Session: Optimization Meets Generative AI: Insights and New Designs
Chair: Minshuo Chen
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)
Talk 1: Fine Tuning And Guidance of Diffusion Models
Speaker: Wenpin Tang
Abstract: The past decade has witnessed the success of generative modeling (e.g. GANs, VAEs,...) in creating high quality samples in a wide variety of data modalities. In the first part of this talk, I will briefly introduce the recently developed diffusion models from a continuous-time perspective. Then in the second part, I will discuss three different approaches to fine-tune the diffusion models: conditioning (classifier guidance), stochastic control and reinforcement learning. Each of these approaches will lead to a nice theory with a few application fields. If time permits, I will also discuss the DPO (Direct preference optimization) approach to fine-tuning text-to-image models.
Talk 2: How Does Gradient Descent Learn Features -- A Local Analysis for Regularized Two-Layer Neural Networks
Speaker: Mo Zhou
Abstract: The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural networks can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works also demonstrate the potential for neural networks to go beyond NTK regime and perform feature learning. Recently, a line of work highlighted the feature learning capabilities of the early stages of gradient-based training. In this paper we consider another mechanism for feature learning via gradient descent through a local convergence analysis. We show that once the loss is below a certain threshold, gradient descent with a carefully regularized objective will capture ground-truth directions. Our results demonstrate that feature learning not only happens at the initial gradient steps, but can also occur towards the end of training.
Talk 3: Theoretical Implications of Training And Sampling Diffusion Models
Speaker: Yuqing Wang
Abstract: Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation. In this talk, I will show a quantitative understanding of the whole generation process, i.e., both training and sampling. More precisely, it conducts a non-asymptotic convergence analysis of denoising score matching under gradient descent. In addition, a refined sampling error analysis for variance exploding models is also provided. The combination of these two results yields a full error analysis, which elucidates (again, but this time theoretically) how to design the training and sampling processes for effective generation. For instance, our theory implies a preference toward noise distribution and loss weighting in training that qualitatively agree with the ones used in Karras et al. 2022. It also provides perspectives on the choices of time and variance schedules in sampling: when the score is well trained, the design in Song et al. 2021 is more preferable, but when it is less trained, the design in Karras et al. 2022 becomes more preferable.
