State Space Models

Figured-bass realization can be described as a sequence of choices constrained both within each sonority and between successive sonorities. This paper gives an explicit mathematical model of a restricted, examination-style four-part realization problem. Pitch spelling, range, chord membership, doubling, omission, spacing, crossing, overlap, melodic motion, consecutive perfect intervals, and selected resolution requirements are expressed as predicates. We distinguish hard constraints from optional preference costs. Four labeled notes are represented visually as the vertices of a quadrilateral and computationally as one ordered voicing state. Legal progressions become paths through a layered graph. We prove that feasibility and minimum-cost realization are polynomial-time problems for a fixed number of voices with explicit finite note domains and fixed local rules. For fixed ranges, a fixed note alphabet, and adjacent-event rules, the number of graph operations is linear in the number of events. Worked two-, four-, and eight-beat examples illustrate legality, optimization, and the failure of a greedy choice. The result concerns the stated formal model; it is not a claim that every musical judgment is captured by local predicates.

Scaling deep learning faces critical bottlenecks: data exhaustion, exponential training costs, and resource concentration. Model merging combines pre-trained checkpoints without gradient descent, offering orders-of-magnitude savings versus retraining. Combining independently trained vision models is difficult when their architectures and parameter shapes differ. Existing weight-space merging methods generally assume aligned, shape-compatible checkpoints, whereas a Vision Transformer (ViT) and a state-space model (SSM) implement token mixing with different operators. We study a hybrid Heterogeneous merging setting that retains both architectures while aligning parameter groups by semantic role. Our proposed Riemannian--Lorentz Parameter Fusion (RLPF) method projects aligned groups to common coordinates, lifts selected coordinates to the Lorentz hyperboloid model of hyperbolic space, computes a regularized geodesic barycenter, and decodes the result into the two branches. A learned gate then combines branch logits for each input. Component groups use fixed curvature values, with normalization parameters treated as Euclidean. In the results available in this manuscript, the fine-tuned system obtains 82.37% on CIFAR-10, 75.04% on Oxford-IIIT Pet, and 78.58% top-1 accuracy on ImageNet-1K; the corresponding best-parent accuracies are 76.54%, 71.42%, and 76.42%. On ImageNet-1K, the reported pre-fine-tuning initialization reaches 77.80%. These results support further study of geometry-aware heterogeneous fusion, but not a training-free single-checkpoint merge: RLPF is a two-branch hybrid whose gate and reported final models are trained.

Robotic systems operating in dynamic environments require visual perception that evolves continuously with the incoming sensory stream. Event cameras provide microsecond temporal resolution and asynchronous sensing, but most learning-based methods accumulate events into frames or temporal bins, introducing an integration delay that can limit fast reaction. Here we propose REACT, a fully spiking state-space model for event-driven temporal perception that processes raw events one by one, without temporal accumulation. REACT uses a complex-valued spiking neuron, C-SiLIF, whose continuous-time dynamics are driven by the physical inter-event interval, allowing its internal state to evolve at the temporal resolution of individual events. We evaluate REACT on gesture recognition and time-to-collision (TTC) estimation from full-field event streams, without a target bounding box or localization input. On EvTTC, REACT achieves a 9.59% relative TTC error with 4.6 ms end-to-end inference latency, within 0.15 percentage points of the best learned method while requiring no target prior. At the dataset's mean approach speed, this latency corresponds to only 4 cm of vehicle motion, compared with 1 m for the fastest competing learned method. REACT further supports anytime TTC prediction, zero-shot transfer to a different driving sequence, and INT8 quantization, reducing the estimated energy consumption from 18.5 to 2.8 mJ per 32,768 events. These results show that event-driven spiking state-space dynamics can provide low-latency, continuously updated temporal perception for reactive robotic systems.

Mixture-of-experts (MoE) inference on consumer hardware is bounded by weight memory: a 35B-class model is 19.5GB at 4-bit, and sparsity shrinks the compute per token, not the bytes that must be held. Naive offloading to SSD does not help on its own, because layer N+1's experts must be chosen before layer N's output exists, so the reads cannot start early enough to hide behind compute. We present Edge0, a streaming MoE inference engine that closes the gap with a prerouter: a per-layer head predicts the next layer's routing one token ahead, and the prediction is consumed as the routing itself, so the staged expert set equals the routed set and nothing is dropped. An unmerged recovery LoRA, trained on the student path, pays back the quality lost to int4 quantization and routing replacement. On a single 24GB machine, Edge0 serves a 35B MoE at 20tok/s inside 3GiB of peak active memory, within a few points of its fp16 teacher on average across five public benchmarks. An 8B tier runs on the same framework, and the framework, checkpoints, and adapters are open source.

Selective state space models (SSMs) have recently emerged as a compelling alternative to transformers, combining competitive performance with substantially improved inference efficiency. At each SSM layer, a sequence of hidden states are propagated by a recurrence, mixing information of different tokens. Despite using a different mechanism, this mixing plays a role analogous to attention in transformers. In fact, recent works have shown that the two architectures may be closer than they first appear, as this recurrence admits a formulation akin to linear attention. In transformers, attention is known to drive the tokens to cluster, i.e., to reach consensus, collapsing in the limit to a single direction. Thus, we ask: does the recurrence at the core of SSMs drive the tokens to consensus, as attention does in transformers? To answer this question, we take a dynamical systems perspective on SSMs, modeling the evolution of tokens across layers as an ordinary differential equation. By exploiting input-to-state stability arguments, we establish local exponential stability of the consensus equilibria and characterize their domain of attraction for time-varying weight matrices, a setting not addressed by previous results. We thereby show that the resemblance between SSMs and transformers does run deeper: the recurrence at the core of SSMs aggregates tokens just as attention does. Numerical experiments on a pretrained Mamba-2 model point to the output gate as the component that regulates the extent of this consensus, preventing the tokens from reaching it in full.

We study the problem of demonstration selection, which involves selecting a subset of examples for prepending to a query to a language model. This problem is closely related to in-context learning and language model inference. Since the inference cost of a transformer model scales quadratically with sequence length, the selection problem becomes especially challenging in a long-context scenario. In this paper, we tackle this problem by building on state space models (SSMs), which require only linear inference time given the input. Our approach involves two algorithms. The first learns a small set of SSMs through distillation of a (trained) transformer model. We partition all the layers into consecutive groups. Then for each group, we estimate a separate state space model to replicate the input-output behavior within the adjacent layers. Second, we map the distilled model outputs to a small set of tokens, and apply these embeddings for demonstration selection in downstream applications. We perform extensive experiments in both synthetic and real-world datasets to validate our approach. We demonstrate that the distilled SSMs only incur an approximation error of less than $0.7\%$ relative to the true output. In downstream evaluation, we show that on several text classification and reasoning tasks, our approach reduces FLOPs by $14.2\times$ and improves accuracy by $6.48\%$ relative to baseline demonstration selection methods.

The Koopman operator has been widely used for time-series prediction in dynamical systems. However, prior work that learns latent ``Koopman spaces'' using neural networks often did not construct a valid Koopman space for forecasting, as these representations may be mathematically inconsistent with the operator-theoretic formulation and fail to capture the intrinsic low-rank structure of system dynamics. To address this issue, we introduce K$^2$SVD, a method that explicitly learns the leading singular functions of the Koopman operator by optimizing a Hilbert-Schmidt objective. This yields a well-defined low-rank approximation of the Koopman operator with an interpretable linear combination, featuring a compact latent space with less than $10\%$ of the dimensions used in previous work. In the learned Koopman space, K$^2$SVD further captures temporal evolution with a linear Gaussian state-space model and performs inference via Kalman filtering, mitigating noise accumulation during multi-step prediction. Empirical results show that K$^2$SVD outperforms state-of-the-art methods across multiple datasets, with significantly faster prediction speeds and lower computational cost than previous efficiency-focused models. This highlights the benefits of principled low-rank Koopman representations and opens up broader potential for applications.

