21 accepted papers
We study inference-time scaling for diffusion models, where the goal is to adapt a pre-trained model to new target distributions without retraining. Existing guidance-based methods are simple but introduce bias, while particle-based corrections suffer from weight degeneracy and high computational co…
In LLM alignment and many other ML applications, one often faces the *Multi-Objective Fine-Tuning* (MOFT) problem, *i.e.*, fine-tuning an existing model with datasets labeled w.r.t. different objectives simultaneously. To address the challenge, we propose a *Conditioned One-Shot* fine-tuning framewo
Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the developm…
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In this work, we propose a comprehensive framework for the error…
Diffusion models have become a leading method for generative modeling of both image and scientific data. As these models are costly to train and \emph{evaluate}, reducing the inference cost for diffusion models remains a major goal. Inspired by the recent empirical success in accelerating diffusion…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear r…
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach combines overdamped Langevin and birth-death dynamics, incorpo…
Bootstrap is a popular methodology for simulating input uncertainty. However, it can be computationally expensive when the number of samples is large. We propose a new approach called **Orthogonal Bootstrap** that reduces the number of required Monte Carlo replications. We decomposes the target bein…
Inferring a diffusion equation from discretely observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments. Assuming that the underlying dynamical process obeys a d-dimension…
Why do neural networks trained with large learning rates for longer time often lead to better generalization? In this paper, we delve into this question by examining the relation between training and testing loss in neural networks. Through visualization of these losses, we note that the training tr…
Learning mappings between infinite-dimensional function spaces have achieved empirical success in many disciplines of machine learning, including generative modeling, functional data analysis, causal inference, and multi-agent reinforcement learning. In this paper, we study the statistical limit of…
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in reducing variance. We examine a prototype estimation proble…
A recent line of work has focused on training machine learning (ML) models in the performative setting, i.e. when the data distribution reacts to the deployed model. The goal in this setting is to learn a model which both induces a favorable data distribution and performs well on the induced distrib…
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem, we focus on a prototype elliptic PDE: the…
In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow dynamics in which one probability distribution follows the…
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions includes Sobolev training for kernel regression, Deep Ritz…
Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer’s risk of default on a loan may induce customers to open more credit lines in orde…
The multiplicative structure of parameters and input data in the first layer of neural networks is explored to build connection between the landscape of the loss function with respect to parameters and the landscape of the model function with respect to input data. By this connection, it is shown th…
Motivated by modern applications, such as online advertisement and recommender systems, we study the top-$k$ extreme contextual bandits problem, where the total number of arms can be enormous, and the learner is allowed to select $k$ arms and observe all or some of the rewards for the chosen arms. W…
A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proportions. Training machine learning models on biased data sets requires correction techniques to compensate for the bias. We…
Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for training deep neural networks, this work presents a mean-field anal…