Selective SSMs

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, $\TildeΔ$ no longer equals the physical time gap $Δ$ between consecutive observations, limiting the ability of these models to handle irregular time series. Continuous time SSMs, such as S5, keep $\TildeΔ\equivΔ$ and therefore handle irregular timestamps natively, 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, $\TildeΔ\equivΔ$ as in S5, 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 best average rank on UEA time series classification and the Physiome ODE regression benchmark, and matches or exceeds the reference baseline model on 6 of 8 natively irregular datasets from astronomy, agriculture, neuromorphic sensing, and climate events. Code available at: https://github.com/TaylanSoydan/TIDES.

Inductive biases influence the behavior and performance of sequential models. In this work, we study an underexplored inductive bias in sequential modeling: continuity in time. We ask a simple question: do models motivated by continuous-time formulations, such as state-space models, actually behave continuously in time, and does this translate into better performance on tasks with continuous temporal structure? To answer this, we formalize model continuity as convergence under temporal refinement, where a model is continuous if its predictions approach an underlying continuous trajectory as the temporal discretization is refined. We show that S4 exhibits stable continuous behavior, whereas S6 (the core of Mamba) can be more sensitive to input amplitude and selective dynamics, despite being derived from a continuous dynamical system. To study whether this distinction matters for learning, we also need a corresponding notion of task continuity. We therefore introduce a metric to quantify the continuity of datasets directly from their temporal structure. Across benchmarks, we find a clear empirical alignment between task continuity, model continuity, and model performance. Beyond an inductive bias, continuity also has practical consequences: we show that it enables a simple temporal subsampling strategy that improves both efficiency and performance.

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

Photoplethysmography (PPG) is increasingly used in wearable affective computing due to its low cost and ease of integration into consumer devices. Recent advances in deep learning have introduced long-range sequence models, such as Transformers, and state-space models, like Mamba, which have demonstrated strong performance on natural language and general time-series tasks. However, it remains unclear whether these architectures offer tangible benefits over widely used Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTMs) for PPG-based affect recognition, given that datasets are typically small and noisy. This work presents a measurement-driven comparison of four deep learning architectures, CNN, CNN-LSTM hybrid, Transformers, and Mamba, for classifying arousal, valence, and relaxation states from wrist-based PPG signals. All models are evaluated under a subject-independent 5-fold cross-validation protocol using identical preprocessing, segmentation, and training pipelines. Our results show that the Transformer and Mamba models achieve performance comparable to that of a CNN baseline, but do not consistently outperform it across all tasks. CNNs remain the most effective overall, providing the highest accuracy with the smallest model size, whereas Transformers have a better balance of F1 scores for Arousal and Relaxation. The study provides the first evaluation of Transformer and Mamba models for PPG-based affect recognition, offering practical guidance on model selection for wearable affective monitoring systems.

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.

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

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

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

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

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

The Mamba model has gained significant attention for its computational advantages over Transformer-based models, while achieving comparable performance across a wide range of language tasks. Like Transformers, Mamba exhibits in-context learning (ICL) capabilities, i.e., making predictions for new tasks based on a prompt containing input-label pairs and a query, without requiring fine-tuning. Despite its empirical success, the theoretical understanding of Mamba remains limited, largely due to the nonlinearity introduced by its gating mechanism. To the best of our knowledge, this paper presents the first theoretical analysis of the training dynamics of a one-layer Mamba model, which consists of a linear attention component followed by a nonlinear gating layer, and its ICL generalization on unseen binary classification tasks, even when the prompt includes additive outliers. Our analysis shows that Mamba leverages the linear attention layer to select informative context examples and uses the nonlinear gating layer to suppress the influence of outliers. By establishing and comparing to the analysis of linear Transformers under the same setting, we show that although Mamba may require more training iterations to converge, it maintains accurate predictions even when the proportion of outliers exceeds the threshold that a linear Transformer can tolerate. These theoretical findings are supported by empirical experiments.

Statutory corpora and judicial decisions are growing faster than legal professionals can read them, while individual judgments often exceed the context limits of standard encoder models. Transformer architectures dominate legal NLP benchmarks, but their quadratic attention complexity can require truncating or fragmenting documents that demand whole-document reasoning. Selective state-space models (SSMs), such as Mamba, offer linear-time sequence modeling and are a promising alternative for long legal documents, yet their performance on legal classification and retrieval remains underexplored. We present a preliminary benchmark comparing Mamba and SSD-Mamba with BERT, DeBERTa, and Longformer across four legal classification tasks (ECtHR, EUR-Lex, SCOTUS, and ILDC/ILC) and two case-retrieval tasks (ECtHR and ILDC), using a shared windowing and aggregation pipeline. The strongest SSM performs within approximately 1.3 percentage points of the strongest transformer across tasks and metrics. SSD-Mamba achieves the best results on most metrics for ECtHR classification, ILDC classification, and ECtHR retrieval, while processing approximately 3 times more tokens per second than DeBERTa and 4 times more than Longformer. DeBERTa remains strongest on SCOTUS and EUR-Lex F1. These results are preliminary because they do not include variance estimates across random seeds or statistical significance testing. Rather than presenting a definitive ranking, we use these findings to motivate further evaluation with repeated-seed experiments, statistical testing, and controls for model capacity and computational efficiency.

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

While transformer-based language models have driven the AI revolution thus far, their computational complexity has spurred growing interest in viable alternatives, such as structured state space sequence models (SSMs) and Selective SSMs. Among these, Mamba (S6) and its variant Mamba-2 have shown remarkable inference speed-ups over transformers while achieving comparable or superior performance on complex language modeling tasks. However, despite these architectural innovations and empirical successes, the fundamental learning capabilities of Mamba remain poorly understood. In this paper, we address this gap by studying in-context learning (ICL) on Markov chains and uncovering an interesting phenomenon: even a single-layer Mamba efficiently learns the in-context Laplacian smoothing estimator, which is both Bayes and minimax optimal. To explain this, we theoretically characterize the representation capacity of Mamba and reveal the fundamental role of convolution in enabling it to represent the optimal Laplacian smoothing. These theoretical insights align strongly with empirical results and, to the best of our knowledge, represent the first formal connection between Mamba and optimal statistical estimators. Finally, we outline promising research directions inspired by these findings.