State Space Models

Also known as SSM

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State space models describe how hidden states evolve over time and generate observations, supporting both probabilistic system identification and neural sequence learning. Approaches range from Kalman filtering, smoothing, and particle or variational inference to structured S4/HiPPO models, selective Mamba scans, and hybrids that combine recurrence with attention. They are applied to long-context language and video, time-series forecasting, and signals such as EEG, with evaluation spanning retrieval and sequence benchmarks as well as real-world prediction tasks. Their recurrent structure can offer linear-time processing and bounded memory, but efficient computation does not guarantee reliable long-range retrieval or state tracking, and practical speed, robustness, and accuracy remain important trade-offs.

Latest papers

299 papers30 papers in the last four weeks, down 12% on the four weeks before. 0.2% of all new papers.

Feb 26, 2026

Interpreting and Steering State-Space Models via Activation Subspace Bottlenecks

State-space models (SSMs) have emerged as an efficient strategy for building powerful language models, avoiding the quadratic complexity of computing attention in transformers. Despite their promise, the interpretability and steerability of modern SSMs remain relatively underexplored. We take a major step in this direction by identifying activation subspace bottlenecks in the Mamba family of SSM models using tools from mechanistic interpretability. We then introduce a test-time steering intervention that simply multiplies the activations of the identified bottlenecks by a scalar. Across 7 SSMs and 6 diverse benchmarks, this intervention improves performance by an average of 8.27%, without requiring any task-specific tuning. Finally, we validate that the identified bottlenecks are indeed hindering performance by modifying them to yield an architecture we call Stable-Mamba, which achieves long-context performance gains when retrained from scratch.

Vamshi Sunku Mohan, Kaustubh Gupta, Aneesha Das +1

AppViewX, Bangalore · Independent Researcher · Microsoft Research, Redmond

State Space Language Models State Space Models Language Model Steering LLM Interpretability Selective SSMs Activation Steering

Feb 26, 2026

HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning

This paper proposes HyperKKL, a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for non-autonomous nonlinear systems. While KKL observers offer a rigorous theoretical framework by immersing nonlinear dynamics into a stable linear latent space, its practical realization relies on solving Partial Differential Equations (PDE) that are analytically intractable. Current existing learning-based approximations of the KKL observer are mostly designed for autonomous systems, failing to generalize to driven dynamics without expensive retraining or online gradient updates. HyperKKL addresses this by employing a hypernetwork architecture that encodes the exogenous input signal to instantaneously generate the parameters of the KKL observer, effectively learning a family of immersion maps parameterized by the external drive. We rigorously evaluate this approach against a curriculum learning strategy that attempts to generalize from autonomous regimes via training heuristics alone. The novel approach is illustrated on four numerical simulations in benchmark examples including the Duffing, Van der Pol, Lorenz, and Rössler systems.

Yahia Salaheldin Shaaban, Salem Lahlou, Abdelrahman Sayed Sayed

MBZUAI, Abu Dhabi, UAE · Univ Gustave Eiffel, COSYS-ESTAS, F-59657 Villeneuve d’Ascq, France

State Space Models

Feb 25, 2026

WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems that encode the past history of the input signal. However, existing projection-based SSMs often rely on polynomial bases with global temporal support, whose inductive biases are poorly matched to signals exhibiting localized or transient structure. In this work, we introduce WaveSSM, a collection of SSMs constructed over wavelet frames. Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization. Empirically, we show that on equal conditions, WaveSSM outperforms orthogonal counterparts as S4 on real-world datasets with transient dynamics, including physiological signals on the PTB-XL dataset and raw audio on Speech Commands.

Ruben Solozabal, Velibor Bojkovic, Hilal Alquabeh +3

MBZUAI · RIKEN AIP

State Space Models Multiscale Time-Series Modeling Non-Stationary Time Series Wavelet Methods

Feb 24, 2026

Benchmarking State Space Models, Transformers, and Recurrent Networks for US Grid Forecasting

Selecting the right deep learning model for power grid forecasting is challenging, as performance heavily depends on the data available to the operator. This paper presents a comprehensive benchmark of five modern neural architectures: two state space models (PowerMamba, S-Mamba), two Transformers (iTransformer, PatchTST), and a traditional LSTM. We evaluate these models on hourly electricity demand across six diverse US power grids for forecast windows between 24 and 168 hours. To ensure a fair comparison, we adapt each model with specialized temporal processing and a modular layer that cleanly integrates weather covariates. Our results reveal that there is no single best model for all situations. When forecasting using only historical load, PatchTST and the state space models provide the highest accuracy. However, when explicit weather data is added to the inputs, the rankings reverse: iTransformer improves its accuracy three times more efficiently than PatchTST. By controlling for model size, we confirm that this advantage stems from the architecture's inherent ability to mix information across different variables. Extending our evaluation to solar generation, wind power, and wholesale prices further demonstrates that model rankings depend on the forecast task: PatchTST excels on highly rhythmic signals like solar, while state space models are better suited for the chaotic fluctuations of wind and price. Ultimately, this benchmark provides grid operators with actionable guidelines for selecting the optimal forecasting architecture based on their specific data environments.

