ResearchResearch paperTraining & Scaling · Reinforcement Learning · Large Language Models1 source · Oct 20, 2026

When Do Gaussian Priors Fail? A Latent Geometry Investigation of RL Fine-Tuning

Latent diffusion models almost universally place a Gaussian prior on the VAE latent space.

RL fine-tuning amplifies this overlap: the score network is under-resolved on the saddle region between modes, dynamic-to-variational amplification rises sharply, and the collapse boundary betac is pushed far above its variational scale.
On the real alanine-dipeptide Boltzmann distribution, a Gaussian-prior VAE collapses at betac = 0.224 while a mode-tracked Gaussian-mixture prior collapses at 0.00316, a 71x gap from the same pipeline.
We trace this gap to a single geometric mediator, dmin/(2 sigma0), and verify the causal chain through controlled interventions: moving geometry at fixed prior, and switching prior at matched geometry (full mediation; prior-label coefficient 0.995x, 95% CI [0.79, 1.25]).
A machine-checked theory skeleton supports the KL pricing structure - a divergent compactness tax under a Gaussian prior versus a finite assignment fee under a mixture - and the position-versus-plateau distinction delimits what is finite-resource from what requires changing the prior.

[1]When Do Gaussian Priors Fail? A Latent Geometry Investigation of RL Fine-Tuning
arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 07:22 PM
Latent diffusion models almost universally place a Gaussian prior on the VAE latent space.
RL fine-tuning amplifies this overlap: the score network is under-resolved on the saddle region between modes, dynamic-to-variational amplification rises sharply, and the collapse boundary beta_c is pushed far above its variational scale.

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