State Space Models

World models enable model-based planning through learned latent dynamics, but imagined rollouts become unstable as the planning horizon grows or the dynamics distribution shifts. We argue that this instability reflects two missing structures in planner-facing latents: history-conditioned memory for approximate Markov completeness, and geometric organization that separates configuration, momentum, and task semantics. We propose HaM-World (HMW), a structured world model that decomposes the latent state into a canonical (q, p) subspace and a context subspace c, while using Mamba selective state-space memory as the history-conditioned input to the same latent dynamics. Within this interface, (q, p) evolves through an energy-derived Hamiltonian vector field plus learnable residual/control dynamics, while c captures semantic, dissipative, and non-conservative factors. This gives the planner a single latent state shared by dynamics prediction, reward/value estimation, imagined rollouts, and CEM action search. On four DeepMind Control Suite tasks, HaM-World reaches the highest Avg. AUC (117.9, +9.5%), reduces long-horizon rollout error to 45% of a strong baseline model, and wins 11/12 k in {3,5,7} MSE cells. Under 12 OOD perturbations spanning dynamics shifts, action delay, and observation masking, HaM-World achieves the highest return in every condition, with average OOD-return gains of 10.2% on Finger Spin and 13.6% on Reacher Easy. Mechanism diagnostics further show bounded action-free Hamiltonian-energy drift, structured energy variation under policy rollouts, and coherent control-induced energy transfer, supporting the intended Soft-Hamiltonian dynamics design.

Structured state space models (SSMs) have recently emerged as a promising foundation for sequence modeling, with Mamba-based architectures demonstrating strong performance through input-dependent state transitions, albeit at considerable complexity. However, their application to time-series classification (TSC) has been largely limited to Mamba-style architectures, leaving the broader SSM design space underexplored. We present the first systematic study spanning diagonal SSMs (S4D) and input-dependent SSMs (Mamba family) on large-scale TSC benchmarks, asking whether such complexity is necessary for top performance. Our results reveal a surprising finding: S4D consistently outperforms Mamba-based variants in both accuracy and efficiency, challenging the assumption that increased complexity translates to meaningful gains in TSC. Building on this, we introduce MS4, lightweight modifications to S4D via a linear input projection and channel-mixing mechanism, and MS4N, a normalized variant that stabilizes state dynamics with negligible overhead. Evaluated on 59 datasets across MONSTER (up to 60 million samples, 50K timesteps, 82 classes) and the UEA benchmark, against 15 baselines, MS4 and MS4N consistently outperform Mamba-based models while remaining more efficient, and MS4N matches or surpasses competing deep learning models that are roughly 2x and 10x larger in parameters. These results position lightweight structured SSMs as a compelling alternative to scaling complexity for TSC.

Accurate analysis of histopathological images is critical for disease diagnosis and treatment planning. Whole-slide images (WSIs), which digitize tissue specimens at gigapixel resolution, are fundamental to this process but require aggregating thousands of patches for slide-level predictions. Multiple Instance Learning (MIL) tackles this challenge with a two-stage paradigm, decoupling tile-level embedding and slide-level prediction. However, most existing methods implicitly embed patch representations in homogeneous Euclidean spaces, overlooking the hierarchical organization and regional heterogeneity of pathological tissues. This limits current models' ability to capture global tissue architecture and fine-grained cellular morphology. To address this limitation, we introduce a hybrid hyperbolic-Euclidean representation that embeds WSI features in dual geometric spaces, enabling complementary modeling of hierarchical tissue structures and local morphological details. Building on this formulation, we develop BatMIL, a WSI classification framework that leverages both geometric spaces. To model long-range dependencies among thousands of patches, we employ a structured state space sequence model (S4) backbone that encodes patch sequences with linear computational complexity. Furthermore, to account for regional heterogeneity, we introduce a chunk-level mixture-of-experts (MoE) module that groups patches into regions and dynamically routes them to specialized subnetworks, improving representational capacity while reducing redundant computation. Extensive experiments on seven WSI datasets spanning six cancer types demonstrate that BatMIL consistently outperforms state-of-the-art MIL approaches in slide-level classification tasks. These results indicate that geometry-aware representation learning offers a promising direction for next-generation computational pathology.

We propose a modular framework for hybrid image restoration that integrates transformer and state-space model (SSM) blocks with a focus on improving runtime efficiency on edge hardware. While transformers provide strong global modeling through self-attention, their attention kernels incur substantial latency on mobile devices, especially for high-resolution inputs. In contrast, SSMs such as Mamba offer lineartime sequence modeling with lower runtime overhead but may underperform on fine grained restoration tasks. To balance accuracy and efficiency, we train lightweight SSM blocks as feature-distilled surrogates of transformer blocks and use them to construct hybrid U-Net-style architectures. To automatically discover effective block combinations, we introduce Efficient Network Search (ENS), a multi-objective search strategy that selects task-specific hybrid configurations from pre-aligned components. ENS optimizes restoration quality while penalizing transformer usage, serving as a lightweight proxy for latency and enabling architecture discovery without repeated hardware profiling. On a Snapdragon 8 Elite CPU, the Restormer baseline requires 10119.52 ms for inference. In contrast, ENS-discovered hybrids significantly reduce runtime: ENS-Deblurring runs in 2973 ms (3.4x faster), ENS-Deraining in 5816 ms (1.74x faster), and ENS-Denoising in 8666 ms (1.17x faster), while maintaining competitive restoration quality.

