State Space Models

State--space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state--space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation--Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state--space modeling and SAEM-based inference in interference-dominated imaging scenarios.

End-to-end OCR increasingly relies on autoregressive sequence models, where the quadratic cost of Transformer attention limits efficient transcription of long, paragraph-level text. State-Space Models (SSMs) such as Mamba offer linear-time decoding and have recently been shown to match Transformer accuracy on printed historical lines, but their behavior as sequences grow from short lines to full paragraphs, and their generalization to handwriting, remain poorly understood. We study how a Mamba-based OCR recognizer scales from lines to paragraphs. We first conduct a systematic exploration of its four core hyperparameters (decoder depth, state dimension, expansion factor, and connector depth) on synthetic paragraphs from 100 to 1,000 characters, identifying the recurrent state dimension and the expansion factor as the dominant levers for long-sequence accuracy. We then compare the recognizer against a Transformer baseline trained under an identical protocol. On clean synthetic paragraphs, both models stay below 1% CER at every length while the SSM runs 1.4 to 4.5 times faster, the speedup growing with sequence length. On real handwriting, however, the SSM lags clearly behind: it reaches 8.2% CER on IAM lines and 10.0% on IAM paragraphs, against 4.2% and 3.5% for the Transformer baseline. Through controlled experiments we show that a substantial part of this gap stems from data scarcity rather than from an intrinsic architectural limit: the autoregressive SSM decoder is markedly data-hungry on long sequences. Our study clarifies when SSMs are a practical choice for large-scale document transcription and when they are not.

While recent advancements in anomaly detection have demonstrated the efficacy of CNN- and Transformer-based approaches, these architectures face inherent limitations: CNNs struggle to capture long-range dependencies, whereas Transformers suffer from quadratic computational complexity. Consequently, Mamba-based architectures have attracted considerable attention, as they successfully combine superior long-range dependency modeling with linear computational complexity. By critically rethinking the structural evolution across the Mamba lineage 1-3 series, this paper proposes MambaADv2, a framework tailored for multi-class unsupervised anomaly detection. MambaADv2 comprises a pre-trained encoder and a Mamba-inspired decoder, equipped with Duality-enhanced State Space (DSS) modules across multiple scales. The proposed DSS module effectively models both global dependencies and local representations by integrating parallel-cascaded Hybrid State Space (HSS) blocks and frequency-enhanced convolution operations. The structure of the Hybrid State Space (HSS) block is tailored by following the SSD-based Mamba lineage and incorporating Mamba3-style position-aware state-space modeling, leveraging the dual computational paths of linear recurrence and parallel matrix formulation to model local continuity and global contextual comparison, thereby better serving the core anomaly detection objective of precisely reconstructing normal representations while magnifying anomalous deviations. Additionally, we propose a semantics-adaptive progressive scanning strategy that decays scanning complexity along the feature pyramid.

Real-time weld-pool perception is critical for closed-loop control in laser wire-feed welding, where sensing, computation, and actuator response introduce unavoidable delay. This paper presents a physics-guided spatiotemporal state space network for lookahead weld-pool segmentation. The model uses historical coaxial grayscale images, welding process parameters, and aligned wire-state electrical signals to predict the future semantic layout of three physically meaningful regions: keyhole, wire, and molten pool. It combines a visual encoder, process- and sensor-conditioned feature normalization, patch-level temporal state space modeling, horizon-conditioned latent prediction, dense future feature prediction, and a motion-aware mask decoder. Auxiliary signed-distance-function supervision, temporal consistency, feature distillation, and fine-grained keyhole losses further constrain the predicted geometry and local motion. Experiments on a 43-sequence laser welding dataset show that the proposed WeldMamba reaches 74.63% mIoU at a 500 ms lookahead. Ablation studies further show that temporal history, patch-level state space modeling, and keyhole motion awareness are the main contributors to robust future segmentation.

Remote photoplethysmography (rPPG) is a camera-based technique for measuring physiological signals, particularly cardiac activity. From the remotely measured signals, heart rate can be estimated, which is crucial for health monitoring. In this study, we investigate a driver health monitoring system based on remote heart rate estimation. However, driving environments represent uncontrolled settings where videos are subject to varying illumination conditions and frequent head movements. We introduce MS-rPPG, a multi-spectral framework that combines RGB with near-infrared (NIR) face video to alleviate rPPG estimation under challenging driving conditions. To combine the complementary features from two spectral videos, we propose a cross-spectral linear modulation (CSLM) strategy based on frequency-domain analysis. Moreover, we introduce MS-Mamba, a novel state space model designed to effectively model long-range temporal dependencies while jointly capturing cross-channel interactions between multi-spectral features. We collected a real-world dataset called MS-Drive, which was recorded from 50 participants while driving the vehicle. The proposed method was evaluated on the MR-NIRP Car dataset and MS-Drive datasets. The experimental results indicate that MS-rPPG shows better robustness and heart rate estimation accuracy than previous methods, highlighting its promise for driver health monitoring. The codes are available at github.com/ziiho08/MS-rPPG.

In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.

Decision-making under partial or adversarial observability requires accurate inference of the environment's latent state and its associated uncertainty. This work analyses adversarial attacks on linear probabilistic state-space models, commonly integrated within reinforcement learning architectures, where the attacker alters observations under likelihood constraints that ensure the perturbations remains consistent. We analyze how such adversarial yet realistic observation shifts influence the latent state and influence policy decisions. This perspective provides a principled pathway toward building more robust reinforcement learning systems, with direct relevance to safety-critical domains such as robotics, where reliable operation under sensor noise, partial failures, and adversarial conditions is essential.

Modeling long-sequence medical time series data, such as electrocardiograms (ECG), poses significant challenges due to high sampling rates, multichannel signal complexity, inherent noise, and limited labeled data. While recent self-supervised learning (SSL) methods, based on various encoder architectures such as convolutional neural networks, have been proposed to learn representations from unlabeled data, they often fall short in capturing long-range dependencies and noise-invariant features. Structured state space models (S4) excel at long-sequence modeling, but existing S4 architectures fail to capture the unique characteristics of multichannel physiological waveforms. In this work, we propose SL-S4Wave, a self-supervised learning framework that combines contrastive learning with a tailored encoder built on structured state space models. The encoder incorporates multi-layer global convolution using multiscale subkernels, enabling the capture of both fine-grained local patterns and long-range temporal dependencies in noisy, high-resolution multichannel waveforms. Extensive experiments on real-world datasets demonstrate that SL-S4Wave (1) consistently outperforms state-of-the-art supervised and self-supervised baselines in a challenging arrhythmia detection task, (2) achieves high performance with significantly fewer labeled examples, showcasing strong label efficiency, and (3) maintains robust performance on long waveform segments, highlighting its capacity to model complex temporal dynamics in long sequences that most existing approaches fail to efficiently model, and (4) transfers effectively to unseen arrhythmia types, underscoring its robust cross-domain generalization. We additionally evaluate SL-S4Wave on multiple EEG tasks, achieving superior performance over strong baselines, demonstrating generalizability of our approach beyond cardiac waveforms.

State Space Models (SSMs) such as Mamba-2 offer linear-time inference but their memory footprint limits edge deployment. Prior ternary SSM work (Slender-Mamba) trains from scratch on 150B tokens; we show a pretrained checkpoint suffices, reducing the marginal token budget by 1,000x. Using grouped quantization-aware training (QAT) with knowledge distillation from a frozen FP16 teacher, we compress Mamba-2 1.3B to 3.61x (2,687 to 744 MB) and achieve 48.1% zero-shot accuracy (7-task average) in just 102M tokens (4 GPU-hours, single H100) -- approaching Bi-Mamba's 48.4% (within +/-0.9pp CI). This QAT-from-pretrained setting reveals zero-ratio collapse, a novel instability caused by learnable quantization scales that does not arise in from-scratch training. We further show that post-hoc correction strategies effective for Transformers fail for SSMs due to error accumulation through the recurrence. These results demonstrate that ternary SSMs do not require expensive from-scratch training: QAT from pretrained checkpoints with KD is a data-efficient alternative.

