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Christopher Re

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6 papers

1 author row

TMLR Journal 2026 Journal Article

A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systems

Xavier Gonzalez
E. Kelly Buchanan
Hyun Dong Lee
Jerry Weihong Liu
Ke Alexander Wang
David M. Zoltowski
Leo Kozachkov
Christopher Re

Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using iterative fixed-point methods, like Newton, Picard, and Jacobi iterations. In this work, we show that these methods can be understood within a common framework based on linear dynamical systems (LDSs), where different iteration schemes arise naturally as approximate linearizations of a nonlinear recursion. Moreover, we theoretically analyze the rates of convergence of these methods, and we verify the predictions of this theory with several case studies. This unifying framework highlights shared principles behind these techniques and clarifies when particular fixed-point methods are most likely to be effective. By bridging diverse algorithms through the language of LDSs, the framework provides a clearer theoretical foundation for parallelizing sequential models and points toward new opportunities for efficient and scalable computation.

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JMLR Journal 2025 Journal Article

Precise High-Dimensional Asymptotics for Quantifying Heterogeneous Transfers

Fan Yang
Hongyang R. Zhang
Sen Wu
Christopher Re
Weijie J. Su

The problem of learning one task using samples from another task is central to transfer learning. In this paper, we focus on answering the following question: when does combining the samples from two related tasks perform better than learning with one target task alone? This question is motivated by an empirical phenomenon known as negative transfer often observed in transfer learning practice. While the transfer effect from one task to another depends on factors such as their sample sizes and the spectrum of their covariance matrices, precisely quantifying this dependence has remained a challenging problem. In order to compare a transfer learning estimator to single-task learning, one needs to compare the risks between the two estimators precisely. Further, the comparison depends on the distribution shifts between the two tasks. This paper applies recent developments of random matrix theory to tackle this challenge in a high-dimensional linear regression setting with two tasks. We provide precise high-dimensional asymptotics for the bias and variance of a classical hard parameter sharing (HPS) estimator in the proportional limit, when the sample sizes of both tasks increase proportionally with dimension at fixed ratios. The precise asymptotics apply to various types of distribution shifts, including covariate shifts, model shifts, and combinations of both. We illustrate these results in a random-effects model to mathematically prove a phase transition from positive to negative transfer as the number of source task samples increases. One insight from the analysis is that a rebalanced HPS estimator, which downsizes the source task when the model shift is high, achieves the minimax optimal rate. The finding regarding phase transition also applies to multiple tasks when feature covariates are shared across all tasks. Simulations validate the accuracy of the high-dimensional asymptotics for finite dimensions. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2025. ( edit, beta )

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TMLR Journal 2023 Journal Article

Holistic Evaluation of Language Models

Percy Liang
Rishi Bommasani
Tony Lee
Dimitris Tsipras
Dilara Soylu
Michihiro Yasunaga
Yian Zhang
Deepak Narayanan

Language models (LMs) are becoming the foundation for almost all major language technologies, but their capabilities, limitations, and risks are not well understood. We present Holistic Evaluation of Language Models (HELM) to improve the transparency of language models. First, we taxonomize the vast space of potential scenarios (i.e. use cases) and metrics (i.e. desiderata) that are of interest for LMs. Then we select a broad subset based on coverage and feasibility, noting what’s missing or underrepresented (e.g. question answering for neglected English dialects, metrics for trustworthiness). Second, we adopt a multi-metric approach: We measure 7 metrics (accuracy, calibration, robustness, fairness, bias, toxicity, and efficiency) for each of 16 core scenarios to the extent possible (87.5% of the time), ensuring that metrics beyond accuracy don’t fall to the wayside, and that trade-offs across models and metrics are clearly exposed. We also perform 7 targeted evaluations, based on 26 targeted scenarios, to more deeply analyze specific aspects (e.g. knowledge, reasoning, memorization/copyright, disinformation). Third, we conduct a large-scale evaluation of 30 prominent language models (spanning open, limited-access, and closed models) on all 42 scenarios, including 21 scenarios that were not previously used in mainstream LM evaluation. Prior to HELM, models on average were evaluated on just 17.9% of the core HELM scenarios, with some prominent models not sharing a single scenario in common. We improve this to 96.0%: now all 30 models have been densely benchmarked on a set of core scenarios and metrics under standardized conditions. Our evaluation surfaces 25 top-level findings concerning the interplay between different scenarios, metrics, and models. For full transparency, we release all raw model prompts and completions publicly for further analysis, as well as a general modular toolkit for easily adding new scenarios, models, metrics, and prompting strategies. We intend for HELM to be a living benchmark for the community, continuously updated with new scenarios, metrics, and models.

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NeurIPS Conference 2013 Conference Paper

An Approximate, Efficient LP Solver for LP Rounding

Srikrishna Sridhar
Stephen Wright
Christopher Re
Ji Liu
Victor Bittorf
Ce Zhang

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program. We propose a scheme that is based on a quadratic program relaxation which allows us to use parallel stochastic-coordinate-descent to approximately solve large linear programs efficiently. Our software is an order of magnitude faster than Cplex (a commercial linear programming solver) and yields similar solution quality. Our results include a novel perturbation analysis of a quadratic-penalty formulation of linear programming and a convergence result, which we use to derive running time and quality guarantees.

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NeurIPS Conference 2012 Conference Paper

Factoring nonnegative matrices with linear programs

Ben Recht
Christopher Re
Joel Tropp
Victor Bittorf

This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a data-driven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C that satisfies X = CX and some linear constraints. The matrix C selects features, which are then used to compute a low-rank NMF of X. A theoretical analysis demonstrates that this approach has the same type of guarantees as the recent NMF algorithm of Arora et al. ~(2012). In contrast with this earlier work, the proposed method has (1) better noise tolerance, (2) extends to more general noise models, and (3) leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the new approach is also superior in practice. An optimized C++ implementation of the new algorithm can factor a multi-Gigabyte matrix in a matter of minutes.

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NeurIPS Conference 2011 Conference Paper

Hogwild!: A Lock-Free Approach to Parallelizing Stochastic Gradient Descent

Benjamin Recht
Christopher Re
Stephen Wright
Feng Niu

Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve state-of-the-art performance on a variety of machine learning tasks. Several researchers have recently proposed schemes to parallelize SGD, but all require performance-destroying memory locking and synchronization. This work aims to show using novel theoretical analysis, algorithms, and implementation that SGD can be implemented without any locking. We present an update scheme called Hogwild which allows processors access to shared memory with the possibility of overwriting each other's work. We show that when the associated optimization problem is sparse, meaning most gradient updates only modify small parts of the decision variable, then Hogwild achieves a nearly optimal rate of convergence. We demonstrate experimentally that Hogwild outperforms alternative schemes that use locking by an order of magnitude.

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