David Hong

Yuangang Li, Justin Tian Jin Chen, Ethan Yu et al.

Large language models (LLMs) increasingly rely on explicit reasoning to solve coding tasks, yet evaluating the quality of this reasoning remains challenging. Existing reasoning evaluators are not designed for coding, and current benchmarks focus primarily on code generation, leaving other coding tasks largely unexplored. We introduce CodeRQ-Bench, the first benchmark for evaluating LLM reasoning quality across three coding task categories: generation, summarization, and classification. Using this benchmark, we analyze 1,069 mismatch cases from existing evaluators, identify five recurring limitations, and derive four design insights for reasoning evaluation in coding tasks. Guided by these insights, we propose VERA, a two-stage evaluator that combines evidence-grounded verification with ambiguity-aware score correction. Experiments on CodeRQ-Bench show that VERA consistently outperforms strong baselines across four datasets, improving AUCROC by up to 0.26 and AUPRC by up to 0.21. We release CodeRQ-Bench at https://github.com/MrLYG/CodeRQ-Bench, supporting future investigations.

Alex Mulrooney, David Hong

Canonical Polyadic (CP) tensor decomposition is a workhorse algorithm for discovering underlying low-dimensional structure in tensor data. This is accomplished in conventional CP decomposition by fitting a low-rank tensor to data with respect to the least-squares loss. Generalized CP (GCP) decompositions generalize this approach by allowing general loss functions that can be more appropriate, e.g., to model binary and count data or to improve robustness to outliers. However, GCP decompositions do not explicitly account for any symmetry in the tensors, which commonly arises in modern applications. For example, a tensor formed by stacking the adjacency matrices of a dynamic graph over time will naturally exhibit symmetry along the two modes corresponding to the graph nodes. In this paper, we develop a symmetric GCP (SymGCP) decomposition that allows for general forms of symmetry, i.e., symmetry along any subset of the modes. SymGCP accounts for symmetry by enforcing the corresponding symmetry in the decomposition. We derive gradients for SymGCP that enable its efficient computation via all-at-once optimization with existing tensor kernels. The form of the gradients also leads to various stochastic approximations that enable us to develop stochastic SymGCP algorithms that can scale to large tensors. We demonstrate the utility of the proposed SymGCP algorithms with a variety of experiments on both synthetic and real data.

Edgar Dobriban, Hamed Hassani, David Hong et al.

It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs. Despite significant progress in the area, foundational open problems remain. In this paper, we address several key questions. We derive exact and approximate Bayes-optimal robust classifiers for the important setting of two- and three-class Gaussian classification problems with arbitrary imbalance, for $\ell_2$ and $\ell_\infty$ adversaries. In contrast to classical Bayes-optimal classifiers, determining the optimal decisions here cannot be made pointwise and new theoretical approaches are needed. We develop and leverage new tools, including recent breakthroughs from probability theory on robust isoperimetry, which, to our knowledge, have not yet been used in the area. Our results reveal fundamental tradeoffs between standard and robust accuracy that grow when data is imbalanced. We also show further results, including an analysis of classification calibration for convex losses in certain models, and finite sample rates for the robust risk.

Shunbo Lei, David Hong, Johanna L. Mathieu et al.

Commercial building heating, ventilation, and air conditioning (HVAC) systems have been studied for providing ancillary services to power grids via demand response (DR). One critical issue is to estimate the counterfactual baseline power consumption that would have prevailed without DR. Baseline methods have been developed based on whole building electric load profiles. New methods are necessary to estimate the baseline power consumption of HVAC sub-components (e.g., supply and return fans), which have different characteristics compared to that of the whole building. Tensor completion can estimate the unobserved entries of multi-dimensional tensors describing complex data sets. It exploits high-dimensional data to capture granular insights into the problem. This paper proposes to use it for baselining HVAC fan power, by utilizing its capability of capturing dominant fan power patterns. The tensor completion method is evaluated using HVAC fan power data from several buildings at the University of Michigan, and compared with several existing methods. The tensor completion method generally outperforms the benchmarks.

Tamara G. Kolda, David Hong

Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of loss functions such as Bernoulli loss for binary data or Huber loss for robust estimation. The stochastic gradient is formed from randomly sampled elements of the tensor and is efficient because it can be computed using the sparse matricized-tensor-times-Khatri-Rao product (MTTKRP) tensor kernel. For dense tensors, we simply use uniform sampling. For sparse tensors, we propose two types of stratified sampling that give precedence to sampling nonzeros. Numerical results demonstrate the advantages of the proposed approach and its scalability to large-scale problems.

Il Yong Chun, David Hong, Ben Adcock et al.

Convolutional analysis operator learning (CAOL) enables the unsupervised training of (hierarchical) convolutional sparsifying operators or autoencoders from large datasets. One can use many training images for CAOL, but a precise understanding of the impact of doing so has remained an open question. This paper presents a series of results that lend insight into the impact of dataset size on the filter update in CAOL. The first result is a general deterministic bound on errors in the estimated filters, and is followed by a bound on the expected errors as the number of training samples increases. The second result provides a high probability analogue. The bounds depend on properties of the training data, and we investigate their empirical values with real data. Taken together, these results provide evidence for the potential benefit of using more training data in CAOL.

David Hong, Tamara G. Kolda, Jed A. Duersch

Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor decomposition that allows other loss functions besides squared error. For instance, we can use logistic loss or Kullback-Leibler divergence, enabling tensor decomposition for binary or count data. We present a variety statistically-motivated loss functions for various scenarios. We provide a generalized framework for computing gradients and handling missing data that enables the use of standard optimization methods for fitting the model. We demonstrate the flexibility of GCP on several real-world examples including interactions in a social network, neural activity in a mouse, and monthly rainfall measurements in India.

John Lipor, David Hong, Yan Shuo Tan et al.

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees, or depend heavily on their initialization. We present a novel geometric approach to the subspace clustering problem that leverages ensembles of the K-subspaces (KSS) algorithm via the evidence accumulation clustering framework. Our algorithm, referred to as ensemble K-subspaces (EKSS), forms a co-association matrix whose (i,j)th entry is the number of times points i and j are clustered together by several runs of KSS with random initializations. We prove general recovery guarantees for any algorithm that forms an affinity matrix with entries close to a monotonic transformation of pairwise absolute inner products. We then show that a specific instance of EKSS results in an affinity matrix with entries of this form, and hence our proposed algorithm can provably recover subspaces under similar conditions to state-of-the-art algorithms. The finding is, to the best of our knowledge, the first recovery guarantee for evidence accumulation clustering and for KSS variants. We show on synthetic data that our method performs well in the traditionally challenging settings of subspaces with large intersection, subspaces with small principal angles, and noisy data. Finally, we evaluate our algorithm on six common benchmark datasets and show that unlike existing methods, EKSS achieves excellent empirical performance when there are both a small and large number of points per subspace.

David Hong, Laura Balzano, Jeffrey A. Fessler

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data. PCA performs well in the presence of moderate noise and even with missing data, but is also sensitive to outliers. PCA is also known to have a phase transition when noise is independent and identically distributed; recovery of the subspace sharply declines at a threshold noise variance. Effective use of PCA requires a rigorous understanding of these behaviors. This paper provides a step towards an analysis of PCA for samples with heteroscedastic noise, that is, samples that have non-uniform noise variances and so are no longer identically distributed. In particular, we provide a simple asymptotic prediction of the recovery of a one-dimensional subspace from noisy heteroscedastic samples. The prediction enables: a) easy and efficient calculation of the asymptotic performance, and b) qualitative reasoning to understand how PCA is impacted by heteroscedasticity (such as outliers).