Single molecule localization microscopy challenge: a biologically inspired benchmark for long-sequence modeling

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.

Whole-slide image (WSI) analysis is challenging due to the gigapixel scale of slides and their inherent hierarchical multi-resolution structure. Existing multiple instance learning (MIL) approaches often model WSIs as unordered collections of patches, which limits their ability to capture structured dependencies between global tissue organization and local cellular patterns. Although recent State Space Models (SSMs) enable efficient modeling of long sequences, how to structure WSI tokens to fully exploit their spatial hierarchy remains an open problem.We propose MoEMambaMIL, a structure-aware SSM framework for WSI analysis that integrates region-nested selective scanning with mixture-of-experts (MoE) modeling. Leveraging multi-resolution preprocessing, MoEMambaMIL organizes patch tokens into region-aware sequences that preserve spatial containment across resolutions. On top of this structured sequence, we decouple resolution-aware encoding and region-adaptive contextual modeling via a combination of static, resolution-specific experts and dynamic sparse experts with learned routing. This design enables efficient long-sequence modeling while promoting expert specialization across heterogeneous diagnostic patterns. Experiments demonstrate that MoEMambaMIL achieves the best performance across 9 downstream tasks.

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems that encode the past history of the input signal. However, existing projection-based SSMs often rely on polynomial bases with global temporal support, whose inductive biases are poorly matched to signals exhibiting localized or transient structure. In this work, we introduce WaveSSM, a collection of SSMs constructed over wavelet frames. Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization. Empirically, we show that on equal conditions, WaveSSM outperforms orthogonal counterparts as S4 on real-world datasets with transient dynamics, including physiological signals on the PTB-XL dataset and raw audio on Speech Commands.