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Xinzhi Zhang

Publications and source records attributed to Xinzhi Zhang.

15 recordsLinked to original sources
arXiv2026

HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan--code--component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

cs.CL↗
arXiv2026

PADiff: Predictive and Adaptive Diffusion Policies for Ad Hoc Teamwork

Ad hoc teamwork (AHT) requires agents to collaborate with previously unseen teammates, which is crucial for many real-world applications. The core challenge of AHT is to develop an ego agent that can predict and adapt to unknown teammates on the fly. Conventional RL-based approaches optimize a single expected return, which often causes policies to collapse into a single dominant behavior, thus failing to capture the multimodal cooperation patterns inherent in AHT. In this work, we introduce PADiff, a diffusion-based approach that captures agent's multimodal behaviors, unlocking its diverse cooperation modes with teammates. However, standard diffusion models lack the ability to predict and adapt in highly non-stationary AHT scenarios. To address this limitation, we propose a novel diffusion-based policy that integrates critical predictive information about teammates into the denoising process. Extensive experiments across three cooperation environments demonstrate that PADiff outperforms existing AHT methods significantly.

cs.AI↗
arXiv2026

OptiMind: Teaching LLMs to Think Like Optimization Experts

Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise. Recent advances in large language models for complex reasoning have spurred interest in automating this task, translating natural language into executable optimization models. Current approaches, however, achieve limited accuracy, hindered by scarce and noisy training data without leveraging domain knowledge. In this work, we systematically integrate optimization expertise to improve formulation accuracy for mixed-integer linear programming, a key family of mathematical programs. Our OptiMind framework leverages semi-automated, class-based error analysis to guide both training and inference, explicitly preventing common mistakes within each optimization class. Our resulting fine-tuned LLM significantly improves formulation accuracy by 20.7% across multiple optimization benchmarks, with consistent gains under test-time scaling methods such as self-consistency and multi-turn feedback, enabling further progress toward robust LLM-assisted optimization formulation.

cs.LG↗
arXiv2025

Upper and Lower Bounds on the Smoothed Complexity of the Simplex Method

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by Spielman and Teng (JACM '04) for this purpose, defines the smoothed complexity of solving a linear program with $d$ variables and $n$ constraints as the expected running time when Gaussian noise of variance $σ^2$ is added to the LP data. We prove that the smoothed complexity of the simplex method is $O(σ^{-3/2} d^{13/4}\log^{7/4} n)$, improving the dependence on $1/σ$ compared to the previous bound of $O(σ^{-2} d^2\sqrt{\log n})$. We accomplish this through a new analysis of the \emph{shadow bound}, key to earlier analyses as well. Illustrating the power of our new method, we use our method to prove a nearly tight upper bound on the smoothed complexity of two-dimensional polygons. We also establish the first non-trivial lower bound on the smoothed complexity of the simplex method, proving that the \emph{shadow vertex simplex method} requires at least $Ω\Big(\min \big(σ^{-1/2} d^{-1/2}\log^{-1/4} d,2^d \big) \Big)$ pivot steps with high probability. A key part of our analysis is a new variation on the extended formulation for the regular $2^k$-gon. We end with a numerical experiment that suggests this analysis could be further improved.

cs.DS↗
arXiv2025

Pseudo-Asynchronous Local SGD: Robust and Efficient Data-Parallel Training

Following AI scaling trends, frontier models continue to grow in size and continue to be trained on larger datasets. Training these models requires huge investments in exascale computational resources, which has in turn driven developtment of distributed deep learning methods. Data parallelism is an essential approach to speed up training, but it requires frequent global communication between workers, which can bottleneck training at the largest scales. In this work, we propose a method called Pseudo-Asynchronous Local SGD (PALSGD) to improve the efficiency of data-parallel training. PALSGD is an extension of Local SGD (Stich, 2018) and DiLoCo (Douillard et al., 2023), designed to further reduce communication frequency by introducing a pseudo-synchronization mechanism. PALSGD allows the use of longer synchronization intervals compared to standard Local SGD. Despite the reduced communication frequency, the pseudo-synchronization approach ensures that model consistency is maintained, leading to performance results comparable to those achieved with more frequent synchronization. Furthermore, we provide a theoretical analysis of PALSGD, establishing its convergence and deriving its convergence rate. This analysis offers insights into the algorithm's behavior and performance guarantees. We evaluated PALSGD on image classification and language modeling tasks. Our results show that PALSGD achieves better performance in less time compared to existing methods like Distributed Data Parallel (DDP), and DiLoCo. Notably, PALSGD trains 18.4% faster than DDP on ImageNet-1K with ResNet-50, 24.4% faster than DDP on TinyStories with GPT-Neo-125M, and 21.1% faster than DDP on TinyStories with GPT-Neo-8M.

