Enrico Ventura, Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello
原文摘要
Classifier-free guidance (CFG) is the de facto standard for conditional sampling in diffusion models, yet it often reduces sample diversity. Using tools from statistical physics, we analyze the emergence of generative distortions induced by CFG, namely the mismatch between the CFG sampling distribution and the true conditional distribution. We study this phenomenon in analytically tractable settings with exact score functions, characterizing its dependence on data dimensionality and the number of classes. For high-dimensional Gaussian mixtures, we use dynamic mean-field theory to show that distortions persist when the number of classes scales exponentially with the data dimension, whereas they vanish in the sub-exponential regime due to a dynamical phase transition. Moreover we found that, in the infinite-class limit, distortions remain unavoidable regardless of dimensionality because of the increasing density of classes. Finally, we show that standard CFG schedules cannot prevent variance shrinkage, and we propose a theoretically grounded guidance schedule incorporating a negative-guidance window that improves both class separability and sample diversity in real-world latent diffusion models.
Matteo Negri, Clarissa Lauditi, Gabriele Perugini, Carlo Lucibello, Enrico M. Malatesta
原文摘要
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we propose and investigate a generalization of the standard setting that we name Random-Features Hopfield Model. Here $P$ binary patterns of length $N$ are generated by applying to Gaussian vectors sampled in a latent space of dimension $D$ a random projection followed by a non-linearity. Using the replica method from statistical physics, we derive the phase diagram of the model in the limit $P,N,D\to\infty$ with fixed ratios $α=P/N$ and $α_D=D/N$. Besides the usual retrieval phase, where the patterns can be dynamically recovered from some initial corruption, we uncover a new phase where the features characterizing the projection can be recovered instead. We call this phenomena the learning phase transition, as the features are not explicitly given to the model but rather are inferred from the patterns in an unsupervised fashion.