# Behavioral Capacity Certificates for Quantized Language Models

arXiv: https://arxiv.org/abs/2609.37887 · HTML: https://mlsanity.com/paper/2609.37887/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache quantization](https://mlsanity.com/inference/kv-cache-quantization/)

## Builds on (most cited first, 18 of 18)

- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach](https://mlsanity.com/paper/1804.05862/) (2018)
- [PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization](https://mlsanity.com/paper/2211.13609/) (2022)
- [Non-Vacuous Generalization Bounds for Large Language Models](https://mlsanity.com/paper/2312.17173/) (2023)
- [Quantize What Counts: More for Keys, Less for Values](https://mlsanity.com/paper/2502.15075/) (2025)
- [SpindleKV: A Novel KV Cache Reduction Method Balancing Both Shallow and Deep Layers](https://mlsanity.com/paper/2507.06517/) (2025)
- [Exploring the Complexity of Deep Neural Networks through Functional Equivalence](https://mlsanity.com/paper/2305.11417/) (2023)
- [Symmetries in PAC-Bayesian Learning](https://mlsanity.com/paper/2510.17303/) (2025)
- [Breaking the 1.58-bit Barrier for Ternary LLMs](https://mlsanity.com/paper/2609.16338/) (2026)

## Abstract (arXiv)

Activation and key-value cache precision change what a quantized language model computes without altering its stored weights. Direct weight-code bounds, however, assign identical complexity to deployments that behave differently and charge separately for weight codes that behave identically. Behavioral Capacity Certificates (BCC) charge for behavior using the aggregate prior mass of complete implementations---weights, scales, activation and cache rules---that induce the same bounded loss. When quantization merges implementations, this shared mass lowers the complexity penalty, and a break-even law determines when the saving survives the cost of validating it. BCC supports a three-step deployment workflow, and our experiments verify each step. First, a forward-only screen shortlists per-layer bit-widths by how often candidate perturbations preserve the reference predictions, with quality comparable to Hessian-guided selection at lower preprocessing cost. Second, margin-certified cells identify weights that can be pruned or sign-flipped without changing the deployed behavior: every permitted combination preserves all declared predictions, and on OLMoE-1B-7B and SmolLM2-1.7B, independent probes bound the probability that any permitted combination changes a prediction on new text. Third, BCC bounds the population loss of the deployed model, nonvacuously for complete decoders and more tightly than the compressed-code route. At equal cache memory, giving keys higher precision than values yields lower NLL and higher prediction agreement on GPT-2, Qwen2.5, and SmolLM2, together with a tighter complexity bound in the GPT-2 audit.