# Training-Inference Kernel Contracts: Bounding Divergence in Post-Training and Deployment

arXiv: https://arxiv.org/abs/2606.07581 · HTML: https://mlsanity.com/paper/2606.07581/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 22 references that are in the map.
- First posted on arXiv 26 May 2026.

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

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [Understanding Reinforcement Learning for Model Training, and future directions with GRAPE](https://mlsanity.com/paper/2509.04501/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Integer Alibi: Localizing Cross-Kernel Divergence in INT8-Quantized LLM Inference](https://mlsanity.com/paper/2608.13756/) (2026)

## Abstract (arXiv)

A modern post-training pipeline often writes one symbol for its policy, pi_theta, while evaluating it through two different programs: a training kernel optimized for autograd and an inference kernel optimized for low-precision, fused, dynamically batched serving. In finite precision, these kernels can induce different distributions at identical weights, with the gap concentrated on slices that aggregate benchmarks under-represent. This paper proposes kernel contracts: a contract-first framework for specifying acceptable divergence between K_train and K_inf. A contract C = (N, S, R, O, Pi) combines numerical, statistical, runtime, and observability clauses with an escalation policy from violations to routing actions. We derive a chain of bounds from logit drift to total-variation distance to bounded reward drift, and specialize it to RL post-training, where per-token importance-ratio drift yields a bound on policy-gradient bias under explicit support and norm assumptions. We also describe a four-stage promotion pipeline, online routing loop, and minimal YAML DSL for contract artifacts. This is a framework and vocabulary paper; we do not report production-scale empirical validation.