Vision Mamba (ViM) models offer a compelling efficiency advantage over Transformers by leveraging the linear complexity of State Space Models (SSMs), yet efficiently deploying them on FPGAs remains challenging. Linear layers struggle with dynamic activation outliers that render static quantization ineffective, while uniform quantization fails to capture the weight distribution at low bit-widths. Furthermore, while associative scan accelerates SSMs on GPUs, its memory access patterns are misaligned with the streaming dataflow required by FPGAs. To address these challenges, we present ViM-Q, a scalable algorithm-hardware co-design for end-to-end ViM inference on the edge. We introduce a hardware-aware quantization scheme combining dynamic per-token activation quantization and per-channel smoothing to mitigate outliers, alongside a custom 4-bit per-block Additive Power-of-Two (APoT) weight quantization. The models are deployed on a runtime-parameterizable FPGA accelerator featuring a linear engine employing a Lookup-Table (LUT) unit to replace multiplications with shift-add operations, and a fine-grained pipelined SSM engine that parallelizes the state dimension while preserving sequential recurrence. Crucially, the hardware supports runtime configuration, adapting to diverse dimensions and input resolutions across the ViM family. Implemented on an AMD ZCU102 FPGA, ViM-Q achieves an average 4.96x speedup and 59.8x energy efficiency gain over a quantized NVIDIA RTX 3090 GPU baseline for low-batch inference on ViM-tiny. This co-design shows a viable path for deploying ViM models on resource-constrained edge devices.

Scalable Vector Graphics (SVG) animation generation is pivotal for professional design due to their structural editability and resolution independence. However, this task remains challenging as it requires bridging discrete code representations with continuous visual dynamics. Existing optimization-based methods often destroy topological consistency, while general-purpose LLMs rely on rigid CSS/SMIL transformations, failing to model geometry-level non-rigid deformations. To address these limitations, we present VAnim, the first LLM-based framework for open-domain text-to-SVG animation. We reconceptualize animation not as sequence generation, but as Sparse State Updates (SSU) on a persistent SVG DOM tree. This paradigm compresses sequence length by over 9.8x while preserving the SVG DOM structure and non-participating elements by construction. To enable precise control, we propose an Identification-First Motion Planning mechanism that grounds textual instructions in explicit visual entities. Furthermore, to overcome the non-differentiable nature of SVG rendering, we employ Rendering-Aware Reinforcement Learning via Group Relative Policy Optimization (GRPO). By leveraging a hybrid reward from a state-of-the-art video perception encoder, we align discrete code updates with high-fidelity visual feedback. We also introduce SVGAnim-134k, the first benchmark for vector animation. Extensive experiments demonstrate that VAnim significantly outperforms state-of-the-art baselines in semantic alignment and structural validity, with additional appendix metrics further validating motion quality and identity preservation.

Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is necessary for identifying dynamic treatment effects, linking control-theoretic observability to causal identifiability, even when hidden confounders affect both treatments and outcomes. We derive a continuous-time adjustment formula expressing potential outcome distributions under treatment trajectories via the measurement model, latent dynamics, and the filtering distribution over latent states given observed histories. We propose Observable Neural ODEs (ObsNODEs), Neural ODE models in observable normal form for causal forecasting. ObsNODEs learn continuous-time dynamics with states reconstructible from observations, enabling outcome prediction under alternative treatment paths. Experiments on synthetic cancer data, semi-synthetic data based on MIMIC-IV, and real-world sepsis data show strong performance over recent sequence models.

We present Density Field State Space Models (DF-SSM), a framework for compressing SSMs to a 1-bit scaffold with int8 low-rank correction. Applied to Mamba-2 1.3B, we achieve a 278 MB model (9.7x smaller than the 2.7 GB FP16 teacher) that runs at 21.4x faster inference on GPU (batch=1, relative to the mamba-ssm reference implementation) while maintaining downstream task performance within 2-4 percentage points of BitMamba-2, a 1.58-bit model trained from scratch on 150B tokens. The distillation itself requires only 32M tokens and 6 hours on a single A100 GPU, though it presupposes a pretrained FP16 teacher. We develop an optimized inference pipeline combining cuBLAS INT8 tensor cores for the scaffold matmul, custom CUDA kernels for stateful SSM and convolution operations, and an AVX-512 CPU backend for efficient deployment on both GPU and CPU. Beyond compression, we investigate the internal knowledge organization of the resulting model, discovering three distinct processing phases: intent classification (layers 0-3, operating in an abstract space with no vocabulary alignment), knowledge retrieval (layers 25-35, where factual associations localize to a 5-layer window), and output formatting (layers 36-47, where category structure dissolves). Through systematic analysis of 445 factual prompts across 19 categories, we find that early-layer classification is syntactic (driven by template structure) rather than semantic, and that the model exhibits well-organized knowledge representations despite weak factual recall--suggesting that representational structure may precede factual strength.