State Space Models (SSMs) have emerged as a compelling alternative to Transformers, enabling sequence modeling with constant memory and linear compute. Although SSMs exhibit reasonable performance and favorable computational characteristics, they continue to lag behind Transformers on tasks that require in-context learning and precise retrieval, slowing their adoption for large-scale language modeling. In this work, we demonstrate that both the success and failure of SSMs in these domains can be explained by studying the role of the gating mechanism, a prevalent component in modern recurrent networks. Specifically, we show through theory and experiments that this gating mechanism causes SSMs to first learn an in-weights "memorization" solution, while delaying, or even preventing, convergence to a correct in-context learning solution. Importantly, this happens even in cases where there are no fundamental limitations due to the architecture or its memory capacity. On the other hand, we find that gating is often beneficial for improving generalization to long sequence lengths. Our results illuminate the crucial role of the gating mechanism in shaping both the training dynamics and generalization of SSMs, and provide a basis for understanding and improving linear-time models.

Transformers and state-space models (SSMs) are the two dominant families of sequence models, and a central open question is how far the analytical knowledge built for transformers transfers to SSMs. We address this through the lens of layer importance which underpins compression, selective fine-tuning, and interpretability across both families. We decompose layer importance into two distinct notions. \emph{Necessity} captures how much the pretrained model depends on a layer's existing contribution, measured by the loss increase from bypassing it. \emph{Plasticity} captures where the model absorbs new information during fine-tuning, measured by the magnitude of task-specific weight updates. Our analysis reveals that the two families behave fundamentally differently: in every evaluated residual transformer up to $14$B parameters, Necessity and Plasticity anti-align across depth, whereas in the evaluated Mamba-style SSMs they point to overlapping regions. The sign of this alignment also predicts downstream adaptation behavior. In the evaluated transformers, concentrating updates in the most plastic layers increases catastrophic forgetting, while this tier-dependent effect disappears in the evaluated Mamba-style SSMs.

High-frequency surgical maneuvers in ophthalmology necessitate high-fidelity temporal modeling, yet characterizing long-range procedural dependencies remains computationally prohibitive for attention-based architectures. Existing models often require aggressive temporal downsampling, which compromises the detection of fine-grained action boundaries and instrument-tissue interactions. To address these scalability constraints, we present OphBiWSSD, a framework that reformulates surgical temporal action localization leveraging Bidirectional State Space Duality. By employing a weight-tied selective scan mechanism that incorporates both preceding and succeeding surgical contexts, our approach facilitates the global synthesis of non-causal temporal cues with linear complexity. This streamlined architecture is well-suited to capture the bidirectional dependencies present in ophthalmic workflows, effectively bridging the gap between local boundary precision and long-range procedural context without incurring the quadratic memory overhead of traditional Transformers. Extensive experiments on the OphNet benchmark demonstrate that OphBiWSSD achieves state-of-the-art temporal localization performance, with mean Average Precisions of 44.42% on phases and 43.08% on operations, surpassing the baselines by 6.80% and 6.66%, respectively. Empirical validation indicates that our approach ensures precise temporal localization and offers a computationally viable pathway for deploying surgical intelligence systems in clinical environments. The code is publicly available at https://github.com/yo3nglau/OphBiWSSD.

In this paper we derive a Probably Approximately Correct (PAC)-Bayesian error bound for partially observed linear time-invariant (LTI) stochastic dynamical systems in state-space form with inputs and sub-Gaussian noise. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. The bound derived in this paper relates the expectation of prediction errors with the prediction error generated by the model on the data used for learning. In addition, we show that it can also be used to derive bounds for the parameter estimation error. In turn, this allows us to provide finite-sample error bounds for the prediction error and parameter estimation error for a wide class of system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

Recent state-space models (SSMs) such as Mamba achieve language modeling performance comparable to transformers despite relying on fundamentally different architectures. This raises an important question: how do these structural differences influence the geometry and functional nature of their internal representations? We study this question through a multi-scale analysis of representations in transformers, SSMs, and hybrid architecture. First, we find that SSMs distribute their representational information evenly across all dimensions, whereas transformer representations are heavily dominated by a single principal direction. By evaluating hybrid architectures, we observe that the representation space becomes increasingly skewed toward a single dominant direction after each attention layer. Next, we explore how the different geometric spread of representations impacts representational capacity through compressibility. Surprisingly, we find that despite their contrasting geometric structures, both architectures exhibit tightly matched effective capacities. We further investigate whether this skewed geometry affects how concepts are encoded. Using rank-constrained probes, we demonstrate that both architectures encode concepts in subspaces of surprisingly similar dimensionality. Furthermore, we demonstrate that the transformers' dominant principal direction does not inherently encode more conceptual information. Finally, we zoom in and examine the alignment between manifolds, either by analyzing representations of specific topics or by looking at the nearest neighborhoods of tokens, and find that they are highly aligned. Ultimately, our analysis suggests that while transformers and SSMs induce different usage of latent space, they display a striking functional convergence at the level of local semantic manifolds.

Data-driven constitutive models for path-dependent plasticity are commonly formulated using nonlinear recurrent neural networks, whose sequential state evolution limits parallel training and whose predictions may depend on the discretization of the applied strain path. We introduce a Constitutive State Space (CSS) model that reformulates structured state-space dynamics as an incremental constitutive operator. The strain increment is decomposed into magnitude and direction: the loading direction drives the latent state-space system, while the increment magnitude enters the zero-order-hold discretization of its continuous-time linear recurrence. This mechanics-tailored construction guarantees stationarity under zero increments, strongly reduces sensitivity to strain-path resolution, and retains the parallel-scan structure of S5 for efficient training on long constitutive histories. The CSS and Minimal State Cell (MSC) architectures are compared for four multiaxial path-dependent material models including isotropic J2 plasticity, pressure-sensitive foam plasticity, and combined isotropic-kinematic hardening. CSS matches or exceeds the prediction accuracy of the MSC, including one order of magnitude lower validation losses for the plastically incompressible materials. Importantly, CSS maintains low errors across large changes in strain-path discretization, whereas the MSC error increases substantially when evaluated at coarser resolutions than used for training. CSS trains substantially faster and requires fewer strain-stress pairs to attain comparable or better accuracy. Analysis of the learned state further reveals latent structure consistent with the dimensionality of the underlying physical constitutive models. These results establish mechanics-tailored structured state-space dynamics as a computational framework for efficient and discretization-robust data-driven constitutive modeling.

Histopathological subtyping relies on the recognition of characteristic histological patterns. These patterns may be expressed by individual tissue structures or by the spatial distribution and co-occurrence of multiple structures, and they often span irregularly shaped tissue regions, termed semantic units in this work. However, conventional patch-based representations may fragment such units and fail to explicitly preserve their internal spatial organization, while efficiently modeling relationships among numerous spatially separated units remains challenging. To address these limitations, we propose the Semantic-Aware Subgraph State Space Model (SASG-SSM), a flexible and efficient framework for whole slide image (WSI) classification. Semantic-Aware Subgraphs (SASGs) first approximate irregularly shaped semantic units by adaptively grouping spatially connected patches guided by class-agnostic visual-semantic priors. By representing patches as graph nodes with adjacency edges, SASGs preserve their internal spatial organization rather than treating them as an unordered set. A Subgraph State Space Module (SG-SSM) subsequently combines a graph neural network encoder for intra-subgraph topology encoding with a Mamba-based state space encoder for efficient contextualization across large numbers of subgraphs. This module integrates local structural information within semantic units with global contextual information arising from their distribution and co-occurrence across the WSI, while efficiently modeling a large number of spatially distributed regions. Extensive experiments across four WSI subtyping datasets demonstrate consistent advantages over representative state-of-the-art methods. Further evaluations under small-cohort and few-shot settings demonstrate robustness and data efficiency under limited training data. Code will be released at https://github.com/HLSvois/SASG-SSM.

