Algorithm- and Data-Dependent Generalization Bounds for Score-Based Generative Models

• URL: http://arxiv.org/abs/2506.03849v1
• Date: Wed, 04 Jun 2025 11:33:04 GMT
• Title: Algorithm- and Data-Dependent Generalization Bounds for Score-Based Generative Models
• Authors: Benjamin Dupuis, Dario Shariatian, Maxime Haddouche, Alain Durmus, Umut Simsekli,
• Abstract summary: Score-based generative models (SGMs) have emerged as one of the most popular classes of generative models.<n>This paper provides the first algorithmic- and data-dependent analysis for SGMs.<n>In particular, we account for the dynamics of the learning algorithm, offering new insights into the behavior of SGMs.
• Score: 27.78637798976204
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 either on discretization aspects or on their statistical performance. In the latter case, bounds have been derived, under various metrics, between the true data distribution and the distribution induced by the SGM, often demonstrating polynomial convergence rates with respect to the number of training samples. However, these approaches adopt a largely approximation theory viewpoint, which tends to be overly pessimistic and relatively coarse. In particular, they fail to fully explain the empirical success of SGMs or capture the role of the optimization algorithm used in practice to train the score network. To support this observation, we first present simple experiments illustrating the concrete impact of optimization hyperparameters on the generalization ability of the generated distribution. Then, this paper aims to bridge this theoretical gap by providing the first algorithmic- and data-dependent generalization analysis for SGMs. In particular, we establish bounds that explicitly account for the optimization dynamics of the learning algorithm, offering new insights into the generalization behavior of SGMs. Our theoretical findings are supported by empirical results on several datasets.

Related papers

• Detecting and Pruning Prominent but Detrimental Neurons in Large Language Models [68.57424628540907]
  Large language models (LLMs) often develop learned mechanisms specialized to specific datasets.<n>We introduce a fine-tuning approach designed to enhance generalization by identifying and pruning neurons associated with dataset-specific mechanisms.<n>Our method employs Integrated Gradients to quantify each neuron's influence on high-confidence predictions, pinpointing those that disproportionately contribute to dataset-specific performance.
  arXiv  Detail & Related papers  (2025-07-12T08:10:10Z)
• Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis [44.468416523840965]
  We develop a theory of algorithm-dependent generalisation for high-dimensional diffusion models.<n>We derive generalisation bounds in terms of score stability, and apply our framework to several fundamental learning settings.
  arXiv  Detail & Related papers  (2025-07-04T18:07:06Z)
• Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis [20.429383584319815]
  We propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator.<n> Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.
  arXiv  Detail & Related papers  (2025-06-01T06:11:38Z)
• Self-Boost via Optimal Retraining: An Analysis via Approximate Message Passing [58.52119063742121]
  Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model performance.<n>This paper addresses the question of how to optimally combine the model's predictions and the provided labels.<n>Our main contribution is the derivation of the Bayes optimal aggregator function to combine the current model's predictions and the given labels.
  arXiv  Detail & Related papers  (2025-05-21T07:16:44Z)
• Preconditioned Inexact Stochastic ADMM for Deep Model [35.37705488695026]
  This paper develops an algorithm, PISA, which enables scalable parallel computing and supports various second-moment schemes.<n>Grounded in rigorous theoretical guarantees, the algorithm converges under the sole assumption of Lipschitz of the gradient.<n> Comprehensive experimental evaluations for or fine-tuning diverse FMs, including vision models, large language models, reinforcement learning models, generative adversarial networks, and recurrent neural networks, demonstrate its superior numerical performance compared to various state-of-the-art Directions.
  arXiv  Detail & Related papers  (2025-02-15T12:28:51Z)
• Toward the Identifiability of Comparative Deep Generative Models [7.5479347719819865]
  We propose a theory of identifiability for comparative Deep Generative Models (DGMs) We show that, while these models lack identifiability across a general class of mixing functions, they surprisingly become identifiable when the mixing function is piece-wise affine. We also investigate the impact of model misspecification, and empirically show that previously proposed regularization techniques for fitting comparative DGMs help with identifiability when the number of latent variables is not known in advance.
  arXiv  Detail & Related papers  (2024-01-29T06:10:54Z)
• Aggregation Weighting of Federated Learning via Generalization Bound Estimation [65.8630966842025]
  Federated Learning (FL) typically aggregates client model parameters using a weighting approach determined by sample proportions. We replace the aforementioned weighting method with a new strategy that considers the generalization bounds of each local model.
  arXiv  Detail & Related papers  (2023-11-10T08:50:28Z)
• Optimal regularizations for data generation with probabilistic graphical models [0.0]
  Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models. We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
  arXiv  Detail & Related papers  (2021-12-02T14:45:16Z)
• Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms [71.62575565990502]
  We prove that the generalization error of an optimization algorithm can be bounded on the complexity' of the fractal structure that underlies its generalization measure. We further specialize our results to specific problems (e.g., linear/logistic regression, one hidden/layered neural networks) and algorithms.
  arXiv  Detail & Related papers  (2021-06-09T08:05:36Z)
• Counterfactual Maximum Likelihood Estimation for Training Deep Networks [83.44219640437657]
  Deep learning models are prone to learning spurious correlations that should not be learned as predictive clues. We propose a causality-based training framework to reduce the spurious correlations caused by observable confounders. We conduct experiments on two real-world tasks: Natural Language Inference (NLI) and Image Captioning.
  arXiv  Detail & Related papers  (2021-06-07T17:47:16Z)
• Generalization Properties of Optimal Transport GANs with Latent Distribution Learning [52.25145141639159]
  We study how the interplay between the latent distribution and the complexity of the pushforward map affects performance. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm.
  arXiv  Detail & Related papers  (2020-07-29T07:31:33Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)
• Hierarchical regularization networks for sparsification based learning on noisy datasets [0.0]
  hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension. Results show the performance of the approach as a data reduction and modeling strategy on both synthetic and real datasets.
  arXiv  Detail & Related papers  (2020-06-09T18:32:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.