Sunki Hong, Jisoo Lee

Gramm AI

Forecasting Benchmarks Electricity Load Forecasting Multivariate Time Series Forecasting State Space Models Time Series Transformers Recurrent Neural Networks

Feb 24, 2026

HiPPO Zoo: Explicit Memory Mechanisms for Interpretable State Space Models

Representing the past in a compressed, efficient, and informative manner is a central problem for systems trained on sequential data. The HiPPO framework, originally proposed by Gu & Dao et al., provides a principled approach to sequential compression by projecting signals onto orthogonal polynomial (OP) bases via structured linear ordinary differential equations. Subsequent works have embedded these dynamics in state space models (SSMs), where HiPPO structure serves as an initialization. Nonlinear successors of these SSM methods such as Mamba are state-of-the-art for many tasks with long-range dependencies, but the mechanisms by which they represent and prioritize history remain largely implicit. In this work, we revisit the HiPPO framework with the goal of making these mechanisms explicit. We show how polynomial representations of history can be extended to support capabilities of modern SSMs such as adaptive memory allocation and associative memory, while retaining direct interpretability in the OP basis. We introduce a unified framework comprising five such extensions, which we collectively refer to as a "HiPPO zoo." Each extension exposes a specific modeling capability through an explicit, interpretable modification of the HiPPO framework. The resulting models adapt their memory online and train in streaming settings with efficient updates. We illustrate the behaviors and modeling advantages of these extensions through a range of synthetic sequence modeling tasks, demonstrating that capabilities typically associated with modern SSMs can be realized through explicit, interpretable polynomial memory structures.

Jack Goffinet, Casey Hanks, David E. Carlson

Department of Computer Science, Duke University, Durham NC, USA · Departments of Civil and Environmental Engineering; Biostatistics and Bioinformatics; and Electrical and Computer Engineering, Duke University, Durham NC, USA

Sequence Modeling State Space Models

Feb 23, 2026

CrossLLM-Mamba: Multimodal State Space Fusion of LLMs for RNA Interaction Prediction

Accurate prediction of RNA-associated interactions is essential for understanding cellular regulation and advancing drug discovery. While Biological Large Language Models (BioLLMs) such as ESM-2 and RiNALMo provide powerful sequence representations, existing methods rely on static fusion strategies that fail to capture the dynamic, context-dependent nature of molecular binding. We introduce CrossLLM-Mamba, a novel framework that reformulates interaction prediction as a state-space alignment problem. By leveraging bidirectional Mamba encoders, our approach enables deep ``crosstalk'' between modality-specific embeddings through hidden state propagation, modeling interactions as dynamic sequence transitions rather than static feature overlaps. The framework maintains linear computational complexity, making it scalable to high-dimensional BioLLM embeddings. We further incorporate Gaussian noise injection and Focal Loss to enhance robustness against hard-negative samples. Comprehensive experiments across three interaction categories, RNA-protein, RNA-small molecule, and RNA-RNA demonstrate that CrossLLM-Mamba achieves state-of-the-art performance. On the RPI1460 benchmark, our model attains an MCC of 0.892, surpassing the previous best by 5.2%. For binding affinity prediction, we achieve Pearson correlations exceeding 0.95 on riboswitch and repeat RNA subtypes. These results establish state-space modeling as a powerful paradigm for multi-modal biological interaction prediction.

Rabeya Tus Sadia, Qiang Ye, Qiang Cheng

Department of Computer Science, University of Kentucky, Lexington, KY, USA · Department of Mathematics, University of Kentucky, Lexington, KY, USA · Institute for Biomedical Informatics, University of Kentucky, Lexington, KY, USA

Cross-Modal Representation Learning State Space Models

Feb 23, 2026

M3S-Net: Multimodal Feature Fusion Network Based on Multi-scale Data for Ultra-short-term PV Power Forecasting

The inherent intermittency and high-frequency variability of solar irradiance, particularly during rapid cloud advection, present significant stability challenges to high-penetration photovoltaic grids. Although multimodal forecasting has emerged as a viable mitigation strategy, existing architectures predominantly rely on shallow feature concatenation and binary cloud segmentation, thereby failing to capture the fine-grained optical features of clouds and the complex spatiotemporal coupling between visual and meteorological modalities. To bridge this gap, this paper proposes M3S-Net, a novel multimodal feature fusion network based on multi-scale data for ultra-short-term PV power forecasting. First, a multi-scale partial channel selection network leverages partial convolutions to explicitly isolate the boundary features of optically thin clouds, effectively transcending the precision limitations of coarse-grained binary masking. Second, a multi-scale sequence to image analysis network employs Fast Fourier Transform (FFT)-based time-frequency representation to disentangle the complex periodicity of meteorological data across varying time horizons. Crucially, the model incorporates a cross-modal Mamba interaction module featuring a novel dynamic C-matrix swapping mechanism. By exchanging state-space parameters between visual and temporal streams, this design conditions the state evolution of one modality on the context of the other, enabling deep structural coupling with linear computational complexity, thus overcoming the limitations of shallow concatenation. Experimental validation on the newly constructed fine-grained PV power dataset demonstrates that M3S-Net achieves a mean absolute error reduction of 6.2% in 10-minute forecasts compared to state-of-the-art baselines. The dataset and source code will be available at https://github.com/she1110/FGPD.

