User-Centric Modeling of Transactional Sequences with Explainable State Space Models

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.

We study how depth, finite precision, state dimension, and chain-of-thought (CoT) affect the expressive power of multi-layer state-space models (SSMs). For the explicit-table $K$-function-composition problem, a canonical benchmark for sequential information propagation, we prove that any $L$-layer SSM solving $(L+3)$-function composition must satisfy $d^2p=Ω(N/L^3)$, where $d$ is the state dimension and $p$ is the per-scalar precision. Conversely, $K$-function composition is solved exactly by a $(K+1)$-layer generalized SSM with $d=1$ and $p=Θ(\log N)$. This gives a worst-case depth hierarchy for this formal problem family. We then distinguish post-input reasoning, in which all thought tokens are generated after the input, from input-interleaved reasoning, in which thought tokens may be inserted while the input stream is being read. Post-input reasoning does not circumvent our communication-based lower-bound pipeline, whereas input-interleaved reasoning admits bidirectional simulations with general deterministic one-pass streaming algorithms at the granularity of persistent memory. Finally, width and precision are not interchangeable under exact step-preserving simulation in the base affine-state model, but become interchangeable through the streaming-memory characterization once input-interleaved reasoning is allowed.

End-to-end OCR increasingly relies on autoregressive sequence models, where the quadratic cost of Transformer attention limits efficient transcription of long, paragraph-level text. State-Space Models (SSMs) such as Mamba offer linear-time decoding and have recently been shown to match Transformer accuracy on printed historical lines, but their behavior as sequences grow from short lines to full paragraphs, and their generalization to handwriting, remain poorly understood. We study how a Mamba-based OCR recognizer scales from lines to paragraphs. We first conduct a systematic exploration of its four core hyperparameters (decoder depth, state dimension, expansion factor, and connector depth) on synthetic paragraphs from 100 to 1,000 characters, identifying the recurrent state dimension and the expansion factor as the dominant levers for long-sequence accuracy. We then compare the recognizer against a Transformer baseline trained under an identical protocol. On clean synthetic paragraphs, both models stay below 1% CER at every length while the SSM runs 1.4 to 4.5 times faster, the speedup growing with sequence length. On real handwriting, however, the SSM lags clearly behind: it reaches 8.2% CER on IAM lines and 10.0% on IAM paragraphs, against 4.2% and 3.5% for the Transformer baseline. Through controlled experiments we show that a substantial part of this gap stems from data scarcity rather than from an intrinsic architectural limit: the autoregressive SSM decoder is markedly data-hungry on long sequences. Our study clarifies when SSMs are a practical choice for large-scale document transcription and when they are not.