State space models (SSMs) achieve linear-time complexity but struggle with multi-channel physiological signals due to three limitations: fixed kernels cannot capture multi-scale temporal dynamics (motor preparation over hundreds of milliseconds vs. execution transients in tens of milliseconds), Markovian state updates restrict global context for periodic oscillations, and channel-independent processing ignores spatial electrode topology. We introduce NAKUL, extending SSMs for medical signal analysis through three contributions: (1) Dynamic Kernel Generation-parallel SSM branches with varying kernel sizes (3, 5, 7, 11 timesteps) are weighted by a meta-network that analyzes input statistics, enabling adaptive temporal scale selection; (2) Spectral Context Modeling-FFT-based operations with learnable Gaussian frequency band filters capture global periodic patterns in $O(N \log N)$ complexity; (3) Graph-Guided Spatial Attention-fixed electrode topology provides spatial biases to multi-head attention for principled cross-channel interaction. On BCI Competition IV-2a motor imagery (our primary benchmark), NAKUL achieves 91.7$\pm$0.6% accuracy, matching EEG-Conformer (92.1$\pm$0.7%) while using 28% fewer parameters (2.5M vs 3.5M) and 2.0$\times$ faster inference (4.3ms vs 8.7ms). The model generalizes to EEG emotion recognition (83.6%), multimodal EEG-fMRI (91.4%), and medical imaging (92.8% on ultrasound), demonstrating architectural versatility. Ablations show dynamic kernels contribute +2.6% and exhibit interpretable scale selection patterns correlated with known neural dynamics.

Recent works have demonstrated that attention-based transformer and large language model (LLM) architectures can achieve strong channel state prediction (CSP) performance by capturing long-range temporal dependencies across channel state information (CSI) sequences. However, these models suffer from quadratic scaling in sequence length, leading to substantial computational cost, memory consumption, and inference latency, which limits their applicability in real-time and resource-constrained wireless deployments. In this paper, we investigate whether selective state space models (SSMs) can serve as a hardware-efficient alternative for CSI prediction. We propose MambaCSP, a hybrid-attention SSM architecture that replaces LLM-based prediction backbones with a linear-time Mamba model. To overcome the local-only dependencies of pure SSMs, we introduce lightweight patch-mixer attention layers that periodically inject cross-token attentions, helping with long-context CSI prediction. Extensive MISO-OFDM simulations show that MambaCSP improves prediction accuracy over LLM-based approaches by 9-12%, while delivering up to 3.0x higher throughput, 2.6x lower VRAM usage, and 2.9x faster inference. Our results demonstrate that hybrid state space architectures provide a promising direction for scalable and hardware-efficient AI-native CSI prediction in future wireless networks.

Vision Mamba, as a state space model (SSM), employs a zero-order hold (ZOH) discretization, which assumes that input signals remain constant between sampling instants. This assumption degrades temporal fidelity in dynamic visual environments and constrains the attainable accuracy of modern SSM-based vision models. In this paper, we present a systematic and controlled comparison of six discretization schemes instantiated within the Vision Mamba framework: ZOH, first-order hold (FOH), bilinear/Tustin transform (BIL), polynomial interpolation (POL), higher-order hold (HOH), and the fourth-order Runge-Kutta method (RK4). We evaluate each method on standard visual benchmarks to quantify its influence in image classification, semantic segmentation, and object detection. Our results demonstrate that POL and HOH yield the largest gains in accuracy at the cost of higher training-time computation. In contrast, the BIL provides consistent improvements over ZOH with modest additional overhead, offering the most favorable trade-off between precision and efficiency. These findings elucidate the pivotal role of discretization in SSM-based vision architectures and furnish empirically grounded justification for adopting BIL as the default discretization baseline for state-of-the-art SSM models.

We establish a mathematical correspondence between state space models, a state-of-the-art architecture for capturing long-range dependencies in data, and an exactly solvable nonlinear oscillator network. As a specific example of this general correspondence, we analyze the diagonal linear time-invariant implementation of the Structured State Space Sequence model (S4). The correspondence embeds S4D, a specific implementation of S4, into a ring network topology, in which recent inputs are encoded, as waves of activity traveling over the one-dimensional spatial layout of the network. We then derive an exact operator expression for the full forward pass of S4D, yielding an analytical characterization of its complete input-output map. This expression reveals that the nonlinear decoder in the system induces interactions between these information-carrying waves that enable classifying real-world sequences. These results generalize across modern SSM architectures, and show that they admit an exact mathematical description with a clear physical interpretation. These insights enable a new level of interpretability for these systems in terms of nonlinear oscillator networks.

