We introduce Resilient Multiple Choice Learning (rMCL), an extension of the MCL approach for conditional distribution estimation in regression settings where multiple targets may be sampled for each training input. Multiple Choice Learning is a simple framework to tackle multimodal density estimation, using the WinnerTakes-All (WTA) loss for a set of hypotheses. In regression settings, the existing MCL variants focus on merging the hypotheses, thereby eventually sacrificing the diversity of the predictions. In contrast, our method relies on a novel learned scoring scheme underpinned by a mathematical framework based on Voronoi tessellations of the output space, from which we can derive a probabilistic interpretation. After empirically validating rMCL with experiments on synthetic data, we further assess its merits on the sound source localization task, demonstrating its practical usefulness and the relevance of its interpretation.

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higherorder optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradientdescent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.

We investigate a practical domain adaptation task, called source-free unsupervised domain adaptation (SFUDA), where the source pretrained model is adapted to the target domain without access to the source data. Existing techniques mainly leverage self-supervised pseudo-labeling to achieve class-wise global alignment [1] or rely on local structure extraction that encourages the feature consistency among neighborhoods [2]. While impressive progress has been made, both lines of methods have their own drawbacks - the "global" approach is sensitive to noisy labels while the "local" counterpart suffers from the source bias. In this paper, we present Divide and Contrast (DaC), a new paradigm for SFUDA that strives to connect the good ends of both worlds while bypassing their limitations. Based on the prediction confidence of the source model, DaC divides the target data into source-like and target-specific samples, where either group of samples is treated with tailored goals under an adaptive contrastive learning framework. Specifically, the source-like samples are utilized for learning global class clustering thanks to their relatively clean labels. The more noisy target-specific data are harnessed at the instance level for learning the intrinsic local structures. We further align the sourcelike domain with the target-specific samples using a memory-based maximum mean discrepancy (MMD) loss to reduce the distribution mismatch. Extensive experiments on VisDA, Office-Home, and the more challenging DomainNet have verified the superior performance of DaC over current state-of-the-art approaches.

This paper investigates simultaneous preference and metric learning from a crowd of respondents. A set of items represented by d-dimensional feature vectors and paired comparisons of the form "item i is preferable to item j" made by each user is given. Our model jointly learns a distance metric that characterizes the crowd's general measure of item similarities along with a latent ideal point for each user reflecting their individual preferences. This model has the flexibility to capture individual preferences, while enjoying a metric learning sample cost that is amortized over the crowd. We first study this problem in a noiseless, continuous response setting (i.e., responses equal to differences of item distances) to understand the fundamental limits of learning. Next, we establish prediction error guarantees for noisy, binary measurements such as may be collected from human respondents, and show how the sample complexity improves when the underlying metric is lowrank. Finally, we establish recovery guarantees under assumptions on the response distribution. We demonstrate the performance of our model on both simulated data and on a dataset of color preference judgments across a large number of users.

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study largescale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NATURALPROVER,a language model that generates proofs by conditioning on background references (e.g.