal map Q and the same Q maps images and text across models. More broadly, this finding enables backward-compatible model upgrades, avoiding costly re-embedding, and has implications for the privacy of learned representations. Our project page: https://canonical-multimodal.github.io/

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of Transformers. For one, we replace dot-product attention by one that uses locality-sensitive hashing, changing its complexity from O(L^2) to O(Llog L), where L is the length of the sequence. Furthermore, we use reversible residual layers instead of the standard residuals, which allows storing activations only once in the training process instead of N times, where N is the number of layers. The resulting model, the Reformer, performs on par with Transformer models while being much more memory-efficient and much faster on long sequences.

COMpression with Bayesian Implicit NEural Representations (COMBINER) is a recent data compression method that addresses a key inefficiency of previous Implicit Neural Representation (INR)-based approaches: it avoids quantization and enables direct optimization of the rate-distortion performance. However, COMBINER still has significant limitations: 1) it uses factorized priors and posterior approximations that lack flexibility; 2) it cannot effectively adapt to local deviations from global patterns in the data; and 3) its performance can be susceptible to modeling choices and the variational parameters' initializations. Our proposed method, Robust and Enhanced COMBINER (RECOMBINER), addresses these issues by 1) enriching the variational approximation while retaining a low computational cost via a linear reparameterization of the INR weights, 2) augmenting our INRs with learnable positional encodings that enable them to adapt to local details and 3) splitting high-resolution data into patches to increase robustness and utilizing expressive hierarchical priors to capture dependency across patches. We conduct extensive experiments across several data modalities, showcasing that RECOMBINER achieves competitive results with the best INR-based methods and even outperforms autoencoder-based codecs on low-resolution images at low bitrates. Our PyTorch implementation is available at https://github.com/cambridge-mlg/RECOMBINER/.

The computational overhead of Vision Transformers in practice stems fundamentally from their deep architectures, yet existing acceleration strategies have primarily targeted algorithmic-level optimizations such as token pruning and attention speedup. This leaves an underexplored research question: can we reduce the number of stacked transformer layers while maintaining comparable representational capacity? To answer this, we propose a branch-based structural reparameterization technique that operates during the training phase. Our approach leverages parallel branches within transformer blocks that can be systematically consolidated into streamlined single-path models suitable for inference deployment. The consolidation mechanism works by gradually merging branches at the entry points of nonlinear components, enabling both feed-forward networks (FFN) and multi-head self-attention (MHSA) modules to undergo exact mathematical reparameterization without inducing approximation errors at test time. When applied to ViT-Tiny, the framework successfully reduces the original 12-layer architecture to 6, 4, or as few as 3 layers while maintaining classification accuracy on ImageNet-1K. The resulting compressed models achieve inference speedups of up to 37% on mobile CPU platforms. Our findings suggest that the conventional wisdom favoring extremely deep transformer stacks may be unnecessarily restrictive, and point toward new opportunities for constructing efficient vision transformers.

Feature pyramid has been an efficient method to extract features at different scales. Development over this method mainly focuses on aggregating contextual information at different levels while seldom touching the inter-level correlation in the feature pyramid. Early computer vision methods extracted scale-invariant features by locating the feature extrema in both spatial and scale dimension. Inspired by this, a convolution across the pyramid level is proposed in this study, which is termed pyramid convolution and is a modified 3-D convolution. Stacked pyramid convolutions directly extract 3-D (scale and spatial) features and outperforms other meticulously designed feature fusion modules. Based on the viewpoint of 3-D convolution, an integrated batch normalization that collects statistics from the whole feature pyramid is naturally inserted after the pyramid convolution. Furthermore, we also show that the naive pyramid convolution, together with the design of RetinaNet head, actually best applies for extracting features from a Gaussian pyramid, whose properties can hardly be satisfied by a feature pyramid. In order to alleviate this discrepancy, we build a scale-equalizing pyramid convolution (SEPC) that aligns the shared pyramid convolution kernel only at high-level feature maps. Being computationally efficient and compatible with the head design of most single-stage object detectors, the SEPC module brings significant performance improvement (>4AP increase on MS-COCO2017 dataset) in state-of-the-art one-stage object detectors, and a light version of SEPC also has sim3.5AP gain with only around 7% inference time increase. The pyramid convolution also functions well as a stand-alone module in two-stage object detectors and is able to improve the performance by sim2AP. The source code can be found at https://github.com/jshilong/SEPC.

