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Xiang Meng

Xiang Meng contributes to research discovery and scholarly infrastructure.

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Published work

6 published item(s)

preprint2026arXiv

ADMM-Q: An Improved Hessian-based Weight Quantizer for Post-Training Quantization of Large Language Models

Quantization is an effective strategy to reduce the storage and computation footprint of large language models (LLMs). Post-training quantization (PTQ) is a leading approach for compressing LLMs. Popular weight quantization procedures, including GPTQ and RTN, suffer in model utility, especially at aggressive quantization levels (sub-4-bit). We propose ADMM-Q, a novel weight quantization algorithm that considers the layer-wise quantization problem. Our algorithm is based on a combinatorial variant of the Alternating Direction Method of Multipliers (ADMM). Our operator-splitting procedure updates weights continuously to minimize the layer-wise reconstruction error, while gradually enforcing the quantization constraints with convergence guarantees. We propose additional algorithmic enhancements (e.g., penalty scheduling, preconditioning, and a local search post-processing step) to make ADMM-Q efficient at LLM scale. ADMM-Q is modular and can be used as a drop-in replacement for any weight quantizer within existing quantization pipelines: ADMM-Q is fully composable with existing techniques including range clipping, learned or random rotations, and activation scaling. Using ADMM-Q in place of GPTQ on Qwen3-8B, we decrease WikiText-2 perplexity in: (i) the W3A16 weight-only setting (12.85 $\rightarrow$ 10.06); (ii) the W4A8 SmoothQuant procedure (9.29 $\rightarrow$ 8.68); and (iii) the W2A4KV4 SpinQuant procedure (66.11 $\rightarrow$ 19.42).

preprint2022arXiv

Coherent modeling of longitudinal causal effects on binary outcomes

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Towards this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the non-causal nuisance parameters. This leads to a series of difficulties in interpretation, estimation and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparametrization of the non-causal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parametrization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parametrization, thereby justifying the restriction to multiplicative SNMMs.

preprint2022arXiv

Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features

Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at scale. A common approach in the literature is to use greedy heuristics, which may not be optimal. Recently there has been significant interest in learning optimal decision trees using various approaches (e.g., based on integer programming, dynamic programming) -- to achieve computational scalability, most of these approaches focus on classification tasks with binary features. In this paper, we present a new discrete optimization method based on branch-and-bound (BnB) to obtain optimal decision trees. Different from existing customized approaches, we consider both regression and classification tasks with continuous features. The basic idea underlying our approach is to split the search space based on the quantiles of the feature distribution -- leading to upper and lower bounds for the underlying optimization problem along the BnB iterations. Our proposed algorithm Quant-BnB shows significant speedups compared to existing approaches for shallow optimal trees on various real datasets.

preprint2022arXiv

REFINE2: A tool to evaluate real-world performance of machine-learning based effect estimators for molecular and clinical studies

Data-adaptive (machine learning-based) effect estimators are increasingly popular to reduce bias in high-dimensional bioinformatic and clinical studies (e.g. real-world data, target trials, -omic discovery). Their relative statistical efficiency (high power) is particularly invaluable in these contexts since sample sizes are often limited due to practical and cost concerns. However, these methods are subject to technical limitations that are dataset specific and involve computational trade-offs. Thus, it is challenging for analysts to identify when such methods may offer benefits or select amongst statistical methods. We present extensive simulation studies of several cutting-edge estimators, evaluating both performance and computation time. Critically, rather than use arbitrary simulation data, we generate synthetic datasets mimicking the observed data structure (plasmode simulation) of a real molecular epidemiologic cohort. We find that machine learning approaches may not always be indicated in such data settings, but that performance is highly context dependent. We present a user-friendly Shiny app REFINE2 (Realistic Evaluations of Finite sample INference using Efficient Estimators) that enables analysts to simulate synthetic data from their own datasets and directly evaluate the performance of several cutting-edge algorithms in those settings. This tool may greatly facilitate the proper selection and implementation of machine-learning-based effect estimators in bioinformatic and clinical study contexts.

preprint2020arXiv

Adaptive Robot-Assisted Feeding: An Online Learning Framework for Acquiring Previously Unseen Food Items

A successful robot-assisted feeding system requires bite acquisition of a wide variety of food items. It must adapt to changing user food preferences under uncertain visual and physical environments. Different food items in different environmental conditions require different manipulation strategies for successful bite acquisition. Therefore, a key challenge is how to handle previously unseen food items with very different success rate distributions over strategy. Combining low-level controllers and planners into discrete action trajectories, we show that the problem can be represented using a linear contextual bandit setting. We construct a simulated environment using a doubly robust loss estimate from previously seen food items, which we use to tune the parameters of off-the-shelf contextual bandit algorithms. Finally, we demonstrate empirically on a robot-assisted feeding system that, even starting with a model trained on thousands of skewering attempts on dissimilar previously seen food items, $ε$-greedy and LinUCB algorithms can quickly converge to the most successful manipulation strategy.

preprint2020arXiv

An exact penalty approach for optimization with nonnegative orthogonality constraints

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization formulation with nonnegative and multiple spherical constraints and an additional single nonlinear constraint. Various constraint qualifications, the first- and second-order optimality conditions of the equivalent formulation are discussed. By establishing a local error bound of the feasible set, we design a class of (smooth) exact penalty models via keeping the nonnegative and multiple spherical constraints. The penalty models are exact if the penalty parameter is sufficiently large other than going to infinity. A practical penalty algorithm with postprocessing is then developed. It uses a second-order method to approximately solve a series of subproblems with nonnegative and multiple spherical constraints. We study the asymptotic convergence of the penalty algorithm and establish that any limit point is a weakly stationary point of the original problem and becomes a stationary point under some additional mild conditions. Extensive numerical results on the projection problem, orthogonal nonnegative matrix factorization problems and the K-indicators model show the effectiveness of our proposed approach.