# Pricing the Risk of Runtime Compression: Anytime-Valid Admission and a Served-Output Law for Compressed Serving State

arXiv: https://arxiv.org/abs/2608.15810 · HTML: https://mlsanity.com/paper/2608.15810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 16 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [MoEQuant: Enhancing Quantization for Mixture-of-Experts Large Language Models via Expert-Balanced Sampling and Affinity Guidance](https://mlsanity.com/paper/2505.03804/) (2025)
- [Model-Preserving Adaptive Rounding](https://mlsanity.com/paper/2505.22988/) (2025)
- [QERA: an Analytical Framework for Quantization Error Reconstruction](https://mlsanity.com/paper/2410.06040/) (2024)
- [EAC-MoE: Expert-Selection Aware Compressor for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2508.01625/) (2025)
- [EAQuant: Enhancing Post-Training Quantization for MoE Models via Expert-Aware Optimization](https://mlsanity.com/paper/2506.13329/) (2025)
- [WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantization](https://mlsanity.com/paper/2603.04956/) (2026)
- [GEMQ: Global Expert-Level Mixed-Precision Quantization for MoE LLMs](https://mlsanity.com/paper/2605.23078/) (2026)
- [MorphServe: Efficient and Workload-Aware LLM Serving via Runtime Quantized Layer Swapping and KV Cache Resizing](https://mlsanity.com/paper/2506.02006/) (2025)
- [Value-and-Structure Alignment for Routing-Consistent Quantization of Mixture-of-Experts Models](https://mlsanity.com/paper/2606.05688/) (2026)
- [DP-LLM: Runtime Model Adaptation with Dynamic Layer-wise Precision Assignment](https://mlsanity.com/paper/2508.06041/) (2025)
- [Runtime-Certified Bounded-Error Quantized Attention](https://mlsanity.com/paper/2605.20868/) (2026)
- [WitCert: Sound Runtime Risk Observability and Gating for KV-Cache Quantization](https://mlsanity.com/paper/2607.28699/) (2026)
- [MoBiE: Efficient Inference of Mixture of Binary Experts under Post-Training Quantization](https://mlsanity.com/paper/2604.06798/) (2026)
- [Runtime Observability for Heterogeneous Attention Memory](https://mlsanity.com/paper/2608.05863/) (2026)

## Abstract (arXiv)

Runtime compression of serving state trades quality for capacity with no priced guarantee: systems adapt precision on load signals with no soundness statement, and certified approaches budget request-level risk by a union bound over a pre-declared event count. We show the union budget exhausts on every long request in a production serving stack (100% of requests), and replace it with an anytime-valid, physically accounted ledger whose bound holds at every one of 352,333 admission calls on live traffic and which, in a pre-registered held-out confirmatory round, halves the exact-fallback rate at matched risk (0.30 -> 0.14) -- coverage is bought at a price the account states. We then price the remaining distance from the certified witness to what a user experiences: a machine-checked design law (TV <= tanh(a_q w_thr)) turns the served-TV target into a threshold knob, and a three-layer audit of its instantiation -- an operator-norm query envelope measured 1.5x from tight, a measured-ellipsoid replacement for the Cauchy-Schwarz ball that buys nothing (0.89x, held-out sound), and the gate's operating point (~700x) -- localizes the entire 1064x gap to the operating point, a price the law now states rather than an unknown. A priced bound is worth nothing on a request one has not seen, so the third link is the quantifier: exchangeable extrapolation across 80 serving histories replaces binary conformal prediction's vacuous certificates with order-statistic bounds that discriminate (0.41 against 0.51 calibration risk). All probabilistic kernels are Lean 4-checked (228 exported theorems, no sorry); which object deserves this machinery at all is settled empirically in a companion paper that adjudicates -- and rejects -- the natural alternative of certifying routing. What ships is an account: risk you can spend, a gap you can read off a law, and a bound that survives the request you have not seen.