Daily Papers

Recent advances in efficient sequence modeling have introduced selective state-space layers, a key component of the Mamba architecture, which have demonstrated remarkable success in a wide range of NLP and vision tasks. While Mamba's empirical performance has matched or surpassed SoTA transformers on such diverse benchmarks, the theoretical foundations underlying its powerful representational capabilities remain less explored. In this work, we investigate the expressivity of selective state-space layers using multivariate polynomials, and prove that they surpass linear transformers in expressiveness. Consequently, our findings reveal that Mamba offers superior representational power over linear attention-based models for long sequences, while not sacrificing their generalization. Our theoretical insights are validated by a comprehensive set of empirical experiments on various datasets.

Sequence models like Transformers and RNNs often overallocate attention to irrelevant context, leading to noisy intermediate representations. This degrades LLM capabilities by promoting hallucinations, weakening long-range and retrieval abilities, and reducing robustness. Recent work has shown that differential design can mitigate this issue in Transformers, improving their effectiveness across various applications. In this paper, we explore whether these techniques, originally developed for Transformers, can be applied to Mamba, a recent architecture based on selective state-space layers that achieves Transformer-level performance with greater efficiency. We show that a naive adaptation of differential design to Mamba is insufficient and requires careful architectural modifications. To address this, we introduce a novel differential mechanism for Mamba, empirically validated on language modeling benchmarks, demonstrating improved retrieval capabilities and superior performance over vanilla Mamba. Finally, we conduct extensive ablation studies and empirical analyses to justify our design choices and provide evidence that our approach effectively mitigates the overallocation problem in Mamba-based models. Our code is publicly available.

A central challenge in sequence modeling is efficiently handling tasks with extended contexts. While recent state-space models (SSMs) have made significant progress in this area, they often lack input-dependent filtering or require substantial increases in model complexity to handle input variability. We address this gap by introducing S7, a simplified yet powerful SSM that can handle input dependence while incorporating stable reparameterization and specific design choices to dynamically adjust state transitions based on input content, maintaining efficiency and performance. We prove that this reparameterization ensures stability in long-sequence modeling by keeping state transitions well-behaved over time. Additionally, it controls the gradient norm, enabling efficient training and preventing issues like exploding or vanishing gradients. S7 significantly outperforms baselines across various sequence modeling tasks, including neuromorphic event-based datasets, Long Range Arena benchmarks, and various physical and biological time series. Overall, S7 offers a more straightforward approach to sequence modeling without relying on complex, domain-specific inductive biases, achieving significant improvements across key benchmarks.

In recent years, Transformers have become the de-facto architecture for sequence modeling on text and a variety of multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs prohibitive compute and memory complexity that scales quadratically w.r.t. the sequence length. A recent architecture, Mamba, based on state space models has been shown to achieve comparable performance for modeling text sequences, while scaling linearly with the sequence length. In this work, we present Mamba-ND, a generalized design extending the Mamba architecture to arbitrary multi-dimensional data. Our design alternatively unravels the input data across different dimensions following row-major orderings. We provide a systematic comparison of Mamba-ND with several other alternatives, based on prior multi-dimensional extensions such as Bi-directional LSTMs and S4ND. Empirically, we show that Mamba-ND demonstrates performance competitive with the state-of-the-art on a variety of multi-dimensional benchmarks, including ImageNet-1K classification, HMDB-51 action recognition, and ERA5 weather forecasting.

Recent advances in deep learning have mainly relied on Transformers due to their data dependency and ability to learn at scale. The attention module in these architectures, however, exhibits quadratic time and space in input size, limiting their scalability for long-sequence modeling. Despite recent attempts to design efficient and effective architecture backbone for multi-dimensional data, such as images and multivariate time series, existing models are either data independent, or fail to allow inter- and intra-dimension communication. Recently, State Space Models (SSMs), and more specifically Selective State Space Models, with efficient hardware-aware implementation, have shown promising potential for long sequence modeling. Motivated by the success of SSMs, we present MambaMixer, a new architecture with data-dependent weights that uses a dual selection mechanism across tokens and channels, called Selective Token and Channel Mixer. MambaMixer connects selective mixers using a weighted averaging mechanism, allowing layers to have direct access to early features. As a proof of concept, we design Vision MambaMixer (ViM2) and Time Series MambaMixer (TSM2) architectures based on the MambaMixer block and explore their performance in various vision and time series forecasting tasks. Our results underline the importance of selective mixing across both tokens and channels. In ImageNet classification, object detection, and semantic segmentation tasks, ViM2 achieves competitive performance with well-established vision models and outperforms SSM-based vision models. In time series forecasting, TSM2 achieves outstanding performance compared to state-of-the-art methods while demonstrating significantly improved computational cost. These results show that while Transformers, cross-channel attention, and MLPs are sufficient for good performance in time series forecasting, neither is necessary.

Facial Expression Recognition (FER) plays a pivotal role in understanding human emotional cues. However, traditional FER methods based on visual information have some limitations, such as preprocessing, feature extraction, and multi-stage classification procedures. These not only increase computational complexity but also require a significant amount of computing resources. Considering Convolutional Neural Network (CNN)-based FER schemes frequently prove inadequate in identifying the deep, long-distance dependencies embedded within facial expression images, and the Transformer's inherent quadratic computational complexity, this paper presents the FER-YOLO-Mamba model, which integrates the principles of Mamba and YOLO technologies to facilitate efficient coordination in facial expression image recognition and localization. Within the FER-YOLO-Mamba model, we further devise a FER-YOLO-VSS dual-branch module, which combines the inherent strengths of convolutional layers in local feature extraction with the exceptional capability of State Space Models (SSMs) in revealing long-distance dependencies. To the best of our knowledge, this is the first Vision Mamba model designed for facial expression detection and classification. To evaluate the performance of the proposed FER-YOLO-Mamba model, we conducted experiments on two benchmark datasets, RAF-DB and SFEW. The experimental results indicate that the FER-YOLO-Mamba model achieved better results compared to other models. The code is available from https://github.com/SwjtuMa/FER-YOLO-Mamba.

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

Efficient long-context language modeling remains a significant challenge in Natural Language Processing (NLP). While Transformers dominate language tasks, they struggle with long sequences due to quadratic computational complexity in training and linearly scaling memory costs during inference. Recent State Space Models (SSMs) such as Mamba offer alternatives with constant memory usage, but they underperform in tasks requiring extensive in-context retrieval. We introduce Taipan, a novel hybrid architecture that combines Mamba-2 with Selective Attention Layers (SALs). These SALs identify tokens requiring long-range interactions, remove less important features, and then augment their representations using the attention module. This approach balances Mamba's efficiency with Transformer-like performance in memory-intensive tasks. By constraining the attention budget, Taipan extends accurate predictions to context lengths of up to 1 million tokens while preserving computational efficiency. Our experiments demonstrate Taipan's superior performance across various scales and tasks, offering a promising solution for efficient long-context language modeling.

Recent advancements in state space models, notably Mamba, have demonstrated significant progress in modeling long sequences for tasks like language understanding. Yet, their application in vision tasks has not markedly surpassed the performance of traditional Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs). This paper posits that the key to enhancing Vision Mamba (ViM) lies in optimizing scan directions for sequence modeling. Traditional ViM approaches, which flatten spatial tokens, overlook the preservation of local 2D dependencies, thereby elongating the distance between adjacent tokens. We introduce a novel local scanning strategy that divides images into distinct windows, effectively capturing local dependencies while maintaining a global perspective. Additionally, acknowledging the varying preferences for scan patterns across different network layers, we propose a dynamic method to independently search for the optimal scan choices for each layer, substantially improving performance. Extensive experiments across both plain and hierarchical models underscore our approach's superiority in effectively capturing image representations. For example, our model significantly outperforms Vim-Ti by 3.1% on ImageNet with the same 1.5G FLOPs. Code is available at: https://github.com/hunto/LocalMamba.

Recent sequence modeling approaches using selective state space sequence models, referred to as Mamba models, have seen a surge of interest. These models allow efficient processing of long sequences in linear time and are rapidly being adopted in a wide range of applications such as language modeling, demonstrating promising performance. To foster their reliable use in real-world scenarios, it is crucial to augment their transparency. Our work bridges this critical gap by bringing explainability, particularly Layer-wise Relevance Propagation (LRP), to the Mamba architecture. Guided by the axiom of relevance conservation, we identify specific components in the Mamba architecture, which cause unfaithful explanations. To remedy this issue, we propose MambaLRP, a novel algorithm within the LRP framework, which ensures a more stable and reliable relevance propagation through these components. Our proposed method is theoretically sound and excels in achieving state-of-the-art explanation performance across a diverse range of models and datasets. Moreover, MambaLRP facilitates a deeper inspection of Mamba architectures, uncovering various biases and evaluating their significance. It also enables the analysis of previous speculations regarding the long-range capabilities of Mamba models.

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

Efficiently modeling sequences with infinite context length has been a long-standing problem. Past works suffer from either the quadratic computation complexity or the limited extrapolation ability on length generalization. In this work, we present Samba, a simple hybrid architecture that layer-wise combines Mamba, a selective State Space Model (SSM), with Sliding Window Attention (SWA). Samba selectively compresses a given sequence into recurrent hidden states while still maintaining the ability to precisely recall memories with the attention mechanism. We scale Samba up to 3.8B parameters with 3.2T training tokens and show that Samba substantially outperforms the state-of-the-art models based on pure attention or SSMs on a wide range of benchmarks. When trained on 4K length sequences, Samba can be efficiently extrapolated to 256K context length with perfect memory recall and show improved token predictions up to 1M context length. As a linear-time sequence model, Samba enjoys a 3.73x higher throughput compared to Transformers with grouped-query attention when processing user prompts of 128K length, and 3.64x speedup when generating 64K tokens with unlimited streaming. A sample implementation of Samba is publicly available in https://github.com/microsoft/Samba.

The Mamba layer offers an efficient selective state space model (SSM) that is highly effective in modeling multiple domains including NLP, long-range sequences processing, and computer vision. Selective SSMs are viewed as dual models, in which one trains in parallel on the entire sequence via IO-aware parallel scan, and deploys in an autoregressive manner. We add a third view and show that such models can be viewed as attention-driven models. This new perspective enables us to compare the underlying mechanisms to that of the self-attention layers in transformers and allows us to peer inside the inner workings of the Mamba model with explainability methods. Our code is publicly available.

