The recent rapid development of well-designed and powerful machine learning (ML) models has significantly transformed our lives. However, the success of these models is often evaluated based on the accuracy of their predictions, which, while important, is not sufficient in many real-world scenarios. In high-stakes applications, it is equally critical to assess the uncertainty of model outputs. Uncertainty quantification (UQ) has long been a central problem in fields like statistics and ML. Several well-established methods, such as Bayesian inference and resampling techniques, have been widely adopted to address UQ. However, Bayesian posterior intervals are only valid if the parametric assumptions of the model are correctly specified, which may not always be the case in practical applications.

Out-of-distribution (OOD) detection is essential for model trustworthiness which aims to sensitively identify semantic OOD samples and robustly generalize for covariate-shifted OOD samples. However, we discover that the superior OOD detection performance of state-of-the-art methods is achieved by secretly sacrificing the OOD generalization ability. Specifically, the classification accuracy of these models could deteriorate dramatically when they encounter even minor noise. This phenomenon contradicts the goal of model trustworthiness and severely restricts their applicability in real-world scenarios. What is the hidden reason behind such a limitation? In this work, we theoretically demystify the ``\textit{sensitive-robust}'' dilemma that lies in many existing OOD detection methods. Consequently, a theory-inspired algorithm is induced to overcome such a dilemma. By decoupling the uncertainty learning objective from a Bayesian perspective, the conflict between OOD detection and OOD generalization is naturally harmonized and a dual-optimal performance could be expected. Empirical studies show that our method achieves superior performance on standard benchmarks. To our best knowledge, this work is the first principled OOD detection method that achieves state-of-the-art OOD detection performance without compromising OOD generalization ability. Our code is available at \href{https://github.com/QingyangZhang/DUL}{https://github.com/QingyangZhang/DUL}.

As the predominant principle, entropy minimization (EM) has been proven to be a simple yet effective cornerstone in existing test-time adaption (TTA) methods. While unfortunately its fatal limitation (i.e., overconfidence) tends to result in model collapse. For this issue, we propose to Conservatively Minimize the Entropy (COME), which is a simple drop-in replacement of traditional EM to elegantly address the limitation. By doing so, COME naturally regularizes the model to favor conservative confidence on unreliable samples. Theoretically, we provide a preliminary analysis to reveal the ability of COME in enhancing the optimization stability by introducing a data-adaptive lower bound on the entropy. Empirically, our method achieves state-of-the-art performance on commonly used benchmarks, showing significant improvements in terms of classification accuracy and uncertainty estimation under various settings including standard, life-long and open-world TTA, i.e., up to 34.5% improvement on accuracy and 15.1% on false positive rate. Endowing machine learning models with self-adjust ability is essential for their deployment in the open world, such as autonomous vehicle control and embodied AI systems. To this end, test-time adaption (TTA) emerges as a promising strategy to enhance the performance in the open world which often encounters unexpected noise or corruption (e.g., data from rainy or snowy weather). Unsupervised losses play a crucial role in model adaptation, which can improve the accuracy of a model on novel distributional test data without the need for additional labeled training data. The initial intuition behind using entropy minimization, given by (Wang et al., 2021) is based on the observation that models tend to be more accurate on samples for which they make predictions with higher confidence. The natural extension of this observation is to encourage models to bolster the confidence on test samples.

Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances.Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be needed in cross-validation (CV) for obtaining a solution with sufficiently small CV error.In this paper we propose a novel framework for computing a lower bound of the CV errors as a function of the regularization parameter, which we call regularization path of CV error lower bounds.The proposed framework can be used for providing a theoretical approximation guarantee on a set of solutions in the sense that how far the CV error of the current best solution could be away from best possible CV error in the entire range of the regularization parameters.We demonstrate through numerical experiments that a theoretically guaranteed a choice of regularization parameter in the above sense is possible with reasonable computational costs.

