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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…
Metropolis-Adjusted Diffusion Models
Kevin H. Lam, Tyler Farghly, Christopher Williams +3
Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to a…
Beyond Real Data: Synthetic Data through the Lens of Regularization
Amitis Shidani, Tyler Farghly, Yang Sun +2
Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we prese…
Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis
Tyler Farghly, Patrick Rebeschini, George Deligiannidis +1
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown…
Generalisation under gradient descent via deterministic PAC-Bayes
Eugenio Clerico, Tyler Farghly, George Deligiannidis +2
We establish disintegrated PAC-Bayesian generalisation bounds for models trained with gradient descent methods or continuous gradient flows. Contrary to standard practice in the PA…
Time-independent Generalization Bounds for SGLD in Non-convex Settings
Tyler Farghly, Patrick Rebeschini
We establish generalization error bounds for stochastic gradient Langevin dynamics (SGLD) with constant learning rate under the assumptions of dissipativity and smoothness, a setti…