Penghui Niu, Taotao Cai, Suqi Zhang +4

School of Artificial Intelligence, Hebei University of Technology, Tianjin 300401, China · University of Southern Queensland, Toowoomba 487-535, Australia · School of Information Engineering, Tianjin University of Commerce, Tianjin 300134, China +3

Solar Power Forecasting Multimodal Fusion Multi-Scale Feature Fusion Multiscale Time-Series Modeling State Space Models

Feb 23, 2026

Fore-Mamba3D: Mamba-based Foreground-Enhanced Encoding for 3D Object Detection

Linear modeling methods like Mamba have been merged as the effective backbone for the 3D object detection task. However, previous Mamba-based methods utilize the bidirectional encoding for the whole non-empty voxel sequence, which contains abundant useless background information in the scenes. Though directly encoding foreground voxels appears to be a plausible solution, it tends to degrade detection performance. We attribute this to the response attenuation and restricted context representation in the linear modeling for fore-only sequences. To address this problem, we propose a novel backbone, termed Fore-Mamba3D, to focus on the foreground enhancement by modifying Mamba-based encoder. The foreground voxels are first sampled according to the predicted scores. Considering the response attenuation existing in the interaction of foreground voxels across different instances, we design a regional-to-global slide window (RGSW) to propagate the information from regional split to the entire sequence. Furthermore, a semantic-assisted and state spatial fusion module (SASFMamba) is proposed to enrich contextual representation by enhancing semantic and geometric awareness within the Mamba model. Our method emphasizes foreground-only encoding and alleviates the distance-based and causal dependencies in the linear autoregression model. The superior performance across various benchmarks demonstrates the effectiveness of Fore-Mamba3D in the 3D object detection task.

Zhiwei Ning, Xuanang Gao, Jiaxi Cao +5

School of Automation and Intelligent Sensing, Shanghai Jiao Tong University · Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University · School of Computer Science and Technology, Zhejiang Normal University +2

3D Object Detection Mamba State Space Models

Feb 23, 2026

DECAF: Dynamic Envelope Context-Aware Fusion for Speech-Envelope Reconstruction from EEG

Reconstructing the speech audio envelope from scalp neural recordings (EEG) is a central task for decoding a listener's attentional focus in applications like neuro-steered hearing aids. Current methods for this reconstruction, however, face challenges with fidelity and noise. Prevailing approaches treat it as a static regression problem, processing each EEG window in isolation and ignoring the rich temporal structure inherent in continuous speech. This study introduces a new, dynamic framework for envelope reconstruction that leverages this structure as a predictive temporal prior. We propose a state-space fusion model that combines direct neural estimates from EEG with predictions from recent speech context, using a learned gating mechanism to adaptively balance these cues. To validate this approach, we evaluate our model on the ICASSP 2023 Stimulus Reconstruction benchmark demonstrating significant improvements over static, EEG-only baselines. Our analyses reveal a powerful synergy between the neural and temporal information streams. Ultimately, this work reframes envelope reconstruction not as a simple mapping, but as a dynamic state-estimation problem, opening a new direction for developing more accurate and coherent neural decoding systems.

Karan Thakkar, Mounya Elhilali

Laboratory for Computational Audio Perception, Johns Hopkins University, USA

EEG Decoding Speech Processing State Space Models

Feb 19, 2026

COMBA: Cross Batch Aggregation for Learning Large Graphs with Context Gating State Space Models

State space models (SSMs) have recently emerged for modeling long-range dependency in sequence data, with much simplified computational costs than modern alternatives, such as transformers. Advancing SMMs to graph structured data, especially for large graphs, is a significant challenge because SSMs are sequence models and the shear graph volumes make it very expensive to convert graphs as sequences for effective learning. In this paper, we propose COMBA to tackle large graph learning using state space models, with two key innovations: graph context gating and cross batch aggregation. Graph context refers to different hops of neighborhood for each node, and graph context gating allows COMBA to use such context to learn best control of neighbor aggregation. For each graph context, COMBA samples nodes as batches, and train a graph neural network (GNN), with information being aggregated cross batches, allowing COMBA to scale to large graphs. Our theoretical study asserts that cross-batch aggregation guarantees lower error than training GNN without aggregation. Experiments on benchmark networks demonstrate significant performance gains compared to baseline approaches. Code and benchmark datasets will be released for public access.