Recent advancements in state-space models (SSMs) have showcased effective performance in modeling long-range dependencies with subquadratic complexity. However, pure SSM-based models still face challenges related to stability and achieving optimal performance on computer vision tasks. Our paper addresses the challenges of scaling SSM-based models for computer vision, particularly the instability and inefficiency of large model sizes. To address this, we introduce a Modulated Group Mamba layer which divides the input channels into four groups and applies our proposed SSM-based efficient Visual Single Selective Scanning (VSSS) block independently to each group, with each VSSS block scanning in one of the four spatial directions. The Modulated Group Mamba layer also wraps the four VSSS blocks into a channel modulation operator to improve cross-channel communication. Furthermore, we introduce a distillation-based training objective to stabilize the training of large models, leading to consistent performance gains. Our comprehensive experiments demonstrate the merits of the proposed contributions, leading to superior performance over existing methods for image classification on ImageNet-1K, object detection, instance segmentation on MS-COCO, and semantic segmentation on ADE20K. Our tiny variant with 23M parameters achieves state-of-the-art performance with a classification top-1 accuracy of 83.3% on ImageNet-1K, while being 26% efficient in terms of parameters, compared to the best existing Mamba design of same model size. Our code and models are available at: https://github.com/Amshaker/GroupMamba.

While Transformers have been the main architecture behind deep learning's success in language modeling, state-space models (SSMs) such as Mamba have recently been shown to match or outperform Transformers at small to medium scale. We show that these families of models are actually quite closely related, and develop a rich framework of theoretical connections between SSMs and variants of attention, connected through various decompositions of a well-studied class of structured semiseparable matrices. Our state space duality (SSD) framework allows us to design a new architecture (Mamba-2) whose core layer is an a refinement of Mamba's selective SSM that is 2-8X faster, while continuing to be competitive with Transformers on language modeling.

Talking head synthesis is vital for virtual avatars and human-computer interaction. However, most existing methods are typically limited to accepting control from a single primary modality, restricting their practical utility. To this end, we introduce ACTalker, an end-to-end video diffusion framework that supports both multi-signals control and single-signal control for talking head video generation. For multiple control, we design a parallel mamba structure with multiple branches, each utilizing a separate driving signal to control specific facial regions. A gate mechanism is applied across all branches, providing flexible control over video generation. To ensure natural coordination of the controlled video both temporally and spatially, we employ the mamba structure, which enables driving signals to manipulate feature tokens across both dimensions in each branch. Additionally, we introduce a mask-drop strategy that allows each driving signal to independently control its corresponding facial region within the mamba structure, preventing control conflicts. Experimental results demonstrate that our method produces natural-looking facial videos driven by diverse signals and that the mamba layer seamlessly integrates multiple driving modalities without conflict.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

Large language models (LLMs) face a daunting challenge due to the excessive computational and memory requirements of the commonly used Transformer architecture. While state space model (SSM) is a new type of foundational network architecture offering lower computational complexity, their performance has yet to fully rival that of Transformers. This paper introduces DenseSSM, a novel approach to enhance the flow of hidden information between layers in SSMs. By selectively integrating shallowlayer hidden states into deeper layers, DenseSSM retains fine-grained information crucial for the final output. Dense connections enhanced DenseSSM still maintains the training parallelizability and inference efficiency. The proposed method can be widely applicable to various SSM types like RetNet and Mamba. With similar model size, DenseSSM achieves significant improvements, exemplified by DenseRetNet outperforming the original RetNet with up to 5% accuracy improvement on public benchmarks.

State Space Models (SSMs) have recently emerged as efficient alternatives to Transformer-Based Models (TBMs) for long-sequence processing, offering linear scaling and lower memory use. Yet, how contextual information flows across layers and tokens in these architectures remains understudied. We present the first unified, token- and layer-level analysis of representation propagation in SSMs and TBMs. Using centered kernel alignment, stability metrics, and probing, we characterize how representations evolve within and across layers. We find a key divergence: TBMs rapidly homogenize token representations, with diversity reemerging only in later layers, while SSMs preserve token uniqueness early but converge to homogenization deeper. Theoretical analysis and parameter randomization further reveal that oversmoothing in TBMs stems from architectural design, whereas in SSMs it arises mainly from training dynamics. These insights clarify the inductive biases of both architectures and inform future model and training designs for long-context reasoning.

Selective state space models (SSMs), such as Mamba, highly excel at capturing long-range dependencies in 1D sequential data, while their applications to 2D vision tasks still face challenges. Current visual SSMs often convert images into 1D sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood connectivity directly in the state space. Instead of relying solely on sequential state transitions, we introduce a structure-aware state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation using the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multiplication framework, providing a deeper understanding of our method. Experimental results demonstrate that Spatial-Mamba, even with a single scan, attains or surpasses the state-of-the-art SSM-based models in image classification, detection and segmentation. Source codes and trained models can be found at https://github.com/EdwardChasel/Spatial-Mamba.

State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

Recent advancements in deep learning have led to widespread use of techniques for audio content generation, notably employing Denoising Diffusion Probabilistic Models (DDPM) across various tasks. Among these, Foley Sound Synthesis is of particular interest for its role in applications for the creation of multimedia content. Given the temporal-dependent nature of sound, it is crucial to design generative models that can effectively handle the sequential modeling of audio samples. Selective State Space Models (SSMs) have recently been proposed as a valid alternative to previously proposed techniques, demonstrating competitive performance with lower computational complexity. In this paper, we introduce MambaFoley, a diffusion-based model that, to the best of our knowledge, is the first to leverage the recently proposed SSM known as Mamba for the Foley sound generation task. To evaluate the effectiveness of the proposed method, we compare it with a state-of-the-art Foley sound generative model using both objective and subjective analyses.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

Few-shot class-incremental learning (FSCIL) confronts the challenge of integrating new classes into a model with minimal training samples while preserving the knowledge of previously learned classes. Traditional methods widely adopt static adaptation relying on a fixed parameter space to learn from data that arrive sequentially, prone to overfitting to the current session. Existing dynamic strategies require the expansion of the parameter space continually, leading to increased complexity. To address these challenges, we integrate the recently proposed selective state space model (SSM) into FSCIL. Concretely, we propose a dual selective SSM projector that dynamically adjusts the projection parameters based on the intermediate features for dynamic adaptation. The dual design enables the model to maintain the robust features of base classes, while adaptively learning distinctive feature shifts for novel classes. Additionally, we develop a class-sensitive selective scan mechanism to guide dynamic adaptation. It minimizes the disruption to base-class representations caused by training on novel data, and meanwhile, forces the selective scan to perform in distinct patterns between base and novel classes. Experiments on miniImageNet, CUB-200, and CIFAR-100 demonstrate that our framework outperforms the existing state-of-the-art methods. The code is available at https://github.com/xiaojieli0903/Mamba-FSCIL.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

Inter-frame modeling is pivotal in generating intermediate frames for video frame interpolation (VFI). Current approaches predominantly rely on convolution or attention-based models, which often either lack sufficient receptive fields or entail significant computational overheads. Recently, Selective State Space Models (S6) have emerged, tailored specifically for long sequence modeling, offering both linear complexity and data-dependent modeling capabilities. In this paper, we propose VFIMamba, a novel frame interpolation method for efficient and dynamic inter-frame modeling by harnessing the S6 model. Our approach introduces the Mixed-SSM Block (MSB), which initially rearranges tokens from adjacent frames in an interleaved fashion and subsequently applies multi-directional S6 modeling. This design facilitates the efficient transmission of information across frames while upholding linear complexity. Furthermore, we introduce a novel curriculum learning strategy that progressively cultivates proficiency in modeling inter-frame dynamics across varying motion magnitudes, fully unleashing the potential of the S6 model. Experimental findings showcase that our method attains state-of-the-art performance across diverse benchmarks, particularly excelling in high-resolution scenarios. In particular, on the X-TEST dataset, VFIMamba demonstrates a noteworthy improvement of 0.80 dB for 4K frames and 0.96 dB for 2K frames.

Models using structured state space sequence (S4) layers have achieved state-of-the-art performance on long-range sequence modeling tasks. An S4 layer combines linear state space models (SSMs), the HiPPO framework, and deep learning to achieve high performance. We build on the design of the S4 layer and introduce a new state space layer, the S5 layer. Whereas an S4 layer uses many independent single-input, single-output SSMs, the S5 layer uses one multi-input, multi-output SSM. We establish a connection between S5 and S4, and use this to develop the initialization and parameterization used by the S5 model. The result is a state space layer that can leverage efficient and widely implemented parallel scans, allowing S5 to match the computational efficiency of S4, while also achieving state-of-the-art performance on several long-range sequence modeling tasks. S5 averages 87.4% on the long range arena benchmark, and 98.5% on the most difficult Path-X task.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

This paper presents a new exploration into a category of diffusion models built upon state space architecture. We endeavor to train diffusion models for image data, wherein the traditional U-Net backbone is supplanted by a state space backbone, functioning on raw patches or latent space. Given its notable efficacy in accommodating long-range dependencies, Diffusion State Space Models (DiS) are distinguished by treating all inputs including time, condition, and noisy image patches as tokens. Our assessment of DiS encompasses both unconditional and class-conditional image generation scenarios, revealing that DiS exhibits comparable, if not superior, performance to CNN-based or Transformer-based U-Net architectures of commensurate size. Furthermore, we analyze the scalability of DiS, gauged by the forward pass complexity quantified in Gflops. DiS models with higher Gflops, achieved through augmentation of depth/width or augmentation of input tokens, consistently demonstrate lower FID. In addition to demonstrating commendable scalability characteristics, DiS-H/2 models in latent space achieve performance levels akin to prior diffusion models on class-conditional ImageNet benchmarks at the resolution of 256times256 and 512times512, while significantly reducing the computational burden. The code and models are available at: https://github.com/feizc/DiS.

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to understand how covariance structure in data, latent state size, and initialization affect the evolution of parameters throughout learning with gradient descent. We show that focusing on the learning dynamics in the frequency domain affords analytical solutions under mild assumptions, and we establish a link between one-dimensional SSMs and the dynamics of deep linear feed-forward networks. Finally, we analyze how latent state over-parameterization affects convergence time and describe future work in extending our results to the study of deep SSMs with nonlinear connections. This work is a step toward a theory of learning dynamics in deep state space models.

