Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization

• URL: http://arxiv.org/abs/2402.01965v3
• Date: Wed, 22 May 2024 19:51:41 GMT
• Title: Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization
• Authors: Fangzhao Zhang, Mert Pilanci,
• Abstract summary: We present a theoretical framework to analyze two-layer neural network-based diffusion models. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.
• Score: 45.72323731094864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In this study, we present a theoretical framework to analyze two-layer neural network-based diffusion models by reframing score matching and denoising score matching as convex optimization. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Although most analyses of diffusion models operate in the asymptotic setting or rely on approximations, we characterize the exact predicted score function and establish convergence results for neural network-based diffusion models with finite data. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.

Related papers

• Supervised Score-Based Modeling by Gradient Boosting [49.556736252628745]
  We propose a Supervised Score-based Model (SSM) which can be viewed as a gradient boosting algorithm combining score matching. We provide a theoretical analysis of learning and sampling for SSM to balance inference time and prediction accuracy. Our model outperforms existing models in both accuracy and inference time.
  arXiv  Detail & Related papers  (2024-11-02T07:06:53Z)
• Nonuniform random feature models using derivative information [10.239175197655266]
  We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. We address the cases of Heaviside and ReLU activation functions, and their smooth approximations (sigmoid and softplus) We suggest simplifications of these exact densities based on approximate derivative data in the input points that allow for very efficient sampling and lead to performance of random feature models close to optimal networks in several scenarios.
  arXiv  Detail & Related papers  (2024-10-03T01:30:13Z)
• BEND: Bagging Deep Learning Training Based on Efficient Neural Network Diffusion [56.9358325168226]
  We propose a Bagging deep learning training algorithm based on Efficient Neural network Diffusion (BEND) Our approach is simple but effective, first using multiple trained model weights and biases as inputs to train autoencoder and latent diffusion model. Our proposed BEND algorithm can consistently outperform the mean and median accuracies of both the original trained model and the diffused model.
  arXiv  Detail & Related papers  (2024-03-23T08:40:38Z)
• The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models [75.33431791218302]
  Deep Neural Network Network (DNN) models are used for programming purposes. In this paper we examine the use of convex neural recovery models. We show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program. We also show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program.
  arXiv  Detail & Related papers  (2023-12-19T23:04:56Z)
• The Hidden Linear Structure in Score-Based Models and its Application [2.1756081703276]
  We show that for well-trained diffusion models, the learned score at a high noise scale is well approximated by the linear score of Gaussian. Our finding of the linear structure in the score-based model has implications for better model design and data pre-processing.
  arXiv  Detail & Related papers  (2023-11-17T22:25:07Z)
• Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models [22.353510613540564]
  We investigate the approximation efficiency of score functions by deep neural networks in generative modeling. We observe score functions can often be well-approximated in graphical models through variational inference denoising algorithms. We provide an efficient sample complexity bound for diffusion-based generative modeling when the score function is learned by deep neural networks.
  arXiv  Detail & Related papers  (2023-09-20T15:51:10Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• A Bayesian Perspective on Training Speed and Model Selection [51.15664724311443]
  We show that a measure of a model's training speed can be used to estimate its marginal likelihood. We verify our results in model selection tasks for linear models and for the infinite-width limit of deep neural networks. Our results suggest a promising new direction towards explaining why neural networks trained with gradient descent are biased towards functions that generalize well.
  arXiv  Detail & Related papers  (2020-10-27T17:56:14Z)
• Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation [23.38076756988258]
  We propose a new single-model based approach to quantify uncertainty in deep neural networks. We use a mean-field approximation formula to compute an analytically intractable integral. Empirically, the proposed approach performs competitively when compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-06-13T07:32:38Z)

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.