The task of out-of-distribution (OOD) detection is crucial for deploying machine learning models in real-world settings. In this paper, we observe that the singular value distributions of the in-distribution (ID) and OOD features are quite different: the OOD feature matrix tends to have a larger dominant singular value than the ID feature, and the class predictions of OOD samples are largely determined by it. This observation motivates us to propose RankFeat, a simple yet effective post hoc approach for OOD detection by removing the rank-1 matrix composed of the largest singular value and the associated singular vectors from the high-level feature. RankFeat achieves state-of-the-art performance and reduces the average false positive rate (FPR95) by 17.90% compared with the previous best method. Extensive ablation studies and comprehensive theoretical analyses are presented to support the empirical results.

Releasing all pairwise shortest path (APSP) distances between vertices on general graphs under weight Differential Privacy (DP) is known as a challenging task. In previous work, to achieve DP with some fixed budget, with high probability the maximal absolute error among all published pairwise distances is roughly O(n) where n is the number of nodes. It was shown that this error could be reduced for some special graphs, which, however, is hard for general graphs. Therefore, whether the approximation error can be reduced to sublinear is posted as an interesting open problem.In this paper, we break the linear barrier on the distance approximation error of previous result, by proposing an algorithm that releases a constructed synthetic graph privately. Computing all pairwise distances on the constructed graph only introduces O(n {1/2}) error in answering all pairwise shortest path distances for fixed privacy parameter.

We present a novel method for tuning the regularization hyper-parameter, \lambda, of a ridge regression that is faster to compute than leave-one-out cross-validation (LOOCV) while yielding estimates of the regression parameters of equal, or particularly in the setting of sparse covariates, superior quality to those obtained by minimising the LOOCV risk. The LOOCV risk can suffer from multiple and bad local minima for finite n and thus requires the specification of a set of candidate \lambda, which can fail to provide good solutions. In contrast, we show that the proposed method is guaranteed to find a unique optimal solution for large enough n, under relatively mild conditions, without requiring the specification of any difficult to determine hyper-parameters. This is based on a Bayesian formulation of ridge regression that we prove to have a unimodal posterior for large enough n, allowing for both the optimal \lambda and the regression coefficients to be jointly learned within an iterative expectation maximization (EM) procedure. Importantly, we show that by utilizing an appropriate preprocessing step, a single iteration of the main EM loop can be implemented in O(\min(n, p)) operations, for input data with n rows and p columns.

Generating precise class-aware pseudo ground-truths, a.k.a, class activation maps (CAMs), is essential for Weakly-Supervised Semantic Segmentation. The original CAM method usually produces incomplete and inaccurate localization maps. To tackle with this issue, this paper proposes an Expansion and Shrinkage scheme based on the offset learning in the deformable convolution, to sequentially improve the recall and precision of the located object in the two respective stages. In the Expansion stage, an offset learning branch in a deformable convolution layer, referred to as expansion sampler'', seeks to sample increasingly less discriminative object regions, driven by an inverse supervision signal that maximizes image-level classification loss. The located more complete object region in the Expansion stage is then gradually narrowed down to the final object region during the Shrinkage stage.

Generating step-by-step "chain-of-thought" rationales improves language model performance on complex reasoning tasks like mathematics or commonsense question-answering. However, inducing language model rationale generation currently requires either constructing massive rationale datasets or sacrificing accuracy by using only few-shot inference. We propose a technique to iteratively leverage a small number of rationale examples and a large dataset without rationales, to bootstrap the ability to perform successively more complex reasoning. This technique, the "Self-Taught Reasoner" (STaR), relies on a simple loop: generate rationales to answer many questions, prompted with a few rationale examples; if the generated answers are wrong, try again to generate a rationale given the correct answer; fine-tune on all the rationales that ultimately yielded correct answers; repeat. We show that STaR significantly improves performance on multiple datasets compared to a model fine-tuned to directly predict final answers, and performs comparably to fine-tuning a 30 \times larger state-of-the-art language model on CommensenseQA. Thus, STaR lets a model improve itself by learning from its own generated reasoning.