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence u mapsto y by simply simulating a linear continuous-time state-space representation x = Ax + Bu, y = Cx + Du. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices A that endow LSSLs with long-range memory. Empirically, stacking LSSL layers into a simple deep neural network obtains state-of-the-art results across time series benchmarks for long dependencies in sequential image classification, real-world healthcare regression tasks, and speech. On a difficult speech classification task with length-16000 sequences, LSSL outperforms prior approaches by 24 accuracy points, and even outperforms baselines that use hand-crafted features on 100x shorter sequences.

State Space Models (SSMs) have emerged as efficient alternatives to Transformers, mitigating their quadratic computational cost. However, the application of Parameter-Efficient Fine-Tuning (PEFT) methods to SSMs remains largely unexplored. In particular, prompt-based methods like Prompt Tuning and Prefix-Tuning, which are widely used in Transformers, do not perform well on SSMs. To address this, we propose state-based methods as a superior alternative to prompt-based methods. This new family of methods naturally stems from the architectural characteristics of SSMs. State-based methods adjust state-related features directly instead of depending on external prompts. Furthermore, we introduce a novel state-based PEFT method: State-offset Tuning. At every timestep, our method directly affects the state at the current step, leading to more effective adaptation. Through extensive experiments across diverse datasets, we demonstrate the effectiveness of our method. Code is available at https://github.com/furiosa-ai/ssm-state-tuning.

Recent years have witnessed great progress in image restoration thanks to the advancements in modern deep neural networks e.g. Convolutional Neural Network and Transformer. However, existing restoration backbones are usually limited due to the inherent local reductive bias or quadratic computational complexity. Recently, Selective Structured State Space Model e.g., Mamba, has shown great potential for long-range dependencies modeling with linear complexity, but it is still under-explored in low-level computer vision. In this work, we introduce a simple but strong benchmark model, named MambaIR, for image restoration. In detail, we propose the Residual State Space Block as the core component, which employs convolution and channel attention to enhance the capabilities of the vanilla Mamba. In this way, our MambaIR takes advantage of local patch recurrence prior as well as channel interaction to produce restoration-specific feature representation. Extensive experiments demonstrate the superiority of our method, for example, MambaIR outperforms Transformer-based baseline SwinIR by up to 0.36dB, using similar computational cost but with a global receptive field. Code is available at https://github.com/csguoh/MambaIR.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

State Space Models (SSMs) have emerged as a promising alternative to the popular transformer-based models and have been increasingly gaining attention. Compared to transformers, SSMs excel at tasks with sequential data or longer contexts, demonstrating comparable performances with significant efficiency gains. In this survey, we provide a coherent and systematic overview for SSMs, including their theoretical motivations, mathematical formulations, comparison with existing model classes, and various applications. We divide the SSM series into three main sections, providing a detailed introduction to the original SSM, the structured SSM represented by S4, and the selective SSM typified by Mamba. We put an emphasis on technicality, and highlight the various key techniques introduced to address the effectiveness and efficiency of SSMs. We hope this manuscript serves as an introduction for researchers to explore the theoretical foundations of SSMs.

We introduce MoS (Mixture of States), a novel fusion paradigm for multimodal diffusion models that merges modalities using flexible, state-based interactions. The core of MoS is a learnable, token-wise router that creates denoising timestep- and input-dependent interactions between modalities' hidden states, precisely aligning token-level features with the diffusion trajectory. This router sparsely selects the top-k hidden states and is trained with an ε-greedy strategy, efficiently selecting contextual features with minimal learnable parameters and negligible computational overhead. We validate our design with text-to-image generation (MoS-Image) and editing (MoS-Editing), which achieve state-of-the-art results. With only 3B to 5B parameters, our models match or surpass counterparts up to 4times larger. These findings establish MoS as a flexible and compute-efficient paradigm for scaling multimodal diffusion models.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Vision transformers have significantly advanced the field of computer vision, offering robust modeling capabilities and global receptive field. However, their high computational demands limit their applicability in processing long sequences. To tackle this issue, State Space Models (SSMs) have gained prominence in vision tasks as they offer linear computational complexity. Recently, State Space Duality (SSD), an improved variant of SSMs, was introduced in Mamba2 to enhance model performance and efficiency. However, the inherent causal nature of SSD/SSMs restricts their applications in non-causal vision tasks. To address this limitation, we introduce Visual State Space Duality (VSSD) model, which has a non-causal format of SSD. Specifically, we propose to discard the magnitude of interactions between the hidden state and tokens while preserving their relative weights, which relieves the dependencies of token contribution on previous tokens. Together with the involvement of multi-scan strategies, we show that the scanning results can be integrated to achieve non-causality, which not only improves the performance of SSD in vision tasks but also enhances its efficiency. We conduct extensive experiments on various benchmarks including image classification, detection, and segmentation, where VSSD surpasses existing state-of-the-art SSM-based models. Code and weights are available at https://github.com/YuHengsss/VSSD.

Structured state space sequence (S4) models have recently achieved state-of-the-art performance on long-range sequence modeling tasks. These models also have fast inference speeds and parallelisable training, making them potentially useful in many reinforcement learning settings. We propose a modification to a variant of S4 that enables us to initialise and reset the hidden state in parallel, allowing us to tackle reinforcement learning tasks. We show that our modified architecture runs asymptotically faster than Transformers in sequence length and performs better than RNN's on a simple memory-based task. We evaluate our modified architecture on a set of partially-observable environments and find that, in practice, our model outperforms RNN's while also running over five times faster. Then, by leveraging the model's ability to handle long-range sequences, we achieve strong performance on a challenging meta-learning task in which the agent is given a randomly-sampled continuous control environment, combined with a randomly-sampled linear projection of the environment's observations and actions. Furthermore, we show the resulting model can adapt to out-of-distribution held-out tasks. Overall, the results presented in this paper show that structured state space models are fast and performant for in-context reinforcement learning tasks. We provide code at https://github.com/luchris429/popjaxrl.

Recent advancements in State Space Models (SSMs) have attracted significant interest, particularly in models optimized for parallel training and handling long-range dependencies. Architectures like Mamba have scaled to billions of parameters with selective SSM. To facilitate broader applications using Mamba, exploring its efficiency is crucial. While token reduction techniques offer a straightforward post-training strategy, we find that applying existing methods directly to SSMs leads to substantial performance drops. Through insightful analysis, we identify the reasons for this failure and the limitations of current techniques. In response, we propose a tailored, unified post-training token reduction method for SSMs. Our approach integrates token importance and similarity, thus taking advantage of both pruning and merging, to devise a fine-grained intra-layer token reduction strategy. Extensive experiments show that our method improves the average accuracy by 5.7% to 13.1% on six benchmarks with Mamba-2 compared to existing methods, while significantly reducing computational demands and memory requirements.

State space models (SSMs) have shown impressive results on tasks that require modeling long-range dependencies and efficiently scale to long sequences owing to their subquadratic runtime complexity. Originally designed for continuous signals, SSMs have shown superior performance on a plethora of tasks, in vision and audio; however, SSMs still lag Transformer performance in Language Modeling tasks. In this work, we propose a hybrid layer named Block-State Transformer (BST), that internally combines an SSM sublayer for long-range contextualization, and a Block Transformer sublayer for short-term representation of sequences. We study three different, and completely parallelizable, variants that integrate SSMs and block-wise attention. We show that our model outperforms similar Transformer-based architectures on language modeling perplexity and generalizes to longer sequences. In addition, the Block-State Transformer demonstrates more than tenfold increase in speed at the layer level compared to the Block-Recurrent Transformer when model parallelization is employed.

Modeling long range dependencies in sequential data is a fundamental step towards attaining human-level performance in many modalities such as text, vision, audio and video. While attention-based models are a popular and effective choice in modeling short-range interactions, their performance on tasks requiring long range reasoning has been largely inadequate. In an exciting result, Gu et al. (ICLR 2022) proposed the Structured State Space (S4) architecture delivering large gains over state-of-the-art models on several long-range tasks across various modalities. The core proposition of S4 is the parameterization of state matrices via a diagonal plus low rank structure, allowing efficient computation. In this work, we show that one can match the performance of S4 even without the low rank correction and thus assuming the state matrices to be diagonal. Our Diagonal State Space (DSS) model matches the performance of S4 on Long Range Arena tasks, speech classification on Speech Commands dataset, while being conceptually simpler and straightforward to implement.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of epsilon-optimal policies reaching a set S_L^{rightarrow} of incrementally L-controllable states. We introduce a novel layered decomposition of the set of incrementally L-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of mathcal{O}(LS^{rightarrow}_{L(1+epsilon)}Gamma_{L(1+epsilon)} A ln^{12}(S^{rightarrow}_{L(1+epsilon)})/epsilon^2), where S^{rightarrow}_{L(1+epsilon)} is the number of states that are incrementally L(1+epsilon)-controllable, A is the number of actions, and Gamma_{L(1+epsilon)} is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of L^2 and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of mathcal{O}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM computation via convolution. To overcome compatibility limitations in parallel convolutional computation, this paper proposes a novel non-recursive non-uniform sample processing strategy. Theoretical analysis of SSMs through the lens of Event-Triggered Control (ETC) theory reveals the Non-Stable State (NSS) problem, where deviations from sampling point requirements lead to error transmission and accumulation, causing the divergence of the SSM's hidden state. Our analysis further reveals that adjustments of input sequences with early memories can mitigate the NSS problem, achieving Sampling Step Adaptation (SSA). Building on this insight, we introduce a simple yet effective plug-and-play mechanism, State Memory Replay (SMR), which utilizes learnable memories to adjust the current state with multi-step information for generalization at sampling points different from those in the training data. This enables SSMs to stably model varying sampling points. Experiments on long-range modeling tasks in autoregressive language modeling and Long Range Arena demonstrate the general effectiveness of the SMR mechanism for a series of SSM models.