Speech codecs serve as bridges between continuous speech signals and large language models, yet face an inherent conflict between acoustic fidelity and semantic preservation. To mitigate this conflict, recent works increasingly adopt dual-tower architectures to decouple semantic and acoustic modeling with separate encoders. However, these dual-tower designs incur substantial architectural overhead. To avoid such complexity, we revisit the single-tower paradigm and propose BiMTokenizer, a low-bitrate speech codec (around 1.1 kbps) combining a bidirectional state-space backbone with Residual Spherical Leech Quantization (RSLQ). The bidirectional backbone strengthens temporal modeling, while RSLQ offers a fixed, well-separated lattice bottleneck for robust semantic and acoustic tokenization without learned-codebook collapse. Experiments show that BiMTokenizer achieves superior acoustic reconstruction and the lowest WER among low-bitrate codec baselines across both clean and noisy environments, while using less than half the parameters of recent dual-tower baselines. Furthermore, its robust semantic representations yield strong performance on downstream speech understanding tasks, confirming that a well-designed single-tower codec can preserve the semantic-acoustic balance at low bitrates. The code and model weights are available at https://github.com/ZhangXinWhut/BiMTokenizer.

Automotive mmWave radar can develop vibration, antenna misalignment, radome blockage, and receive-channel degradation that corrupt the signal before perception begins. Data for these faults are scarce because each condition must be induced and measured on physical hardware. We introduce Rad-R, a raw-ADC dataset captured with a 4-chip 77GHz TI MMWCAS-RF-EVM cascade (192 virtual channels). Unlike existing raw-radar datasets, Rad-R pairs each recording with a controlled hardware fault at a calibrated severity, an independent physical severity measurement, and frame-synchronised IMU, temperature, GPS, and camera streams. Rad-R is a single-session dataset, so our generalisation claims are confined to a controlled cross-severity protocol in which train and test use physically distinct captures. A reproducible benchmark evaluates seven representative vision backbones and the proposed raw-IQ Mamba SSM (RadrNet) under within-clip, chirp-wise anytime, few-shot cross-capture, and controlled cross-severity protocols. Within-clip performance is near-saturated ($>0.98$ macro-F1), whereas cross-severity generalisation remains difficult: the absolute-phase RadrNet-DS falls to $0.49$ macro-F1. RadrNet-DS-CI replaces absolute phase with per-frame-standardised magnitude and relative chirp-to-chirp phase and ranks first on the controlled benchmark ($0.663$ vs. $0.628$ for the strongest RD-CNN; three seeds); the RadrNet family also leads on the anytime and few-shot budgets. A descriptive cross-modal analysis further finds that radar micro-Doppler covaries with independently measured IMU vibration energy (pooled Spearman $ρ=0.41$ across conditions). The complete dataset and code will be released publicly under permissive licences.

Sequence models---the architecture family behind large language models and, increasingly, state-of-the-art image recognition---have redefined how machines learn from high-dimensional data. Yet population estimation from satellite imagery, a task that underpins infrastructure planning, public health, and disaster response, has scarcely benefited: leading systems still bind population to a uniform raster, disaggregating census counts onto grid cells through weighting surfaces built from ancillary data (e.g., in WorldPop and LandScan), which can introduce systematic spatial bias, and predicting population per grid cell with convolutional neural networks. In this approach, the administrative-unit structure in which the census was actually collected is discarded. We close this gap with MambaPop, which renders each administrative unit as a single polygon-masked satellite image and treats tract-level population estimation as a sequence-modeling problem over its image patches, pairing each tract image directly with its population label and eliminating the disaggregation step entirely. Built on the hybrid state-space--attention MambaVision backbone, MambaPop is, to our knowledge, the first method to learn population directly from an administrative unit's own image as well as the first to apply a state-space based (Mamba) hybrid architecture to the population estimation task. Across all $\sim$84{,}000 contiguous-US census tracts of the 2020 census, MambaPop attains a mean absolute error (MAE) of $1{,}141$ persons per tract, matching the strongest convolutional baseline (YOLOv11, MAE $1{,}122$).

Accurate air quality forecasting is essential for public health and urban environmental management, but remains challenging because pollutant channels differ in periodicity and distribution drift, while their concentration trajectories contain both multi-scale dependencies and rapid changes. Recent methods have improved spatial dependency learning and meteorological covariate modeling. However, pollutant channels are still passed through the same normalization rule and temporal backbone, using a shared latent representation for channel-specific distributions and changes at different rates. To address this limitation, we propose AirFlow, a pollutant-aware dual-stream framework that operates on station multivariate observations without additional graph propagation or predefined signal decomposition. Specifically, AirFlow designs two novel blocks: (1) a statistic-guided normalization routing mechanism that selects a normalization path for each pollutant according to its 24-hour autocorrelation and distribution drift; and (2) a hierarchical dual-stream state model that combines multi-scale state space propagation with learnable response coefficients, where gated bidirectional cross-attention exchanges information and adaptively fuses the resulting representations. Experiments on real-world data from multiple cities show that AirFlow achieves the best performance in 34 of 36 metrics comparisons, with reductions of up to 11.11% root mean square error over the state-of-the-art baseline. AirFlow also requires only 0.0483M parameters and 0.0215G FLOPs, achieving high forecasting accuracy with low computational overhead.

Estimating counterfactual outcomes over time from longitudinal observational data is central to clinical decision support. Existing methods rely on domain confusion -- adversarial training that renders representations invariant to treatment assignment -- yet this invariance creates a mutual information conflict: it suppresses treatment-correlated covariate signals necessary for accurate outcome prediction. We formalise this tension via a Jensen-Shannon divergence bound on counterfactual prediction error and develop two complementary models. CSSD (Causal State-Space model with Direct decoder) adapts selective State Space Models with a parallel multi-step decoder that eliminates accumulated rollout error by producing all prediction horizons simultaneously in a single forward pass. CSSPD (Causal State-Space model with Predictive regularisation and Direct decoder) augments CSSD with Contrastive Predictive Coding and Local Information Maximisation to reinforce temporal predictability in the balancing representation and recover local covariate information destroyed by domain confusion. On MIMIC-III, CSSPD achieves lower counterfactual RMSE than the Causal Transformer at every horizon tau >= 2 at O(T) encoder cost, with gains from 0.02 (2-step) to 0.07 (6-step). On Cancer Simulation across confounding strengths gamma in {0,1,2,3,4}, CSSPD outperforms CT at gamma <= 3 (margins 25.9%--37.0%), and CSSD achieves the lowest overall average RMSE (12.7% reduction over CT), confirming the MI conflict analysis. To our knowledge, this is the first work to formalise the balancing-prediction MI conflict and propose a structured resolution through complementary predictive and information-theoretic training objectives.

State-space models (SSMs) provide a powerful theoretical framework to enable parallel training of recurrent networks. We expand on previous work adapting SSMs to spiking models to provide a novel interpretation of resonate-and-fire (R&F) neural networks which is compatible both with real and spiking inputs, parallel and recurrent execution, has clear connections to hyperdimensional (HD) computing, and maintains biologically-realistic features. We demonstrate an implementation of this approach which integrates an STFT, recurrent memory, and attentional features within a single spike-compatible network.

Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem? We give a provable pipeline for doing so. Starting from observations of an unknown nonlinear dynamical system, we first learn an implicit spectral predictor using Observation Spectral Filtering (OSF), a convex method that competes with the best linear observer for the system. We then apply spectral-to-LDS distillation to convert this predictor into an explicit recurrent linear dynamical system. Our main theorem shows that the average prediction error of the distilled LDS decomposes into an exponentially-small distillation term and the OSF learning term governed by the Luenberger complexity of the best observer. The guarantee is dimension-free: it depends on observer complexity rather than on the latent dimension needed to represent the nonlinear system. To our knowledge, this yields the first end-to-end provable method for extracting a best-in-hindsight LDS representation of nonlinear dynamics through convex learning followed by provable distillation. Experiments on linear LDS benchmarks and MuJoCo behavior cloning show that the train-then-distill pipeline produces compact LDS predictors that match or outperform directly trained baselines.