Wastewater treatment plants (WWTPs) need digital-twin-style decision support tools that can simulate plant response under prescribed control plans, tolerate irregular and missing sensing, and remain informative over 12-36 h planning horizons. Meeting these requirements with full-scale plant data remains an open engineering-AI challenge. We present CCSS-RS, a controlled continuous-time state-space model that separates historical state inference from future control and exogenous rollout. The model combines typed context encoding, gain-weighted forcing of prescribed and forecast drivers, semigroup-consistent rollouts, and Student-t plus hurdle outputs for heavy-tailed and zero-inflated WWTP sensor data. On the public Avedøre full-scale benchmark, with 906,815 timesteps, 43% missingness, and 1-20 min irregular sampling, CCSS-RS achieves RMSE 0.696 and CRPS 0.349 at H=1000 across 10,000 test windows. This reduces RMSE by 40-46% relative to Neural CDE baselines and by 31-35% relative to simplified internal variants. Four case studies using a frozen checkpoint on test data demonstrate operational value: oxygen-setpoint perturbations shift predicted ammonium by -2.3 to +1.4 over horizons 300-1000; a smoothed setpoint plan ranks first in multi-criterion screening; context-only sensor outages raise monitored-variable RMSE by at most 10%; and ammonium, nitrate, and oxygen remain more accurate than persistence throughout the rollout. These results establish CCSS-RS as a practical learned simulator for offline scenario screening in industrial wastewater treatment, complementary to mechanistic models.

Visual state-space models (SSMs) are increasingly promoted as efficient alternatives to Vision Transformers, yet their practical advantages remain unclear under fair comparison because existing studies rarely isolate encoder effects from decoder and training choices. We present a strictly controlled benchmark of representative visual SSM families, including VMamba, MambaVision, and Spatial-Mamba, for remote-sensing semantic segmentation, in which only the encoder varies across experiments. Evaluated on LoveDA and ISPRS Potsdam under a unified 4-stage feature interface and a fixed lightweight decoder, the benchmark reveals three main findings, intra-family scaling yields only modest gains, cross-domain generalization is strongly asymmetric, and boundary delineation is the dominant failure mode under distribution shift. Although visual SSMs achieve favorable accuracy-efficiency trade-offs relative to the controlled CNN and Transformer baselines considered here, the results suggest that future improvements are more likely to come from robustness-oriented design and boundary-aware decoding than from encoder scaling alone. By isolating encoder behavior under a unified and reproducible protocol, this study establishes a practical reference benchmark for the design and evaluation of future Mamba-based segmentation backbones

Traditional Task and Motion Planning (TAMP) systems depend on physics models for motion planning and discrete symbolic models for task planning. Although physics model are often available, symbolic models (consisting of symbolic state interpretation and action models) must be meticulously handcrafted or learned from labeled data. This process is both resource-intensive and constrains the solution to the specific domain, limiting scalability and adaptability. On the other hand, Visual Language Models (VLMs) show desirable zero-shot visual understanding (due to their extensive training on heterogeneous data), but still achieve limited planning capabilities. Therefore, integrating VLMs with classical planning for long-horizon reasoning in TAMP problems offers high potential. Recent works in this direction still lack generality and depend on handcrafted, task-specific solutions, e.g. describing all possible objects in advance, or using symbolic action models. We propose a framework that generalizes well to unseen problem instances. The method requires only lifted predicates describing relations among objects and uses VLMs to ground them from images to obtain the symbolic state. Planning is performed with domain-independent heuristic search using goal-count and width-based heuristics, without need for action models. Symbolic search over VLM-grounded state-space outperforms direct VLM-based planning and performs on par with approaches that use a VLM-derived heuristic. This shows that domain-independent search can effectively solve problems across domains with large combinatorial state spaces. We extensively evaluate on extensively evaluate our method and achieve state-of-the-art results on the ProDG and ViPlan benchmarks.

Salient object detection (SOD) requires modeling both long-range contextual dependencies and fine-grained structural details, which remains challenging for convolutional, transformer-based, and Mamba-based state space models. While recent Mamba-based state space approaches enable efficient global reasoning, they often struggle to recover precise object boundaries. In contrast, diffusion models capture strong structural priors through iterative denoising, but their use in discriminative dense prediction is still limited due to computational cost and integration challenges. In this work, we propose DGSSM, a diffusion-guided state space (Mamba) framework that formulates multimodal salient object detection as a progressive denoising process. The framework integrates diffusion structural priors with multi-scale state space encoding, adaptive saliency prompting, and an iterative Mamba diffusion refinement mechanism to improve boundary accuracy. A boundary-aware refinement head and self-distillation strategy further enhance spatial coherence and feature consistency. Extensive experiments on 13 public benchmarks across RGB, RGB-D, and RGB-T settings demonstrate that DGSSM consistently outperforms state-of-the-art methods across multiple evaluation metrics while maintaining a compact model size. These results suggest that diffusion-guided state space modeling is an effective and generalizable paradigm for multimodal dense prediction tasks.