Given the remarkable achievements in image generation through diffusion models, the research community has shown increasing interest in extending these models to video generation. Recent diffusion models for video generation have predominantly utilized attention layers to extract temporal features. However, attention layers are limited by their memory consumption, which increases quadratically with the length of the sequence. This limitation presents significant challenges when attempting to generate longer video sequences using diffusion models. To overcome this challenge, we propose leveraging state-space models (SSMs). SSMs have recently gained attention as viable alternatives due to their linear memory consumption relative to sequence length. In the experiments, we first evaluate our SSM-based model with UCF101, a standard benchmark of video generation. In addition, to investigate the potential of SSMs for longer video generation, we perform an experiment using the MineRL Navigate dataset, varying the number of frames to 64 and 150. In these settings, our SSM-based model can considerably save memory consumption for longer sequences, while maintaining competitive FVD scores to the attention-based models. Our codes are available at https://github.com/shim0114/SSM-Meets-Video-Diffusion-Models.

A central objective in computer vision is to design models with appropriate 2-D inductive bias. Desiderata for 2D inductive bias include two-dimensional position awareness, dynamic spatial locality, and translation and permutation invariance. To address these goals, we leverage an expressive variation of the multidimensional State Space Model (SSM). Our approach introduces efficient parameterization, accelerated computation, and a suitable normalization scheme. Empirically, we observe that incorporating our layer at the beginning of each transformer block of Vision Transformers (ViT) significantly enhances performance for multiple ViT backbones and across datasets. The new layer is effective even with a negligible amount of additional parameters and inference time. Ablation studies and visualizations demonstrate that the layer has a strong 2-D inductive bias. For example, vision transformers equipped with our layer exhibit effective performance even without positional encoding

We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed algorithms, state-free inference does not incur any significant memory or computational cost with an increase in state size. We achieve this using properties of the proposed frequency domain transfer function parametrization, which enables direct computation of its corresponding convolutional kernel's spectrum via a single Fast Fourier Transform. Our experimental results across multiple sequence lengths and state sizes illustrates, on average, a 35% training speed improvement over S4 layers -- parametrized in time-domain -- on the Long Range Arena benchmark, while delivering state-of-the-art downstream performances over other attention-free approaches. Moreover, we report improved perplexity in language modeling over a long convolutional Hyena baseline, by simply introducing our transfer function parametrization. Our code is available at https://github.com/ruke1ire/RTF.

Seeking answers effectively for long videos is essential to build video question answering (videoQA) systems. Previous methods adaptively select frames and regions from long videos to save computations. However, this fails to reason over the whole sequence of video, leading to sub-optimal performance. To address this problem, we introduce a state space layer (SSL) into multi-modal Transformer to efficiently integrate global semantics of the video, which mitigates the video information loss caused by frame and region selection modules. Our SSL includes a gating unit to enable controllability over the flow of global semantics into visual representations. To further enhance the controllability, we introduce a cross-modal compositional congruence (C^3) objective to encourage global semantics aligned with the question. To rigorously evaluate long-form videoQA capacity, we construct two new benchmarks Ego-QA and MAD-QA featuring videos of considerably long length, i.e. 17.5 minutes and 1.9 hours, respectively. Extensive experiments demonstrate the superiority of our framework on these new as well as existing datasets.

State-space models (SSMs) offer a promising architecture for sequence modeling, providing an alternative to Transformers by replacing expensive self-attention with linear recurrences. In this paper, we propose a simple yet effective trick to enhance SSMs within given computational budgets by sparsifying them. Our intuition is that tokens in SSMs are highly redundant due to gradual recurrent updates, and dense recurrence operations block the delivery of past information. In particular, we observe that upper layers of SSMs tend to be more redundant as they encode global information, while lower layers encode local information. Motivated by this, we introduce Simba, a hierarchical sparsification method for SSMs based on token pruning. Simba sparsifies upper layers more than lower layers, encouraging the upper layers to behave like highways. To achieve this, we propose a novel token pruning criterion for SSMs, measuring the global impact of tokens on the final output by accumulating local recurrences. We demonstrate that Simba outperforms the baseline model, Mamba, with the same FLOPS in various natural language tasks. Moreover, we illustrate the effect of highways, showing that Simba not only enhances efficiency but also improves the information flow across long sequences. Code is available at https://github.com/woominsong/Simba.

Recent studies have shown that, relative position encoding performs well in selective state space model scanning algorithms, and the architecture that balances SSM and Attention enhances the efficiency and effectiveness of the algorithm, while the sparse activation of the mixture of experts reduces the training cost. I studied the effectiveness of using different position encodings in structured state space dual algorithms, and the more effective SSD-Attn internal and external function mixing method, and designed a more efficient cross domain mixture of experts. I found that the same matrix is very wonderful in different algorithms, which allows us to establish a new hybrid sparse architecture: Cheems. Compared with other hybrid architectures, it is more efficient and more effective in language modeling tasks.

Structured State Space Models (SSMs) have emerged as alternatives to transformers. While SSMs are often regarded as effective in capturing long-sequence dependencies, we rigorously demonstrate that they are inherently limited by strong recency bias. Our empirical studies also reveal that this bias impairs the models' ability to recall distant information and introduces robustness issues. Our scaling experiments then discovered that deeper structures in SSMs can facilitate the learning of long contexts. However, subsequent theoretical analysis reveals that as SSMs increase in depth, they exhibit another inevitable tendency toward over-smoothing, e.g., token representations becoming increasingly indistinguishable. This fundamental dilemma between recency and over-smoothing hinders the scalability of existing SSMs. Inspired by our theoretical findings, we propose to polarize two channels of the state transition matrices in SSMs, setting them to zero and one, respectively, simultaneously addressing recency bias and over-smoothing. Experiments demonstrate that our polarization technique consistently enhances the associative recall accuracy of long-range tokens and unlocks SSMs to benefit further from deeper architectures. All source codes are released at https://github.com/VITA-Group/SSM-Bottleneck.

For the deployment of neural networks in resource-constrained environments, prior works have built lightweight architectures with convolution and attention for capturing local and global dependencies, respectively. Recently, the state space model has emerged as an effective global token interaction with its favorable linear computational cost in the number of tokens. Yet, efficient vision backbones built with SSM have been explored less. In this paper, we introduce Efficient Vision Mamba (EfficientViM), a novel architecture built on hidden state mixer-based state space duality (HSM-SSD) that efficiently captures global dependencies with further reduced computational cost. In the HSM-SSD layer, we redesign the previous SSD layer to enable the channel mixing operation within hidden states. Additionally, we propose multi-stage hidden state fusion to further reinforce the representation power of hidden states, and provide the design alleviating the bottleneck caused by the memory-bound operations. As a result, the EfficientViM family achieves a new state-of-the-art speed-accuracy trade-off on ImageNet-1k, offering up to a 0.7% performance improvement over the second-best model SHViT with faster speed. Further, we observe significant improvements in throughput and accuracy compared to prior works, when scaling images or employing distillation training. Code is available at https://github.com/mlvlab/EfficientViM.

A high-performance image compression algorithm is crucial for real-time information transmission across numerous fields. Despite rapid progress in image compression, computational inefficiency and poor redundancy modeling still pose significant bottlenecks, limiting practical applications. Inspired by the effectiveness of state space models (SSMs) in capturing long-range dependencies, we leverage SSMs to address computational inefficiency in existing methods and improve image compression from multiple perspectives. In this paper, we integrate the advantages of SSMs for better efficiency-performance trade-off and propose an enhanced image compression approach through refined context modeling, which we term MambaIC. Specifically, we explore context modeling to adaptively refine the representation of hidden states. Additionally, we introduce window-based local attention into channel-spatial entropy modeling to reduce potential spatial redundancy during compression, thereby increasing efficiency. Comprehensive qualitative and quantitative results validate the effectiveness and efficiency of our approach, particularly for high-resolution image compression. Code is released at https://github.com/AuroraZengfh/MambaIC.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Visual Model-Based Reinforcement Learning (MBRL) promises to encapsulate agent's knowledge about the underlying dynamics of the environment, enabling learning a world model as a useful planner. However, top MBRL agents such as Dreamer often struggle with visual pixel-based inputs in the presence of exogenous or irrelevant noise in the observation space, due to failure to capture task-specific features while filtering out irrelevant spatio-temporal details. To tackle this problem, we apply a spatio-temporal masking strategy, a bisimulation principle, combined with latent reconstruction, to capture endogenous task-specific aspects of the environment for world models, effectively eliminating non-essential information. Joint training of representations, dynamics, and policy often leads to instabilities. To further address this issue, we develop a Hybrid Recurrent State-Space Model (HRSSM) structure, enhancing state representation robustness for effective policy learning. Our empirical evaluation demonstrates significant performance improvements over existing methods in a range of visually complex control tasks such as Maniskill gu2023maniskill2 with exogenous distractors from the Matterport environment. Our code is avaliable at https://github.com/bit1029public/HRSSM.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

State Space Models (SSMs) have become the leading alternative to Transformers for sequence modeling. Their primary advantage is efficiency in long-context and long-form generation, enabled by fixed-size memory and linear scaling of computational complexity. We begin this work by showing a simple theoretical result stating that SSMs cannot accurately solve any ``truly long-form'' generation problem (in a sense we formally define), undermining their main competitive advantage. However, we show that this limitation can be mitigated by allowing SSMs interactive access to external tools. In fact, we show that given the right choice of tool access and problem-dependent training data, SSMs can learn to solve any tractable problem and generalize to arbitrary problem length/complexity (i.e., achieve length generalization). Following our theoretical finding, we demonstrate that tool-augmented SSMs achieve remarkable length generalization on a variety of arithmetic, reasoning, and coding tasks. These findings highlight SSMs as a potential efficient alternative to Transformers in interactive tool-based and agentic settings.

To mitigate the computational complexity in the self-attention mechanism on long sequences, linear attention utilizes computation tricks to achieve linear complexity, while state space models (SSMs) popularize a favorable practice of using non-data-dependent memory pattern, i.e., emphasize the near and neglect the distant, to processing sequences. Recent studies have shown the priorities by combining them as one. However, the efficiency of linear attention remains only at the theoretical level in a causal setting, and SSMs require various designed constraints to operate effectively on specific data. Therefore, in order to unveil the true power of the hybrid design, the following two issues need to be addressed: (1) hardware-efficient implementation for linear attention and (2) stabilization of SSMs. To achieve this, we leverage the thought of tiling and hierarchy to propose CHELA (short-long Convolutions with Hardware-Efficient Linear Attention), which replaces SSMs with short-long convolutions and implements linear attention in a divide-and-conquer manner. This approach enjoys global abstraction and data-dependent selection from stable SSM and linear attention while maintaining real linear complexity. Our comprehensive experiments on the Long Range Arena benchmark and language modeling tasks demonstrate the effectiveness of the proposed method.