Muon is a recent optimizer that orthogonalizes the update to each weight matrix with a Newton-Schulz iteration, which performs steepest descent under the spectral norm. Almost all the evidence for it comes from Transformer models, and its behavior on state-space models is largely unreported. We compare Muon with AdamW on Mamba-2 130M under a controlled protocol that varies only which weight groups are trained with Muon. The benefit is localized. Muon on the output projection alone beats Muon on the input projection or on both. The advantage is mainly one of token efficiency. It holds on two corpora and two token budgets, and persists when training continues well past the compute-optimal point. Conditioning does not explain the gain. Muon lowers the condition number of whichever projection it trains, but the better-conditioned input projection is not the one that helps.

Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that \textbf{state propagation alone is sufficient}. We propose the \textbf{Complex State Propagator (CSP)}, a minimalistic recurrent architecture that \textbf{only propagates hidden states} across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a \textbf{block-level skip connection} alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves \textbf{100% accuracy} with perfect F1 scores across canonical tasks.

Retrieval-augmented generation (RAG) imposes a prefill cost proportional to retrieved context length, and -- with Transformer backbones -- a KV-cache that grows with each generated token. State-Space Models (SSMs) avoid the second cost by construction; we eliminate the first, collapsing prefill from $O(L_{context})$ to $O(1)$ per query. We introduce PRECOG (Pre-Computed Context Injection), a retrieval mechanism that exploits a property unique to SSMs: the fixed-size, position-agnostic recurrent hidden state is a complete summary of everything the model has read. PRECOG pre-encodes document corpora offline as SSM hidden states and injects the best-matching state directly at query time, bypassing in-context re-ingestion entirely. The same state-injection mechanism enables SMC (Structured Memory Consolidation): a hierarchical persistent memory with cognitive-domain clustering, an adjustable fidelity-vs-storage dial, and $O(1)$ session initialization, which consolidates short-term episodic states into long-term semantic memory and fuses both with retrieved corpus states at query time. We demonstrate the system on TENNs-LLM, a 1.2B-parameter gated-SSM language model with a 192 KB hidden state. PRECOG matches in-context RAG answer quality, reducing prefill latency from $\sim$27 s to $<$6 ms on edge hardware -- a $\sim$4500$\times$ speedup that crosses the threshold from unusable to interactive. The mechanism is architecturally impossible for Transformer KV-caches, which are position-entangled and grow linearly with context length.

Adverse weather image restoration aims to recover clear visibility from degraded images in complex weather conditions. Existing works attempt to address this problem by modeling relationships between pixels, however, this paradigm defies the spatially non-uniformity fact of degradations and learns non-discriminative features from semantic-conflict regions. In this paper, we propose SSR, a \textbf{S}emantic-center guilded \textbf{S}tate space model for image \textbf{R}estoration. The key idea of SSR is to shift the conventional scanning strategy of pixel-serial to semantic-guilded one. Specifically, we introduce a Superpixel-guided Selective Scan Mechanism ($\text{S}^3$M), which first partitions the image into perceptually coherent regions via superpixel clustering and then performs relations modeling within the semantic-related regions. Moreover, a Region-level Gating Mechanism (RGM) is developed to perform intra-region calibration by modulating degradation outliers within each semantic superpixel unit along the channel dimension. Extensive experiments on \textbf{6} well-established benchmarks demonstrate that SSR performs favorably against state-of-the-art models with competitive computational cost.

Ultra-high-definition (UHD) image restoration must balance the aggregation of spatially recurring degradation cues with the preservation of localized image structures. Compact aggregation can reduce redundant processing but may attenuate edges, textures, and other fine structures. Existing approaches manage UHD restoration cost through downsampling, window partitioning, or cluster-based token reduction; yet many of them do not explicitly retain information that is poorly represented by shared aggregation. In this study, we propose a Context-Detail Decoupled State Space Model (CoDe-SSM) for UHD restoration, which processes aggregated context and clustering residuals in separate pathways. The context modeling pathway, implemented by the Global Cluster Scan Module (GCSM), aggregates features into $K$ input-dependent cluster centers and applies selective SSM reasoning over the resulting fixed-order sequence, enabling cross-region context sharing while decoupling computational cost from spatial resolution. The detail recovery pathway, implemented by the Local High-Frequency Module (LHFM), processes the clustering residual with an input-derived high-frequency mask and a sparse mixture of convolutional experts. Extensive experiments on five UHD benchmarks and five degradation types demonstrate that our explicit context-detail decoupling strategy yields substantial gains in restoration quality while maintaining desirable efficiency.

State-of-the-art intracortical brain-to-text systems pair a neural-sequence phone decoder with an external language model. Two design axes remain underexplored: whether selective state-space models (Mamba) improve on recurrent decoders, and how the output target (phonetic vs.\ character) interacts with that choice. On the public Brain-to-Text '25 benchmark, we study a controlled 2x2 grid (GRU vs.\ hybrid Mamba decoder; phonetic vs.\ character targets) trained with a CTC objective under one reproducible protocol. The recurrent baseline remains strongest: the best phonetic GRU reaches 12.62% PER and 21.19% WER, while the best textual GRU after LM rescoring reaches 13.39% CER and 26.28% WER. The Mamba hybrid is competitive but does not surpass it. Ablations isolate architectural contributions, and error analysis shows representation-dependent failures: articulatory-like phoneme confusions vs.\ lexical and word-boundary errors.

Existing vector-sketch models treat recognition and generation as separate tasks, leaving a gap for streaming interfaces that must understand a drawing as it is being made. We present SketchMamba, a single causal sequence model that continuously classifies a sketch from any partial prefix while simultaneously generating its continuation. We achieve this by applying a dense per-step classification loss to a selective state-space backbone. Evaluated on a 58-class subset of the Quick, Draw! dataset, SketchMamba yields 94.93% final-step accuracy and a progressive-accuracy Area Under the Curve (AUC) of 0.706, crossing 90% of its final accuracy by the time 70% of the strokes are drawn. In a matched-budget comparison, the 1.55 million-parameter backbone ties a causal Transformer while outperforming recurrent and convolutional baselines. Ablations confirm that the dense supervision regime, rather than the architecture alone, drives the early-prediction capability. The results demonstrate that a single causal hidden state can unify progressive recognition and autoregressive generation without auxiliary encoders or task-specific branching.

Long-sequence memory tracking places two opposing demands on a recurrent state: near-lossless retention of stored bindings over long horizons, and active overwriting of stale ones. In our diagnostic suite, the strongest efficient baselines tend to solve only one side well. Continuous-time-parameterized state-space models (SSMs) such as Mamba obtain their discrete recurrence by zero-order-hold discretization of a continuous-time system; we argue that this detour is unnecessary for memory tracking and parameterize the discrete transition directly. Naju (Native Adaptive Junction Unit) factorizes the recurrent update, schematically $x_n = f_n\odot x_{n-1} + i_n\odot(B_n u_n)$, into an explicit discrete pole (a learned forget gate $f_n$), an independent write gain $i_n$, and input-dependent write/read maps. Since the sigmoid pole satisfies $0<f_n<1$, each frozen local coordinate is Schur-stable by construction, and the full time-varying recurrence satisfies a fading-memory/BIBO bound under uniform boundedness assumptions, with no stability regularizer. We formalize the key structural limitation of coupled designs: any non-expansive complementary single-gate recurrence ties the effective retention $r$ and write gain $w$ through $|r|+w\le 1$, so near-complete retention forces weak writing; decoupling $f_n$ from $i_n$ removes this constraint. Empirically, Naju is the only evaluated model that remains strong on both retention and overwriting at 4x the training length. Beyond the diagnostic suite, we evaluate Naju on WikiText-103 language modeling, Long Range Arena, and multi-query associative recall. Across these settings, Naju consistently combines strong long-range memory with competitive or superior performance, outperforming the Mamba baselines in the principal comparisons while remaining competitive with the Transformer and preserving linear-time, linear-memory scaling.

