18 papers
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…
Distribution Matching Distillation for Continuous Diffusion Language Models
Paul Le Van Kiem, Dario Shariatian, Umut Simsekli +1
Continuous diffusion language models generate all tokens in parallel, yet high-quality generation can still require hundreds of network evaluations (NFEs). We study how distributio…
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…
Uniform Diffusion Models Revisited: Leave-One-Out Denoiser and Absorbing State Reformulation
Samson Gourevitch, Yazid Janati, Dario Shariatian +4
Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Mode…
Variational Inference for Lévy Process-Driven SDEs via Neural Tilting
Yaman Kindap, Manfred Opper, Benjamin Dupuis +2
Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While Lé…
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…
Latent-Augmented Discrete Diffusion Models
Dario Shariatian, Alain Durmus, Umut Simsekli +1
Discrete diffusion models have emerged as a powerful class of models and a promising route to fast language generation, but practical implementations typically rely on factored rev…
On the Interaction of Compressibility and Adversarial Robustness
Melih Barsbey, Antônio H. Ribeiro, Umut Şimşekli +1
As demands for resource efficiency and safety in modern neural networks intensify, substantial research effort has gone into model compression and adversarial robustness. Yet despi…
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…
The Surprising Agreement Between Convex Optimization Theory and Learning-Rate Scheduling for Large Model Training
Fabian Schaipp, Alexander Hägele, Adrien Taylor +2
We show that learning-rate schedules for large model training behave surprisingly similar to a performance bound from non-smooth convex optimization theory. We provide a bound for…
Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms
Rayna Andreeva, Benjamin Dupuis, Rik Sarkar +2
We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neur…
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…