Study Finds Language Models' Context Sensitivity Follows Polynomial Rather Than Exponential Decay
A new arXiv preprint establishes that autoregressive language models' sensitivity to context truncation decays polynomially rather than geometrically, and derives tight theoretical bounds on memory requirements for KV cache compression. The work frames KV cache compression as a sequential Wyner-Ziv source coding problem and validates the polynomial decay law empirically across four models from two families ranging from 0.5B to 3B parameters. The findings matter because they provide the first rigorous characterization of the memory-distortion tradeoff for suffix-only cache policies, showing sliding-window schemes are order-optimal within that policy class.
Researchers have posted a preprint to arXiv showing that the next-token prediction distribution in autoregressive language models is far more sensitive to distant context than previously assumed: the sensitivity decays as a power law rather than exponentially, with the polynomial fit outperforming an exponential fit by roughly an order of magnitude in extrapolation accuracy. The study tests this across four models spanning two architectural families and parameter counts from 0.5B to 3B, and confirms the result is not an artifact of positional encodings via a position-preserving ablation. Theoretically, the authors cast online KV cache compression as a sequential Wyner-Ziv source coding problem on the model's natural filtration, using the next-step query as decoder-side information. Under the polynomial truncation-sensitivity assumption, they prove that suffix-only (sliding-window) cache policies require a window of size Θ(ε^{-1/α}) to achieve distortion ε, establishing both an achievability result via an explicit block-Markov scheme and a matching converse under a two-sided Bayes-risk condition. Empirically, recency-based eviction strategies suppress distortion by roughly two orders of magnitude compared to random token retention at equal memory budgets, consistent with the derived power-law scaling. Whether recurrent or propagating cache summaries can surpass the suffix-only lower bound remains an open question explicitly flagged by the authors.
What's missing
The study's own open questions and limitations include: (1) it is unresolved whether recurrent or propagating cache summary schemes can beat the Θ(ε^{-1/α}) scaling established for suffix-only policies; (2) the rate-of-convergence exponent of the block-Markov scheme matches the converse only under additional forward-decay and regularity hypotheses not implied by truncation sensitivity alone, differing by a factor of two otherwise; and (3) the work has not yet undergone formal peer review.
What different sources said
- arXiv cs.AICenter
Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression
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