The Automunge open source python library platform for tabular data pre-processing automates feature engineering data transformations of numerical encoding and missing data infill to received tidy data on bases fit to properties of columns in a designated train set for consistent and efficient application to subsequent data pipelines such as for inference, where transformations may be applied to distinct columns in "family tree" sets with generations and branches of derivations. Included in the library of transformations are methods to extract structure from bounded categorical string sets by way of automated string parsing, in which comparisons between entries in the set of unique values are parsed to identify character subset overlaps which may be encoded by appended columns of boolean overlap detection activations or by replacing string entries with identified overlap partitions. Further string parsing options, which may also be applied to unbounded categoric sets, include extraction of numeric substring partitions from entries or search functions to identify presence of specified substring partitions. The aggregation of these methods into "family tree" sets of transformations are demonstrated for use to automatically extract structure from categoric string compositions in relation to the set of entries in a column, such as may be applied to prepare categoric string set encodings for machine learning without human intervention.

Recent advancements in Mamba have shown promising results in image restoration. These methods typically flatten 2D images into multiple distinct 1D sequences along rows and columns, process each sequence independently using selective scan operation, and recombine them to form the outputs. However, such a paradigm overlooks two vital aspects: i) the local relationships and spatial continuity inherent in natural images, and ii) the discrepancies among sequences unfolded through totally different ways. To overcome the drawbacks, we explore two problems in Mamba-based restoration methods: i) how to design a scanning strategy preserving both locality and continuity while facilitating restoration, and ii) how to aggregate the distinct sequences unfolded in totally different ways. To address these problems, we propose a novel Mamba-based Image Restoration model (MaIR), which consists of Nested S-shaped Scanning strategy (NSS) and Sequence Shuffle Attention block (SSA). Specifically, NSS preserves locality and continuity of the input images through the stripe-based scanning region and the S-shaped scanning path, respectively. SSA aggregates sequences through calculating attention weights within the corresponding channels of different sequences. Thanks to NSS and SSA, MaIR surpasses 40 baselines across 14 challenging datasets, achieving state-of-the-art performance on the tasks of image super-resolution, denoising, deblurring and dehazing. The code is available at https://github.com/XLearning-SCU/2025-CVPR-MaIR.

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem of extracting relevant context information from long sequences in NLP and realistic scenes in CV. A classical neural network component, a Multi-Layer Perceptron (MLP), complements the attention mechanism. Its necessity is frequently justified by its capability of modeling nonlinear relationships. However, the attention mechanism itself is nonlinear through its internal use of similarity measures. A possible hypothesis is that this nonlinearity is sufficient for modeling typical application problems. As the MLPs usually contain the most trainable parameters of the whole model, their omission would substantially reduce the parameter set size. Further components can also be reorganized to reduce the number of parameters. Under some conditions, query and key matrices can be collapsed into a single matrix of the same size. The same is true about value and projection matrices, which can also be omitted without eliminating the substance of the attention mechanism. Initially, the similarity measure was defined asymmetrically, with peculiar properties such as that a token is possibly dissimilar to itself. A possible symmetric definition requires only half of the parameters. We have laid the groundwork by testing widespread CV benchmarks: MNIST and CIFAR-10. The tests have shown that simplified transformer architectures (a) without MLP, (b) with collapsed matrices, and (c) symmetric similarity matrices exhibit similar performance as the original architecture, saving up to 90% of parameters without hurting the classification performance.

Explicitly disentangling style and content in vision models remains challenging due to their semantic overlap and the subjectivity of human perception. Existing methods propose separation through generative or discriminative objectives, but they still face the inherent ambiguity of disentangling intertwined concepts. Instead, we ask: Can we bypass explicit disentanglement by learning to merge style and content invertibly, allowing separation to emerge naturally? We propose SCFlow, a flow-matching framework that learns bidirectional mappings between entangled and disentangled representations. Our approach is built upon three key insights: 1) Training solely to merge style and content, a well-defined task, enables invertible disentanglement without explicit supervision; 2) flow matching bridges on arbitrary distributions, avoiding the restrictive Gaussian priors of diffusion models and normalizing flows; and 3) a synthetic dataset of 510,000 samples (51 styles times 10,000 content samples) was curated to simulate disentanglement through systematic style-content pairing. Beyond controllable generation tasks, we demonstrate that SCFlow generalizes to ImageNet-1k and WikiArt in zero-shot settings and achieves competitive performance, highlighting that disentanglement naturally emerges from the invertible merging process.

