Looped SSMs: Depth-Recurrence and Input Reshaping for Time Series Classification

• URL: http://arxiv.org/abs/2605.16048v1
• Date: Fri, 15 May 2026 15:18:12 GMT
• Title: Looped SSMs: Depth-Recurrence and Input Reshaping for Time Series Classification
• Abstract summary: We show that a looped SSM with $k$ parameters iterated $L$ times consistently closely matches or outperforms a standard SSM.<n>We also show that input reshaping is an equally neglected design axis.
• Score: 50.994194925685434
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: State Space Models (SSMs) are inherently recurrent along the sequence dimension, yet depth-recurrence - reusing the same block repeatedly across layers, as recently applied in looped transformers - has not been explored in this model family. We show that a looped SSM with $k$ parameters iterated $L$ times consistently closely matches or outperforms a standard SSM with $k \cdot L$ independent parameters across four architectures (LRU, S5, LinOSS, LrcSSM) and six time series classification benchmarks, despite operating within a strictly smaller hypothesis space, as we formally establish. Since the larger model contains the looped model as a special case, this dominance cannot be explained by expressivity and instead points to parameter sharing across depth as a beneficial inductive bias that simplifies optimization. These results demonstrate that depth-recurrence is orthogonal to sequence-recurrence and independently beneficial. We further show that input reshaping is an equally neglected design axis: concatenating timesteps for low-dimensional inputs, or flattening and rechunking the joint feature-time dimension for high-dimensional ones, yields accuracy gains of 1-6% across all models, confirmed over 5 random seeds. Both techniques provide standalone improvements that compound when combined, suggesting that depth and input reshaping are two independent and underexplored design axes for SSMs on time series.

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