Propelled by the rapid advancement of deep learning technologies, the YOLO series has set a new benchmark for real-time object detectors. Researchers have continuously explored innovative applications of reparameterization, efficient layer aggregation networks, and anchor-free techniques on the foundation of YOLO. To further enhance detection performance, Transformer-based structures have been introduced, significantly expanding the model's receptive field and achieving notable performance gains. However, such improvements come at a cost, as the quadratic complexity of the self-attention mechanism increases the computational burden of the model. Fortunately, the emergence of State Space Models (SSM) as an innovative technology has effectively mitigated the issues caused by quadratic complexity. In light of these advancements, we introduce Mamba-YOLO a novel object detection model based on SSM. Mamba-YOLO not only optimizes the SSM foundation but also adapts specifically for object detection tasks. Given the potential limitations of SSM in sequence modeling, such as insufficient receptive field and weak image locality, we have designed the LSBlock and RGBlock. These modules enable more precise capture of local image dependencies and significantly enhance the robustness of the model. Extensive experimental results on the publicly available benchmark datasets COCO and VOC demonstrate that Mamba-YOLO surpasses the existing YOLO series models in both performance and competitiveness, showcasing its substantial potential and competitive edge.The PyTorch code is available at:https://github.com/HZAI-ZJNU/Mamba-YOLO

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

Video diffusion models have recently shown promise for world modeling through autoregressive frame prediction conditioned on actions. However, they struggle to maintain long-term memory due to the high computational cost associated with processing extended sequences in attention layers. To overcome this limitation, we propose a novel architecture leveraging state-space models (SSMs) to extend temporal memory without compromising computational efficiency. Unlike previous approaches that retrofit SSMs for non-causal vision tasks, our method fully exploits the inherent advantages of SSMs in causal sequence modeling. Central to our design is a block-wise SSM scanning scheme, which strategically trades off spatial consistency for extended temporal memory, combined with dense local attention to ensure coherence between consecutive frames. We evaluate the long-term memory capabilities of our model through spatial retrieval and reasoning tasks over extended horizons. Experiments on Memory Maze and Minecraft datasets demonstrate that our approach surpasses baselines in preserving long-range memory, while maintaining practical inference speeds suitable for interactive applications.

Active inference is a first principles approach for understanding the brain in particular, and sentient agents in general, with the single imperative of minimizing free energy. As such, it provides a computational account for modelling artificial intelligent agents, by defining the agent's generative model and inferring the model parameters, actions and hidden state beliefs. However, the exact specification of the generative model and the hidden state space structure is left to the experimenter, whose design choices influence the resulting behaviour of the agent. Recently, deep learning methods have been proposed to learn a hidden state space structure purely from data, alleviating the experimenter from this tedious design task, but resulting in an entangled, non-interpreteable state space. In this paper, we hypothesize that such a learnt, entangled state space does not necessarily yield the best model in terms of free energy, and that enforcing different factors in the state space can yield a lower model complexity. In particular, we consider the problem of 3D object representation, and focus on different instances of the ShapeNet dataset. We propose a model that factorizes object shape, pose and category, while still learning a representation for each factor using a deep neural network. We show that models, with best disentanglement properties, perform best when adopted by an active agent in reaching preferred observations.

Autoregressive (AR) diffusion enables streaming, interactive long-video generation by producing frames causally, yet maintaining coherence over minute-scale horizons remains challenging due to accumulated errors, motion drift, and content repetition. We approach this problem from a memory perspective, treating video synthesis as a recurrent dynamical process that requires coordinated short- and long-term context. We propose VideoSSM, a Long Video Model that unifies AR diffusion with a hybrid state-space memory. The state-space model (SSM) serves as an evolving global memory of scene dynamics across the entire sequence, while a context window provides local memory for motion cues and fine details. This hybrid design preserves global consistency without frozen, repetitive patterns, supports prompt-adaptive interaction, and scales in linear time with sequence length. Experiments on short- and long-range benchmarks demonstrate state-of-the-art temporal consistency and motion stability among autoregressive video generator especially at minute-scale horizons, enabling content diversity and interactive prompt-based control, thereby establishing a scalable, memory-aware framework for long video generation.

The most fundamental capability of modern AI methods such as Large Language Models (LLMs) is the ability to predict the next token in a long sequence of tokens, known as ``sequence modeling." Although the Transformers model is the current dominant approach to sequence modeling, its quadratic computational cost with respect to sequence length is a significant drawback. State-space models (SSMs) offer a promising alternative due to their linear decoding efficiency and high parallelizability during training. However, existing SSMs often rely on seemingly ad hoc linear recurrence designs. In this work, we explore SSM design through the lens of online learning, conceptualizing SSMs as meta-modules for specific online learning problems. This approach links SSM design to formulating precise online learning objectives, with state transition rules derived from optimizing these objectives. Based on this insight, we introduce a novel deep SSM architecture based on the implicit update for optimizing an online regression objective. Our experimental results show that our models outperform state-of-the-art SSMs, including the Mamba model, on standard sequence modeling benchmarks and language modeling tasks.

Efficient state space models (SSMs), such as linear recurrent neural networks and linear attention variants, offer computational advantages over Transformers but struggle with tasks requiring long-range in-context retrieval-like text copying, associative recall, and question answering over long contexts. Previous efforts to address these challenges have focused on architectural modifications, often reintroducing computational inefficiencies. In this paper, we propose a novel training procedure, Birdie, that significantly enhances the in-context retrieval capabilities of SSMs without altering their architecture. Our approach combines bidirectional input processing with dynamic mixtures of specialized pre-training objectives, optimized via reinforcement learning. We introduce a new bidirectional SSM architecture that seamlessly transitions from bidirectional context processing to causal generation. Experimental evaluations demonstrate that Birdie markedly improves performance on retrieval-intensive tasks such as multi-number phone book lookup, long paragraph question-answering, and infilling. This narrows the performance gap with Transformers, while retaining computational efficiency. Our findings highlight the importance of training procedures in leveraging the fixed-state capacity of SSMs, offering a new direction to advance their capabilities. All code and pre-trained models are available at https://www.github.com/samblouir/birdie, with support for JAX and PyTorch.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Selective state space models (SSMs) represented by Mamba have demonstrated their computational efficiency and promising outcomes in various tasks, including automatic speech recognition (ASR). Mamba has been applied to ASR task with the attention-based encoder-decoder framework, where the cross-attention mechanism between encoder and decoder remains. This paper explores the capability of Mamba as the decoder-only architecture in ASR task. Our MAmba-based DEcoder-ONly approach (MADEON) consists of a single decoder that takes speech tokens as a condition and predicts text tokens in an autoregressive manner. To enhance MADEON, we further propose speech prefixing that performs bidirectional processing on speech tokens, which enriches the contextual information in the hidden states. Our experiments show that MADEON significantly outperforms a non-selective SSM. The combination of speech prefixing and the recently proposed Mamba-2 yields comparable performance to Transformer-based models on large datasets.

State space models (SSMs) with selection mechanisms and hardware-aware architectures, namely Mamba, have recently demonstrated significant promise in long-sequence modeling. Since the self-attention mechanism in transformers has quadratic complexity with image size and increasing computational demands, the researchers are now exploring how to adapt Mamba for computer vision tasks. This paper is the first comprehensive survey aiming to provide an in-depth analysis of Mamba models in the field of computer vision. It begins by exploring the foundational concepts contributing to Mamba's success, including the state space model framework, selection mechanisms, and hardware-aware design. Next, we review these vision mamba models by categorizing them into foundational ones and enhancing them with techniques such as convolution, recurrence, and attention to improve their sophistication. We further delve into the widespread applications of Mamba in vision tasks, which include their use as a backbone in various levels of vision processing. This encompasses general visual tasks, Medical visual tasks (e.g., 2D / 3D segmentation, classification, and image registration, etc.), and Remote Sensing visual tasks. We specially introduce general visual tasks from two levels: High/Mid-level vision (e.g., Object detection, Segmentation, Video classification, etc.) and Low-level vision (e.g., Image super-resolution, Image restoration, Visual generation, etc.). We hope this endeavor will spark additional interest within the community to address current challenges and further apply Mamba models in computer vision.

We introduce a novel state-space architecture for diffusion models, effectively harnessing spatial and frequency information to enhance the inductive bias towards local features in input images for image generation tasks. While state-space networks, including Mamba, a revolutionary advancement in recurrent neural networks, typically scan input sequences from left to right, they face difficulties in designing effective scanning strategies, especially in the processing of image data. Our method demonstrates that integrating wavelet transformation into Mamba enhances the local structure awareness of visual inputs and better captures long-range relations of frequencies by disentangling them into wavelet subbands, representing both low- and high-frequency components. These wavelet-based outputs are then processed and seamlessly fused with the original Mamba outputs through a cross-attention fusion layer, combining both spatial and frequency information to optimize the order awareness of state-space models which is essential for the details and overall quality of image generation. Besides, we introduce a globally-shared transformer to supercharge the performance of Mamba, harnessing its exceptional power to capture global relationships. Through extensive experiments on standard benchmarks, our method demonstrates superior results compared to DiT and DIFFUSSM, achieving faster training convergence and delivering high-quality outputs. The codes and pretrained models are released at https://github.com/VinAIResearch/DiMSUM.git.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.

Recurrent neural networks (RNNs) have recently demonstrated strong performance and faster inference than Transformers at comparable parameter budgets. However, the recursive gradient computation with the backpropagation through time (or BPTT) algorithm remains the major computational bottleneck. In this work, we propose a novel method that replaces BPTT with a fixed gradient feedback mechanism, yielding an efficient approximation of the exact gradient propagation based on the assumption of time stationarity. Our approach leverages state-space model (SSM) principles to define a structured feedback matrix that directly propagates gradients from future time steps. This formulation bypasses the need for recursive gradient backpropagation, significantly reducing training overhead while preserving the network's ability to capture long-term dependencies. The experiments on language modeling benchmarks exhibit competitive perplexity scores, while significantly reducing the training costs. These promising results suggest that designing a feedback method like an SSM can fully exploit the efficiency advantages of RNNs for many practical applications.