Structured State Space Models (SSMs), including the S4 and S4D architectures, have recently emerged as powerful alternatives to attention-based models for capturing long-range dependencies in sequential data. Despite their strong empirical performance, deploying these models in time- and resource-constrained settings remains challenging due to their computational and memory demands. In this paper, we propose a novel incremental, operator-level pruning approach for S4- and S4D-based models that significantly reduces inference cost while preserving predictive performance. To the best of our knowledge, this is the first work to systematically investigate structured operator pruning for SSMs. Our method progressively prunes model operators by interleaving structured masking with fine-tuning, while jointly monitoring accuracy and inference latency. We implement this approach within a unified training and evaluation framework that enables systematic exploration of efficiency-accuracy trade-offs. Experiments across multiple benchmark datasets show that pruning up to 70% of the model operators preserves the performance of the original models in most cases, while substantially reducing inference latency. These results demonstrate that structured operator pruning is an effective and previously unexplored strategy for improving the efficiency of SSMs and facilitate their deployment in practical, resource-constrained scenarios.

Mamba-based state space models offer linear-time long-range modeling for high-resolution dense prediction, but sequential state-space propagation can attenuate boundary-sensitive and detail-sensitive responses that are critical in multi-class semantic segmentation. We propose Reload-Mamba, a semantic segmentation framework that addresses this propagation-induced response dilution through three segmentation-specific designs: (i) a boundary-supervised local detail prior that is explicitly trained with ground-truth boundary masks to identify regions requiring response restoration; (ii) a class-uncertainty-aware Reload Gate that incorporates per-pixel class entropy from a pre-reload auxiliary head as an additional gating signal, a formulation that is informative only under multi-class dense prediction; and (iii) a hierarchical multi-level Reload mechanism that applies anti-dilution refinement at three decoder levels and fuses the restored representations top-down. Built upon a ConvNeXt-Tiny encoder with a multi-scale decoder and four-directional Mamba scanning with pixel-wise directional attention, Reload-Mamba achieves 47.9% single-scale (48.9% multi-scale) mIoU on ADE20K and 83.2% single-scale mIoU on Cityscapes. With ResNet-101 + COCO pre-training under the standard DeepLab-style protocol, Reload-Mamba reaches 87.8% mIoU on PASCAL VOC 2012 val. Controlled ablations show that each of the three segmentation-specific designs contributes beyond a direct port of the prior anti-dilution architecture proposed for binarization, cumulatively improving over the direct-port baseline by +2.2 mIoU on ADE20K.

Text-guided Open-vocabulary Object Counting (TOOC) aims to estimate the number of objects described by text prompts, which is particularly challenging in dense scenes with large scale variations. Existing TOOC approaches predominantly rely on Transformers, whose quadratic complexity with respect to image resolution limits their scalability. Mamba offers a promising alternative due to its linear complexity. However, previous Mamba-based methods have two main limitations. On the one hand, the inherent causal formulation of Mamba constrains the bidirectional spatial dependency modeling required by non-causal vision tasks. On the other hand, existing Mamba-based vision models often overlook the unconstrained high entropy in the spatial token responses, which can weaken local details and high-frequency cues. To address these limitations, we propose MambaCount, an efficient framework built on the Spatial Sparse State Space Duality (S^4D) block. Specifically, we analyze and reconstruct the decay dynamics of hidden states in Mamba to alleviate the dependency constraints introduced by causal modeling. Moreover, we introduce a Spatial Token Selection (STS) sub-block to reduce the unconstrained high entropy in spatial token responses within Mamba. In addition, we design Multi-Granularity Prototypes (MGP) to identify object-like regions at different semantic levels, improving cross-modal alignment and interpretability. Extensive experiments on FSC-147 demonstrate that MambaCount achieves state-of-the-art performance among methods without secondary querying, obtaining a test MAE of 12.23, while retaining linear complexity.

State-space models (SSMs) are the standard formalism for Bayesian treatment of dynamical systems, with natural applications in statistics, signal processing, and machine learning. Despite their importance in both theory and application, dynamical systems have proven difficult to incorporate in modern probabilistic programming languages (PPLs), making state-of-the-art methods less accessible to practitioners and introducing friction in following the "Bayesian workflow." We introduce dynestyx, a probabilistic programming library with first-class support for SSMs, including state-of-the-art methods in the estimation of both states and parameters. Through a single, unified interface, users may specify arbitrary priors for discrete-time or continuous-time dynamical systems, perform inference over mixed-effect data, and make state and parameter estimates with principled uncertainty quantification.

Fine-grained action recognition demands temporal reasoning that general-purpose architectures address through different cost-accuracy tradeoffs: 3D dense operators couple computation to the input volume, while difference-based methods approximate motion through rigid, hand-crafted subtraction of uncontextualized features - each reflecting a deliberate design choice with corresponding limitations in expressiveness or flexibility. We present MamBOA, a backbone-agnostic temporal framework built upon a novel interleaved scan structure that recasts the selective state-space recurrence (S6) as a native motion synthesizer. By interleaving consecutive feature representations extracted from a pretrained backbone into a single alternating sequence, the proposed scan structurally drives the recurrence to encode both temporal observations of each position within a shared hidden state, separated by only a single decay step - rendering the inter-frame transition an intrinsic component of the state dynamics rather than an externally computed quantity. A cascade of dedicated alignment and decoding operations then distills this joint encoding into an explicit motion representation, which a dual-path pooling mechanism adaptively aggregates by balancing attention-driven selection with uniform temporal coverage. The framework interfaces seamlessly with CNN, Transformer, and Mamba backbone families, adding only ~2.1 GFLOPs per feature pair. On Diving48, MamBOA achieves 85.02% Top-1 accuracy with an image-pretrained backbone and 86.24% with a video-pretrained backbone processing the entire video in a single forward pass - demonstrating that structurally induced state-space dynamics constitute a principled and general foundation for motion modeling.

Document image binarization aims to separate foreground text from degraded backgrounds while preserving thin, broken, and low-contrast strokes. Although deep learning methods have improved binarization performance, most existing approaches rely on convolutional, transformer-based, or generative architectures, while Mamba-based state space models remain largely unexplored for this task. In this work, we investigate Mamba-based feature propagation and observe that direct state-space propagation may dilute weak foreground cues during long-range modeling, especially faint ink traces, fragmented characters, and boundary-sensitive stroke details. To address this problem, we propose DeepMine-Mamba, a Mamba-based binarization framework equipped with a novel Anti-Dilution Gate that estimates propagation-induced feature changes and selectively restores stroke-sensitive local responses while suppressing unnecessary background enhancement. Experiments on DIBCO/H-DIBCO benchmarks under a strict leave-one-year-out protocol show that DeepMine-Mamba achieves competitive overall performance, with strong average FM and Fps across benchmark years. Ablation results further show that the Anti-Dilution Gate is the key component for mitigating propagation-induced foreground dilution and improving stroke preservation.

Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables. Existing state-space models process time series by scanning tokenized temporal or spatial sequences, discarding the evolutionary geometric structure. We address this limitation by introducing manifold constraints into state-space modeling: treating the cross-variable correlation structure as a continuous trajectory on the symmetric positive definite manifold, whose Riemannian geometric features, tangent space linearity, and Frechet mean centrality act as a principled geometric regularizer that guides and stabilizes the selective scanning dynamics of SSMs. We propose SPDM, a geometry-aware SSM architecture that realizes this principle through two cooperating mechanisms: a manifold trajectory path that projects dynamically evolving covariance matrices from the SPD manifold to a Euclidean tangent space, and a geometric gating scheme that directly modulates SSM's internal selective parameters based on geometric signals derived from the manifold trajectory. The parameterization preserves the linear-time complexity of the Mamba parallel scan while embedding rich structural constraints, making the architecture preserve prediction accuracy and computational efficiency simultaneously. Extensive experiments on eleven real-world benchmark datasets establish state-of-the-art forecasting performance, and further studies confirm that geometrically constrained state-space dynamics are the dominant architectural factor behind its performance gains.