cs.LG↗
arXiv2025

On the Emergence of Thinking in LLMs I: Searching for the Right Intuition

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT \cite{li2024chain,merrill2023expresssive}.

cs.AI↗
arXiv2024

Cost efficiency of fMRI studies using resting-state vs task-based functional connectivity

We investigate whether and how we can improve the cost efficiency of neuroimaging studies with well-tailored fMRI tasks. The comparative study is conducted using a novel network science-driven Bayesian connectome-based predictive method, which incorporates network theories in model building and substantially improves precision and robustness in imaging biomarker detection. The robustness of the method lays the foundation for identifying predictive power differential across fMRI task conditions if such difference exists. When applied to a clinically heterogeneous transdiagnostic cohort, we found shared and distinct functional fingerprints of neuropsychological outcomes across seven fMRI conditions. For example, emotional N-back memory task was found to be less optimal for negative emotion outcomes, and gradual-onset continuous performance task was found to have stronger links with sensitivity and sociability outcomes than with cognitive control outcomes. Together, our results show that there are unique optimal pairings of task-based fMRI conditions and neuropsychological outcomes that should not be ignored when designing well-powered neuroimaging studies.

stat.AP↗
arXiv2023

A Hyperbolic Extension of Kadison-Singer Type Results

In 2013, Marcus, Spielman, and Srivastava resolved the famous Kadison-Singer conjecture. It states that for $n$ independent random vectors $v_1,\cdots, v_n$ that have expected squared norm bounded by $ε$ and are in the isotropic position in expectation, there is a positive probability that the determinant polynomial $\det(xI - \sum_{i=1}^n v_iv_i^\top)$ has roots bounded by $(1 + \sqrtε)^2$. An interpretation of the Kadison-Singer theorem is that we can always find a partition of the vectors $v_1,\cdots,v_n$ into two sets with a low discrepancy in terms of the spectral norm (in other words, rely on the determinant polynomial). In this paper, we provide two results for a broader class of polynomials, the hyperbolic polynomials. Furthermore, our results are in two generalized settings: $\bullet$ The first one shows that the Kadison-Singer result requires a weaker assumption that the vectors have a bounded sum of hyperbolic norms. $\bullet$ The second one relaxes the Kadison-Singer result's distribution assumption to the Strongly Rayleigh distribution. To the best of our knowledge, the previous results only support determinant polynomials [Anari and Oveis Gharan'14, Kyng, Luh and Song'20]. It is unclear whether they can be generalized to a broader class of polynomials. In addition, we also provide a sub-exponential time algorithm for constructing our results.

math.PR↗
arXiv2021

BU-Trace: A Permissionless Mobile System for Privacy-Preserving Intelligent Contact Tracing

The coronavirus disease 2019 (COVID-19) pandemic has caused an unprecedented health crisis for the global. Digital contact tracing, as a transmission intervention measure, has shown its effectiveness on pandemic control. Despite intensive research on digital contact tracing, existing solutions can hardly meet users' requirements on privacy and convenience. In this paper, we propose BU-Trace, a novel permissionless mobile system for privacy-preserving intelligent contact tracing based on QR code and NFC technologies. First, a user study is conducted to investigate and quantify the user acceptance of a mobile contact tracing system. Second, a decentralized system is proposed to enable contact tracing while protecting user privacy. Third, an intelligent behavior detection algorithm is designed to ease the use of our system. We implement BU-Trace and conduct extensive experiments in several real-world scenarios. The experimental results show that BU-Trace achieves a privacy-preserving and intelligent mobile system for contact tracing without requesting location or other privacy-related permissions.