Jiajun Shen, Yufei Jin, Yi He +1

Florida Atlantic University · William & Mary

Graph Representation Learning Graph Neural Networks State Space Models

Feb 19, 2026

2Mamba2Furious: Linear in Complexity, Competitive in Accuracy

Linear attention transformers have become a strong alternative to softmax attention due to their efficiency. However, linear attention tends to be less expressive and results in reduced accuracy compared to softmax attention. To bridge the accuracy gap between softmax attention and linear attention, we manipulate Mamba-2, a very strong linear attention variant. We first simplify Mamba-2 down to its most fundamental and important components, evaluating which specific choices make it most accurate. From this simplified Mamba variant (Mamba-2S), we improve the A-mask and increase the order of the hidden state, resulting in a method, which we call 2Mamba, that is nearly as accurate as softmax attention, yet much more memory efficient for long context lengths. We also investigate elements to Mamba-2 that help surpass softmax attention accuracy. Code is provided for all our experiments.

Gabriel Mongaras, Eric C. Larson

Lyle School of Engineering Southern Methodist University Dallas, TX 75205

Linear Attention Memory-Efficient Attention State Space Models

Feb 5, 2026

HealthMamba: An Uncertainty-aware Spatiotemporal Graph State Space Model for Effective and Reliable Healthcare Facility Visit Prediction

Healthcare facility visit prediction is essential for optimizing healthcare resource allocation and informing public health policy. Despite advanced machine learning methods being employed for better prediction performance, existing works usually formulate this task as a time-series forecasting problem without considering the intrinsic spatial dependencies of different types of healthcare facilities, and they also fail to provide reliable predictions under abnormal situations such as public emergencies. To advance existing research, we propose HealthMamba, an uncertainty-aware spatiotemporal framework for accurate and reliable healthcare facility visit prediction. HealthMamba comprises three key components: (i) a Unified Spatiotemporal Context Encoder that fuses heterogeneous static and dynamic information, (ii) a novel Graph State Space Model called GraphMamba for hierarchical spatiotemporal modeling, and (iii) a comprehensive uncertainty quantification module integrating three uncertainty quantification mechanisms for reliable prediction. We evaluate HealthMamba on four large-scale real-world datasets from California, New York, Texas, and Florida. Results show HealthMamba achieves around 6.0% improvement in prediction accuracy and 3.5% improvement in uncertainty quantification over state-of-the-art baselines.

Dahai Yu, Lin Jiang, Rongchao Xu +1

Department of Computer Science, Florida State University

Spatiotemporal Forecasting State Space Models Spatial Context Modeling Uncertainty Quantification

Jan 30, 2026

Learning-to-Defer in Non-Stationary Time Series via Switching State-Space Models

Learning-to-defer (L2D) lets a predictor decide, at each round, whether to issue its own forecast or pay for an expert's. In non-stationary time series this decision must keep adapting, although deployment reveals only the consulted expert's forecast while a historical archive records every expert with the target. L2D-SLDS learns from this archive a switching state-space model of the target and all expert forecasts, whose shared and expert-specific states describe how experts move together and apart. Its predictive law supplies the internal forecast and the expected cost of every consultation, which a greedy router minimizes, and one consultation also updates the beliefs about unconsulted and unavailable experts. We prove sublinear regret against a changing conditional-risk oracle without exploration, when the candidate models are accurate and either the archive separates them or live feedback reveals cost differences. On three real datasets, L2D-SLDS has the lowest cost among eight bandit routers and adapts its consultation rate to the fee.

Yannis Montreuil, Letian Yu, Axel Carlier +2

School of Computing National University of Singapore · Université de Toulouse Fédération ENAC ISAE-SUPAERO ONERA · Institute for Infocomm Research A*STAR, Singapore

Cost-Sensitive Learning Adaptive Model Routing Learning to Defer Decision-Focused Learning Non-Stationary Time Series Forecasting State Space Models

Jan 14, 2026

Parallelizable memory recurrent units

With the emergence of massively parallel processing units, parallelization has become a desirable property for new sequence models. The ability to parallelize the processing of sequences with respect to the sequence length during training is one of the main factors behind the uprising of the Transformer architecture. However, Transformers lack efficiency at sequence generation, as they need to reprocess all past timesteps at every generation step. Recently, state-space models (SSMs) emerged as a more efficient alternative. These new kinds of recurrent neural networks (RNNs) keep the efficient update of the RNNs while gaining parallelization by getting rid of nonlinear dynamics (or recurrence). SSMs can reach state-of-the-art performance through the efficient training of potentially very large networks, but still suffer from limited representation capabilities. In particular, SSMs cannot exhibit persistent memory, or the capacity of retaining information for an infinite duration, because of their monostability. In this paper, we introduce a new family of RNNs, the memory recurrent units (MRUs), that combine the persistent memory capabilities of nonlinear RNNs with the parallelizable computations of SSMs. These units leverage multistability as a source of persistent memory, while getting rid of transient dynamics for efficient computations. We then derive a specific implementation as proof-of-concept: the bistable memory recurrent unit (BMRU). This new RNN is compatible with the parallel scan algorithm. We show that BMRU achieves good results in tasks with long-term dependencies, and can be combined with SSMs to create parallelizable hybrid networks that have both transient dynamics and persistent memory.

