SSM Adapters via Hankel Reduced-order Modeling: Injection Site Determines Task Suitability in Long-Context Fine-Tuning

• URL: http://arxiv.org/abs/2606.26290v1
• Date: Wed, 24 Jun 2026 18:36:31 GMT
• Title: SSM Adapters via Hankel Reduced-order Modeling: Injection Site Determines Task Suitability in Long-Context Fine-Tuning
• Abstract summary: We introduce Hankel Reduced order Model (HRM) adapter, an SSM-based residual module for such tasks.<n>By leveraging the time-invariance of the system matrix $barA$, HRM enables an exact FFT-based parallel scan, achieving computational parity with LoRA.<n> Gate analysis reveals that HRM effectively learns to modulate recurrence, providing a robust architectural alternative to low-rank adaptation for long-context sequence modeling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: While parameter-efficient fine-tuning (PEFT) typically targets attention projectors, its efficacy for tasks requiring sequential state accumulation remains under-explored. We examine if PEFT for such tasks can benefit from state space model (SSMs) adapters, and if MLP blocks are better injection sites. We introduce Hankel Reduced order Model (HRM) adapter, an SSM-based residual module initialized via Balanced Truncation of empirical Hankel Grammians. By leveraging the time-invariance of the system matrix $\bar{A}$, HRM enables an exact FFT-based parallel scan, achieving computational parity with LoRA across all context lengths. In iso-parametric evaluations on Mistral-7B (8.4M trainable parameters), HRM outperforms LoRA variants on LongBench tasks, including QuALITY (+34.8\% relative accuracy) and QMSum (+71.6\% relative ROUGE-1). HRM further demonstrates consistent superiority across 18 configurations of synthetic state-tracking (DFA, Parity) and character-level language modeling (enwik8). Gate analysis reveals that HRM adapters effectively learn to modulate recurrence, providing a robust architectural alternative to low-rank adaptation for long-context sequence modeling.

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