cs.SI↗
arXiv2020

Generalizing Complex Hypotheses on Product Distributions: Auctions, Prophet Inequalities, and Pandora's Problem

This paper explores a theory of generalization for learning problems on product distributions, complementing the existing learning theories in the sense that it does not rely on any complexity measures of the hypothesis classes. The main contributions are two general sample complexity bounds: (1) $\tilde{O} \big( \frac{nk}{ε^2} \big)$ samples are sufficient and necessary for learning an $ε$-optimal hypothesis in any problem on an $n$-dimensional product distribution, whose marginals have finite supports of sizes at most $k$; (2) $\tilde{O} \big( \frac{n}{ε^2} \big)$ samples are sufficient and necessary for any problem on $n$-dimensional product distributions if it satisfies a notion of strong monotonicity from the algorithmic game theory literature. As applications of these theories, we match the optimal sample complexity for single-parameter revenue maximization (Guo et al., STOC 2019), improve the state-of-the-art for multi-parameter revenue maximization (Gonczarowski and Weinberg, FOCS 2018) and prophet inequality (Correa et al., EC 2019), and provide the first and tight sample complexity bound for Pandora's problem.

cs.GT↗
arXiv2019

A Dual-gate MoS2 Photodetector Based on Interface Coupling Effect

Two-dimensional (2D) transition metal dichalcogenides (TMDs) based photodetectors have shown great potential for the next generation optoelectronics. However, most of the reported MoS2 photodetectors function under the photogating effect originated from the charge-trap mechanism, which is difficult for quantitative control. Such devices generally suffer from a poor compromise between response speed and responsivity (R) and large dark current. Here, a dual-gated (DG) MoS2 phototransistor operating based on the interface coupling effect (ICE) is demonstrated. By simultaneously applying a negative top-gate voltage (VTG) and positive back-gate voltage (VBG) to the MoS2 channel, the photo-generated holes can be effectively trapped in the depleted region under TG. An ultrahigh R of ~1E5 A/W and detectivity (D*) of ~1E14 Jones have been achieved in several devices with different thickness under Pin of 53 uW/cm2 at VTG=-5 V. Moreover, the response time of the DG phototransistor can also be modulated based on the ICE. Based on these systematic measurements of MoS2 DG phototransistors, the results show that the ICE plays an important role in the modulation of photoelectric performances. Our results also pave the way for the future optoelectrical application of 2D TMDs materials and prompt for further investigation in the DG structured phototransistors.

physics.app-ph↗
arXiv2019

Smoothed complexity of local Max-Cut and binary Max-CSP

We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most $\smash{ϕn^{O(\sqrt{\log n})}}$, where $n$ is the number of nodes in the graph and $ϕ$ is a parameter that measures the magnitude of perturbations applied on its edge weights. This improves the previously best upper bound of $ϕn^{O(\log n)}$ by Etscheid and Röglin. Our result is based on an analysis of long sequences of flips, which shows~that~it is very unlikely for every flip in a long sequence to incur a positive but small improvement in the cut weight. We also extend the same upper bound on the smoothed complexity of FLIP to all binary Maximum Constraint Satisfaction Problems.

cs.DS↗
arXiv2019

Settling the Sample Complexity of Single-parameter Revenue Maximization

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an $ε$-net of the mechanism space, explicitly or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. Our lower bounds are also unified under a meta construction of hard instances.

cs.GT↗
arXiv2018

Angles and Schauder basis in Hilbert spaces

Let $\mathcal{H}$ be a complex separable Hilbert space. We prove that if $\{f_{n}\}_{n=1}^{\infty}$ is a Schauder basis of the Hilbert space $\mathcal{H}$, then the angles between any two vectors in this basis must have a positive lower bound. Furthermore, we investigate that $\{z^{σ^{-1}(n)}\}_{n=1}^{\infty}$ can never be a Schauder basis of $L^{2}(\mathbb{T},ν)$, where $\mathbb{T}$ is the unit circle, $ν$ is a finite positive discrete measure, and $σ: \mathbb{Z} \rightarrow \mathbb{N}$ is an arbitrary surjective and injective map.

math.FA↗