Selective SSMs

Volume Electron Microscopy (VEM) is crucial for 3D tissue imaging but often produces anisotropic data with poor axial resolution, hindering visualization and downstream analysis. Existing methods for isotropic reconstruction often suffer from neglecting abundant axial information and employing simple downsampling to simulate anisotropic data. To address these limitations, we propose VEMamba, an efficient framework for isotropic reconstruction. The core of VEMamba is a novel 3D Dependency Reordering paradigm, implemented via two key components: an Axial-Lateral Chunking Selective Scan Module (ALCSSM), which intelligently re-maps complex 3D spatial dependencies (both axial and lateral) into optimized 1D sequences for efficient Mamba-based modeling, explicitly enforcing axial-lateral consistency; and a Dynamic Weights Aggregation Module (DWAM) to adaptively aggregate these reordered sequence outputs for enhanced representational power. Furthermore, we introduce a realistic degradation simulation and then leverage Momentum Contrast (MoCo) to integrate this degradation-aware knowledge into the network for superior reconstruction. Extensive experiments on both simulated and real-world anisotropic VEM datasets demonstrate that VEMamba achieves highly competitive performance across various metrics while maintaining a lower computational footprint. The source code is available on GitHub: https://github.com/I2-Multimedia-Lab/VEMamba

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

Selective state space models (SSMs) have rapidly become a compelling backbone for large language models, especially for long-context workloads. Yet in deployment, their inference performance is often bounded by the memory capacity, bandwidth, and latency limits of a single GPU, making multi-GPU execution increasingly necessary. Although tensor parallelism (TP) is widely used to scale Transformer inference, applying it to selective SSM blocks is non-trivial because the SSM mixer couples large projections with a sequence-wise recurrent state update and local mixing whose efficiency depends on preserving locality and avoiding synchronization in the critical path. This paper presents a communication-efficient TP design for selective SSM inference that addresses three practical engineering challenges: enabling TTFT improvements via an SSM state cache across prefill and decode, partitioning the mixer's packed parameter tensor so that recurrent updates remain local while minimizing communication, and reducing TP aggregation overhead with quantized AllReduce. We evaluate on three representative SSM-based LLMs spanning pure-SSM and hybrid architectures - Mamba, Falcon-Mamba, and Zamba - on NVIDIA A6000 and A100 clusters. Our experiments show substantial throughput gains from tensor-parallel SSM inference, improving batch-request throughput by ~1.6-2.1x on 2 GPUs and ~2.6-4.0x on 4 GPUs for Mamba, with the largest benefits at long context lengths, and achieving a further ~10-18% throughput improvement from quantized all-reduce by lowering synchronization bandwidth overhead.

We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL). Unlike interpretations framing Transformers as performing implicit gradient descent, we formalize ICL as meta-learning over latent sequence tasks. For tasks governed by Linear Gaussian State Space Models (LG-SSMs), we prove a meta-trained selective SSM asymptotically implements the Bayes-optimal predictor, converging to the posterior predictive mean. We further establish a statistical separation from gradient descent, constructing tasks with temporally correlated noise where the optimal Bayesian predictor strictly outperforms any empirical risk minimization (ERM) estimator. Since Transformers can be seen as performing implicit ERM, this demonstrates selective SSMs achieve lower asymptotic risk due to superior statistical efficiency. Experiments on synthetic LG-SSM tasks and a character-level Markov benchmark confirm selective SSMs converge faster to Bayes-optimal risk, show superior sample efficiency with longer contexts in structured-noise settings, and track latent states more robustly than linear Transformers. This reframes ICL from "implicit optimization" to "optimal inference," explaining the efficiency of selective SSMs and offering a principled basis for architecture design.

Stereo depth estimation is fundamental to underwater robotic perception, yet suffers from severe domain shifts caused by wavelength-dependent light attenuation, scattering, and refraction. Recent approaches leverage monocular foundation models with GRU-based iterative refinement for underwater adaptation; however, the sequential gating and local convolutional kernels in GRUs necessitate multiple iterations for long-range disparity propagation, limiting performance in large-disparity and textureless underwater regions. In this paper, we propose StereoAdapter-2, which replaces the conventional ConvGRU updater with a novel ConvSS2D operator based on selective state space models. The proposed operator employs a four-directional scanning strategy that naturally aligns with epipolar geometry while capturing vertical structural consistency, enabling efficient long-range spatial propagation within a single update step at linear computational complexity. Furthermore, we construct UW-StereoDepth-80K, a large-scale synthetic underwater stereo dataset featuring diverse baselines, attenuation coefficients, and scattering parameters through a two-stage generative pipeline combining semantic-aware style transfer and geometry-consistent novel view synthesis. Combined with dynamic LoRA adaptation inherited from StereoAdapter, our framework achieves state-of-the-art zero-shot performance on underwater benchmarks with 17% improvement on TartanAir-UW and 7.2% improvment on SQUID, with real-world validation on the BlueROV2 platform demonstrates the robustness of our approach. Code: https://github.com/AIGeeksGroup/StereoAdapter-2. Website: https://aigeeksgroup.github.io/StereoAdapter-2.

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.

Multi-modal medical image synthesis is pivotal for alleviating clinical data scarcity, yet existing methods fail to reconcile global anatomical consistency with high-fidelity local detail. We propose FermatSyn, which addresses three persistent limitations: (1) SAM2-based Prior Encoder that injects domain-aware anatomical knowledge via LoRA$^{+}$ efficient fine-tuning of a frozen SAM2 Vision Transformer; (2) Hierarchical Residual Downsampling Module (HRDM) coupled with a Cross-scale Integration Network (CIN) that preserves high-frequency lesion details and adaptively fuses global--local representations; and (3) continuity constrained Fermat Spiral Scanning strategy within a Bidirectional Fermat Scan Mamba (BFS-Mamba), constructing an approximately isotropic receptive field that substantially reduces the directional bias of raster or spiral serialization. Experiments on SynthRAD2023, BraTS2019, BraTS-MEN, and BraTS-MET show FermatSyn surpasses state-of-the-art methods in PSNR, SSIM, FID, and 3D structural consistency. Downstream segmentation on synthesized images yields no significant difference from real-image training ($p{>}0.05$), confirming clinical utility. Code is available at https://github.com/exsinger-hub/ FermatSyn.

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.