New Methods Estimate LLM Distribution Differences Efficiently.

Eric Price, Kevin Tian, Zhiyang Xun, Yusong Zhu· July 23, 2026 View original

Summary

This paper introduces efficient methods for estimating the total variation (TV) distance between two autoregressive distributions, like those from different LLM inference engines, under various access models (sample, logit, noisy logit). The techniques offer a robust way to quantify differences in model outputs, even when KL divergence is infinite, and are empirically validated.

This research addresses the critical challenge of quantifying the differences between the output distributions of large language models (LLMs), especially when various implementation choices and optimizations lead to divergent behaviors even with identical weights. The authors propose novel methods for estimating the total variation (TV) distance between two length-n autoregressive distributions, offering a robust alternative to KL divergence which can be infinite in certain scenarios. The study explores three access models for estimation: sample access, logit access, and noisy logit access, providing query complexity bounds for each. For instance, logit access achieves an optimal O(n/ε²) queries. The theoretical findings are complemented by empirical evaluations, demonstrating the practicality of these algorithms by measuring the distance between LLMs served by different engines like SGLang and vLLM. This work provides valuable tools for developers and researchers to ensure consistency and understand the impact of deployment choices on model behavior.

Why it matters

For professionals deploying and evaluating LLMs, accurately measuring the divergence between model outputs from different inference engines or optimization strategies is crucial for quality control, debugging, and ensuring consistent user experiences.

How to implement this in your domain

  1. 1Utilize the proposed TV distance estimation methods to compare the output distributions of different LLM inference engines or deployment configurations.
  2. 2Integrate these estimation techniques into your LLM evaluation pipelines to detect subtle shifts in model behavior due to optimizations or hardware changes.
  3. 3Develop monitoring tools that track TV distance over time to ensure consistency and identify potential regressions in deployed LLMs.
  4. 4Apply these methods to validate the impact of quantization or custom kernels on the statistical properties of your LLM outputs.

Who benefits

AI/ML DevelopmentCloud ComputingSoftware Quality AssuranceResearch & Development

Key takeaways

  • LLM deployment choices can significantly alter output distributions, even with identical weights.
  • Total variation distance is a robust metric for comparing LLM distributions, unlike KL divergence.
  • Efficient algorithms are presented for estimating TV distance under various access models.
  • This work provides practical tools for ensuring consistency and quality in LLM deployments.

Original post by Eric Price, Kevin Tian, Zhiyang Xun, Yusong Zhu

"arXiv:2607.19510v1 Announce Type: new Abstract: Modern LLM deployments use a number of implementation choices and inference optimizations (e.g., batching, custom kernels, and quantization) on top of fixed weights, so two engines serving "the same model" can produce meaningfully d…"

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Originally posted by Eric Price, Kevin Tian, Zhiyang Xun, Yusong Zhu on X · view source

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