The state space models, employing recursively propagated features, demonstrate strong representation capabilities comparable to Transformer models and superior efficiency. However, constrained by the inherent geometric constraints of sequences, it still falls short in modeling long-range dependencies. To address this issue, we propose the GrootVL network, which first dynamically generates a tree topology based on spatial relationships and input features. Then, feature propagation is performed based on this graph, thereby breaking the original sequence constraints to achieve stronger representation capabilities. Additionally, we introduce a linear complexity dynamic programming algorithm to enhance long-range interactions without increasing computational cost. GrootVL is a versatile multimodal framework that can be applied to both visual and textual tasks. Extensive experiments demonstrate that our method significantly outperforms existing structured state space models on image classification, object detection and segmentation. Besides, by fine-tuning large language models, our approach achieves consistent improvements in multiple textual tasks at minor training cost.

In the realm of medical image segmentation, both CNN-based and Transformer-based models have been extensively explored. However, CNNs exhibit limitations in long-range modeling capabilities, whereas Transformers are hampered by their quadratic computational complexity. Recently, State Space Models (SSMs), exemplified by Mamba, have emerged as a promising approach. They not only excel in modeling long-range interactions but also maintain a linear computational complexity. In this paper, leveraging state space models, we propose a U-shape architecture model for medical image segmentation, named Vision Mamba UNet (VM-UNet). Specifically, the Visual State Space (VSS) block is introduced as the foundation block to capture extensive contextual information, and an asymmetrical encoder-decoder structure is constructed with fewer convolution layers to save calculation cost. We conduct comprehensive experiments on the ISIC17, ISIC18, and Synapse datasets, and the results indicate that VM-UNet performs competitively in medical image segmentation tasks. To our best knowledge, this is the first medical image segmentation model constructed based on the pure SSM-based model. We aim to establish a baseline and provide valuable insights for the future development of more efficient and effective SSM-based segmentation systems. Our code is available at https://github.com/JCruan519/VM-UNet.

State Space Models (SSMs) have the advantage of keeping linear computational complexity compared to attention modules in transformers, and have been applied to vision tasks as a new type of powerful vision foundation model. Inspired by the observations that the final prediction in vision transformers (ViTs) is only based on a subset of most informative tokens, we take the novel step of enhancing the efficiency of SSM-based vision models through token-based pruning. However, direct applications of existing token pruning techniques designed for ViTs fail to deliver good performance, even with extensive fine-tuning. To address this issue, we revisit the unique computational characteristics of SSMs and discover that naive application disrupts the sequential token positions. This insight motivates us to design a novel and general token pruning method specifically for SSM-based vision models. We first introduce a pruning-aware hidden state alignment method to stabilize the neighborhood of remaining tokens for performance enhancement. Besides, based on our detailed analysis, we propose a token importance evaluation method adapted for SSM models, to guide the token pruning. With efficient implementation and practical acceleration methods, our method brings actual speedup. Extensive experiments demonstrate that our approach can achieve significant computation reduction with minimal impact on performance across different tasks. Notably, we achieve 81.7\% accuracy on ImageNet with a 41.6\% reduction in the FLOPs for pruned PlainMamba-L3. Furthermore, our work provides deeper insights into understanding the behavior of SSM-based vision models for future research.

Recent work has shown that state space models such as Mamba are significantly worse than Transformers on recall-based tasks due to the fact that their state size is constant with respect to their input sequence length. But in practice, state space models have fairly large state sizes, and we conjecture that they should be able to perform much better at these tasks than previously reported. We investigate whether their poor copying and recall performance could be due in part to training difficulties rather than fundamental capacity constraints. Based on observations of their "attention" maps, we propose a structured initialization technique that allows state space layers to more readily mimic attention. Across a variety of architecture settings, our initialization makes it substantially easier for Mamba to learn to copy and do associative recall from scratch.

We describe a novel approach for developing realistic digital models of dynamic range compressors for digital audio production by analyzing their analog prototypes. While realistic digital dynamic compressors are potentially useful for many applications, the design process is challenging because the compressors operate nonlinearly over long time scales. Our approach is based on the structured state space sequence model (S4), as implementing the state-space model (SSM) has proven to be efficient at learning long-range dependencies and is promising for modeling dynamic range compressors. We present in this paper a deep learning model with S4 layers to model the Teletronix LA-2A analog dynamic range compressor. The model is causal, executes efficiently in real time, and achieves roughly the same quality as previous deep-learning models but with fewer parameters.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one update, and has exponentially small retrieval errors. It has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. The new update rule is equivalent to the attention mechanism used in transformers. This equivalence enables a characterization of the heads of transformer models. These heads perform in the first layers preferably global averaging and in higher layers partial averaging via metastable states. The new modern Hopfield network can be integrated into deep learning architectures as layers to allow the storage of and access to raw input data, intermediate results, or learned prototypes. These Hopfield layers enable new ways of deep learning, beyond fully-connected, convolutional, or recurrent networks, and provide pooling, memory, association, and attention mechanisms. We demonstrate the broad applicability of the Hopfield layers across various domains. Hopfield layers improved state-of-the-art on three out of four considered multiple instance learning problems as well as on immune repertoire classification with several hundreds of thousands of instances. On the UCI benchmark collections of small classification tasks, where deep learning methods typically struggle, Hopfield layers yielded a new state-of-the-art when compared to different machine learning methods. Finally, Hopfield layers achieved state-of-the-art on two drug design datasets. The implementation is available at: https://github.com/ml-jku/hopfield-layers

We present a model inspired by the Global Workspace Theory that integrates specialized modules to perform a sequential reasoning task. A controller selectively routes information between modules through the workspace using a gating mechanism. This approach allows the model to chain operations by iteratively broadcasting information between specialized domains, mimicking System-2 reasoning. We evaluate the model's performance on a simple addition task, where two addends must be summed. The task can be solved by routing information sequentially through an Input module, an Increment module (multiple times), and finally an Output module. We consider two implementations of this system with increasing complexity. First, using hand-designed modules operating on one-hot digit representations, the controller (a LSTM recurrent network) learns to select the appropriate modules (input, increment, output) in the appropriate sequence. Second, we replace the hand-designed modules with learned representation modules for MNIST images and an increment module trained on the task objectives; here again, the controller learns the appropriate sequential module selection to solve the task. Finally, we show that the Global Workspace model, while having fewer parameters, outperforms LSTMs and Transformers when tested on unseen addition operations (both interpolations and extrapolations of addition operations seen during training). Our results highlight the potential of architectures inspired by the Global Workspace Theory to enhance deep learning's reasoning capabilities.

Representations are at the core of all deep reinforcement learning (RL) methods for both Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). Many representation learning methods and theoretical frameworks have been developed to understand what constitutes an effective representation. However, the relationships between these methods and the shared properties among them remain unclear. In this paper, we show that many of these seemingly distinct methods and frameworks for state and history abstractions are, in fact, based on a common idea of self-predictive abstraction. Furthermore, we provide theoretical insights into the widely adopted objectives and optimization, such as the stop-gradient technique, in learning self-predictive representations. These findings together yield a minimalist algorithm to learn self-predictive representations for states and histories. We validate our theories by applying our algorithm to standard MDPs, MDPs with distractors, and POMDPs with sparse rewards. These findings culminate in a set of preliminary guidelines for RL practitioners.

Selective state-space models (SSMs) like Mamba overcome some of the shortcomings of Transformers, such as quadratic computational complexity with sequence length and large inference-time memory requirements from the key-value cache. Moreover, recent studies have shown that SSMs can match or exceed the language modeling capabilities of Transformers, making them an attractive alternative. In a controlled setting (e.g., same data), however, studies so far have only presented small scale experiments comparing SSMs to Transformers. To understand the strengths and weaknesses of these architectures at larger scales, we present a direct comparison between 8B-parameter Mamba, Mamba-2, and Transformer models trained on the same datasets of up to 3.5T tokens. We also compare these models to a hybrid architecture consisting of 43% Mamba-2, 7% attention, and 50% MLP layers (Mamba-2-Hybrid). Using a diverse set of tasks, we answer the question of whether Mamba models can match Transformers at larger training budgets. Our results show that while pure SSMs match or exceed Transformers on many tasks, they lag behind Transformers on tasks which require strong copying or in-context learning abilities (e.g., 5-shot MMLU, Phonebook) or long-context reasoning. In contrast, we find that the 8B Mamba-2-Hybrid exceeds the 8B Transformer on all 12 standard tasks we evaluated (+2.65 points on average) and is predicted to be up to 8x faster when generating tokens at inference time. To validate long-context capabilities, we provide additional experiments evaluating variants of the Mamba-2-Hybrid and Transformer extended to support 16K, 32K, and 128K sequences. On an additional 23 long-context tasks, the hybrid model continues to closely match or exceed the Transformer on average. To enable further study, we release the checkpoints as well as the code used to train our models as part of NVIDIA's Megatron-LM project.

In generative models, two paradigms have gained attraction in various applications: next-set prediction-based Masked Generative Models and next-noise prediction-based Non-Autoregressive Models, e.g., Diffusion Models. In this work, we propose using discrete-state models to connect them and explore their scalability in the vision domain. First, we conduct a step-by-step analysis in a unified design space across two types of models including timestep-independence, noise schedule, temperature, guidance strength, etc in a scalable manner. Second, we re-cast typical discriminative tasks, e.g., image segmentation, as an unmasking process from [MASK]tokens on a discrete-state model. This enables us to perform various sampling processes, including flexible conditional sampling by only training once to model the joint distribution. All aforementioned explorations lead to our framework named Discrete Interpolants, which enables us to achieve state-of-the-art or competitive performance compared to previous discrete-state based methods in various benchmarks, like ImageNet256, MS COCO, and video dataset FaceForensics. In summary, by leveraging [MASK] in discrete-state models, we can bridge Masked Generative and Non-autoregressive Diffusion models, as well as generative and discriminative tasks.