Selective State Space Models (SSMs), notably Mamba, employ diagonal state transitions that limit both memory retention and bilinear computational capacity. We propose a factorized bilinear input modulation that augments the SSM with a state-input product, interpretable as a finite-dimensional Koopman bilinear form. After introducing a shared state across channels (Coupled SSM), the modulation admits three implementations. Coupled Bilinear Input Modulation (seq-BIM) retains the full bilinear product on the input side at the cost of sequential computation, Coupled Gated Modulation (GM) linearizes it into a gate modulation that is compatible with the parallel scan, and Parallel Bilinear Input Modulation (p-BIM) places the same bilinear product on the state transition while remaining parallel-scannable. Experiments on a multiple input-delay pendulum (memory retention) and NARMA-10 (bilinear computation) reveal a clear dissociation. GM substantially improves memory retention but not bilinear computation, while both seq-BIM and p-BIM improve both. A pathway ablation confirms that the two downstream routes of the bilinear signal serve complementary roles. The improvement is statistically robust, with the bilinear variants consistently outperforming the other variants on bilinear computation. Furthermore, only the bilinear variants benefit from increasing the SSM state dimension, while coupling or gate modulation alone show no improvement, establishing the bilinear mechanism as uniquely capable of exploiting larger state spaces.

We introduce a new framework for room acoustics modelling based on a state-space model of the boundary integral equation representing the sound field in a room. Whereas state-space models of linear time-invariant systems are traditionally constructed by means of a state vector and a 4-tuple of system matrices, the state-space representation introduced in this work consists of a state function representing the pressure distribution at the room boundary, and a 4-tuple of integral operators. We refer to this representation as a boundary integral operator state-space (BIOSS) model and provide a physical interpretation for each of the integral operators. As many mathematical operations on vectors and matrices translate to functions and operators, the BIOSS representation can be manipulated to obtain two transfer function representations, having either a feedback or a parallel feedforward structure. Consequently, various equivalent representations for room acoustics are obtained in the BIOSS framework, in the time or frequency domain, and in continuous or discrete space. We discuss two future directions for how the proposed framework can be fertile for research on room acoustics modelling. Firstly, we identify equivalences between the BIOSS framework and various existing room acoustics models (boundary element models, delay networks, geometric models), which may be used to establish relations between existing models and to develop novel room acoustics models. Secondly, we postulate on how concepts from state-space theory, such as observability, controllability, and state realization, can be used for developing new inference and control methods for room acoustics.

Accurate traffic forecasting is crucial for intelligent transportation systems, supporting effective traffic management, congestion reduction, and informed urban planning. However, traditional models often fail to adequately capture the intricate spatio-temporal dependencies present in traffic data. To overcome these limitations, we introduce GAMMA-Net, a novel approach that integrates Graph Attention Networks (GAT) with multi-axis Selective State Space Models (Mamba). The GAT component uses a self-attention mechanism to dynamically adjust the influence of nodes within the traffic network, enabling adaptive spatial dependency modeling based on real-time conditions. Simultaneously, the Mamba module efficiently models long-term temporal and spatial dynamics without the heavy computational cost of conventional recurrent architectures. Extensive experiments on several benchmark traffic datasets, including METR-LA, PEMS-BAY, PEMS03, PEMS04, PEMS07, and PEMS08, show that GAMMA-Net consistently outperforms existing state-of-the-art models across different prediction horizons, achieving up to a 16.25% reduction in Mean Absolute Error (MAE) compared to baseline models. Ablation studies highlight the critical contributions of both the spatial and temporal components, emphasizing their complementary role in improving prediction accuracy. In conclusion, the GAMMA-Net model sets a new standard in traffic forecasting, offering a powerful tool for next-generation traffic management and urban planning. The code for this study is available at https://github.com/hdy6438/GAMMA-Net

Pathological diagnosis is highly reliant on image analysis, where Regions of Interest (ROIs) serve as the primary basis for diagnostic evidence, while whole-slide image (WSI)-level tasks primarily capture aggregated patterns. To extract these critical morphological features, ROI-level Foundation Models (FMs) based on Vision Transformers (ViTs) and large-scale self-supervised learning (SSL) have been widely adopted. However, three core limitations remain in their application to ROI analysis: (1) cross-magnification domain shift, as fixed-scale pretraining hinders adaptation to diverse clinical settings; (2) inadequate local-global relationship modeling, wherein the ViT backbone of FMs suffers from high computational overhead and imprecise local characterization; (3) insufficient fine-grained sensitivity, as traditional self-attention mechanisms tend to overlook subtle diagnostic cues. To address these challenges, we propose SSMamba, a hybrid SSL framework that enables effective fine-grained feature learning without relying on large external datasets. This framework incorporates three domain-adaptive components: Mamba Masked Image Modeling (MAMIM) for mitigating domain shift, a Directional Multi-scale (DMS) module for balanced local-global modeling, and a Local Perception Residual (LPR) module for enhanced fine-grained sensitivity. Employing a two-stage pipeline, SSL pretraining on target ROI datasets followed by supervised fine-tuning (SFT), SSMamba outperforms 11 state-of-the-art (SOTA) pathological FMs on 10 public ROI datasets and surpasses 8 SOTA methods on 6 public WSI datasets. These results validate the superiority of task-specific architectural designs for pathological image analysis.

