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Francis Bach

4 papers indexed

arxivcs.LG2026-07-09

Eigenvalue Calibration for Semantic Embeddings of Large Language Models

Sebastian G. Gruber, Nassim Walha, Francis Bach, Florian Buettner

Uncertainty quantification is central to the reliable deployment of large language models (LLMs), and eigenvalues of semantic embeddings have recently emerged as a key tool in state-of-the-art methods. However, conventional calibration results developed for classification probabi…

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arxivcs.LG2026-07-02

DecompRL: Solving Harder Problems by Learning Modular Code Generation

Juliette Decugis, Fabian Gloeckle, Francis Bach, Taco Cohen, Gabriel Synnaeve

How can Large Language Models (LLMs) solve problems they currently cannot? Repeated sampling scales test-time compute but GPU cost grows linearly with attempts, while reinforcement learning (RL) with verifiable rewards improves single-attempt accuracy at the expense of sample div…

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arxivcs.LGmath.OCmath.STstat.ML2026-07-02

Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model

Francis Bach

We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix. By affine invariance, the model is written as q $\sim$ N(0, I), p $\sim$ N($Δ$, I), with linear features, where $Δ$ is a mean vector. The variational estimator…

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arxivcs.LGcs.AI2026-07-01

Don't Let Gains FADE: Breaking Down Policy Gradient Weights in RL

Juliette Decugis, Sean O'Brien, Francis Bach, Gabriel Synnaeve, Taco Cohen

Reinforcement learning post-training dramatically improves LLM reasoning, but suffers from training instability and diversity collapse. Advantage functions offer an appealing fix: they reshape the training objective, reweight which rollouts drive learning, and are trivial to impl…

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