Cross-Entropy Games and Frost Training

Arthur Renard; Franck Gabriel; Valentin Hartmann; Clément Hongler

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arXiv · 2605.27701

Cross-Entropy Games and Frost Training

Arthur Renard·Franck Gabriel·Valentin Hartmann·Clément Hongler

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Abstract

We present Frost Training, a method for improving Monte Carlo-based policy optimization for a large family of LLM-as-a-judge tasks called Cross-Entropy Games. The key idea is to exploit the gradient of the reward function in embedding space. This signal is used in the Greedy Coordinate Gradient (GCG) jailbreaking technique; we demonstrate for the first time that it can also be used to boost model training. We validate our method using GRPO training for maximum-likelihood infilling. Frost Training improves the model's ability to generate high-scoring outputs, reaching higher maximum scores in a best-of-k setting, and does so at an increased speed.

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Arthur Renard, Franck Gabriel, Valentin Hartmann, Clément Hongler. 2026-05-26. Cross-Entropy Games and Frost Training. https://arxiv.org/abs/2605.27701

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