Florent De Geeter, Gaspard Lambrechts, Damien Ernst +1

Montefiore Institute, University of Liege, Liege, Belgium

Recurrent Neural Networks State Space Models

Jan 4, 2026

Modeling Information Blackouts in Missing Not-At-Random Time Series Data

Traffic forecasting systems rely on fixed sensor networks that frequently exhibit contiguous blackouts. Such outages are usually treated as ignorable missingness, although dropout can depend on unobserved traffic conditions. We study this possibility with an MNAR-aware latent state-space model that combines linear traffic dynamics with a Bernoulli missingness channel whose probability depends on the latent state. Inference uses an Extended Kalman Filter (EKF) followed by Rauch-Tung-Striebel (RTS) smoothing, and parameters are learned by approximate EM. We evaluate Seattle using a leakage-free, month-balanced set of 300 unique all-horizon-aligned blackout windows. On this benchmark, MAR-LDS attains 4.264 mph pooled imputation RMSE and MNAR-LDS improves it to 4.177 (difference -0.086); the detector-cluster bootstrap 95% interval is [-0.182,-0.002]. A causal one-step predicted latent representation raises missingness ROC-AUC from 0.685 using observed-only features to 0.784. We further test whether this compact probabilistic model remains competitive with substantially larger neural time-series architectures under the identical masked-imputation protocol. MNAR-LDS ranks second in pooled RMSE and outperforms 8 of 9 evaluated neural architectures; it is within 1.22% of the best neural result, with no statistically resolved difference under detector-cluster bootstrap, while achieving lower P95 error, lower long-blackout RMSE, and orders of magnitude fewer stored scalar entries. MNAR roughly doubles end-to-end training time relative to MAR and increases EKF+RTS inference time by 41%, making the accuracy-complexity-cost tradeoff explicit. Controlled state-dependent blackouts further show larger gains when dropout is genuinely informative, including a 6.34% reduction in 30-minute forecast RMSE relative to MAR.

Aman Sunesh, Allan Ma, Siddarth Nilol

New York University

Time Series Imputation Incomplete Data Imputation Traffic Flow Estimation State Space Models

Dec 22, 2025

Lag Operator SSMs: A Geometric Framework for Structured State Space Modeling

Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multistage process of continuous-time modeling and subsequent discretization, which can obscure intuition. We introduce a direct, first-principles framework for constructing discrete-time SSMs that is both flexible and modular. Our approach is based on a novel lag operator, which geometrically derives the discrete-time recurrence by measuring how the system's basis functions undergo what we call a domain expansion from one timestep to the next. The resulting state matrices are computed via a single inner product involving this operator, enabling a modular design space for creating novel SSMs by flexibly combining different basis functions and time-warping schemes. To validate our framework, we demonstrate that a specific instance exactly recovers the recurrence of the influential HiPPO model. Numerical simulations confirm our derivation, providing new theoretical tools for designing flexible and robust sequence models.

Sutashu Tomonaga, Kenji Doya, Noboru Murata

Okinawa Institute of Science and Technology · Waseda University

Sequence Modeling State Space Models

Nov 19, 2025

Recursive Entropic Variational Inference for Nonlinear State-Space Models

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic consistency constraints. This framework gives rise to a family of forward-backward algorithms whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models, we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.

Hany Abdulsamad, Ángel F. García-Fernández, Simo Särkkä

Amsterdam Machine Learning Lab University of Amsterdam, Netherlands · Information Processing and Telecommunications Center Universidad Politécnica de Madrid, Spain · ELLIS Institute Finland Department of Electrical Engineering and Automation Aalto University, Finland

Bayesian Filtering Variational Inference State Space Models

Nov 17, 2025

Naga: Vedic Encoding for Deep State Space Models

This paper presents Naga, a deep State Space Model (SSM) encoding approach inspired by structural concepts from Vedic mathematics. The proposed method introduces a bidirectional representation for time series by jointly processing forward and time-reversed input sequences. These representations are then combined through an element-wise (Hadamard) interaction, resulting in a Vedic-inspired encoding that enhances the model's ability to capture temporal dependencies across distant time steps. We evaluate Naga on multiple long-term time series forecasting (LTSF) benchmarks, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, and ILI. The experimental results show that Naga outperforms 28 current state of the art models and demonstrates improved efficiency compared to existing deep SSM-based approaches. The findings suggest that incorporating structured, Vedic-inspired decomposition can provide an interpretable and computationally efficient alternative for long-range sequence modeling.

Melanie Schaller, Nick Janssen, Bodo Rosenhahn

Sequence Modeling State Space Models Long-Term Time Series Forecasting Multivariate Time Series Forecasting

Oct 29, 2025

PyDPF: A Python Package for Differentiable Particle Filtering

State-space models (SSMs) are a widely used tool in time series analysis. In the complex systems that arise from real-world data, it is common to employ particle filtering (PF), an efficient Monte Carlo method for estimating the hidden state corresponding to a sequence of observations. Applying particle filtering requires specifying both the parametric form and the parameters of the system, which are often unknown and must be estimated. Gradient-based optimisation techniques cannot be applied directly to standard particle filters, as the filters themselves are not differentiable. However, several recently proposed methods modify the resampling step to make particle filtering differentiable. In this paper, we present an implementation of several such differentiable particle filters (DPFs) with a unified API built on the popular PyTorch framework. Our implementation makes these algorithms easily accessible to a broader research community and facilitates straightforward comparison between them. We validate our framework by reproducing experiments from several existing studies and demonstrate how DPFs can be applied to address several common challenges with state space modelling.