Medical time series, such as electrocardiograms (ECG) and electroencephalograms (EEG), exhibit complex temporal dynamics and structured cross-channel dependencies, posing fundamental challenges for automated analysis. Conventional convolutional and recurrent models struggle to capture long-range dependencies, while Transformer-based approaches incur quadratic complexity and often introduce redundant interactions that are misaligned with the intrinsic structure of physiological signals. To address these limitations, we propose MedMamba, a principle-driven multi-scale bidirectional state space architecture tailored for medical time series classification. Our design is guided by three key inductive biases of physiological signals: spatial centralization, multi-timescale temporal composition, and non-causal contextual dependency. These principles are instantiated through a lightweight channel-mixing module for cross-channel reparameterization, multi-scale convolutional tokenization for temporal decomposition, and bidirectional Mamba blocks for efficient global context modeling with linear complexity. Extensive experiments on six benchmark datasets spanning EEG, ECG, and human activity signals demonstrate that MedMamba consistently outperforms state-of-the-art methods across diverse modalities. Notably, it achieves 85.97% accuracy on PTB and establishes new state-of-the-art performance on the challenging ADFTD dataset (54.72% accuracy and 52.01% F1-score). Strong results on long-sequence benchmarks, such as SleepEDF, further validate its capability in modeling long-range dependencies. Moreover, MedMamba achieves a speedup of 4.6x in inference, highlighting its practicality for real-time clinical deployment. These results suggest that principle-guided state space modeling offers an effective and scalable alternative to Transformer-based approaches for medical time series analysis.

Despite recent advances in state space models (SSMs) such as Mamba across various sequence domains, research on their standalone capacity for time series classification (TSC) has remained limited. We propose MambaSL, a framework that minimally redesigns the selective SSM and projection layers of a single-layer Mamba, guided by four TSC-specific hypotheses. To address benchmarking limitations -- restricted configurations, partial University of East Anglia (UEA) dataset coverage, and insufficiently reproducible setups -- we re-evaluate 20 strong baselines across all 30 UEA datasets under a unified protocol. As a result, MambaSL achieves state-of-the-art performance with statistically significant average improvements, while ensuring reproducibility via public checkpoints for all evaluated models. Together with visualizations, these results demonstrate the potential of Mamba-based architectures as a TSC backbone.

Recent advances in Deep Learning (DL) have strengthened data-driven System Identification (SysID), with Neural and Fuzzy Ordinary Differential Equation (NODE/FODE) models achieving high accuracy in nonlinear dynamic modeling. Yet, system states in these frameworks are often reconstructed without clear physical meaning, and input contributions to the state derivatives remain difficult to interpret. To address these limitations, we propose Explainable FODE (xFODE), an interpretable SysID framework with integrated DL-based training. In xFODE, we define states in an incremental form to provide them with physical meanings. We employ fuzzy additive models to approximate the state derivative, thereby enhancing interpretability per input. To provide further interpretability, Partitioning Strategies (PSs) are developed, enabling the training of fuzzy additive models with explainability. By structuring the antecedent space during training so that only two consecutive rules are activated for any given input, PSs not only yield lower complexity for local inference but also enhance the interpretability of the antecedent space. To train xFODE, we present a DL framework with parameterized membership function learning that supports end-to-end optimization. Across benchmark SysID datasets, xFODE matches the accuracy of NODE, FODE, and NLARX models while providing interpretable insights.

Vision State Space Models (SSMs) like Vim, VMamba, and SiMBA rely on complex scanning strategies to adapt sequential SSMs to process 2D images, introducing computational overhead and architectural complexity. We propose HAMSA, a scanning-free SSM operating directly in the spectral domain. HAMSA introduces three key innovations: (1) simplified kernel parameterization-a single Gaussian-initialized complex kernel replacing traditional (A, B, C) matrices, eliminating discretization instabilities; (2) SpectralPulseNet (SPN)-an input-dependent frequency gating mechanism enabling adaptive spectral modulation; and (3) Spectral Adaptive Gating Unit (SAGU)-magnitude-based gating for stable gradient flow in the frequency domain. By leveraging FFT-based convolution, HAMSA eliminates sequential scanning while achieving O(L log L) complexity with superior simplicity and efficiency. On ImageNet-1K, HAMSA reaches 85.7% top-1 accuracy (state-of-the-art among SSMs), with 2.2 X faster inference than transformers (4.2ms vs 9.2ms for DeiT-S) and 1.4-1.9X speedup over scanning-based SSMs, while using less memory (2.1GB vs 3.2-4.5GB) and energy (12.5J vs 18-25J). HAMSA demonstrates strong generalization across transfer learning and dense prediction tasks.