We propose a hybrid approach for user-centric modeling of transactional event sequences that combines contrastive representation learning (CoLES) with State Space Models (SSMs). While contrastive methods yield high-quality compressed user representations, existing encoders -- RNNs and Transformers -- suffer from vanishing gradients or quadratic complexity, respectively. Mamba, a selective SSM, efficiently handles long-range dependencies but remains underexplored for personalized user analysis. We investigate two integration strategies: (1)~initializing the Mamba hidden state with a CoLES embedding, and (2)~prepending the projected CoLES embedding as a prefix token to the input sequence. Both approaches supply the model with an informative user prior from the first step. Experiments on three public datasets -- Age (multiclass age-group prediction), MBD (multi-label product acquisition), and Taobao (binary purchase prediction) -- demonstrate consistent improvements over standalone Mamba and CoLES with a linear classifier, with the hybrid models converging 2--3$\times$ faster than the plain SSM baseline. Explainability analysis via discretization-step maps and Integrated Gradients reveals selective event filtering on behavior-rich datasets and identifies the most informative transaction features.

Modern power systems increasingly require probabilistic forecasts amid interacting uncertainties from renewable intermittency, flexible demand, market volatility, and weather-dependent generation. However, existing methods often treat multi-scale decomposition, exogenous-variable alignment, and probabilistic output as separate steps, obscuring how predictable structures and uncertainty-bearing fluctuations jointly shape the forecast distribution. This paper proposes a state-space exogenous-context and temporal-frequency resolution architecture for general probabilistic energy forecasting. Its central premise is that trend-periodic components primarily determine the baseline trajectory, whereas high-frequency residuals and external perturbations govern the spread and asymmetry of forecast uncertainty. Accordingly, the architecture adaptively separates deterministic and residual streams, aligns exogenous context with both, refines the deterministic backbone through multi-resolution spectral-temporal state-space modeling, and estimates ordered quantile boundaries from their complementary representations. Experiments on load, price, solar, and wind forecasting achieve the best continuous ranked probability score in 14 of 18 settings, reducing average CRPS by 5.74% and upper-tail quantile risk by 7.27% over the strongest baselines. These results support deterministic-stochastic separation as an effective design principle for general probabilistic energy forecasting.

Polarimetric synthetic aperture radar (PolSAR) image classification is a representative task for physics-aware GeoAI, where land-cover semantics are closely coupled with electromagnetic scattering mechanisms. Many existing complex-valued networks can preserve amplitude-phase information, but they are often limited in long-range spatial dependency modeling and usually incorporate polarimetric priors only as input-level or shallow auxiliary features. As a result, physical knowledge is insufficiently used to guide deep feature evolution. To address this issue, this paper proposes CV-SSMNet, a physics-aware complex-valued state-space network with scattering-aware feature modulation for PolSAR image classification. The proposed method builds a complex-valued state-space model (CV-SSM) in the original complex domain to capture long-range spatial dependencies while preserving polarimetric amplitude-phase coupling. Meanwhile, seven physically meaningful scattering priors, are encoded as FiLM-style modulation signals to adaptively recalibrate complex-valued representations during feature evolution. CV-SSMNet further integrates multi-scale complex convolutions, branch-wise CV-SSM encoding, prior-guided recalibration, and lightweight global context aggregation, enabling physically guided representation learning from local scattering structures to global spatial context. Experiments on three L-band benchmark datasets and an additional P-band BIOMASS evaluation demonstrate that CV-SSMNet achieves competitive accuracy, improved regional consistency, and better boundary preservation, supporting the effectiveness of embedding polarimetric scattering mechanisms into complex-valued long-range GeoAI representation learning.

Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium. Under stated conditions, ECG-separation is sound but incomplete in our examples. Back-door/half-trek routes identify observed queries. Yet for an untouched rotationally symmetric Gaussian block, second moments determine only a source-frame rotation, across which distinct-variable effects generically change. Unknown sensing creates a separate ambiguity. In passive stable linear models without self-effects, unknown wiring and full-rank unknown sensing leave $B$ completely unidentified for $d\ge2$. Under LiNG, non-Gaussianity removes the source rotation; mechanism interventions separate sensing from interactions. With unknown support, invariant sensing, aligned responses, and well-posed single-target interventions identify $(H,B)$ up to declared equivalence. Of $d$ targets, $d-1$ suffice exactly when the sole untargeted node directly parents all others; otherwise $d$ are needed. Acquisition probes are excluded; known wiring gives no universal count. With nonlinear sensing, isotropic Gaussian source blocks admit hidden twists within and across blocks in labelled environments preserving required radial laws. Conversely, under stated positivity, informative one-block changes, rank, and irreducibility conditions, the finest independent source-block representation is identified within the stated alternative class up to block permutation and blockwise coordinate changes, but not downstream mechanisms or the sensor/interaction split. Together, these results show which causal conclusions equilibrium data support and which require targeted experiments.

Low-rank adaptation introduces a static learned update applied identically to every input. The update provides task-level adaptation but does not explicitly represent token-level or instance-level state variation. A family of adapters is proposed that introduces selective state-space control at two complementary granularities. At the token level, MaLoRA (Mamba-modulated low-rank adaptation) makes the adapter's scaling factor a dynamic input-dependent function with recurrent state across tokens, in contrast to the stateless modulators of prior work. The token-level adapter improves over low-rank adaptation. On the other hand, it differentiates tokens by structural role but not by contextual relevance, which motivates placing evidence selection at the context level. At the context level, MaRA (Mamba Retrieval Adapter) tracks cross-segment reasoning state and selects the segments most relevant to the query. State-space controlled retrieval of approximately three million parameters exceeds an eight-billion-parameter dense retriever on supporting-paragraph recall. Although base models perform poorly on the task without adaptation (14 to 25 F1), MaRA recovers the evidence relevance latent in their representations. Across three frozen backbones and two multi-hop reasoning benchmarks, the end-to-end family improves reasoning accuracy on every cell of the 3-by-2 grid, by +6.4 F1 (+10.0% relative) on average over the LoRA baseline.

We propose parameter-efficient SSM-based U-Net architectures for 3D medical image segmentation. Convolutional U-Nets afford O(n) local mixing per layer but lack explicit global context; transformers provide global reasoning at O(n^2) cost in sequence length $n$. State-space models (SSMs), such as Mamba, offer $O(n)$ global propagation per block. Yet, existing medical SSM segmenters rely on fixed scan patterns and large parameter budgets. Dynamic Adaptive Scan (DAS), which learns data-dependent reordering before selective scan, has not been applied to medical imaging or extended to 3D volumes. We propose DAMamba-UNet3D, a hybrid encoder-decoder that integrates tri-plane 3D-DAS blocks at encoder stages E2-E4 while retaining convolutions elsewhere (~5.3M parameters). On BraTS 2020 five-fold cross-validation, DAMamba-UNet3D achieves mean Dice 0.815+/-0.013 (full-volume per-case evaluation) at ~13x lower parameter cost than SegMamba (0.824+-0.014, ~70M). At comparable scale, DAMamba-L (~70M), a wide DAS-native variant with encoder-only DAMamba and a convolutional bottleneck, reaches 0.829+-0.012, surpassing retrained SegMamba by 0.5pt. Component ablations show that encoder-only DAS placement is critical as bottleneck and decoder SSM blocks lower Dice. Together, the results suggest that learned tri-plane DAS in a hybrid U-Net is competitive with, and under our large-scale design may improve upon, SegMamba's fixed Tri-orientated Mamba (ToM) scanning on BraTS 2020. Code: https://github.com/marafathussain/DAMamba-UNet3D.