Medical knowledge graphs (MKGs) infused with clinical knowledge have been increasingly used to model electronic health records (EHRs) to support interpretable predictions in healthcare domain. However, existing MKG-based approaches are limited in capturing pairwise relations between clinical concepts (e.g., conditions, procedures, and medications), and restricts their ability to model higher-order interactions among co-occurring or semantically related concepts. In addition, most representation learning methods that leverage MKGs either collapse temporal information across visits or lack an explicit mechanism for modeling long-range temporal dependencies, which is critical for clinical tasks such as mortality prediction. To mitigate these limitations, we propose HoT-SSM, a parameter efficient and higher-order temporal graph reasoning with state space models. For each visit, HoT-SSM constructs hypergraphs by grouping semantically related clinical concepts into hyperedges using domain knowledge, thereby preserving visit-level clinical context. Further, to model the temporal dynamics while learning the representations, we introduce a novel dynamic hypergraph-based state space model that explicitly captures patients latent state evolution over time while preserving long-range information. The learned representations are used for downstream clinical prediction and reasoning. Experiments on MIMIC-III and MIMIC-IV datasets shows significant performance improvement over the current state-of-the-art models, demonstrating the effectiveness of jointly modeling higher-order clinical interactions and long-range temporal dependencies.

Koopman theory turns nonlinear dynamics into a linear spectral problem. In computation, however, everything depends on a hard finite-dimensional choice: the observables must be expressive, nearly invariant under the dynamics, and, ideally, compatible with composition. Deep Koopman methods learn flexible coordinates, whereas structure-preserving methods enforce operator identities on fixed dictionaries. We combine these ideas by introducing Deep Embedded Multiplicative Dynamic Mode Decomposition (DeepMDMD), a method that learns a latent space and a partition of it, while enforcing the Koopman product rule as an exact algebraic constraint. Training alternates between an exact multiplicative operator update and a differentiable latent-clustering step that promotes Koopman closure. The result is a finite transition map on learned latent cells. Its nonzero spectrum lies on the unit circle, its dictionary is shaped by the dynamics rather than by ambient geometry, and forecasts are made in latent coordinates before being decoded to physical space. Across Hamiltonian, chaotic, and fluid examples, DeepMDMD learns dictionaries that are far more compact and dynamically coherent than those produced by geometric MDMD partitions. It reduces spectral pollution, reveals richer continuous-spectrum structure, and gives stable forecasts under severe noise. In high-dimensional flows, including a 158,624-dimensional cylinder wake and a noisy $Re=20,000$ lid-driven cavity, it preserves coherent structures and long-time spectral statistics where state-space MDMD fails. These results suggest a practical rule for Koopman learning: learn the coordinates, constrain the algebra.

We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state-space dynamics. This is achieved by simultaneous training of the AE and the state-space model. In addition, we extend the discrete ROM formulation to a sequence-based model, which processes state and input histories to improve prediction accuracy while preserving the control-affine structure. We motivate our framework by applying feedback linearization to the derived models, and we present guidelines for its efficient use. The proposed framework is assessed on two numerical examples and its performance is compared to a baseline model, where the AE identifies a latent space with linear state-space dynamics. The assessment involves evaluating the prediction accuracy of the ROM on test data and its effectiveness in controlling the system to a desired state or trajectory.

The Transformer's quadratic complexity with input length imposes an unsustainable computational load on large language models (LLMs). In contrast, the Selective Scan Structured State-Space Model, or Mamba, addresses this computational challenge effectively. This paper explores a query-based cross-modal projector designed to bolster Mamba's efficiency for vision-language modeling by compressing visual tokens based on input through the cross-attention mechanism. This innovative projector also removes the need for manually designing the 2D scan order of original image features when converting them into an input sequence for Mamba LLM. Experimental results across various vision-language understanding benchmarks show that the proposed cross-modal projector enhances Mamba-based multimodal LLMs, boosting both performance and throughput.

Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs (CTDG-SSM) from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator (CTT-HiPPO), a novel memory-based reformulation of HiPPO to jointly encode temporal dynamics and graph structure. The solution from CTT-HiPPO is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs (CTDG-SSM). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation. Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, CTDG-SSM achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.

Correspondence pruning aims to identify inliers from an initial set of correspondences. Most existing Graph Neural Network (GNN)-based methods rely on geometric features mapped from coarse Euclidean coordinates, which struggle to capture the subtle geometric consistencies presented by inliers. While Mamba-based methods possess global receptive fields and long sequence modeling capabilities, they tend to accumulate substantial inconsistent features within the hidden state space, making it difficult to distinguish inliers from outliers. In this paper, we integrate frequency domain perception into this task for the first time and propose SFMambaNet, a novel Spectral-Frequency enhanced Mamba-based two-view correspondence pruning network. Our method is collaboratively composed of two components: First, we design a Local Spectral-Geometric Attention (LSGA) block. LSGA incorporates spectral positional encoding into local graph interactions and introduces multi-scale Mamba processing to enhance the capture of subtle geometric consistencies and improve local feature discriminability. Building upon this, we design a Spectral-Integrated Global Mamba (SIGM) block. SIGM embeds a frequency gating mechanism within the state space, utilizing the frequency information provided by LSGA to explicitly suppress high-frequency noise accumulation within hidden states and mitigate the propagation of inconsistent features. This enhances inlier-outlier separability and achieves robust global context modeling capabilities with nearly linear complexity. Extensive experiments demonstrate that SFMambaNet outperforms current state-of-the-art methods on several challenging tasks. The code is available at https://github.com/Kirito14IT/SFMambaNet.

In multi-modal image registration, the primary challenge lies in shared structural information extraction. Compared to Transformers, Structured State Space Duality (SSD) offers greater global structural feature extraction with higher efficiency during training and inference. Inspired by these advantages, we propose a novel algorithm for multi-modal image registration, named RegNetMamba-2. Our algorithm incorporates SSD into coarse-to-fine matching process to extract local and global structural features effectively. Firstly, SSD is applied in three different scales for multi-modal feature extraction in our network. To strengthen local representation, we pay more attention on foreground edge and structural information by feature scaling function of SSD. Secondly, for shared feature extraction of input images and multi-modal feature fusion in all scales, we propose cross-modality feature fusion model based on SSD, consisting of Cross-Modality feature Interaction (CMI) module and Multi-Scale feature Fusion (MSF) module. CMI module is designed for cross-modality feature extraction of each scale by SSD in cross form. MSF module is designed to employ a progressive upward fusion in feature-level to obtain fine features, consisting of multi-modal features in all scales. Following coarse-to-fine, the features in 1/8 scale from CMI and 1/2 scale from MSF are collected to calculate matching probability scores. Then we respectively establish matching process by correspondences of pixel-wise. Extensive experiments demonstrate that comparing with state-of-the-art deep-learning based algorithms, RegNetMamba-2 has achieved good effects in both performance and efficiency for multi-modal image registration on the following datasets: VIS-SAR (OSDataset), VIS-IR (LGHD/RoadSence) and VIS-NIR (RGB-NIR sense).

