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This paper addresses a critical numerical instability in quantizing the recurrent states of Linear-attention and SSM models, where dynamic scaling fails to prevent error compounding over long contexts. The authors demonstrate that yoking the quantizer scale to a full-precision reference mitigates norm explosion but reveals that resolution limits remain a fundamental barrier, rendering group-wise INT4 ineffective beyond short horizons without architectural changes. Ultimately, the study argues that simply locating outliers is insufficient and that managing scale dynamics is essential for viable long-context inference in state-space architectures.
When Dynamic Scaling Fails: A Scale-State Feedback Governs Recurrent-State Quantization in Linear-Attention and SSM LLMs
arXiv:2610.15139v1 Announce Type: new Abstract: Linear-attention and state-space LLMs carry long context in a fixed-size recurrent state, and quantizing that state is the natural way to cut its cost during long decode. Unlike a weight tensor, the state is rewritten at every step, so a quantizer applied at each step sits inside the recurrence and its errors compound. INT4 that leaves synthetic recall perfectly intact at the start destroys it a thousand steps later. The mechanism is a feedback between the quantizer scale and the state it is derived from. Yoking that scale to a full-precision reference removes the resulting norm explosion entirely, yet recovers only 1.8 of the 5.4 nats lost, so numerical instability and functional degradation are separable failures. The remainder is a resolution problem that locating outliers does not solve, since every outlier-aware scheme here loses to plain persistent scaling. Allocating bits across layers does help, but under article-disjoint splits a learned allocation collapses onto the trivial rule of protecting the first few layers. Run out to 32K, group-wise INT4 is worth no more than discarding the state. Contain the scale rather than locate outliers, and report the decode horizon at which a bit-width was certified.
Abstract:Linear-attention and state-space LLMs carry long context in a fixed-size recurrent state, and quantizing that state is the natural way to cut its cost during long decode. Unlike a weight tensor, the state is rewritten at every step, so a quantizer applied at each step sits inside the recurrence and its errors compound. INT4 that leaves synthetic recall perfectly intact at the start destroys it a thousand steps later. The mechanism is a feedback between the quantizer scale and the state it is derived from. Yoking that scale to a full-precision reference removes the resulting norm explosion entirely, yet recovers only 1.8 of the 5.4 nats lost, so numerical instability and functional degradation are separable failures. The remainder is a resolution problem that locating outliers does not solve, since every outlier-aware scheme here loses to plain persistent scaling. Allocating bits across layers does help, but under article-disjoint splits a learned allocation collapses onto the trivial rule of protecting the first few layers. Run out to 32K, group-wise INT4 is worth no more than discarding the state. Contain the scale rather than locate outliers, and report the decode horizon at which a bit-width was certified.
14 pages, 6 figures, 7 tables. NeurIPS 2026 Workshop on Long-Context Foundation Models (non-archival). Extended version: adds a cross-architecture containment comparison on Mamba-2 and corrects two claims in the workshop version. Code and project page: this https URL
Machine Learning (cs.LG)
arXiv:2610.15139 [cs.LG]
(or arXiv:2610.15139v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.15139 arXiv-issued DOI via DataCite (pending registration)
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