Implicit neural representations (INR) have gained significant popularity for signal and image representation for many end-tasks, such as superresolution, 3D modeling, and more. Most INR architectures rely on sinusoidal positional encoding, which accounts for high-frequency information in data. However, the finite encoding size restricts the model's representational power. Higher representational power is needed to go from representing a single given image to representing large and diverse datasets. Our approach addresses this gap by representing an image with a polynomial function and eliminates the need for positional encodings. Therefore, to achieve a progressively higher degree of polynomial representation, we use element-wise multiplications between features and affine-transformed coordinate locations after every ReLU layer. The proposed method is evaluated qualitatively and quantitatively on large datasets like ImageNet. The proposed Poly-INR model performs comparably to state-of-the-art generative models without any convolution, normalization, or self-attention layers, and with far fewer trainable parameters. With much fewer training parameters and higher representative power, our approach paves the way for broader adoption of INR models for generative modeling tasks in complex domains. The code is available at https://github.com/Rajhans0/Poly_INR

Panoptic segmentation involves a combination of joint semantic segmentation and instance segmentation, where image contents are divided into two types: things and stuff. We present Panoptic SegFormer, a general framework for panoptic segmentation with transformers. It contains three innovative components: an efficient deeply-supervised mask decoder, a query decoupling strategy, and an improved post-processing method. We also use Deformable DETR to efficiently process multi-scale features, which is a fast and efficient version of DETR. Specifically, we supervise the attention modules in the mask decoder in a layer-wise manner. This deep supervision strategy lets the attention modules quickly focus on meaningful semantic regions. It improves performance and reduces the number of required training epochs by half compared to Deformable DETR. Our query decoupling strategy decouples the responsibilities of the query set and avoids mutual interference between things and stuff. In addition, our post-processing strategy improves performance without additional costs by jointly considering classification and segmentation qualities to resolve conflicting mask overlaps. Our approach increases the accuracy 6.2\% PQ over the baseline DETR model. Panoptic SegFormer achieves state-of-the-art results on COCO test-dev with 56.2\% PQ. It also shows stronger zero-shot robustness over existing methods. The code is released at https://github.com/zhiqi-li/Panoptic-SegFormer.

Relative position encoding (RPE) is important for transformer to capture sequence ordering of input tokens. General efficacy has been proven in natural language processing. However, in computer vision, its efficacy is not well studied and even remains controversial, e.g., whether relative position encoding can work equally well as absolute position? In order to clarify this, we first review existing relative position encoding methods and analyze their pros and cons when applied in vision transformers. We then propose new relative position encoding methods dedicated to 2D images, called image RPE (iRPE). Our methods consider directional relative distance modeling as well as the interactions between queries and relative position embeddings in self-attention mechanism. The proposed iRPE methods are simple and lightweight. They can be easily plugged into transformer blocks. Experiments demonstrate that solely due to the proposed encoding methods, DeiT and DETR obtain up to 1.5% (top-1 Acc) and 1.3% (mAP) stable improvements over their original versions on ImageNet and COCO respectively, without tuning any extra hyperparameters such as learning rate and weight decay. Our ablation and analysis also yield interesting findings, some of which run counter to previous understanding. Code and models are open-sourced at https://github.com/microsoft/Cream/tree/main/iRPE.