State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy. Black-box deep learning has shown promise as an alternative. However, these methods rely on the availability of large datasets and potentially available physical knowledge is neglected. We propose the PG-RSSNN, a physics-guided recurrent state-space neural network that incorporates recurrent structures to enable the use of non-saturating activation functions in multi-step prediction. It mitigates the vanishing gradients and eliminates the risk of numerical divergence in training seen in existing structures that feed back state estimates. Results across multiple systems with various physical model imperfections, from linear state-space models with Gaussian noise to a robotic arm and a cascaded water tank system, show that the proposed PG-RSSNN maintains stable training behavior, and improves multi-step predictions, as compared with black-box neural networks and physics-only models, even with limited training data and when physical models are only partially known.

The detection and segmentation of infrared small targets have important application significance in the fields of surveillance and security, maritime rescue and so on. Due to the low occupancy of these targets in long-distance imaging, the mainstream visual state space model is inefficient and difficult to accurately model the target edge. The existing infrared state space models do not deviate from the mainstream visual state space structure framework from the structural properties of infrared small targets. In order to solve this problem, this paper proposes the RPCASSM network based on the model paradigm of robust principal component analysis(RPCA), which aims to design the background state space module(BSSM) and the target state space module(TSSM) by the nature of the infrared small target in the spatial domain. The BSSM aims to use the saliency of spatial heterogeneous signals to design a spatial probe scanning mechanism(SPCM) to model background information. The TSSM designs a deformable prompt scanning mechanism(DPCM) by using the sparsity and local highlight of the target to focus on the deformable space of the target for state space modeling. According to the above design, we effectively solve the problem that the existing mainstream vision state space model is difficult to accurately model the edge structure of infrared small target. Experimental results on the existing benchmark data sets prove the effectiveness of the RPCASSM design. Our code will be made public at \href{https://github.com/PepperCS/RPCASSM}{RPCASSM}.

Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings. However, modern-sized datasets have made overparameterized deep networks the preferred methods of choice due to their predictive power and favorable computational scaling. While many posterior approximations exist, all incur approximation errors. Recent work accounts for this error in the form of computational uncertainty but comes at the cost of quadratic complexity and assumes fixed model hyperparameters. Here we extend this development to model selection, including a novel training loss and optimization scheme, which yields tractable inference in large state-spaces. We introduce a framework, the Computation-Aware State-Space Model (CASSM), specifically designed for the scale-imbalanced regime, where the number of trials is significantly lower than the number of recorded neurons. In this regime, for both synthetic and real data, we show that our method is competitive with data-hungry deep networks, with significantly improved uncertainty calibration over previous attempts to scale Bayesian methods. Our experiments provide a roadmap to neuroscience researchers in choosing from a host of potential dynamical latent variable models given key dataset properties and constraints.

We present Harmonic, a hierarchical state space model (SSM) for language modeling. The architecture stacks three recurrent levels at progressively slower timescales; each level receives the prediction error of the level below as input, rather than its raw hidden state. On enwiki8 with equal token budgets, Harmonic outperforms a comparable Transformer (28M params) by +1.4% at 1K tokens, +6.7% at 8K tokens, and +11.4% at 32K tokens (bpt, lower is better). It also outperforms Mamba at every tested length by 0.7--1.8%. At 64K tokens, both Mamba and Transformer run out of memory on an 80GB H100; Harmonic trains successfully, reaching 6.169 bpt. Results replicate on WikiText-103 (H-TF gap +1.7% to +7.2% across 1K--32K). At 1B parameter scale, replacing all attention layers in TinyLlama 1.1B with HarmonicBlock eliminates the RoPE positional encoding limit: the resulting Hallamonic model maintains stable loss across sequence lengths 1K--8K on two independent clean benchmarks (Lambada and fineweb-edu held-out), while TinyLlama degrades catastrophically past its 2K-token RoPE limit (gap: +9.4 bpt at seq=8K on Lambada). Compute is O(L) per forward pass vs. O(L^2) for attention. Logs: https://github.com/Omibranch/harmonic-logs.

Energy consumption prediction is essential for efficient grid management, demand-side optimization, and sustainable energy planning. Although advanced machine learning methods have been employed for better prediction performance, existing works have two key limitations: (1) they usually formulate this task as a purely time-series prediction problem without explicitly modeling the spatial dependencies among different regions, and (2) they fail to provide reliable predictions with uncertainty estimates under abnormal situations such as extreme weather events. To advance existing research, we propose EnergyMamba, an uncertainty-aware spatiotemporal learning framework for accurate and reliable energy consumption prediction, which comprises two key components: (i) a novel Graph-Enhanced Selective State Space Model (GE-Mamba) that injects spatial context learned from the grid topology into the temporal dynamics, enabling coupled spatiotemporal modeling, and (ii) an Adaptive Sequential Conformalized Quantile Regression (AS-CQR) module, which includes locally adaptive normalization and an online feedback mechanism to dynamically calibrate prediction intervals under potential distribution shifts. We evaluate EnergyMamba on four large-scale real-world datasets from Florida, New York, and California. Results show EnergyMamba achieves around 5% improvement in prediction accuracy and 6% improvement in uncertainty quantification over 15 state-of-the-art baselines.

Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering. Physics-informed neural networks (PINNs) learn PDE solutions from governing equations. However, accurately capturing temporal evolution remains challenging. Recent sequence-model-based approaches parameterize time evolution using general-purpose sequence models, which capture temporal dependencies but do not explicitly encode the structured dynamics of PDE solutions. In addition, their memory requirements can scale unfavorably with sequence length and resolution, limiting applicability in large-scale or high-dimensional settings. This work introduces a PINN approach that incorporates oscillatory state-space dynamics to represent the modal structure of PDE solutions. The proposed method leverages a linear-oscillator-based temporal evolution, together with a PDE-aware spectral basis in space. This design enables closed-form spatial differentiation and consistent enforcement of boundary conditions. The method is evaluated on forward, inverse, and high-dimensional PDE problems, including cases up to 100 spatial dimensions. The results show improved accuracy and reduced memory usage compared to recent sequence-model-based PINN approaches. Overall, this work highlights the benefits of incorporating structured dynamical priors into the temporal evolution of neural PDE solvers and suggests designing more physics-aligned and computationally efficient PINN architectures.

Electroencephalography (EEG) is a critical, non-invasive method to monitor electrical brain activity. EEGs can span anywhere from a couple seconds to multiple hours, posing a major hurdle for existing deep learning methods due to two major factors: (1) existing EEG models are predominantly built upon the attention mechanism, incurring quadratic scaling as the sequence length increases, and (2) raw EEG signals must be processed in a sliding-window fashion due to fixed-length input requirements, preventing global understanding of the entire signal. To this extent, we propose CaMBRAIN - the first Causal, Mamba-based state space model (SSM) capable of real-time inference of EEG signals, arguing that bidirectional approaches are needlessly expensive given the causal, unidirectional nature of EEG. However, training such a model is non-trivial, as crucial EEG events can be extremely brief - within fractions of a second - yet separated by long intervals spanning minutes. Current EEG methods use self-supervised objectives that optimize for signal reconstruction, but these are not well suited for streaming SSMs; they fail to explicitly train the hidden state to retain the salient long-range context needed for streaming inference. We therefore introduce a multi-stage self-supervised training pipeline specifically tailored to encourage long-range memory retention and strong performance on EEG signals, while preserving the linear-time complexity of state space models. CaMBRAIN achieves state-of-the-art (SOTA) results across 3 different EEG datasets with >10x higher throughput than existing models, enabling the first model capable of long-range, continuous inference of variable-length EEG signals.

