Diffusion models trained on a finite dataset first learn to generate novel, high-quality samples and only much later collapse onto their training set. We identify the mechanism behind this separation of timescales and the object that probes it. The training dynamics of the score function are governed---exactly, and at...
Raphaël Urfin, Tony Bonnaire, Giulio Biroli et al.· 1 citation
Score-based generative models generate new samples by integrating a time-dependent drift that carries Gaussian noise onto the target distribution. In practice this drift is modeled by a neural network, trained on a loss integrated over time $t$ with a weighting schedule $w(t)$. Along the backward dynamics, and for mult...
J. Klinger, Raphaël Urfin, Giulio Biroli et al.· 0 citations
Conventional wisdom in deep learning holds that overparameterization---having more parameters $p$ than training samples $n$---is benign: larger models generalize better and, even without regularization, interpolating models generalize well, the test error following a double-descent curve. One might expect the same beni...
Raphaël Urfin, Tony Bonnaire, Giulio Biroli et al.· 0 citations
It is found that τmem increases linearly with the training set size n, whereas τgen remains constant, which creates a growing window of training times with n where models generalize effectively, despite showing strong memorization if training continues beyond it.
Tony Bonnaire, Raphaël Urfin, Giulio Biroli et al.· Journal of Statistical Mecha...· 2 citations
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