Prior efforts in light-weight model development mainly centered on CNN and Transformer-based designs yet faced persistent challenges. CNNs adept at local feature extraction compromise resolution while Transformers offer global reach but escalate computational demands O(N^2). This ongoing trade-off between accuracy and efficiency remains a significant hurdle. Recently, state space models (SSMs), such as Mamba, have shown outstanding performance and competitiveness in various tasks such as language modeling and computer vision, while reducing the time complexity of global information extraction to O(N). Inspired by this, this work proposes to explore the potential of visual state space models in light-weight model design and introduce a novel efficient model variant dubbed EfficientVMamba. Concretely, our EfficientVMamba integrates a atrous-based selective scan approach by efficient skip sampling, constituting building blocks designed to harness both global and local representational features. Additionally, we investigate the integration between SSM blocks and convolutions, and introduce an efficient visual state space block combined with an additional convolution branch, which further elevate the model performance. Experimental results show that, EfficientVMamba scales down the computational complexity while yields competitive results across a variety of vision tasks. For example, our EfficientVMamba-S with 1.3G FLOPs improves Vim-Ti with 1.5G FLOPs by a large margin of 5.6% accuracy on ImageNet. Code is available at: https://github.com/TerryPei/EfficientVMamba.

Model-based reinforcement learning (RL) algorithms designed for handling complex visual observations typically learn some sort of latent state representation, either explicitly or implicitly. Standard methods of this sort do not distinguish between functionally relevant aspects of the state and irrelevant distractors, instead aiming to represent all available information equally. We propose a modified objective for model-based RL that, in combination with mutual information maximization, allows us to learn representations and dynamics for visual model-based RL without reconstruction in a way that explicitly prioritizes functionally relevant factors. The key principle behind our design is to integrate a term inspired by variational empowerment into a state-space model based on mutual information. This term prioritizes information that is correlated with action, thus ensuring that functionally relevant factors are captured first. Furthermore, the same empowerment term also promotes faster exploration during the RL process, especially for sparse-reward tasks where the reward signal is insufficient to drive exploration in the early stages of learning. We evaluate the approach on a suite of vision-based robot control tasks with natural video backgrounds, and show that the proposed prioritized information objective outperforms state-of-the-art model based RL approaches with higher sample efficiency and episodic returns. https://sites.google.com/view/information-empowerment

Many control tasks exhibit similar dynamics that can be modeled as having common latent structure. Hidden-Parameter Markov Decision Processes (HiP-MDPs) explicitly model this structure to improve sample efficiency in multi-task settings. However, this setting makes strong assumptions on the observability of the state that limit its application in real-world scenarios with rich observation spaces. In this work, we leverage ideas of common structure from the HiP-MDP setting, and extend it to enable robust state abstractions inspired by Block MDPs. We derive instantiations of this new framework for both multi-task reinforcement learning (MTRL) and meta-reinforcement learning (Meta-RL) settings. Further, we provide transfer and generalization bounds based on task and state similarity, along with sample complexity bounds that depend on the aggregate number of samples across tasks, rather than the number of tasks, a significant improvement over prior work that use the same environment assumptions. To further demonstrate the efficacy of the proposed method, we empirically compare and show improvement over multi-task and meta-reinforcement learning baselines.

Deep neural networks (DNNs) have remarkably succeeded in various image processing tasks. However, their large size and computational complexity present significant challenges for deploying them in resource-constrained environments. This paper presents an innovative approach for integrating Mamba Architecture within a Progressive Knowledge Distillation (PKD) process to address the challenge of reducing model complexity while maintaining accuracy in image classification tasks. The proposed framework distills a large teacher model into progressively smaller student models, designed using Mamba blocks. Each student model is trained using Selective-State-Space Models (S-SSM) within the Mamba blocks, focusing on important input aspects while reducing computational complexity. The work's preliminary experiments use MNIST and CIFAR-10 as datasets to demonstrate the effectiveness of this approach. For MNIST, the teacher model achieves 98% accuracy. A set of seven student models as a group retained 63% of the teacher's FLOPs, approximating the teacher's performance with 98% accuracy. The weak student used only 1% of the teacher's FLOPs and maintained 72% accuracy. Similarly, for CIFAR-10, the students achieved 1% less accuracy compared to the teacher, with the small student retaining 5% of the teacher's FLOPs to achieve 50% accuracy. These results confirm the flexibility and scalability of Mamba Architecture, which can be integrated into PKD, succeeding in the process of finding students as weak learners. The framework provides a solution for deploying complex neural networks in real-time applications with a reduction in computational cost.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

Transformers and their variants have achieved great success in speech processing. However, their multi-head self-attention mechanism is computationally expensive. Therefore, one novel selective state space model, Mamba, has been proposed as an alternative. Building on its success in automatic speech recognition, we apply Mamba for spoofing attack detection. Mamba is well-suited for this task as it can capture the artifacts in spoofed speech signals by handling long-length sequences. However, Mamba's performance may suffer when it is trained with limited labeled data. To mitigate this, we propose combining a new structure of Mamba based on a dual-column architecture with self-supervised learning, using the pre-trained wav2vec 2.0 model. The experiments show that our proposed approach achieves competitive results and faster inference on the ASVspoof 2021 LA and DF datasets, and on the more challenging In-the-Wild dataset, it emerges as the strongest candidate for spoofing attack detection. The code has been publicly released in https://github.com/swagshaw/XLSR-Mamba.

Recurrent Neural Networks (RNNs) offer fast inference on long sequences but are hard to optimize and slow to train. Deep state-space models (SSMs) have recently been shown to perform remarkably well on long sequence modeling tasks, and have the added benefits of fast parallelizable training and RNN-like fast inference. However, while SSMs are superficially similar to RNNs, there are important differences that make it unclear where their performance boost over RNNs comes from. In this paper, we show that careful design of deep RNNs using standard signal propagation arguments can recover the impressive performance of deep SSMs on long-range reasoning tasks, while also matching their training speed. To achieve this, we analyze and ablate a series of changes to standard RNNs including linearizing and diagonalizing the recurrence, using better parameterizations and initializations, and ensuring proper normalization of the forward pass. Our results provide new insights on the origins of the impressive performance of deep SSMs, while also introducing an RNN block called the Linear Recurrent Unit that matches both their performance on the Long Range Arena benchmark and their computational efficiency.

State-space models are a low-complexity alternative to transformers for encoding long sequences and capturing long-term dependencies. We propose LOCOST: an encoder-decoder architecture based on state-space models for conditional text generation with long context inputs. With a computational complexity of O(L log L), this architecture can handle significantly longer sequences than state-of-the-art models that are based on sparse attention patterns. We evaluate our model on a series of long document abstractive summarization tasks. The model reaches a performance level that is 93-96% comparable to the top-performing sparse transformers of the same size while saving up to 50% memory during training and up to 87% during inference. Additionally, LOCOST effectively handles input texts exceeding 600K tokens at inference time, setting new state-of-the-art results on full-book summarization and opening new perspectives for long input processing.

As foundational models reshape scientific discovery, a bottleneck persists in dynamical system reconstruction (DSR): the ability to learn across system hierarchies. Many meta-learning approaches have been applied successfully to single systems, but falter when confronted with sparse, loosely related datasets requiring multiple hierarchies to be learned. Mixture of Experts (MoE) offers a natural paradigm to address these challenges. Despite their potential, we demonstrate that naive MoEs are inadequate for the nuanced demands of hierarchical DSR, largely due to their gradient descent-based gating update mechanism which leads to slow updates and conflicted routing during training. To overcome this limitation, we introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on K-means and least squares. Extensive experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten parametric ordinary differential equations. However, our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points. Further analysis with synthetic and neuroscientific time series suggests that the quality of the contextual representations generated by MixER is closely linked to the presence of hierarchical structure in the data.

Recent work proposed state-space models (SSMs) as an efficient alternative to transformer-based LLMs. Can these models be pruned to further reduce their computation costs? We adapt several pruning methods to the SSM structure, and apply them to four SSM-based LLMs across multiple tasks. We find that such models are quite robust to some pruning methods (e.g. WANDA), while using other methods lead to fast performance degradation.

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function piproptoe^{-U} is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose Masked Diffusion Neural Sampler (MDNS), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this challenge, alternative architectures such as linear attention, State Space Models (SSMs), and Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives. While connections between these approaches exist, such models are commonly developed in isolation and there is a lack of theoretical understanding of the shared principles underpinning these architectures and their subtle differences, greatly influencing performance and scalability. In this paper, we introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation. Our framework facilitates rigorous comparisons, providing new insights on the distinctive characteristics of each model class. For instance, we compare linear attention and selective SSMs, detailing their differences and conditions under which both are equivalent. We also provide principled comparisons between softmax attention and other model classes, discussing the theoretical conditions under which softmax attention can be approximated. Additionally, we substantiate these new insights with empirical validations and mathematical arguments. This shows the DSF's potential to guide the systematic development of future more efficient and scalable foundation models.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Representation learning and exploration are among the key challenges for any deep reinforcement learning agent. In this work, we provide a singular value decomposition based method that can be used to obtain representations that preserve the underlying transition structure in the domain. Perhaps interestingly, we show that these representations also capture the relative frequency of state visitations, thereby providing an estimate for pseudo-counts for free. To scale this decomposition method to large-scale domains, we provide an algorithm that never requires building the transition matrix, can make use of deep networks, and also permits mini-batch training. Further, we draw inspiration from predictive state representations and extend our decomposition method to partially observable environments. With experiments on multi-task settings with partially observable domains, we show that the proposed method can not only learn useful representation on DM-Lab-30 environments (that have inputs involving language instructions, pixel images, and rewards, among others) but it can also be effective at hard exploration tasks in DM-Hard-8 environments.

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to predict sequences of desirable physical quantities (e.g. force, inertial measurements). While classical approaches are powerful for locally-linear prediction problems, they often fall short when using real-world sensors. These sensors are typically non-linear, are affected by extraneous variables (e.g. vibration), and exhibit data-dependent drift. For many problems, the prediction task is exacerbated by small labeled datasets since obtaining ground-truth labels requires expensive equipment. In this work, we present Hierarchical State-Space Models (HiSS), a conceptually simple, new technique for continuous sequential prediction. HiSS stacks structured state-space models on top of each other to create a temporal hierarchy. Across six real-world sensor datasets, from tactile-based state prediction to accelerometer-based inertial measurement, HiSS outperforms state-of-the-art sequence models such as causal Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments further indicate that HiSS demonstrates efficient scaling to smaller datasets and is compatible with existing data-filtering techniques. Code, datasets and videos can be found on https://hiss-csp.github.io.