Data-driven methods have revolutionized ocean modeling, yet current approaches rely heavily on complete reanalysis datasets, imposing computational constraints and limiting model performance to that of the training data. Here, we present a generative state-space model and an optimization framework that enable learning directly from sparse and noisy observations. The model is essentially a hidden Markov model with a continuous state space, where oceanic physical quantities are treated as hidden states and measurements as observations, enabling a unified representation of ocean fields and observational data. Both the initial-state and state-transition modules are implemented as neural networks to capture the complexity and temporal evolution of ocean states, while the emission module is formulated as a masked Gaussian distribution. To train the model from sparse observations, we derive an optimization framework based on the expectation-maximization (EM) algorithm. The framework alternately reconstructs high-fidelity ocean fields via Langevin dynamics and optimizes deep neural networks to capture temporal evolution. Theoretical analysis shows that the framework maximizes the likelihood of observations under the generative model. For efficiency, we assume that ocean-state evolution follows a stationary, ergodic, and Markovian stochastic process and adopt only length-two state sequences during optimization. Experiments on CMIP6 simulation data and FY-3D satellite data demonstrate high-fidelity reconstruction and accurate prediction, showing that sparse observations can directly improve the model's representation of ocean-state dynamics. This work offers a scalable pathway for next-generation Earth system models to learn directly from sparse, incomplete real-world observations.

Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.

Recent advances in deep-learning-based nonlinear system identification have led to encoder-based estimation of neural state-space (ANN-SS) models that achieve state-of-the-art performance in offline settings by estimating initial model states from past input-output data. These methods are typically used in multiple-shooting-based offline identification, and online learning of these models remains largely unexplored. This paper presents a batch-wise learning pipeline and a direct recursive identification algorithm for subspace encoder-based ANN-SS models. We provide convergence analysis of the recursive formulation and validate its performance through extensive simulation studies. The results demonstrate that the proposed approach enables computationally efficient online adaptation with high model accuracy.

In this paper we propose DCVC-Mamba (DCVC-MB), a neural video codec framework for B-frame coding. Our approach incorporates an IBP frame strategy for low-delay B-frame coding, a spatio-temporal fusion model based on state-space models for bidirectional temporal prediction, and an entropy-aware skipping mechanism that selectively omits coding certain latents to reduce entropy coding times. In addition to our model contributions we also implement two inference-time strategies that enhance compression performance. Experimental evaluation shows that DCVC-MB compares favorably to existing NVCs and traditional codecs. The method demonstrates BD-rate reductions of up to $8.98\%$ on average compared to prior neural video codecs, and improvements of up to $30.45\%$ and $1.81\%$ over the VTM-19.0-LDP and VTM-19.0-RA(Inter-GoP=16) benchmarks, respectively, contributing to advances in neural video compression.

State space models (SSMs), notably Mamba, have recently emerged as efficient alternatives to self-attention with linear computational complexity. We investigate the integration of Mamba into YOLO26, the latest non-maximum suppression (NMS)-free object detection framework, by proposing MambaPSA, a lightweight Mamba-based replacement for the C2PSA block at the end of the backbone. To complement this study, we additionally insert a bidirectional Vision Mamba (BiViM) module at the P3, P4, and P5 levels of the neck. Experiments on PASCAL VOC 2007+2012 show that MambaPSA reduces parameters by 2.9%, FLOPs by 12.1%, and improves CPU inference throughput by 17.6% (from 17 to 20 FPS) with negligible accuracy change (-0.1 mAP50:95), while the P4 BiViM placement yields the best accuracy gain (+0.9 mAP50:95). These results suggest that SSMs offer a favorable efficiency-accuracy trade-off when replacing attention-based blocks in NMS-free lightweight detectors.

Global Station Weather Forecasting (GSWF) is pivotal for localized and extreme weather prediction over key regions. Despite efforts to exploit look-back windows, existing methods show limited accuracy gains and struggle with extreme events and error accumulation. These limitations stem from overreliance on short-term patterns, which are insufficient to capture chaotic weather dynamics, especially under partial observations. To address this problem, we propose a novel Triaxial State Space Model (TSSM) with a history-enhanced Temporal-VariableHistorical paradigm, which incorporates period-aligned historical weather data to compensate for long-term, large-scale periodic, and full-window weather patterns beyond the temporal lookback window. Specifically, TSSM stacks historical samples into period-aligned batches, where forecasting is causally supported by historical and current observations. Temporal, variable, and historical scanning are designed to capture axial temporal dependencies, variable correlations, and historical evolution. This structure is hierarchically shared to model seasonal to extreme events while alleviating misalignment across historical patterns. TSSM achieves SOTA performance on Weather-5K, the largest station weather dataset to date, with 10% and 61% gains in accuracy and extreme event metrics, and obtains 95% best or second-best results on human-involved datasets. Its advantages are more pronounced in long-horizon and iterative forecasting, reaching a 37.5% gain at 240h and up to 103.5% under a 48h times 5 iterative setting. Moreover, TSSM retains > 90% performance under up to 80% missing observations, compared with < 43% for baselines, demonstrating robustness and practical potential for reliable GSWF in global in-situ observation networks.

Selective state-space models such as Mamba route information through a bank of first-order modes whose input coupling is set by a learned selection mechanism. We give an exact instrument for measuring how a trained model uses these modes. Because the state matrix is diagonal, each channel's output decomposes exactly into per-mode contributions, and a per-(layer, channel, window) Gram tensor yields the exact output error of dropping any subset of modes, offline, at any budget. Validated against the reference implementation to a relative error of $2.3\times10^{-7}$ on the Mamba-1 family where it is exact, the instrument predicts a layer's deployed pruning error to a median relative deviation of $5\times10^{-7}$ over $4{,}464$ configurations, its floor set by the reconstruction. Applying the instrument across the Mamba-1 family (130M--2.8B), the deployed 7B Falcon-Mamba, and Mamba-2, we find that trained models re-allocate their state space with the input: which modes carry the signal migrates across contexts, and at the most affected layers a per-input oracle roughly halves the output error of a fixed mode set. Frozen-signal counterfactuals attribute the migration primarily to the input-dependent write map $B_t$; the timestep usually identified with selectivity carries almost none of it. Input-scheduled mode pruning on this measurement outperforms static, Hankel-based, and layer-adaptive rankings at every scale from 130M to the deployed 7B Falcon-Mamba, and at half the state budget it matches the unpruned model. Because the scheduler reads each window's mode usage from a first pass, this demonstrates realizable headroom; we claim no deployed compute or memory saving.

State Space Models (SSMs) have emerged as a powerful paradigm for efficient long-sequence modeling, offering parallel training and fast linear-time recurrent inference. However, like other recurrent architectures, SSMs must compress an unbounded history into a fixed-size state, which limits context retention and makes precise retrieval over long-range context inherently difficult. To overcome this limitation, we propose Delay State Space Models (DSSMs), a delay differential equation (DDE)-inspired extension of diagonal SSMs that augments discrete SSM recurrences with explicit delayed-state feedback. Making explicit delayed feedback practical requires new stability parameterization, history management, and FFT-training tools. We address these challenges with a practical discretization and parameterization grounded in a simple delay-independent stability condition. To bypass direct time-domain kernel construction, we derive the DSSM transfer function and compute kernels in the frequency domain, using a kernel contour shift to suppress aliasing and recover accurate FFT training. Empirically, DSSMs substantially improve targeted delayed-retrieval tasks while outperforming S4D on most standard sequence metrics and remaining close on the others.

Fixed-state sequence models compress an unbounded past into a bounded state, which caps their associative recall at roughly the state dimension; attention escapes the cap by keeping a key-value entry for every token, at quadratic compute and a cache that grows with the sequence. We study the middle ground: a sparse cache that allocates a slot only when an input is novel, so its size tracks the number of distinct items rather than the number of tokens. The allocation rule is the DP-means clustering rule, the small-variance limit of a Dirichlet-process mixture, used not as latent-variable inference but as the key-value memory operator for a deep recurrent backbone. We develop it in two forms, a static cache with a fixed concentration and a surprise-adaptive variant whose concentration follows the recent novelty rate. On a controlled associative-recall benchmark with redundancy we show that the cache matches full-attention recall while storing only the distinct items, that it dominates a fixed-budget eviction cache on the recall-versus-size frontier, and that on a state-space backbone it answers both a recall query and a long-range aggregate at the lowest memory of any model tested. The allocation is learnable end to end: a two-parameter novelty-threshold gate trained on the task loss alone recovers the rule exactly, whereas an over-parameterized gate fails, so the operative ingredient is the inductive bias rather than capacity. The evidence is a family of controlled mechanism studies at modest scale, with the distinct-items property confirmed on four real streams (recommendation, systems logs, clinical events, and insurance claims); a real-backbone, real-corpus language validation is pursued in a companion study.

