# PIMSM: Physics-Informed Multi-Scale Mamba for Stable Neural Representations under Distribution Shift

arXiv: https://arxiv.org/abs/2605.16351 · HTML: https://mlsanity.com/paper/2605.16351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Physiological signal modeling, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- State-space sequence models (S4, Mamba) / [Physiological signal modeling](https://mlsanity.com/ssm/physiological-signal-modeling/)

## Builds on (most cited first, 16 of 16)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Towards a general-purpose foundation model for fMRI analysis](https://mlsanity.com/paper/2506.11167/) (2025)
- [Omni-fMRI: A Universal Atlas-Free fMRI Foundation Model](https://mlsanity.com/paper/2601.23090/) (2026)
- [SLIM-Brain: A Data- and Training-Efficient Foundation Model for fMRI Data Analysis](https://mlsanity.com/paper/2512.21881/) (2025)
- [ms-Mamba: Multi-scale Mamba for Time-Series Forecasting](https://mlsanity.com/paper/2504.07654/) (2025)
- [Scale-Free and Multifractal Time Dynamics of fMRI Signals during Rest and Task](https://mlsanity.com/paper/1308.4385/) (2013)
- [MS-SSM: A Multi-Scale State Space Model for Efficient Sequence Modeling](https://mlsanity.com/paper/2512.23824/) (2025)
- [Spatiotemporal Learning of Brain Dynamics from fMRI Using Frequency-Specific Multi-Band Attention for Cognitive and Psychiatric Applications](https://mlsanity.com/paper/2503.23394/) (2025)
- [STM3: Mixture of Multiscale Mamba for Long-Term Spatio-Temporal Time-Series Prediction](https://mlsanity.com/paper/2508.12247/) (2025)

## Abstract (arXiv)

Scientific foundation models are expected to reuse representations under changes in dataset, acquisition protocol, and deployment domain, yet many sequence backbones treat scientific temporal structure as an unconstrained pattern to be fitted. We argue that this misses a central property of natural dynamical systems: neural and atmospheric time series are organized by interacting processes across multiple physical timescales, and failure to preserve this multiscale structure contributes to brittleness under distribution shift. We formalize this failure mode as temporal kernel mismatch, where a model fits in-distribution dynamics with an effective memory policy that is not anchored to the signal's physical timescales, leading to representation drift and degraded transfer. We propose Physics-Informed Multi-Scale Mamba (PIMSM), a state-space architecture that maps spectrum-estimated transition points between frequency regimes (knee frequencies) to scale-specific discretization parameters and anchors them to acquisition time units. On Human Connectome Project fMRI, PIMSM improves robustness and representation stability under severe temporal-context truncation, extreme low-resource transfer, and resting-state-to-task-state generalization. Without modality-specific adaptation, the same architecture also attains the lowest variable-wise MAE across all reported horizons and variables on Weather-5K held-out-station spatial out-of-distribution forecasting. These results support temporal-scale alignment as a practical inductive bias for scientific foundation models that must preserve structure, not only fit correlations, under deployment shift.