11 papers · 1 filter
Discrete Diffusion Models are Minimax Optimal Under Sparsity
Luca Blunda, Tyler Farghly, Umut Simsekli +1
Discrete diffusion models have emerged as a leading alternative to autoregressive models for generating text and other categorical data, yet their theoretical foundations remain le…
Tightening the Score Matching Gap for Diffusion Models
Benjamin Dupuis, Tyler Farghly, Maxime Haddouche +2
Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution. Their training and evaluation primarily rely on an Evidence Lo…
Benign Overfitting Does Not Occur in Diffusion Models
Tyler Farghly, Benjamin Dupuis, Alain Durmus +1
Benign overfitting and double descent have come to shape our understanding of generalization in deep learning, establishing that overfitting is not only compatible with good genera…
Rényi Differential Privacy for Heavy-Tailed SDEs via Fractional Poincaré Inequalities
Benjamin Dupuis, Mert Gürbüzbalaban, Umut Şimşekli +3
Characterizing the differential privacy (DP) of learning algorithms has become a major challenge in recent years. In parallel, many studies suggested investigating the behavior of…
Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
Benjamin Dupuis, Dario Shariatian, Maxime Haddouche +2
Score-based generative models (SGMs) have emerged as one of the most popular classes of generative models. A substantial body of work now exists on the analysis of SGMs, focusing e…
Algorithmic Stability of Stochastic Gradient Descent with Momentum under Heavy-Tailed Noise
Thanh Dang, Melih Barsbey, A K M Rokonuzzaman Sonet +3
Understanding the generalization properties of optimization algorithms under heavy-tailed noise has gained growing attention. However, the existing theoretical results mainly focus…
Generalization Bounds for Markov Algorithms through Entropy Flow Computations
Benjamin Dupuis, Maxime Haddouche, George Deligiannidis +1
Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time no…
Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets
Benjamin Dupuis, Paul Viallard, George Deligiannidis +1
We propose data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on "random sets" in a…
Tighter Generalisation Bounds via Interpolation
Paul Viallard, Maxime Haddouche, Umut Şimşekli +1
This paper contains a recipe for deriving new PAC-Bayes generalisation bounds based on the -divergence, and, in addition, presents PAC-Bayes generalisation bounds where we…
Tracking the Median of Gradients with a Stochastic Proximal Point Method
Fabian Schaipp, Guillaume Garrigos, Umut Simsekli +1
There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corru…
Generalization Bounds for Heavy-Tailed SDEs through the Fractional Fokker-Planck Equation
Benjamin Dupuis, Umut Şimşekli
Understanding the generalization properties of heavy-tailed stochastic optimization algorithms has attracted increasing attention over the past years. While illuminating interestin…