Recent works have indicated redundancy across transformer blocks, prompting the research of depth compression to prune less crucial blocks. However, current ways of entire-block pruning suffer from risks of discarding meaningful cues learned in those blocks, leading to substantial performance degradation. As another line of model compression, channel pruning can better preserve performance, while it cannot reduce model depth and is challenged by inconsistent pruning ratios for individual layers. To pursue better model compression and acceleration, this paper proposes FlattenGPT, a novel way to detect and reduce depth-wise redundancies. By flatting two adjacent blocks into one, it compresses the network depth, meanwhile enables more effective parameter redundancy detection and removal. FlattenGPT allows to preserve the knowledge learned in all blocks, and remains consistent with the original transformer architecture. Extensive experiments demonstrate that FlattenGPT enhances model efficiency with a decent trade-off to performance. It outperforms existing pruning methods in both zero-shot accuracies and WikiText-2 perplexity across various model types and parameter sizes. On LLaMA-2/3 and Qwen-1.5 models, FlattenGPT retains 90-96\% of zero-shot performance with a compression ratio of 20\%. It also outperforms other pruning methods in accelerating LLM inference, making it promising for enhancing the efficiency of transformers.

The self-attention-based model, transformer, is recently becoming the leading backbone in the field of computer vision. In spite of the impressive success made by transformers in a variety of vision tasks, it still suffers from heavy computation and intensive memory costs. To address this limitation, this paper presents an Interpretability-Aware REDundancy REDuction framework (IA-RED^2). We start by observing a large amount of redundant computation, mainly spent on uncorrelated input patches, and then introduce an interpretable module to dynamically and gracefully drop these redundant patches. This novel framework is then extended to a hierarchical structure, where uncorrelated tokens at different stages are gradually removed, resulting in a considerable shrinkage of computational cost. We include extensive experiments on both image and video tasks, where our method could deliver up to 1.4x speed-up for state-of-the-art models like DeiT and TimeSformer, by only sacrificing less than 0.7% accuracy. More importantly, contrary to other acceleration approaches, our method is inherently interpretable with substantial visual evidence, making vision transformer closer to a more human-understandable architecture while being lighter. We demonstrate that the interpretability that naturally emerged in our framework can outperform the raw attention learned by the original visual transformer, as well as those generated by off-the-shelf interpretation methods, with both qualitative and quantitative results. Project Page: http://people.csail.mit.edu/bpan/ia-red/.

Traditional image-to-3D models often struggle with scenes containing multiple objects due to biases and occlusion complexities. To address this challenge, we present REPARO, a novel approach for compositional 3D asset generation from single images. REPARO employs a two-step process: first, it extracts individual objects from the scene and reconstructs their 3D meshes using off-the-shelf image-to-3D models; then, it optimizes the layout of these meshes through differentiable rendering techniques, ensuring coherent scene composition. By integrating optimal transport-based long-range appearance loss term and high-level semantic loss term in the differentiable rendering, REPARO can effectively recover the layout of 3D assets. The proposed method can significantly enhance object independence, detail accuracy, and overall scene coherence. Extensive evaluation of multi-object scenes demonstrates that our REPARO offers a comprehensive approach to address the complexities of multi-object 3D scene generation from single images.

Model merging aims to enable multi-task learning by integrating the capabilities of multiple models fine-tuned from the same pre-trained checkpoint into a single model. Its core challenge is inter-task interference among task-specific parameter updates. In this paper, we analyze the output shifts induced by task updates and observe that their energy is concentrated in a small number of principal directions. We call the subspace spanned by these directions the essential subspace. In contrast, most remaining directions carry little task-relevant energy, but their accumulation across multiple task updates can cause severe interference during merging. Motivated by this observation, we propose Essential Subspace Decomposition (ESD), which decomposes each task update according to the principal components of its activation shift. Based on ESD, we introduce Essential Subspace Merging (ESM), a training-free static merging method that orthogonalizes and fuses essential components into one compact multi-task model. We further extend ESM to ESM++, a training-free dynamic merging method that decomposes task-specific residuals into low-rank experts and selects the most relevant expert through prototype-based routing during forward inference. Extensive experiments across multiple task sets and model scales demonstrate that ESM and ESM++ effectively preserves task knowledge while reducing inter-task interference.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

Transformer architectures rely on position encodings to model the spatial structure of input data. Rotary Position Encoding (RoPE) is a widely used method in language models that encodes relative positions through fixed, block-diagonal, rotation matrices applied to key-query interactions. We hypothesize that this inductive bias limits their RoPE's effectiveness for modalities with high dimensional structure. Lie Relative Encodings (LieRE) introduce a principled generalization of RoPE, aimed at increasing the representational capacity of positional encodings in transformers. Instead of fixed 2D rotations, LieRE learns dense skew-symmetric matrices (Lie algebra elements), which are then differentiable mapped to form high-dimensional rotation matrices (Lie group elements). This results in richer, learnable, and continuous, encodings of both relative and absolute positional information. We demonstrate the effectiveness of LieRE on 2D and 3D vision tasks, showing that it generalizes well to higher input resolutions while maintaining computational efficiency. The code and checkpoints are publicly available at https://github.com/StanfordMIMI/LieRE.