We study how depth, finite precision, state dimension, and chain-of-thought (CoT) affect the expressive power of multi-layer state-space models (SSMs). For the explicit-table $K$-function-composition problem, a canonical benchmark for sequential information propagation, we prove that any $L$-layer SSM solving $(L+3)$-function composition must satisfy $d^2p=Ω(N/L^3)$, where $d$ is the state dimension and $p$ is the per-scalar precision. Conversely, $K$-function composition is solved exactly by a $(K+1)$-layer generalized SSM with $d=1$ and $p=Θ(\log N)$. This gives a worst-case depth hierarchy for this formal problem family. We then distinguish post-input reasoning, in which all thought tokens are generated after the input, from input-interleaved reasoning, in which thought tokens may be inserted while the input stream is being read. Post-input reasoning does not circumvent our communication-based lower-bound pipeline, whereas input-interleaved reasoning admits bidirectional simulations with general deterministic one-pass streaming algorithms at the granularity of persistent memory. Finally, width and precision are not interchangeable under exact step-preserving simulation in the base affine-state model, but become interchangeable through the streaming-memory characterization once input-interleaved reasoning is allowed.

It remains challenging to assess driver fatigue from untrimmed videos under constrained computational budgets, due to the difficulty of modeling long-range temporal dependencies in subtle facial expressions. Some existing approaches rely on computationally heavy architectures, whereas others employ traditional lightweight pairwise graph networks, despite their limited capacity to model high-order synergies and global temporal context. Therefore, we propose HST-HGN, a novel Heterogeneous Spatial-Temporal Hypergraph Network driven by Bidirectional State Space Models. Spatially, we introduce a hierarchical hypergraph network to fuse pose-disentangled geometric topologies with multi-modal texture patches dynamically. This formulation encapsulates high-order synergistic facial deformations, effectively overcoming the limitations of conventional methods. In temporal terms, a Bi-Mamba module with linear complexity is applied to perform bidirectional sequence modeling. This explicit temporal-evolution filtering enables the network to distinguish highly ambiguous transient actions, such as yawning versus speaking, while encompassing their complete physiological lifecycles. Extensive evaluations across diverse fatigue benchmarks demonstrate that HST-HGN achieves state-of-the-art performance. In particular, our method strikes a balance between discriminative power and computational efficiency, making it well-suited for real-time in-cabin edge deployment.

Automatic violence detection from video is challenging because violent interactions may be distant, occluded, or only partially visible. Audio can provide complementary evidence for violent events that are difficult to recognize from visual information alone. However, audio itself may be absent, dubbed, or dominated by environmental noise, making the central challenge not whether to incorporate audio but how to adapt reliance on it according to the visual scene. We introduce \emph{AViS-Mamba}, an audiovisual Mamba-based architecture in which the visual stream directly governs the behavior of the audio stream. At each layer of the audio encoder, a compact visual representation produces a modulation vector that conditions the encoder's internal temporal operators together with a routing gate that regulates the strength of this visual intervention. Rather than fusing or reweighting features after they have been extracted, visual context directly shapes the temporal dynamics of the audio encoder. We further propose Adaptive AV-InfoNCE, a contrastive objective that learns to balance the audio-to-video and video-to-audio alignment directions rather than weighting them uniformly. On the audio-valid NTU-CCTV and DVD benchmarks, AViS-Mamba establishes state-of-the-art results, attaining 88.59% and 75.74% accuracy. We demonstrate that adaptive visual conditioning consistently outperforms fixed routing and improves performance under degraded and missing-audio conditions. Layer-wise analysis further reveals that the model adapts the audio stream selectively across network depth rather than applying a single global routing policy.

