Study Finds Language Models' Context Sensitivity Follows Polynomial Rather Than Exponential Decay
Researchers analyzing KV cache compression in autoregressive language models discovered that the next-token prediction's sensitivity to context truncation decays polynomially rather than exponentially. This finding, tested across four models ranging from 0.5-3B parameters, suggests that sliding-window cache policies can compress memory more efficiently than previously understood. The result has implications for optimizing memory usage in large language models while maintaining prediction accuracy.
A new preprint from arXiv presents a theoretical and empirical analysis of how autoregressive language models degrade when their context (stored in KV caches) is truncated. Using rate-distortion theory framed as sequential Wyner-Ziv source coding, the authors demonstrate that the next-token distribution's sensitivity to context loss follows a power law (polynomial decay) rather than an exponential one—an improvement of an order of magnitude in extrapolation accuracy. The finding was validated across four models in two families with 0.5-3B parameters, with the decay pattern confirmed to be independent of positional encoding artifacts. Under this polynomial truncation-sensitivity model, the authors prove that suffix-only cache policies (like sliding windows) require memory scaling as O(ε^{-1/α}) to achieve distortion ε, with a matching lower bound showing this is necessary. Empirically, recency-based eviction policies suppress distortion by roughly two orders of magnitude compared to random retention at equal memory budget.
What's missing
The paper leaves open whether recurrent or propagating cache summaries could beat the polynomial scaling bound for suffix-only policies. Additionally, the rate-of-convergence exponent for the explicit block-Markov scheme matches the converse only under additional forward-decay and regularity hypotheses not implied by truncation sensitivity alone, and differs by a factor of two otherwise—suggesting the theoretical characterization is incomplete for general cases.
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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