John-Joseph Brady, Benjamin Cox, Yunpeng Li +1

King’s College London · Max-Planck Institut für Physik · University of Edinburgh

Particle Filtering Bayesian Filtering Differentiable Programming State Space Models

Oct 26, 2025

Beyond Semantics: How Temporal Biases Shape Retrieval in Transformer and State-Space Models

In-context learning is governed by both temporal and semantic relationships, shaping how Large Language Models (LLMs) retrieve contextual information. Analogous to human episodic memory, where the retrieval of specific events is enabled by separating events that happened at different times, this work probes the ability of various pretrained LLMs, including transformer and state-space models, to differentiate and retrieve temporally separated events. Specifically, we prompted models with sequences containing multiple presentations of the same token, which reappears at the sequence end. By fixing the positions of these repeated tokens and permuting all others, we removed semantic confounds and isolated temporal effects on next-token prediction. Across diverse sequences, models consistently placed the highest probabilities on tokens following a repeated token, but with a notable bias for those nearest the beginning or end of the input. An ablation experiment linked this phenomenon in transformers to induction heads. Extending the analysis to unique semantic contexts with partial overlap further demonstrated that memories embedded in the middle of a prompt are retrieved less reliably. Despite architectural differences, state-space and transformer models showed comparable temporal biases. Our findings deepen the understanding of temporal biases in in-context learning and offer an illustration of how these biases can enable temporal separation and episodic retrieval.

Anooshka Bajaj, Deven Mahesh Mistry, Sahaj Singh Maini +2

Department of Computer Science Indiana University Bloomington

In-Context Learning Induction Heads State Space Models

Oct 22, 2025

Data Efficient Any Transformer-to-Mamba Distillation via Attention Bridge

State-space models (SSMs) have emerged as promising alternatives to Transformers for sequence modeling. However, training competitive SSMs from scratch remains computationally intensive, and the ecosystem around them is far less mature than that of Transformers. Moreover, the architectural differences between SSMs and Transformers make it challenging to efficiently transfer knowledge from pretrained Transformers. In this work, we propose Cross-architecture distillation via Attention Bridge (CAB), a distillation framework that transfers attention-related representations from Transformer teachers to state-space student models. Unlike conventional knowledge distillation that supervises only final predictions, CAB enables token-level intermediate supervision through a lightweight bridge and flexible layer-wise alignment. By aligning Transformer attention-related representations with Mamba's token-dependent state projections, CAB facilitates efficient cross-architecture knowledge transfer without inference-time overhead. Experiments on image classification and language modeling demonstrate that CAB improves Transformer-to-SSM distillation, particularly under limited-supervision settings. Overall, CAB provides an efficient pathway for transferring Transformer representations to SSM-based models, helping bridge the gap between mature Transformer ecosystems and emerging SSM ecosystems.

Penghao Wang, Yuhao Zhou, Mengxuan Wu +3

National University of Singapore · The University of Texas at Austin

Cross-Architecture Knowledge Distillation Knowledge Distillation State Space Models

Oct 17, 2025

Cortical-SSM: A Deep State Space Model for Motor Imagery Decoding from EEG Signals

Classification of electroencephalogram (EEG) signals obtained during motor imagery (MI) has substantial application potential, including communication assistance and rehabilitation support for patients with motor impairments. These signals remain inherently susceptible to physiological artifacts (e.g., eye blinking and swallowing), which pose persistent challenges. Although Transformer-based approaches for classifying EEG signals have been widely adopted, they often struggle to capture fine-grained dependencies within them. To overcome these limitations, we propose Cortical-SSM, a novel architecture that extends deep state space models to capture integrated dependencies of EEG signals across temporal, spatial, and frequency domains. We validated our method across two large-scale public MI EEG datasets containing more than 50 subjects. Our method outperformed baseline methods on both benchmarks. Furthermore, visual explanations derived from our model indicate that it effectively captures neurophysiologically relevant regions of EEG signals. These results indicate that Cortical-SSM provides a robust and interpretable alternative to attention-based architectures for MI EEG decoding. By enabling physiologically grounded feature learning, our method advances the reliability of subject-independent EEG classification and supports the development of practical and clinically deployable brain-computer interface systems.