End-to-end OCR for historical newspapers remains challenging, as models must handle long text sequences, degraded print quality, and complex layouts. While Transformer-based recognizers dominate current research, their quadratic complexity limits efficient paragraph-level transcription and large-scale deployment. We investigate linear-time State-Space Models (SSMs), specifically Mamba, as a scalable alternative to Transformer-based sequence modeling for OCR. We present to our knowledge, the first OCR architecture based on SSMs, combining a CNN visual encoder with bi-directional and autoregressive Mamba sequence modeling, and conduct a large-scale benchmark comparing SSMs with Transformer- and BiLSTM-based recognizers. Multiple decoding strategies (CTC, autoregressive, and non-autoregressive) are evaluated under identical training conditions alongside strong neural baselines (VAN, DAN, DANIEL) and widely used off-the-shelf OCR engines (PERO-OCR, Tesseract OCR, TrOCR, Gemini). Experiments on historical newspapers from the Bibliotheque nationale du Luxembourg, with newly released >99% verified gold-standard annotations, and cross-dataset tests on Fraktur and Antiqua lines, show that all neural models achieve low error rates (~2% CER), making computational efficiency the main differentiator. Mamba-based models maintain competitive accuracy while halving inference time and exhibiting superior memory scaling (1.26x vs 2.30x growth at 1000 chars), reaching 6.07% CER at the severely degraded paragraph level compared to 5.24% for DAN, while remaining 2.05x faster. We release code, trained models, and standardized evaluation protocols to enable reproducible research and guide practitioners in large-scale cultural heritage OCR available at https://github.com/MarcoPerson/ssm-ocr-benchmark.

Transformers excel at in-context retrieval but suffer from quadratic complexity with sequence length, while State Space Models (SSMs) offer efficient linear-time processing but have limited retrieval capabilities. We investigate whether hybrid architectures combining Transformers and SSMs can achieve the best of both worlds on two synthetic in-context retrieval tasks. The first task, n-gram retrieval, requires the model to reproduce an n-gram that succeeds the query within the input sequence. The second task, position retrieval, presents the model with a query token and requires it to perform a two-hop lookup: first locating the corresponding element in the sequence, and then outputting its positional index. Under controlled conditions, we assess data efficiency, length generalization, robustness to out of domain training examples, and learned representations across Transformers, SSMs, and hybrid architectures. We find that hybrid models outperform SSMs and match or exceed Transformers in terms of data efficiency and extrapolation for tasks that require precise information retrieval from the input context. However, Transformers maintain superiority in position retrieval tasks. Through representation analysis, we discover that SSM-based models develop locality-aware embeddings where tokens representing adjacent positions become neighbors in embedding space, forming interpretable structures. This property is absent in Transformers as causal attention is sufficient for acquiring positional associations, and the introduction of positional encoding amplifies this behavior, leading to improvement in data efficiency. SSMs on the other hand update their internal representations incrementally and without positional encodings, are required to learn these associations. Our findings reveal fundamental differences in how Transformers and SSMs, and hybrid models learn positional associations.

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.

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.

Image super-resolution (SR) is a critical technology for overcoming the inherent hardware limitations of sensors. However, existing approaches mainly focus on directly enhancing the final resolution, often neglecting effective control over error propagation and accumulation during intermediate stages. Recently, Mamba has emerged as a promising approach that can represent the entire reconstruction process as a state sequence with multiple nodes, allowing for intermediate intervention. Nonetheless, its fixed linear mapper is limited by a narrow receptive field and restricted flexibility, which hampers its effectiveness in fine-grained images. To address this, we created a nonlinear state predictive control model \textbf{MambaX} that maps consecutive spectral bands into a latent state space and generalizes the SR task by dynamically learning the nonlinear state parameters of control equations. Compared to existing sequence models, MambaX 1) employs dynamic state predictive control learning to approximate the nonlinear differential coefficients of state-space models; 2) introduces a novel state cross-control paradigm for multimodal SR fusion; and 3) utilizes progressive transitional learning to mitigate heterogeneity caused by domain and modality shifts. Our evaluation demonstrates the superior performance of the dynamic spectrum-state representation model in both single-image SR and multimodal fusion-based SR tasks, highlighting its substantial potential to advance spectrally generalized modeling across arbitrary dimensions and modalities.

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.

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.

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.

Selective State-Space Models (SSMs) such as Mamba have become central to long-sequence modeling. Still, their stability is poorly understood: their state-space coefficients are modulated online by a token-dependent gating signal, making the recurrence neither linear time-invariant nor classically nonlinear. We study continuous-time selective SSMs through passivity, dissipativity, and Input-to-State Stability (ISS), explicitly separating the selection signal $x(\cdot)$ from the driving input $u(\cdot)$. We obtain four results: exponential forgetting under strict dissipativity; a canonical $\mathrm{AUC}_{\mathrm{loc}}$ quadratic storage for the frozen-selection subsystem that accommodates discontinuous gating; a parametric LMI together with universal kernel constraints and "irreversible forgetting" under universal quadratic storage; and sufficient conditions for global ISS uniformly over admissible selection schedules. We then bridge to practice by deriving a sampled block LMI for the Mamba selective-scan core, which is used as a differentiable training-time regularizer. Across seven standard time-series datasets and four prediction horizons, the regularizer reduces sampled Mamba-core LMI violations by roughly $92\%$ in $28/28$ pairs at a clean-MSE cost of less than $0.018\%$. It improves internal Mamba passivity and state-norm diagnostics under injected perturbations. Our results turn classical control-theoretic tools into verifiable structural and training criteria for selective SSMs, while honestly scoping which guarantees transfer to a deep selective-scan architecture.

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.

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.

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.