A learning-enabled disturbance-rejection framework based on a Neural Extended State Observer (Neural-ESO) is presented in this letter. Unlike existing learning-based control methods that largely rely on the learned model once deployed, Neural-ESO adopts a dual-pathway architecture: a predictive pathway uses a neural network to provide a feedforward disturbance estimate that accelerates convergence, while a corrective pathway employs a conventional ESO to compensate prediction errors and prevent over-reliance on the neural component. Using Lyapunov theory and a small-gain analysis, we show that enforcing a Lipschitz bound on the learning component guarantees uniform ultimate boundedness of the closed-loop error dynamics. The proposed framework is validated on a quadrotor landing task subject to strong ground-effect disturbances across normal and out-of-distribution scenarios, demonstrating accuracy-robustness trade-off and greater operational reliability during training, deployment, and transfer compared with state-of-the-art baselines.

With the proliferation of AI-generated content, sophisticated multimedia manipulation has raised critical concerns about malicious applications such as opinion manipulation and evidence fabrication, making Audio-Visual Temporal Forgery Localization (AV-TFL) an urgent research frontier. Existing TFL methods have progressed along two main paradigms: Transformer-based temporal modeling and channel-wise multimodal fusion. While these approaches capture temporal dependencies and cross-modal correlations, they process all frequency components indiscriminately, leading to overfitting on high-frequency noise and limited robustness under real-world data degradation. Through systematic frequency domain analysis, we find that forgery-discriminative patterns concentrate in the low/mid-frequency range (normalized frequency 0-0.15), while high-frequency components primarily introduce noise, removing them even improves detection performance by +1.4%. Based on this phenomenon, we propose UniSkip-Mamba, a frequency-aware State Space Model framework that incorporates Unified Multimodal Sequence Fusion to preserve cross-modal phase relationships, and Skip-Scanning Mamba Blocks that implement frequency-aware regularization through a novel Group-Scan-Merge mechanism, naturally biasing learning toward discriminative low/mid-frequency patterns (0-0.15) while maintaining representational completeness. We achieve state-of-the-art (SOTA) performance: 63.4% AP@0.95 on LAV-DF (+9.8% improvement) and 63.58% mAP on AV-Deepfake1M (+14.32% improvement), with 6x faster inference. Our frequency-domain analysis provides theoretical justification from a signal processing perspective for why skip-scanning inherently improves both accuracy and robustness.

State Space Models (SSMs) have emerged as an alternative to Vision Transformers, yet most vision SSMs inherit directional token scanning from causal sequence modeling. While effective for sequential data, directional scanning introduces spatial bias and orientation-sensitive representations. We present Vision Non-Causal Trapezoidal Mamba (VNCT), a second-order non-causal vision SSM that enables all image tokens to interact in a single pass, eliminating direSctional scanning and achieving low single-image inference latency. VNCT exhibits more orientation-robust representations, showing reduced performance degradation under image rotations and flips, while improving Boundary IoU by up to 3.7 points, leading to more accurate boundary preservation and object localization. Across ImageNet-1K classification, COCO object detection and instance segmentation, and ADE20K semantic segmentation, VNCT consistently outperforms both directional-scanning vision SSMs and first-order non-causal SSMs. These results show that directional scanning is unnecessary for high-performance vision SSMs and that second-order non-causal state-space modeling offers a simple, efficient, and robust alternative for visual recognition.

In this paper, we present the Invariant-Variant Disentangled State-Space Model (IVD-SSM), our submission to SemEval-2026 Task 4 on Narrative Story Similarity and Narrative Representation Learning. Evaluating narrative similarity is a profound computational challenge that requires models to look past concrete, superficial elements such as specific names, actors, objects, or settings to isolate and compare abstract patterns of causality and plot progression. To model these extended causal chains without the quadratic bottlenecks of standard Transformers, we leverage a hybrid State-Space Model (Jamba-1.5-Mini). Building upon this backbone, we introduce the Structurally Gated Alignment (SGA) head, a novel, differentiable algorithmic architecture. The SGA head operates on two scales: a heavily strided Macro-path maps the coarse structural skeleton of a story, which then acts as a gating mechanism to filter a full-resolution Micro-path, actively suppressing semantic noise and superficial keyword overlaps. Evaluated on both pairwise comparative judgments (Track A) and dense representation learning (Track B), our approach demonstrates that explicitly disentangling structural invariants from lexical variants provides a robust, principled framework for deep narrative understanding.

Images captured by consumer electronic devices, such as mobile phones and digital cameras, often suffer from low-light degradation due to sensor limitations and imaging pipelines, which degrades visual quality and affects downstream vision tasks. Existing methods based on Convolutional Neural Networks (CNNs) and Transformers have dominated current low-light image enhancement (LIE) due to their excellent ability to model hierarchical features. However, CNNs operate in local receptive fields that cannot model long-range dependencies, while Transformers overcome this problem but incur substantial computational costs. To address these challenges, we propose MambaLIE, a Scene Light Intensity-Boosted Low-Light Image Enhancement method based on a State Space Model (SSM). We first introduce scene light intensity to improve the structural distribution of illumination, which is then gated with the low-light input to guide enhancement. To better model the illumination while maintaining computational efficiency, we propose the Locally Enhanced State Space Model (LESSM) for efficient light enhancement. Our LESSM contains two branches: an SSM branch and a Local Enhanced branch, where the former is used to model the long-range dependencies with linear time complexity, while the latter is used to enhance local feature representations. Extensive experiments demonstrate that MambaLIE outperforms state-of-the-art CNN-based and Transformer-based LIE methods on four widely used synthetic benchmarks and five publicly available real-world benchmarks in terms of accuracy, speed, and model size, making it suitable for practical deployment on resource-constrained devices.

Hierarchical state-space models (HSSMs) offer a promising approach to long-horizon prediction by segmenting sequences into temporal chunks. However, their performance hinges on how chunk boundaries are determined. While prior HSSMs typically rely on fixed-length chunking or similarity-based boundary detection, these methods often misalign with the intrinsic temporal structure of the data. We argue that chunking should instead be driven by prediction errors, which more directly indicate when longer-range context becomes necessary. Nevertheless, integrating surprise-based chunking into HSSMs introduces critical challenges, including hierarchical collapse during end-to-end training and the absence of surprise signals during open-loop prediction. To address these issues, we propose Surprise-based Nested Temporal Abstraction (SUNTA), a method that employs a decoupled training strategy to preserve surprise signals and uses internal inconsistency as a top-down surprise metric to determine chunk boundaries within imagined rollouts. Experiments on video prediction tasks in 2D and 3D environments demonstrate that SUNTA outperforms baselines, uniquely maintaining accurate predictions over 250 timesteps, whereas all baselines degrade within the first 10 timesteps.

Rotational Scanning Computed Laminography (RCL) is widely utilized for the Non-Destructive Testing (NDT) of large planar components. However, to facilitate rapid inspection, continuous sparse-view scanning is often employed, where the angular integration effect during exposure induces rotational blur in the projection domain. Furthermore, the data incompleteness inherent in sparse sampling manifests as sparse artifacts in the reconstructed image domain. To address these cross-domain degradations, this paper proposes RCL-Mamba, a measurement-oriented dual-domain State Space Model (SSM)-based image restoration network. The framework adopts a cascaded joint processing strategy: it first corrects the rotational blur in the projection domain and subsequently suppresses the sparse artifacts in the image domain. Additionally, we design a Mamba-CNN dual-branch module to adaptively balance large-scale blur correction with local detail recovery. Evaluations on both simulated datasets and real-world Printed Circuit Board (PCB) scans demonstrate that RCL-Mamba outperforms existing baselines in blur removal, artifact suppression, and structural preservation. Line-profile-based structural measurement further verifies that the proposed method better preserves via/pad boundaries and slender trace profiles. Crucially, by reducing the required scanning views from 512 to 64, our method enhances inspection efficiency by approximately 8-fold without compromising reconstruction quality, offering a robust measurement-oriented restoration solution for high-throughput RCL inspection with improved structural measurement fidelity.