Shuntaro Suzuki, Shunya Nagashima, Komei Sugiura

Keio University

MI Classification Brain-Computer Interfaces EEG Decoding State Space Models

Oct 8, 2025

Contextual Representation Flow Across Depth in State-Space and Transformer Architectures

State Space Models (SSMs) have emerged as efficient, linear-time alternatives to Transformer-Based Models (TBMs) for long-context processing. However, their different mechanisms raise an important question: how does contextual representation flow across depth differ between these model families and their hybrids? We examine this question across twenty-one pretrained models, combining token-wise spectral diversity, layer-wise variation on seven datasets, and answer-location probing on two retrieval tasks. This joint analysis reveals that TBMs retain most of their token diversity at the output, whereas SSMs reach richer intermediate diversity but retain less of it on average, with late-layer compression. Comparisons with reinitialized weights reveal that these profiles depend on pretrained weights, while hybrids combine strong answer-location accessibility with architecture-dependent geometry, showing that high accessibility need not require the steadiest representation flow. Finally, we conduct theoretical case studies connecting these contrasts to mechanism-level differences: query-time token mixing in TBMs, repeated recurrent updates in SSMs, and preserved attention updates in hybrids.

Nhat M. Hoang, Do Xuan Long, Cong-Duy Nguyen +3

Nanyang Technological University, Singapore · National University of Singapore

State Space Models State Space Language Models Transformer Representation Geometry in Language Models Long-Context Modeling

Sep 25, 2025

Aligning Inductive Bias for Data-Efficient Generalization in State Space Models

The remarkable success of modern AI has been closely tied to scaling laws, yet the finite supply of high-quality data makes data efficiency--learning more from less--an increasingly important frontier. A model's inductive bias is a critical lever for data efficiency, but foundational sequence models such as State Space Models (SSMs) often rely on fixed, task-agnostic biases. When this fixed prior is misaligned with the underlying structure of a task, the model may require additional samples to overcome its own bias before learning the relevant signal. In this work, we introduce a principled framework for understanding and aligning the inductive bias of linear time-invariant SSMs. We first formalize this bias through an SSM-induced kernel and show theoretically and empirically that its spectrum is governed by the model's frequency response. This characterization motivates Task-Dependent Initialization (TDI), a fast power-spectrum matching method that aligns the initial SSM bias with the task's spectral characteristics before downstream training. Across controlled synthetic experiments, trainable one-layer SSMs, and deep SSMs on diverse real-world benchmarks, TDI can improve data-efficient generalization primarily when task-relevant spectral structure is present and the default SSM bias is spectrally mismatched. Our results provide both a theoretical lens and a practical tool for task-adaptive inductive bias, suggesting a path toward more data-efficient sequence modeling.

Qiyu Chen, Guozhang Chen

School of Computer Science, National Key Laboratory for Multimedia Information Processing, Peking University, China · School of Physics, Peking University, China

Sequence Modeling Data-Efficient Learning State Space Models

Aug 13, 2025

EEGDM: Label-Efficient EEG Representation Learning with Generative Diffusion Model

Electroencephalography (EEG) is a critical tool for monitoring brain activity and diagnosing neurological disorders such as epilepsy. However, learning meaningful representations from raw EEG signals remains challenging due to limited annotations, substantial inter-subject variability, and complex temporal dynamics. Recent EEG foundation models (FMs) have demonstrated promising performance through transformer-based architectures and large-scale self-supervised pretraining, yet they often incur substantial computational costs and exhibit diminishing returns with increasing model and dataset scale, limiting their practicality in clinical settings. To address these challenges, we propose EEGDM, a diffusion-based EEG representation learning framework. Specifically, EEGDM introduces a Structured State-Space Model for Diffusion Pretraining (SSMDP) that effectively captures long-range temporal dependencies through generative diffusion training on unlabeled EEG data. The representations are subsequently leveraged for downstream tasks via our Latent Fusion Module (LFM), which integrates multi-layer latent features of SSMDP. We evaluate EEGDM on three EEG benchmarks spanning EEG event classification (TUEV), seizure detection (CHB-MIT), and seizure classification (IIIC). Compared with existing state-of-the-art methods, including EEG FMs, EEGDM achieves competitive performance across diverse tasks and datasets, exceeding existing methods in most cases while requiring substantially fewer samples for both pretraining and downstream adaptation. These results demonstrate that diffusion-based learning can unlock more discriminative EEG representations, with direct implications for epilepsy diagnosis and management. Our source code and pretrained checkpoints are publicly available at: https://github.com/jhpuah/EEGDM.

Jia Hong Puah, Sim Kuan Goh, Ziwei Zhang +6

School of Artificial Intelligence and Robotics, Xiamen University Malaysia · School of Energy and Chemical Engineering, Xiamen University Malaysia · Department of Biomedical Engineering, Universiti Malaya +3

Electroencephalography EEG Seizure Detection Representation Learning Self-Supervised Time Series Representation Learning Diffusion Models Data-Efficient Learning+1

Jul 18, 2025

State Space Models Naturally Produce Time Cell and Oscillatory Behaviors and Scale to Abstract Cognitive Functions

A grand challenge in modern neuroscience is bridging the gap between the microscale neural circuits and cognitive functions. While extensive knowledge exists about neuronal connectivity and biophysics, how low-level phenomena give rise to abstract behaviors remains largely unresolved. Here, we propose that a mathematical framework based on State Space Models offers mathematical sufficiency and computational plausibility to generate response profiles that resemble time cells, ramping activity, and oscillatory responses. Our results suggest that such behaviors can emerge from a structured multi-timescale complex rotational basis, which enables optimized history compression and naturally generates structured temporal dynamics even prior to training, mirroring recent findings in biological circuits. Learning exploits and adapts to the pre-existing temporal basis for specific tasks. We show that the model can readily scale to abstract cognitive functions such as event counting, supporting its use as a computationally tractable framework for understanding neural activities.

