Exact Memory-Time Optimization for Prefix-Cached Language Model Serving
Retaining language-model prefix states trades recomputation against storage time. Optimizing each cached block independently can overcount savings: a resident block is usable only when the required preceding prefix is also available. We introduce Prefix-Certificate Retention (PCR), an exact finite-trace formulation for static, grouped, reset-on-access timeouts. Usable-prefix rewards become nodes whose prerequisites are timeout thresholds and preceding hit certificates. The resulting maximum-weight closure reduces to one minimum cut, with graph size linear in the number of block lookups and timeout choices. A breakpoint theorem extends the construction to all nonnegative timeouts without d...
| Authors | Shivam Gupta |
|---|---|
| Primary category | cs.LG |
| Published | 2 October 2026 |
| Last updated at source | 2 October 2026 |
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