Large pre-trained models have achieved outstanding results in sequence modeling. The Transformer block and its attention mechanism have been the main drivers of the success of these models. Recently, alternative architectures, such as Selective Structured State Space Models (SSMs), have been proposed to address the inefficiencies of Transformers. This paper explores the compression of SSM-based models, particularly Mamba and its hybrids. We study the sensitivity of these models to the removal of selected components at different granularities to reduce the model size and computational overhead, thus improving their efficiency while maintaining accuracy. The proposed solutions, collectively referred to as Mamba-Shedder, achieve a speedup of up to 1.4x during inference, demonstrating that model efficiency can be improved by eliminating several redundancies with minimal impact on the overall model performance. The code is available at https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning.

Attention mechanisms have been widely used to capture long-range dependencies among nodes in Graph Transformers. Bottlenecked by the quadratic computational cost, attention mechanisms fail to scale in large graphs. Recent improvements in computational efficiency are mainly achieved by attention sparsification with random or heuristic-based graph subsampling, which falls short in data-dependent context reasoning. State space models (SSMs), such as Mamba, have gained prominence for their effectiveness and efficiency in modeling long-range dependencies in sequential data. However, adapting SSMs to non-sequential graph data presents a notable challenge. In this work, we introduce Graph-Mamba, the first attempt to enhance long-range context modeling in graph networks by integrating a Mamba block with the input-dependent node selection mechanism. Specifically, we formulate graph-centric node prioritization and permutation strategies to enhance context-aware reasoning, leading to a substantial improvement in predictive performance. Extensive experiments on ten benchmark datasets demonstrate that Graph-Mamba outperforms state-of-the-art methods in long-range graph prediction tasks, with a fraction of the computational cost in both FLOPs and GPU memory consumption. The code and models are publicly available at https://github.com/bowang-lab/Graph-Mamba.

State space models (SSMs) have high performance on long sequence modeling but require sophisticated initialization techniques and specialized implementations for high quality and runtime performance. We study whether a simple alternative can match SSMs in performance and efficiency: directly learning long convolutions over the sequence. We find that a key requirement to achieving high performance is keeping the convolution kernels smooth. We find that simple interventions--such as squashing the kernel weights--result in smooth kernels and recover SSM performance on a range of tasks including the long range arena, image classification, language modeling, and brain data modeling. Next, we develop FlashButterfly, an IO-aware algorithm to improve the runtime performance of long convolutions. FlashButterfly appeals to classic Butterfly decompositions of the convolution to reduce GPU memory IO and increase FLOP utilization. FlashButterfly speeds up convolutions by 2.2times, and allows us to train on Path256, a challenging task with sequence length 64K, where we set state-of-the-art by 29.1 points while training 7.2times faster than prior work. Lastly, we introduce an extension to FlashButterfly that learns the coefficients of the Butterfly decomposition, increasing expressivity without increasing runtime. Using this extension, we outperform a Transformer on WikiText103 by 0.2 PPL with 30% fewer parameters.

Stateful policies play an important role in reinforcement learning, such as handling partially observable environments, enhancing robustness, or imposing an inductive bias directly into the policy structure. The conventional method for training stateful policies is Backpropagation Through Time (BPTT), which comes with significant drawbacks, such as slow training due to sequential gradient propagation and the occurrence of vanishing or exploding gradients. The gradient is often truncated to address these issues, resulting in a biased policy update. We present a novel approach for training stateful policies by decomposing the latter into a stochastic internal state kernel and a stateless policy, jointly optimized by following the stateful policy gradient. We introduce different versions of the stateful policy gradient theorem, enabling us to easily instantiate stateful variants of popular reinforcement learning and imitation learning algorithms. Furthermore, we provide a theoretical analysis of our new gradient estimator and compare it with BPTT. We evaluate our approach on complex continuous control tasks, e.g., humanoid locomotion, and demonstrate that our gradient estimator scales effectively with task complexity while offering a faster and simpler alternative to BPTT.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Establishing semantic correspondences between images is a fundamental yet challenging task in computer vision. Traditional feature-metric methods enhance visual features but may miss complex inter-correlation relationships, while recent correlation-metric approaches are hindered by high computational costs due to processing 4D correlation maps. We introduce MambaMatcher, a novel method that overcomes these limitations by efficiently modeling high-dimensional correlations using selective state-space models (SSMs). By implementing a similarity-aware selective scan mechanism adapted from Mamba's linear-complexity algorithm, MambaMatcher refines the 4D correlation map effectively without compromising feature map resolution or receptive field. Experiments on standard semantic correspondence benchmarks demonstrate that MambaMatcher achieves state-of-the-art performance.

Despite the significant achievements of Vision Transformers (ViTs) in various vision tasks, they are constrained by the quadratic complexity. Recently, State Space Models (SSMs) have garnered widespread attention due to their global receptive field and linear complexity with respect to the input length, demonstrating substantial potential across fields including natural language processing and computer vision. To improve the performance of SSMs in vision tasks, a multi-scan strategy is widely adopted, which leads to significant redundancy of SSMs. For a better trade-off between efficiency and performance, we analyze the underlying reasons behind the success of the multi-scan strategy, where long-range dependency plays an important role. Based on the analysis, we introduce Multi-Scale Vision Mamba (MSVMamba) to preserve the superiority of SSMs in vision tasks with limited parameters. It employs a multi-scale 2D scanning technique on both original and downsampled feature maps, which not only benefits long-range dependency learning but also reduces computational costs. Additionally, we integrate a Convolutional Feed-Forward Network (ConvFFN) to address the lack of channel mixing. Our experiments demonstrate that MSVMamba is highly competitive, with the MSVMamba-Tiny model achieving 82.8% top-1 accuracy on ImageNet, 46.9% box mAP, and 42.2% instance mAP with the Mask R-CNN framework, 1x training schedule on COCO, and 47.6% mIoU with single-scale testing on ADE20K.Code is available at https://github.com/YuHengsss/MSVMamba.

Reinforcement learning (RL) has made a lot of advances for solving a single problem in a given environment; but learning policies that generalize to unseen variations of a problem remains challenging. To improve sample efficiency for learning on such instances of a problem domain, we present Self-Paced Context Evaluation (SPaCE). Based on self-paced learning, \spc automatically generates \task curricula online with little computational overhead. To this end, SPaCE leverages information contained in state values during training to accelerate and improve training performance as well as generalization capabilities to new instances from the same problem domain. Nevertheless, SPaCE is independent of the problem domain at hand and can be applied on top of any RL agent with state-value function approximation. We demonstrate SPaCE's ability to speed up learning of different value-based RL agents on two environments, showing better generalization capabilities and up to 10x faster learning compared to naive approaches such as round robin or SPDRL, as the closest state-of-the-art approach.

This work introduces Structured Linear Controlled Differential Equations (SLiCEs), a unifying framework for sequence models with structured, input-dependent state-transition matrices that retain the maximal expressivity of dense matrices whilst being cheaper to compute. The framework encompasses existing architectures, such as input-dependent block-diagonal linear recurrent neural networks and DeltaNet's diagonal-plus-low-rank structure, as well as two novel variants based on sparsity and the Walsh-Hadamard transform. We prove that, unlike the diagonal state-transition matrices of S4D and Mamba, SLiCEs employing block-diagonal, sparse, or Walsh-Hadamard matrices match the maximal expressivity of dense matrices. Empirically, SLiCEs solve the A_5 state-tracking benchmark with a single layer, achieve best-in-class length generalisation on regular language tasks among parallel-in-time models, and match the performance of log neural controlled differential equations on six multivariate time-series classification datasets while cutting the average time per training step by a factor of twenty.

Effectively modeling long spatiotemporal sequences is challenging due to the need to model complex spatial correlations and long-range temporal dependencies simultaneously. ConvLSTMs attempt to address this by updating tensor-valued states with recurrent neural networks, but their sequential computation makes them slow to train. In contrast, Transformers can process an entire spatiotemporal sequence, compressed into tokens, in parallel. However, the cost of attention scales quadratically in length, limiting their scalability to longer sequences. Here, we address the challenges of prior methods and introduce convolutional state space models (ConvSSM) that combine the tensor modeling ideas of ConvLSTM with the long sequence modeling approaches of state space methods such as S4 and S5. First, we demonstrate how parallel scans can be applied to convolutional recurrences to achieve subquadratic parallelization and fast autoregressive generation. We then establish an equivalence between the dynamics of ConvSSMs and SSMs, which motivates parameterization and initialization strategies for modeling long-range dependencies. The result is ConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling. ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizon Moving-MNIST experiment while training 3X faster than ConvLSTM and generating samples 400X faster than Transformers. In addition, ConvS5 matches or exceeds the performance of state-of-the-art methods on challenging DMLab, Minecraft and Habitat prediction benchmarks and enables new directions for modeling long spatiotemporal sequences.

State representation learning, or the ability to capture latent generative factors of an environment, is crucial for building intelligent agents that can perform a wide variety of tasks. Learning such representations without supervision from rewards is a challenging open problem. We introduce a method that learns state representations by maximizing mutual information across spatially and temporally distinct features of a neural encoder of the observations. We also introduce a new benchmark based on Atari 2600 games where we evaluate representations based on how well they capture the ground truth state variables. We believe this new framework for evaluating representation learning models will be crucial for future representation learning research. Finally, we compare our technique with other state-of-the-art generative and contrastive representation learning methods. The code associated with this work is available at https://github.com/mila-iqia/atari-representation-learning

State-space models (SSMs), such as Mamba Gu & Dao (2034), have been proposed as alternatives to Transformer networks in language modeling, by incorporating gating, convolutions, and input-dependent token selection to mitigate the quadratic cost of multi-head attention. Although SSMs exhibit competitive performance, their in-context learning (ICL) capabilities, a remarkable emergent property of modern language models that enables task execution without parameter optimization, remain underexplored compared to Transformers. In this study, we evaluate the ICL performance of SSMs, focusing on Mamba, against Transformer models across various tasks. Our results show that SSMs perform comparably to Transformers in standard regression ICL tasks, while outperforming them in tasks like sparse parity learning. However, SSMs fall short in tasks involving non-standard retrieval functionality. To address these limitations, we introduce a hybrid model, \variant, that combines Mamba with attention blocks, surpassing individual models in tasks where they struggle independently. Our findings suggest that hybrid architectures offer promising avenues for enhancing ICL in language models.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.