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in $W_\infty$. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

3D shape completion from partial scans remains challenging for unseen categories and noisy real-world observations, where geometry alone is often insufficient for inferring missing structure. We present DinoComplete, a deterministic and efficient shape completion framework that augments geometric reconstruction with voxel-aligned semantic priors distilled from DINO features. First, we construct multi-view DINO feature volumes aligned with ShapeNet data and train a student network to predict dense semantic features directly from incomplete shapes. These predicted features capture global structure and part-aware semantic context while remaining aligned with the underlying geometry. We then integrate these distilled features into a completion network, where geometric and semantic voxel representations are fused through voxel state-space modeling. To enable efficient long-range reasoning without sacrificing resolution, we introduce a multi-scale voxel Mamba module that refines the fused features by combining full-grid and chunk-wise sequence modeling. Experiments on unseen ShapeNet categories and ScanNet objects show that DinoComplete achieves stronger completion quality than prior deterministic and generative based completion methods while using fewer parameters, requiring lower memory, and achieving faster inference. Our results demonstrate that distilling semantic priors from visual foundation models improves generalization and robustness in 3D shape completion.

High-fidelity 3D Gaussian head avatar generation is critical for applications such as AR/VR, telepresence, and digital humans. Existing methods depend on multi-view datasets, 3D captures, or intermediate 2D view synthesis. In contrast, we learn both conditional and unconditional 3D head models from randomly sampled 2D images alone, without using multi-view data, 3D supervision, or intermediate view generation. We introduce MVCHead, a single-shot state space model that enforces multi-view consistency (MVC) directly in the 3D representation while regressing 3D Gaussians under these constraints. At its core, we propose a Hierarchical State Space (HiSS) block that progressively refines Gaussians from coarse to fine, while capturing long-range dependencies. Within each HiSS block, we modify Mamba's standard unidirectional scan with the proposed Hierarchical Bi-directional State Scan (HiBiSS) that aligns recurrence with the axes along which multi-view inconsistencies are strongest. Finally, we design an SE(3) Multi-view Critic that judges whether a set of self-renders arises from a single underlying 3D configuration, rewarding cross-view pixel alignment without observing real multi-view pairs. MVCHead achieves state-of-the-art perceptual quality, surpasses prior methods in both texture and geometric consistency, and maintains comparable shape consistency. To demonstrate scalability, we release FaceGS-10K, the first large-scale dataset of ready-to-use 3D Gaussian head assets for training and evaluation of 3D head models. Project Page and code: https://humansensinglab.github.io/MVCHead/

Medical time series are central to healthcare, enabling continuous monitoring and supporting timely clinical decisions. Despite recent progress, existing methods struggle to jointly model local-global dynamics and handle nonstationarities like baseline drift, while often failing to capture latent channel interactions. To address these challenges, we propose MedMamba, an end-to-end architecture that integrates state space models with domain-specific inductive biases. Specifically, MedMamba first employs multi-scale convolutional embeddings to capture discriminative local morphology. Second, to mitigate nonstationarity, we introduce a tri-branch differential state space encoder that processes raw, temporal-difference, and frequency-domain views, fusing them to emphasize informative patterns while suppressing drift. Furthermore, to uncover latent channel correlations, we design a spatial graph Mamba module that learns a directed dependency structure regularized toward sparsity and acyclicity, which obviates the need for predefined graphs. Extensive experiments on five real-world datasets demonstrate that MedMamba achieves state-of-the-art performance while maintaining linear computational complexity, and ablation studies validate each component's contribution.Code is available at https://github.com/zhangda1018/MedMamba.

Sonar imaging is the primary modality for underwater target detection, yet small targets remain difficult to detect due to insufficient pixel coverage, low acoustic contrast, and scale ambiguity across imaging ranges. CNN-based detectors extract local features efficiently but cannot suppress noise-induced false alarms without global acoustic context. Transformer-based methods capture long-range dependencies at quadratic computational cost. Existing Mamba-based vision models offer efficient linear-cost scanning but lack multi-scale semantic alignment across pyramid levels, multi-receptive-field fusion, and small-target-aware training supervision needed for reliable sonar detection. This letter proposes Mamba Dilated-Scale Fusion (MambaDSF), a hybrid framework addressing these limitations through three contributions: a Mamba Enhanced Feature Pyramid (MambaEFP) backbone that jointly captures local echo cues and global acoustic context at linear complexity; a Dilate Fusion Mamba (DFMamba) encoder that enforces multi-scale feature alignment across pyramid levels; and Scale-Adaptive Weighted IoU (SA-WIoU) and Cross-Scale Coherence (CSC) losses that stabilize small-target training. MambaDSF achieves 91.5% mAP50 on the UATD forward-looking sonar benchmark with 28.7 million parameters, surpassing all compared detectors. On a small-target subset the gain reached +2.2 percentage points, and cross-domain evaluation on FLS and MD-FLS confirms the generalization of the proposed architecture. The codes are publicly available at https://github.com/IDontKnowAAA/MambaDSF.

Diffusion models excel at generating diverse and multimodal trajectories for robotic planning, yet their iterative denoising process introduces latency that is incompatible with high-frequency closed-loop control. To address this problem, we propose Dynamic Neural Koopman Distillation, a framework that distills multistep diffusion inference into a single forward pass while retaining the multimodal expressivity of the teacher model. Specifically, we introduce a Factorized Dynamic Koopman layer that models the denoising process through a factorized latent transition with state-dependent modal gains. We evaluate the proposed method on standard D4RL MuJoCo locomotion benchmarks and a physical Kinova manipulator, comparing against one-step baselines. The results show that our method significantly outperforms existing one-step distillation approaches on the reported locomotion tasks, and reduces the inference latency to the millisecond regime compared with the teacher policy. Hardware experiments further demonstrate that our method enables smooth and fast closed-loop execution while maintaining task success and comparable accuracy. A project page is available at https://fdkoopman.github.io/.

Accelerated MRI reconstruction requires recovering missing details while preserving anatomically coherent structures across large spatial regions. State-space models such as Mamba provide efficient long-range modeling, making them attractive learned regularizers for unrolled reconstruction. However, in a data-consistency-coupled unrolled solver, different stages operate on different reconstruction iterates, where the resident carrier should preserve coherent reconstruction content across stages while stage-dependent non-resident evidence is tied to the current update. Treating these roles uniformly can place persistent resident-carrier evidence and update-dependent non-resident evidence into the same recurrent content route. We therefore propose SO-Mamba, a state-ownership Mamba regularizer that assigns reconstruction evidence within each Mamba stage to recurrent residency, state-interface access, and non-state output correction. SO-Mamba implements this ownership rule with a State-Ownership Router (SOR), which constructs a resident carrier for recurrent content and routes non-resident evidence to affine modulation of the B/C state interfaces and an output correction outlet. The resident carrier supplies the Mamba content route, while the non-resident evidence stream adapts the state interfaces and contributes through the output outlet without entering the recurrent content route. We further introduce a two-level outer-band leakage diagnostic that separates hidden-state storage from readout expression by measuring outer-band energy in the selective-scan state trajectory and the post-scan Mamba readout. Experiments on five public MRI reconstruction benchmarks spanning diverse anatomies, sampling patterns, and coil configurations show that SO-Mamba consistently improves over CNN-, Transformer-, and Mamba-based baselines with competitive computational efficiency.

State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference, which for SSMs is in general a very challenging problem due to the intractability of the likelihood. Recently, neural estimation methods, such as sequential neural likelihood (SNL), have shown promising results in Bayesian inference problems. In this paper, we show that SNL, when applied to the SSM setting, suffers important limitations, such as requiring a large amount of simulated samples to achieve a moderate performance, scaling poorly with sequence length, while not being amortized. We then introduce a novel inference algorithm called truncated-SNL (T-SNL), which addresses the limitations of SNL. Our algorithm is more accurate, more stable and robust during training, more scalable to longer temporal sequences, and can be amortized when new observations become available. Our experiments show that T-SNL is sample-efficient, robust, and flexible algorithm which outperforms other approaches.

