Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression

Researchers develop theoretical bounds for KV cache compression in language models, discovering that context sensitivity decays polynomially rather than exponentially. Their findings enable more efficient memory-aware cache policies that reduce memory requirements while maintaining model performance, with practical implications for deploying larger models on resource-constrained systems.

This research addresses a fundamental efficiency problem in deploying autoregressive language models: the Key-Value (KV) cache grows linearly with sequence length, creating bottlenecks for long-context inference. The team's core discovery—that token prediction sensitivity to context truncation follows a power law rather than exponential decay—has substantial implications for how systems allocate memory during inference.

The polynomial decay finding emerged consistently across multiple model architectures (0.5-3B parameters), verified through independent measurement techniques and ablations controlling for positional encoding effects. This suggests the phenomenon reflects genuine model behavior rather than artifacts. The researchers formalize this insight through sequential Wyner-Ziv source coding theory, establishing that suffix-only cache policies require memory scaling of Θ(ε^-1/α) to achieve distortion ε—where α is the empirically measured decay exponent.

Practically, this theory predicts real-world performance. Recency-based eviction policies (sliding windows and sink-plus-recent schemes) suppress distortion by roughly two orders of magnitude compared to random retention at equivalent memory budgets. These findings benefit inference optimization across deployment contexts—from edge devices to cloud services where compute and memory costs directly impact profitability. The open question of whether recurrent or summary-based cache methods can beat polynomial scaling leaves room for further innovation.

For AI infrastructure providers and model deployers, this work provides theoretical grounding for cache optimization decisions, moving the field from heuristic approaches toward principled trade-offs between memory consumption and output quality. The polynomial law enables better prediction of performance degradation curves, improving resource planning accuracy.

• →Context sensitivity in language models decays polynomially, not exponentially, enabling more precise memory-distortion trade-off calculations
• →Sliding-window cache policies achieve near-optimal scaling of O(ε^-1/α) memory requirement for suffix-only schemes
• →Recency-biased eviction strategies outperform random cache retention by two orders of magnitude at equal memory budgets
• →Theoretical framework based on sequential Wyner-Ziv coding successfully predicts observed degradation in concrete cache policies
• →Findings apply consistently across multiple model architectures, suggesting fundamental principles rather than model-specific artifacts