Deep learning-based music source separation has gained a lot of interest in the last decades. Most of the existing methods operate with either spectrograms or waveforms. Spectrogram based models learn suitable masks for separating magnitude spectrogram into different sources, and waveform-based models directly generate waveforms of individual sources. The two types of models have complementary strengths; the former is superior given harmonic sources such as vocals, while the latter demonstrates better results for percussion and bass instruments. In this work, we improved upon the state-of-the-art (SoTA) models and successfully combined the best of both worlds. The backbones of the proposed framework, dubbed Danna-Sep, are two spectrogram-based models including a modified X-UMX and U-Net, and an enhanced Demucs as the waveform-based model. Given an input of mixture, we linearly combined respective outputs from the three models to obtain the final result. We showed in the experiments that, despite its simplicity, Danna-Sep surpassed the SoTA models by a large margin in terms of Source-to-Distortion Ratio.

Current learned image compression models typically exhibit high complexity, which demands significant computational resources. To overcome these challenges, we propose an innovative approach that employs hierarchical feature extraction transforms to significantly reduce complexity while preserving bit rate reduction efficiency. Our novel architecture achieves this by using fewer channels for high spatial resolution inputs/feature maps. On the other hand, feature maps with a large number of channels have reduced spatial dimensions, thereby cutting down on computational load without sacrificing performance. This strategy effectively reduces the forward pass complexity from \(1256 \, kMAC/Pixel\) to just \(270 \, kMAC/Pixel\). As a result, the reduced complexity model can open the way for learned image compression models to operate efficiently across various devices and pave the way for the development of new architectures in image compression technology.

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where C^{(ell)}=E[h^{(ell)}h^{(ell)top}], and track deviations from a random-matrix bulk. Across model scales (1.5B--30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, Ω(h)=1-|h|_1/(d|h|_2), exhibits a discontinuity near a critical normalized depth γ_capprox 0.42 in sufficiently large models. We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics. The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space, which we call Transient Class Objects (TCOs). We provide theoretical conditions connecting logical separability to spectral decay and validate the predicted signatures with layerwise probes on multiple open-weight model families.

The seminal Fast Johnson-Lindenstrauss (Fast JL) transform by Ailon and Chazelle (SICOMP'09) embeds a set of n points in d-dimensional Euclidean space into optimal k=O(varepsilon^{-2} ln n) dimensions, while preserving all pairwise distances to within a factor (1 pm varepsilon). The Fast JL transform supports computing the embedding of a data point in O(d ln d +k ln^2 n) time, where the d ln d term comes from multiplication with a d times d Hadamard matrix and the k ln^2 n term comes from multiplication with a sparse k times d matrix. Despite the Fast JL transform being more than a decade old, it is one of the fastest dimensionality reduction techniques for many tradeoffs between varepsilon, d and n. In this work, we give a surprising new analysis of the Fast JL transform, showing that the k ln^2 n term in the embedding time can be improved to (k ln^2 n)/alpha for an alpha = Omega(min{varepsilon^{-1}ln(1/varepsilon), ln n}). The improvement follows by using an even sparser matrix. We also complement our improved analysis with a lower bound showing that our new analysis is in fact tight.