State Space Models (SSMs) have emerged as a powerful and efficient alternative to Transformers, demonstrating linear-time complexity and exceptional sequence modeling capabilities. However, their application to vision tasks remains challenging. First, existing vision SSMs largely depend on manually designed fixed scanning methods to flatten image patches into sequences, which imposes predefined geometric structures and increases the complexity. Second, the broader adoption of vision SSMs is hindered in domains that require query-based interactions between distinct information streams. This is a result of the inherently causal and self-referential nature of SSMs designed for 1D sequence modeling tasks. This fusion mechanism is indispensable for critical perception tasks such as multi-view 3D fusion. To address these limitations, we propose Deformba, a context adaptive method that dynamically augments the spatial structural information while maintaining the linear complexity of SSMs. Deformba also allows multi-modal fusion like cross attention. To demonstrate the effectiveness and general applicability of Deformba, we test its performance on general 2D vision tasks such as image classification, object detection, and segmentation, as well as 3D vision tasks like BEV perception. Extensive experiments show that Deformba achieves strong performance across various visual perception benchmarks.

Latent state space systems are ubiquitous in statistical modelling, arising naturally when time series are observed through noisy measurements. However, training deep state space models (DSSMs) at scale remains difficult. Two largely distinct strategies have emerged for training DSSMs. The first, auto-encoding DSSMs, trains generative models by optimising a variational lower bound. The second backpropagates through the outputs of classical sequential Monte Carlo (SMC) algorithms. Such approaches can train DSSMs for both discriminative and generative tasks, but their inherently sequential forward passes scale poorly on modern hardware. We propose \emph{parallel variational Monte Carlo} (PVMC), a new training method that bridges these paradigms and robustly trains DSSMs for both discriminative and generative tasks. Across a set of benchmark experiments, PVMC matches or exceeds state-of-the-art performance while training $10\times$ faster than the fastest competing SMC-based approach.

State-space models (SSMs) face a fundamental trade-off between efficiency and expressivity that is mainly dictated by the structure of the model's transition matrix. Unstructured transition matrices enable maximal expressivity, as measured by their ability to model finite-state automaton (FSA) transitions, but come at a prohibitively high compute and memory cost. In contrast, most structured transition matrix forms are highly efficient both in runtime and memory consumption, but suffer from limited expressivity. Building on recent work on structured sparse SSMs, we propose Flash PD-SSM, a novel SSM that achieves comparable throughput to widely-used structured SSMs with significantly better expressivity guarantees. Flash PD-SSM maintains a trainable set of structured sparse matrices, a single one of which is discretely selected at each time-step, enabling FSA expressiveness at the level of unstructured matrices while maintaining the efficiency required for training models at scale. First, we validate Flash PD-SSM against a suite of alternative models on synthetic mechanistic and state-tracking tasks, finding that its theoretical expressivity is achieved in practice. Second, on multivariate time-series tasks involving sequences of length over 17,000, we find that Flash PD-SSM defines a new state-of-the-art (SoTA) accuracy among competing SSM methods. Finally, we demonstrate that Flash PD-SSM is an effective drop-in replacement for hybrid LLMs, yielding improvements both in natural language state-tracking and in common language modeling scenarios. The model exhibits increased throughput and decreased memory consumption compared to SSMs widely used in frontier language models.

Semantic segmentation of multi-source remote sensing images is a fundamental task for Earth observation applications. Existing methods often struggle with insufficient multi-scale context modeling and suboptimal cross-modal feature fusion, limiting their performance in complex high-resolution scenes. To this end, we propose Axial-Relation Guided Fusion Mamba (ARG-Mamba), a state space model-based framework for optical-elevation remote sensing image segmentation. Specifically, we introduce a Multi-Scale State Space Module to capture both fine-grained local details and global contextual dependencies with linear computational complexity. Moreover, an Axial-Relation Guided Fusion Module is designed to explicitly model global cross-modal correlations along horizontal and vertical axes, enabling efficient feature fusion between optical and elevation modalities. Extensive experiments conducted on the ISPRS Vaihingen and Potsdam datasets demonstrate that our ARG-Mamba consistently outperforms state-of-the-art methods while maintaining favorable computational efficiency. The code will be made publicly available at \url{https://github.com/oucailab/ARG-Mamba}.

Fully homomorphic encryption (FHE) changes sequence-model design because rotations, encrypted products, ciphertext materialization, multiplicative depth, and bootstrapping pressure can dominate ordinary neural-network costs. This paper presents public-decay homomorphic state space models (HSSMs), recurrent/state-space blocks whose carried state is updated through ciphertext-plaintext public decay while ciphertext-ciphertext multiplication remains on a local write path. The design keeps a fixed encrypted state across the sequence. The evaluated workflow separates client-side tokenization, frozen fastText lookup, projection, clipping, encryption, decryption, and thresholding from server-side encrypted evaluation over bounded projected features. On full Rotten Tomatoes and SST-2 validation splits, the encrypted HSSM path exactly matches plaintext classifications and reaches 0.7505 and 0.7420 accuracy. Against HE-friendly polynomial attention on the same fastText workloads, HSSM matches or exceeds full-sequence task quality while running about 5x faster. Paired L40S operation-level rows show 1.34-1.62x lower latency than cached final-token polynomial attention, 30-258x lower latency than full-sequence polynomial attention, and lower logical encrypted-state footprint. A T = 16/32 comparator with encrypted public-linear input and Q/K/V projections shows projected HSSM succeeding under depth 8/ring 32768, while projected attention succeeds under depth 10/ring 65536. A matched T = 8 OpenFHE/FIDESlib trace finishes at final level 3 and noise-scale degree 2 on both backends. These results make public-decay carry a practical FHE co-design lever for encrypted sequence inference from bounded projected features.

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

A fundamental challenge in point cloud object detection lies in the conflict between the extreme sparsity of distant points and the need for remote context understanding. The existing methods typically use 1D serialization to expand the receptive field, which inevitably discards already scarce local geometric details and reduces detection of distant and small objects. To address this issue, we propose 3DTMDet, a novel detection network that synergistically combines state space models (Mamba) with Transformers. The core idea is to utilize SSM's linear complexity and advantages in long sequence modeling to effectively capture global interactions between sparse and distant points, while using Transformer modules with local attention to encode fine-grained geometric structures in local point sets, preserving accurate shape information. We propose the 3D Hybrid Mamba Transformer (3DHMT) block, which uses an SSM-Attention-SSM pipeline to balance global context understanding and local detail preservation, effectively alleviating the tension between receptive field enlargement and geometric preservation in remote detection. In addition, we introduced a voxel generation block inspired by LiDAR physics, which diffuses features along the sensor observation direction to reconstruct the complete object structure of occlusion and distant areas. Extensive experiments conducted on the KITTI and ONCE datasets have shown that 3DTMDet outperforms state-of-the-art detectors. The code is available at https://github.com/QiuBingwen/3DTMDet.

Human trajectory forecasting is crucial for safe navigation in crowded environments, requiring models that balance accuracy with computational efficiency. Efficiently modeling social interactions is key to performance in dense crowds. Yet, most recent methods rely on attention mechanisms, which are effective at capturing complex dependencies, but incur quadratic computational costs that scale poorly with the growing number of neighbors. Recently, Selective State-Space Models have provided a linear-time alternative; however, their inherently sequential design is misaligned with the unstructured and dynamic nature of social interactions. To address this challenge, we propose Social-Mamba, a forecasting architecture that reformulates social interactions as structured sequential processes. At its core is the Cycle Mamba block, a novel module that enables continuous bidirectional information flow. Social-Mamba organizes agents on an egocentric grid and introduces social triplet factorization, which decomposes interactions into temporal, egocentric, and goal-centric scans. These are dynamically integrated through a learnable social gate and global scan to generate accurate and efficient trajectory predictions. Extensive experiments on five trajectory forecasting benchmarks show that Social-Mamba achieves state-of-the-art accuracy while offering superior parameter efficiency and computational scalability. Furthermore, embedding Social-Mamba into a flow-matching framework further enhances both accuracy and efficiency, establishing it as a flexible and robust foundation for future trajectory forecasting research. The code is publicly available: https://github.com/vita-epfl/Social-Mamba

The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks in which the neurons' states are governed by time-varying dynamics. The proposed model provides the learnable time-varying dynamics through a dictionary of basis functions, where each basis function evolves differently over time. We evaluate the proposed approach on both synthetic data from switching systems and a speech denoising task where real audio is corrupted with switching dynamics noise. The results show that the proposed time-varying model consistently outperforms its time-invariant counterparts while maintaining comparable computational complexity. Our investigations also reveal which aspects of the time-varying dynamics of the data most need to be captured by the proposed time-invariant models, how the additional freedom provided by time-varying basis functions should be allocated across model components, and to what extent larger models can compensate for time-invariant limitations.