This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagrangian mechanics formulation. As in Lagrangian neural networks (LNNs), we parameterize the kinetic and potential energies with neural networks. The unknown external forces in the Lagrangian formulation are modeled as white Gaussian noise. The corresponding Euler--Lagrange equations then yield a continuous-time stochastic state-space model (SSM) that describes the system dynamics. The neural network parameters and system states are then jointly learned via a maximum-likelihood method using Gaussian-approximation-based Bayesian filters. The effectiveness of the proposed method is demonstrated on pendulum and Duffing oscillator examples, and its performance is compared with conventional LNNs and with approximate Bayesian filters using known system models.

State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memory degradation over extended horizons due to poorly conditioned first-order updates and unbalanced update geometry. We introduce MuonSSM, a general framework that stabilizes SSM training by explicitly conditioning the geometry of memory updates rather than the recurrent transition matrix. MuonSSM augments SSMs with a momentum-based pathway and a lightweight Newton Schulz transformation on low-rank input injections, yielding bounded and spectrally conditioned updates while preserving parallel scan complexity. Theory shows that MuonSSM improves gradient propagation, mitigates spectral amplification, and enriches memory representations over long horizons. Extensive experiments across language, vision, and time-series benchmarks show consistent gains in accuracy, robustness, and long-context performance when integrated into diverse SSM backbones. These results establish geometric conditioning of updates as a principled pathway to stable, scalable sequence modeling.

Visual Object Tracking (VOT) and Moving Object Segmentation (MOS) are two fundamental tasks in computer vision that involve both spatial and temporal object dynamics. Existing methods rely predominantly on visual cues and thus often falter in real-world scenarios where object motions are inherently complex and nonlinear. To address this limitation, we propose SUMO, a zero-shot, training-free, unified framework integrating nonlinear dynamics with vision-based segmentation for accurate and consistent VOT and MOS. Specifically, we develop a nonlinear State Space Model (SSM) inspired by robotics principles to capture the complex object dynamics. Building on this model, we propose a Selective Unscented Filter (SUF) for accurate state estimation, which features a joint scoring mechanism and dynamically fuses multi-source predictions to identify the most plausible object state over time. Furthermore, we apply a memory selection mechanism to evaluate the reliability of memory frames. Our extensive experimental results show that SUMO achieves state-of-the-art performance on both VOT and MOS tasks.

Nowadays mobile robots have wide engineering applications. Simultaneous localization and mapping (SLAM) is an important task of these robots. The major and common algorithms used for this task are based on extended Kalman filter (EKF). One of the main problems in EKF-based SLAM is its divergence. The nonlinearity of motion and observation models and linearization error are the main reasons for the divergence. There have been some efforts to address this problem with limited success. In this paper, by applying a simple compass and using an effective transformation, we transform the non-linear state space model into a linear model. Then, by applying the original KF to this model, we reach a new method, which is called LMKF SLAM. We show that the LMKF SLAM is significantly superior to the state-of-the-art methods, especially EKF-based SLAMs, both in accuracy, convergence, and computational complexity. The proposed method is also more stable with respect to the uncertainty of sensors values and changes in system parameters. Experimental results verify these points.

Sea state prediction is essential for operational maritime applications and coupled earth system modeling, yet current spectral wave models remain computationally prohibitive for many use cases, including online coupling to climate simulations and making probabilistic (ensemble-based) predictions. While deep learning has recently demonstrated strong performance in weather forecasting, existing AI-based wave models are predominantly deterministic and largely limited to bulk variables such as significant wave height, leaving probabilistic sea state estimation largely unexplored. In this work, we propose a diffusion-based generative model for global sea state estimation that conditions on a relatively long history (5 days) of global wind forcing. This generative model directly samples the complex conditional distribution of sea state without autoregressive time-stepping. Unlike prior approaches, our framework naturally extends beyond bulk variables to estimate partition-related variables and derived quantities, such as Stokes drift and mean square slope. Trained on a 30-year global WAVEWATCH-III hindcast, the model achieves substantial computational acceleration compared with numerical spectral models while delivering skillful predictions and a calibrated ensemble spread for the bulk variables. Our results suggest that diffusion-based sea state sampling offers a promising path toward probabilistic wave forecasting and efficient coupling of sea state information into broader earth system models.

While parameter-efficient fine-tuning (PEFT) typically targets attention projectors, its efficacy for tasks requiring sequential state accumulation remains under-explored. We examine if PEFT for such tasks can benefit from state space model (SSMs) adapters, and if MLP blocks are better injection sites. We introduce Hankel Reduced order Model (HRM) adapter, an SSM-based residual module initialized via Balanced Truncation of empirical Hankel Grammians. By leveraging the time-invariance of the system matrix $\bar{A}$, HRM enables an exact FFT-based parallel scan, achieving computational parity with LoRA across all context lengths. In iso-parametric evaluations on Mistral-7B (8.4M trainable parameters), HRM outperforms LoRA variants on LongBench tasks, including QuALITY (+34.8% relative accuracy) and QMSum (+71.6% relative ROUGE-1). HRM further demonstrates consistent superiority across 18 configurations of synthetic state-tracking (DFA, Parity) and character-level language modeling (enwik8). Gate analysis reveals that HRM adapters effectively learn to modulate recurrence, providing a robust architectural alternative to low-rank adaptation for long-context sequence modeling.

State Space Models (SSMs), designed for long-range modeling, offer linear computational complexity and strong capabilities in capturing long-range dependencies. In the field of remote sensing, SSMs have gained popularity due to their effectiveness in addressing unique challenges such as dense visual predictions, multi-modal remote sensing data, and temporal remote sensing data, which have also yielded significant advancements in customized architectures. This paper presents a comprehensive review of SSM-based approaches in remote sensing, covering most of the relevant studies since SSMs were first introduced to the field. We offer a multi-dimensional analysis examining SSM applications in remote sensing tasks and discussing advancements in architecture design. This paper not only synthesizes the rapid progress in SSM-based research but also identifies key challenges and future opportunities. By providing a detailed perspective, this paper aims to serve as a foundational resource for remote sensing researchers, offering actionable insights to foster further advancements in this evolving domain. We will keep tracing related works at https://github.com/QinzheYang/Awesome-RS-State-Space-Model.

In-camera JPEG previews are ubiquitous in raw image formats and provide an sRGB reference at negligible storage cost. Although existing metadata-based reconstruction frameworks can exploit this side information when recovering raw images, their context models often become computationally expensive especially at high resolution, eg, 4K raw image, given that attention mechanisms scale quadratically with feature maps, hindering its practical application. To address these limitations, we propose MambaRaw, a JPEG-conditioned metadata-based raw image reconstruction framework that uses State Space Models (SSMs) to estimate entropy parameters efficiently. Our key contribution comprises a Spatial-Energy Coupled Context Modeling mechanism with two lightweight modules: (1) TileMambaBlock, which performs Mamba-style selective scanning only on information-dense tiles to improve the efficiency; and (2) Energy-Aware Refinement (EAR), an identity-initialized residual module that enhance feature representation to match the long-tail energy distribution of raw signals. Extensive experiments on three camera datasets (Sony, Olympus, Samsung) show consistent improvements over strong metadata-based baselines and set a new state of the art for JPEG-guided raw reconstruction with great efficiency. Notably, at low metadata bitrates, MambaRaw increases PSNR by 1.2--1.4 dB and reduces end-to-end coding latency by about 9%. Code is released at https://github.com/Peizeli1/MambaRaw.

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.