Sen Lu, Xiaoyu Zhang, Mingtao Hu +3

Electrical Engineering and Computing Science, University of Michigan

State Space Models Computational Cognitive Modeling

Mar 25, 2025

Keyframe-Centric State-Space Modeling for Burst Image Super-Resolution

Burst image super-resolution (BISR) reconstructs a high-resolution keyframe by aggregating complementary sub-pixel evidence from a short burst of low-resolution frames. Existing methods often process all burst frames with heavy backbones or maintain deep cross-frame interaction throughout the network, leading to redundant computation on non-key frames and limiting scalability with burst length. In this work we propose BurstMamba, a BISR architecture built on a simple principle: allocate most compute to reconstructing the keyframe, and process the burst primarily to extract sub-pixel priors. To this end, BurstMamba decouples BISR into a high-capacity keyframe super-resolution stream and a lightweight burst stream that interacts with it only through stage-wise residual injection. To improve burst-to-keyframe transfer, we introduce Gather -> Aggregate -> Scatter (GAS), which uses correspondence only for cross-frame message passing while preserving native-view features through a residual connection, and a wavelet-conditioned state update that biases selective routing toward high-frequency regions. Across SyntheticSR, RealBSR-RAW, and RealBSR-RGB, BurstMamba achieves state-of-the-art results. Extensive ablations show that the proposed compute separation, GAS, and wavelet-conditioned routing each contribute to the model's accuracy and scaling.

Ozan Unal, Steven Marty, Dengxin Dai

Computer Vision Lab, Huawei Research Center Zurich, Switzerland

Image Super-Resolution State Space Models

Jul 8, 2024

Mamba-FSCIL: Dynamic Adaptation with Selective State Space Model for Few-Shot Class-Incremental Learning

Few-shot class-incremental learning (FSCIL) aims to incrementally learn novel classes from limited examples while preserving knowledge of previously learned classes. Existing methods face a critical dilemma: static architectures rely on a constant parameter space to learn from data that arrive sequentially, making them prone to overfitting to the current session, while dynamic architectures continually expand the parameter space, leading to increased complexity. In this study, we explore the potential of Selective State Space Models (SSMs) for FSCIL. Mamba leverages its input-dependent parameters to dynamically adjust its processing patterns and generate content-aware scan patterns without session-wise projector expansion. This enables it to configure distinct processing for base and novel classes, helping preserve existing knowledge while adapting to new ones. To leverage Mamba's potential for FSCIL, we design two key modules: First, we propose a dual selective SSM projector that generates input-conditioned state-space parameters from intermediate features for dynamic adaptation. The dual design structurally decouples base and novel-class processing, employing a frozen base branch to maintain stable base-class features and a dynamic incremental branch that adaptively learns distinctive feature shifts for novel classes. Second, we develop a class-sensitive selective scan mechanism to guide dynamic adaptation of the incremental branch. It reduces the disruption to base-class representations caused by training on novel data, and meanwhile, encourages the selective scan to perform in distinct patterns between base and novel classes. Extensive experiments on miniImageNet, CIFAR-100, and CUB-200 demonstrate that Mamba-FSCIL achieves state-of-the-art performance.

Xiaojie Li, Yibo Yang, Jianlong Wu +4

School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen, China · Pengcheng Laboratory, Shenzhen, China · King Abdullah University of Science and Technology, Jeddah, Saudi Arabia +1

Class-Incremental Learning Incremental Learning Few-Shot Image Classification State Space Models

Mar 12, 2024

SSM Meets Video Diffusion Models: Efficient Long-Term Video Generation with Structured State Spaces

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 computational costs, which increase quadratically with the sequence length. This limitation presents significant challenges when generating longer video sequences using diffusion models. To overcome this challenge, we propose leveraging state-space models (SSMs) as temporal feature extractors. SSMs (e.g., Mamba) have recently gained attention as promising alternatives due to their linear-time memory consumption relative to sequence length. In line with previous research suggesting that using bidirectional SSMs is effective for understanding spatial features in image generation, we found that bidirectionality is also beneficial for capturing temporal features in video data, rather than relying on traditional unidirectional SSMs. We conducted comprehensive evaluations on multiple long-term video datasets, such as MineRL Navigate, across various model sizes. For sequences up to 256 frames, SSM-based models require less memory to achieve the same FVD as attention-based models. Moreover, SSM-based models often deliver better performance with comparable GPU memory usage. Our codes are available at https://github.com/shim0114/SSM-Meets-Video-Diffusion-Models.

Yuta Oshima, Shohei Taniguchi, Masahiro Suzuki +1

The University of Tokyo

Video Diffusion Models Long-Horizon Video Generation Diffusion Model Acceleration State Space Models