Online surgical phase recognition (SPR) underpins context-aware operating-room systems and requires committing to a prediction at every frame from past context alone. Surgical video poses three demands that natural-video recognizers do not jointly address: procedures span tens of thousands of frames, time flows non-uniformly as long routine stretches are punctuated by brief phase-defining transitions, and the visual domain is narrow so backbone features are strongly correlated across channels. Existing recognizers either let per-frame cost grow with elapsed length, or hold cost bounded but advance state at a uniform rate with channel-independent dynamics, leaving the latter two demands unaddressed. We present SurgicalMamba, a causal SPR model built on Mamba2's structured state-space duality (SSD) that holds per-frame cost at O(d). It introduces three SSD-compatible components that jointly address these demands: a dual-path SSD block that separates long- and short-term regimes at the level of recurrent state; intensity-modulated stepping, a continuous-time time-warp that adapts the slow path's effective rate to phase-relevant information; and state regramming, a per-chunk Cayley rotation that opens cross-channel mixing in the otherwise axis-aligned SSM recurrence. The learned rotation planes inherit a phase-aligned structure without any direct supervision, offering an interpretable internal signature of surgical workflow. Across seven public SPR benchmarks, SurgicalMamba reaches state-of-the-art accuracy and phase-level Jaccard under strict online evaluation: 94.6%/82.7% on Cholec80 (+0.7 pp/+2.2 pp over the strongest prior) and 89.5%/68.9% on AutoLaparo (+1.7 pp/+2.0 pp), at 238.74 fps on a single GPU. Ablations isolate the contribution of each component. The code is publicly available at https://github.com/sukjuoh/Surgical-Mamba.

Building black-box models for dynamical systems from data is a challenging problem in machine learning, especially when asymptotic stability guarantees are required. In this paper, we introduce a novel stability-ensuring and backpropagation-compatible projection scheme based on the Schur decomposition for the state matrix of linear discrete-time state-space layers, as well as an alternative pre-factorized formulation of the methodology. The proposed methods dynamically project the quasi-triangular factor of the state matrix's real Schur decomposition onto its nearest stable peer, ensuring stable dynamics with minimal overparameterization. Experiments on synthetic linear systems demonstrate that the method achieves accuracy and convergence rates comparable to those of state-of-the-art stable-system identification techniques, despite a marginal increase in computational complexity. Furthermore, the lower weight count facilitates convergence during training without sacrificing accuracy in stacked neural-network architectures with static nonlinearities targeting real-world datasets. These results suggest that the Schur-based projection provides a numerically robust framework for identifying complex dynamics on par with the State of the Art while satisfying strict asymptotic-stability requirements.

Guided depth super-resolution (GDSR) reconstructs HR depth maps from LR inputs with HR RGB guidance. Existing methods either model each modality independently or rely on computationally expensive attention mechanisms with quadratic complexity, hindering the establishment of efficient and semantically interactive joint representations. In this paper, we observe that feature maps from different modalities exhibit semantic-level correlations during feature extraction. This motivates us to develop a more flexible approach enabling dense, semantically-aware deep interactions between modalities. To this end, we propose a novel GDSR framework centered around the Interactive State Space Model. Specifically, we design a cross-modal local scanning mechanism that enables fine-grained semantic interactions between RGB and depth features. Leveraging the Mamba architecture, our framework achieves global modeling with linear complexity. Furthermore, a cross-modal matching transform module is introduced to enhance interactive modeling quality by utilizing representative features from both modalities. Extensive experiments demonstrate competitive performance against state-of-the-art methods.

Radar-camera depth estimation must turn an ultra-sparse, all-weather, metric radar signal into a dense per-pixel depth map. Existing methods -- concatenation, confidence-aware gating, sparse supervision, graph-based extraction -- combine radar and image features outside the backbone's sequence operator, and even cross-modal Mamba variants leave the selection mechanism itself unimodal. We argue that the selection mechanism is the right place for radar to enter. We introduce Radar-Modulated Selection (RMS), a minimal and principled way to inject radar into Mamba's selective scan: radar modulates the scan from within, adding zero-initialised perturbations to the step size $Δ$ and readout $\mathbf{C}$ while leaving the input projection $\mathbf{B}$ and state dynamics $\mathbf{A}$ image-only. The construction is exactly equivalent to a pretrained image-only Mamba at initialisation, ensuring radar only influences the model where it improves accuracy. Two further properties follow that out-of-scan fusion cannot offer: linear-cost cross-modal coupling at every recurrence step, and a natural fallback to the image-only backbone when radar is absent. We deploy RMS in a Multi-View Scan Pyramid (MVSP) that matches the fusion operator to radar's spatial reach at each scale. SemoDepth achieves state-of-the-art performance on nuScenes, reducing MAE by 34.0%, 29.9%, and 29.9% over the previous best at 0--50, 0--70, and 0--80m, while attaining the lowest single-frame latency (26.8ms). A further ablation shows that out-of-scan feature blending adds no accuracy on top of RMS, providing empirical validation that in-scan selection can replace out-of-scan fusion.

State Space Models (SSMs) have emerged as a compelling alternative to attention models for long-range vision tasks, offering input-dependent recurrence with linear complexity. However, most efficient SSM variants reduce computation cost by modifying scan routes, resolutions, or traversal patterns, while largely leaving the recurrent dynamics implicit. Consequently, the model's state-dependent memory behavior is difficult to control, particularly in compact backbones where long scan paths can exceed the effective memory horizon. We propose Token-Conditioned Poles SSM (TCP-SSM), a structured selective SSM framework that improves efficiency while making recurrence dynamics explicit and interpretable through stable poles. TCP-SSM builds each scan operator with 1) real poles that model monotone or sign-alternating decay, and 2) complex-conjugate poles that capture damped oscillatory responses. Using bounded radius and angle modulation, TCP-SSM converts shared base poles into token-dependent poles, allowing each scan step to adapt its memory behavior to the current visual token while preserving pole stability. For practical scalability, we integrate grouped pole sharing with a lightweight low-rank input pathway, yielding an efficient scan operator that preserves linear-time scan complexity. Across image classification, semantic segmentation, and object detection, TCP-SSM reduces SSM computation complexity up to 44% in Vision Mamba-style models while maintaining or surpassing baseline accuracy.

Vision state space models inherit the efficiency and long-range modeling ability of Mamba-style selective scans. However, their performance depends critically on the representation of two-dimensional visual features as one-dimensional token sequences. Existing scan operators range from predefined geometric traversals to dynamic coordinate-based samplers that reroute tokens through predicted offsets and interpolation. While effective, these mechanisms primarily adapt paths or sampling locations, rather than explicitly modeling which local patches should exchange information before global state-space mixing. This motivates a simple question: \emph{can graphs help vision state space models see better?} We introduce \textbf{GraphScan}, a graph-induced dynamic scanning operator for Vision SSMs. For each token, GraphScan constructs a spatially bounded local graph, learns feature-conditioned affinities with relative positional bias, and produces the output token by one-step message passing over its semantic neighborhood. The resulting tokens are locally grounded before being processed by the selective SSM for global aggregation. GraphScan preserves token count and linear scaling in image size, while replacing coordinate-conditioned interpolation with feature-conditioned semantic routing. Integrated into a hierarchical backbone, \textbf{GraphScan-Mamba} achieves state-of-the-art performance among Vision SSMs across image classification, object detection, instance segmentation, and semantic segmentation, with modest computational overhead. Our analysis further shows that GraphScan induces interpretable displacement fields over the token lattice, providing a semantic and spatially grounded view of dynamic scanning. These results suggest that future Vision SSMs should treat scanning not merely as geometric serialization, but as learned local semantic routing before global state-space modeling.