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs). However, since PDEs are typically discretized into large-scale meshes with complex geometries, it is challenging for Transformers to capture intricate physical correlations directly from massive individual points. Going beyond superficial and unwieldy meshes, we present Transolver based on a more foundational idea, which is learning intrinsic physical states hidden behind discretized geometries. Specifically, we propose a new Physics-Attention to adaptively split the discretized domain into a series of learnable slices of flexible shapes, where mesh points under similar physical states will be ascribed to the same slice. By calculating attention to physics-aware tokens encoded from slices, Transovler can effectively capture intricate physical correlations under complex geometrics, which also empowers the solver with endogenetic geometry-general modeling capacity and can be efficiently computed in linear complexity. Transolver achieves consistent state-of-the-art with 22% relative gain across six standard benchmarks and also excels in large-scale industrial simulations, including car and airfoil designs. Code is available at https://github.com/thuml/Transolver.

In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this to topological concepts such as homeomorphism and embedding. We then investigate what are continuous and discontinuous representations for 2D, 3D, and n-dimensional rotations. We demonstrate that for 3D rotations, all representations are discontinuous in the real Euclidean spaces of four or fewer dimensions. Thus, widely used representations such as quaternions and Euler angles are discontinuous and difficult for neural networks to learn. We show that the 3D rotations have continuous representations in 5D and 6D, which are more suitable for learning. We also present continuous representations for the general case of the n-dimensional rotation group SO(n). While our main focus is on rotations, we also show that our constructions apply to other groups such as the orthogonal group and similarity transforms. We finally present empirical results, which show that our continuous rotation representations outperform discontinuous ones for several practical problems in graphics and vision, including a simple autoencoder sanity test, a rotation estimator for 3D point clouds, and an inverse kinematics solver for 3D human poses.

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

Adversarial examples mislead deep neural networks with imperceptible perturbations and have brought significant threats to deep learning. An important aspect is their transferability, which refers to their ability to deceive other models, thus enabling attacks in the black-box setting. Though various methods have been proposed to boost transferability, the performance still falls short compared with white-box attacks. In this work, we observe that existing input transformation based attacks, one of the mainstream transfer-based attacks, result in different attention heatmaps on various models, which might limit the transferability. We also find that breaking the intrinsic relation of the image can disrupt the attention heatmap of the original image. Based on this finding, we propose a novel input transformation based attack called block shuffle and rotation (BSR). Specifically, BSR splits the input image into several blocks, then randomly shuffles and rotates these blocks to construct a set of new images for gradient calculation. Empirical evaluations on the ImageNet dataset demonstrate that BSR could achieve significantly better transferability than the existing input transformation based methods under single-model and ensemble-model settings. Combining BSR with the current input transformation method can further improve the transferability, which significantly outperforms the state-of-the-art methods. Code is available at https://github.com/Trustworthy-AI-Group/BSR

Concept erasure serves as a vital safety mechanism for removing unwanted concepts from text-to-image (T2I) models. While extensively studied in U-Net and dual-stream architectures (e.g., Flux), this task remains under-explored in the recent emerging paradigm of single-stream diffusion transformers (e.g., Z-Image). In this new paradigm, text and image tokens are processed as a single unified sequence via shared parameters. Consequently, directly applying prior erasure methods typically leads to generation collapse. To bridge this gap, we introduce Z-Erase, the first concept erasure method tailored for single-stream T2I models. To guarantee stable image generation, Z-Erase first proposes a Stream Disentangled Concept Erasure Framework that decouples updates and enables existing methods on single-stream models. Subsequently, within this framework, we introduce Lagrangian-Guided Adaptive Erasure Modulation, a constrained algorithm that further balances the sensitive erasure-preservation trade-off. Moreover, we provide a rigorous convergence analysis proving that Z-Erase can converge to a Pareto stationary point. Experiments demonstrate that Z-Erase successfully overcomes the generation collapse issue, achieving state-of-the-art performance across a wide range of tasks.

Recent work demonstrated Transformers' ability to efficiently copy strings of exponential sizes, distinguishing them from other architectures. We present the Causal Relation Network (CausalRN), an all-MLP sequence modeling architecture that can match Transformers on the copying task. Extending Relation Networks (RNs), we implemented key innovations to support autoregressive sequence modeling while maintaining computational feasibility. We discovered that exponentially-activated RNs are reducible to linear time complexity, and pre-activation normalization induces an infinitely growing memory pool, similar to a KV cache. In ablation study, we found both exponential activation and pre-activation normalization are indispensable for Transformer-level copying. Our findings provide new insights into what actually constitutes strong in-context retrieval.