Selective state space models (SSMs), such as Mamba, achieve strong per-token expressivity by making the time discretization step $\TildeΔ$ a learned function of the input. However, in doing so, $\TildeΔ$ ceases to represent a physical sampling interval, limiting its irregular time series modeling capability. Continuous-time SSMs, such as S5, preserve the physical meaning of $\TildeΔ$ and handle irregular timestamps natively ($\TildeΔ\equivΔ)$, but their dynamics remain linear time-invariant (LTI), limiting per-token expressivity. We propose \textbf{TIDES}, a selective SSM variant that reconciles selective and continuous architectures by moving input-dependence off the step size and onto the diagonal state matrix. As a result, $\TildeΔ$ retains its physical meaning, tied to the state discretization, allowing the model to handle irregular timestamps natively without sacrificing the per-token expressivity that makes selective SSMs effective. We show this on a novel \emph{Fading Flash} experimental benchmark, a compact controlled diagnostic for sequence models that jointly tests input-dependence and extrapolation to out-of-distribution $Δ$ values, and isolates the distinct failure modes of current state-of-the-art architectures that TIDES avoids by construction. On large-scale benchmarks, TIDES sets the new state-of-the-art average rank on UEA time-series classification and the Physiome-ODE regression benchmark. Code available at: https://github.com/TaylanSoydan/TIDES.

Effective sequence modeling fundamentally requires balancing the retention of unbounded history with the high-resolution detection of abrupt short-term variations common in real-world phenomena. However, existing state space models (SSMs) relying on high-order polynomial projection operators (HiPPO) face a critical trade-off where uniform measures dilute recent information to maintain timescale invariance, while exponential measures sacrifice global context to capture local dynamics. This paper proposes a Fractional Recurrent Architecture for Computational Temporal Analysis of Long sequences (FRACTAL), a novel architecture integrating fractional measure theory into recursive memory updates to address this limitation. By deriving projection operators with analytically characterized spectral properties and a tunable singularity index, the proposed method amplifies sensitivity to recent signal perturbations while preserving the spectral structure that encodes scale-invariant memory dynamics. This theoretical innovation is instantiated within a simplified diagonalized state space framework by modulating input projection initialization to enable simultaneous capture of multi-scale temporal features. FRACTAL achieves an average score of 87.11% on the Long Range Arena benchmark, including 61.85% on the ListOps task, outperforming the S5 model.

Recent event-based image reconstruction methods predominantly rely on Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) to process complementary event information. However, these architectures face fundamental limitations: CNNs often fail to capture global feature correlations, whereas ViTs incur quadratic computational complexity (e.g., $O(n^2)$), hindering their application in high-resolution scenarios. To address these bottlenecks, we introduce EmambaIR, an Efficient visual State Space Model designed for image reconstruction using spatially sparse and temporally continuous event streams. Our framework introduces two key components: the cross-modal Top-k Sparse Attention Module (TSAM) and the Gated State-Space Module (GSSM). TSAM efficiently performs pixel-level top-k sparse attention to guide cross-modal interactions, yielding rich yet sparse fusion features. Subsequently, GSSM utilizes a nonlinear gated unit to enhance the temporal representation of vanilla linear-complexity ($O(n)$) SSMs, effectively capturing global contextual dependencies without the typical computational overhead. Extensive experiments on six datasets across three diverse image reconstruction tasks - motion deblurring, deraining, and High Dynamic Range (HDR) enhancement - demonstrate that EmambaIR significantly outperforms state-of-the-art methods while offering substantial reductions in memory consumption and computational cost. The source code and data are publicly available at: https://github.com/YunhangWickert/EmambaIR

Online goal recognition in continuous domains poses two central challenges: efficiently encoding large trajectories and effectively comparing them. Recent work addresses these challenges by using custom state-space representations and metrics to compare observations against hypotheses. However, these approaches often overlook well-established encoding techniques used in other domains that offer substantial advantages. This paper introduces a novel method for online goal recognition that leverages path signatures, a compact, expressive representation of rough path theory that efficiently captures key semantic features of trajectories, enabling more meaningful comparisons between them. Experiments show that our method consistently outperforms the state of the art in predictive accuracy and online planning efficiency, while remaining competitive offline.

Hybrid State-Space models combine Attention with recurrent State-Space Model (SSM) layers, balancing eidetic memory from Attention with compressed fading memory from SSMs. This yields smaller Key-Value caches and faster decoding than Transformers, along with a richer architectural design space. Exploring that design space at scale has so far required training from scratch, a barrier that has kept most large-model Hybrid research within a narrow range of architectures. We introduce Priming, a method that turns Hybrid architecture design from a pre-training problem into a knowledge transfer one. Priming initializes a Hybrid model from a pre-trained Transformer and, through short alignment and post-training phases, recovers downstream quality using less than 0.5% of the source model's pre-training token budget. Priming is agnostic to the source Transformer family (e.g., Qwen, Llama, Mistral), model class (dense or Mixture-of-Experts), and model scale. Priming enables us to run the first controlled comparison of SSM layer types at scale under identical conditions. We evaluate, Gated KalmaNet (GKA), Gated DeltaNet (GDN), and Mamba-2, and show that their expressiveness hierarchy, GKA>GDN>Mamba-2, directly predicts downstream performance on long-context reasoning tasks. We scale Priming to 8B/32B reasoning models with native 128K contexts. Our Hybrid GKA 32B improves over its source Qwen3-32B by +3.8 average reasoning points, while staying within 1% of a Transformer post-trained on the same data and enabling up to 2.3x higher decode throughput. To foster research on Hybrid architectures, we release a model zoo of primed Hybrid models for long-context reasoning and instruction following, together with the Priming training and inference code (Sequence Parallelism algorithms for long-context training, optimized GKA kernels, and vLLM serving plugin), all under Apache~2.0 License.

Inferring the evolution of high-dimensional and multi-modal (e.g., spatio-temporal) physical fields from irregular sparse measurements in real time is a fundamental challenge in science and engineering. Existing approaches, including diffusion-based generative models and functional tensor methods, typically operate in offline settings, depend on full temporal observations, or incur substantial inference cost. We propose StreamPhy, an end-to-end framework that enables efficient and accurate streaming inference of full-field physical dynamics from incoming irregular sparse measurements. The framework integrates a data-adaptive observation encoder that is robust to arbitrary observation patterns, a structured state-space model that supports memory-efficient online updates across irregular time intervals, and an expressive Functional Tensor Feature-wise Linear Modulation (FT-FiLM) decoder for continuous-field generation. We prove that FT-FiLM is more expressive than the functional Tucker model, admitting a richer function class for handling complex dynamics. Experiments on three representative physical systems under challenging sampling patterns show that StreamPhy consistently outperforms state-of-the-art baselines, with at least 48% improvement in accuracy and up to 20--100X faster inference than diffusion-based methods.

We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled by Volterra series and their autoregressive variants, as well as systems admitting Hammerstein-type state-space realizations. We apply the proposed framework to the problem of data-driven modeling of such systems, i.e., when simulation or control objectives for an unknown system are carried out without an explicit system identification step. To that end, we link the behavioral approach to two data-driven modeling methods in a vector-valued RKHS: (1) minimum-norm interpolation and (2) subspace identification.