BZPEERReading, trust and collaboration for research
Menu

Discover

GraphFollow connections around a paper, topic or saved view.

Workspaces

HomePick up where your research flow left off.InboxHandle requests, replies and notifications from one place.CollectionsCurate reading lists, evidence sets and shareable dossiers.ResearchSee your private provenance graph, trail and imports.CollaborationMove from discovery into focused discussion rooms.PublishDraft, preview and publish full-text research articles.

Network

ExpertsFind specialists worth following or asking for help.CommunitiesJoin research circles organized around shared work.PartnersSee external organizations active around the same topics.

Opportunities

ListingsBrowse roles, calls and collaborations with clearer fit signals.

Account

Log inReturn to your reading and collaboration workspace.Create accountStart saving work, following people and joining teams.
Log inCreate account

Researcher profile

Zaiwen Wen

Zaiwen Wen contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.OCArtificial IntelligenceMachine Learningcond-mat.str-eleess.SPphysics.chem-phphysics.comp-phquant-ph

Trust snapshot

Quick read

Trust 21 - EmergingVerification L1Unclaimed author
10works
0followers
8topics
4close collaborators

Actions

Decide how to stay connected

Follow researcher0

Identity and collaboration

How to connect with this researcher

Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.

Log in to claim

Direct collaboration

Open a focused conversation when the fit is right

Claim this author entity first to unlock direct invitations.

Research graph

See the researcher in context

Open full explorer

Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.

Building this graph slice

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

10 published item(s)

preprint2026arXiv

CAM-Bench: A Benchmark for Computational and Applied Mathematics in Lean

Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving computational and applied mathematics underrepresented. We introduce CAM-Bench, a Lean 4 theorem-proving benchmark of 1,000 Lean proof targets in computational and applied mathematics, with coverage spanning optimization, numerical linear algebra, and numerical analysis. These problems are adapted from textbook exercises and often depend on locally introduced definitions, notation, algorithms, and elementary results. To construct CAM-Bench, we develop a dependency-recovery pipeline that reconstructs the local textbook context needed to state each problem faithfully. It then normalizes each problem into a standalone informal theorem and translates it into a Lean target. We validate the resulting formal problems through Lean compilation and semantic review, checking both formal correctness and semantic alignment with the original exercises. For each problem, we release the raw exercise, recovered context, normalized informal theorem, and final Lean target. CAM-Bench complements existing formal mathematics benchmarks by targeting applied mathematics problems that rely on textbook concepts and elementary theorems, many of which are not directly available as standard Mathlib4 lemmas. We evaluate widely used large language models and formalization agents on CAM-Bench, and analyze common failure modes in tracking local assumptions, applying elementary results, decomposing proofs, and maintaining long-horizon control in Lean.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling

Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver code, existing benchmarks are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but instance information is conveyed through visual artifacts such as tables, graphs, maps, schedules, and dashboards. We introduce multimodal optimization modeling, a benchmark setting in which models must construct both a mathematical formulation and executable solver code from a text-and-visual problem specification. To evaluate this setting, we develop a solver-grounded framework that generates structured optimization instances, verifies each with an exact solver, and builds both the model-facing inputs and hidden reference files from the same verified source. We instantiate the framework as MM-OptBench, a benchmark of 780 solver-verified instances spanning 6 optimization families, 26 subcategories, and 3 structural difficulty levels. We evaluate 9 multimodal large language models (MLLMs), including 6 frontier general-purpose models and 3 math-specialized models, with aggregate, family-level, difficulty-level, and failure-mode analyses. The results show that the task remains far from solved: the best two models reach 52.1% and 51.3% pass@1, while on average across the six general-purpose MLLMs, pass@1 is 43.4% on easy instances and 15.9% on hard instances. All three math-specialized MLLMs solve 0/780 instances. Failure attribution shows that errors arise both when extracting instance data from text and visuals and when turning extracted data into solver-correct formulations and code. MM-OptBench provides a testbed for solver-grounded, decision-oriented multimodal intelligence.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits

Parameter shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evaluate the cost function at different parameter shifts, then use specific coefficients to combine them linearly to obtain the exact derivatives. In this work, we propose an extended parameter shift rule (EPSR) which generalizes a broad range of existing PSRs and has the following two advantages. First, EPSR offers an infinite number of possible parameter shifts, allowing the selection of the optimal parameter shifts to minimize the final derivative variance and thereby obtaining the more accurate derivative estimates with limited quantum resources. Second, EPSR extends the scope of the PSRs in the sense that EPSR can handle arbitrary Hermitian operator $H$ in gate $U(x) = \exp (iHx)$ in the parameterized quantum circuits, while existing PSRs are valid only for simple Hermitian generators $H$ such as simple Pauli words. Additionally, we show that the widely used ``general PSR'', introduced by Wierichs et al. (2022), is a special case of our EPSR, and we prove that it yields globally optimal shifts for minimizing the derivative variance under the weighted-shot scheme. Finally, through numerical simulations, we demonstrate the effectiveness of EPSR and show that the usage of the optimal parameter shifts indeed leads to more accurate derivative estimates.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Near-Optimal Primal-Dual Method for Off-Policy Learning in CMDP

As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish an $Ω\left(\frac{\min\left\{|\mathcal{S}||\mathcal{A}|,|\mathcal{S}|+I\right\} C^*}{(1-γ)^3ε^2}\right)$ sample complexity lower bound for the offline CMDP problem, where $I$ stands for the number of constraints. By introducing a simple but novel deviation control mechanism, we propose a near-optimal primal-dual learning algorithm called DPDL. This algorithm provably guarantees zero constraint violation and its sample complexity matches the above lower bound except for an $\tilde{\mathcal{O}}((1-γ)^{-1})$ factor. Comprehensive discussion on how to deal with the unknown constant $C^*$ and the potential asynchronous structure on the offline dataset are also included.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Unified Primal-Dual Algorithm Framework for Inequality Constrained Problems

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers many existing algorithms such as PDHG, Chambolle-Pock (CP), GDA, OGDA and linearized ALM, but also guides us to design a new efficient algorithm called Simi-OGDA (SOGDA). Second, it enables us to study the role of the augmented penalty term in the convergence analysis. Interestingly, a properly selected penalty not only improves the numerical performance of the above methods, but also theoretically enables the convergence of algorithms like PDHG and SOGDA. Under properly designed step sizes and penalty term, our unified framework preserves the $\mathcal{O}(1/N)$ ergodic convergence while not requiring any prior knowledge about the magnitude of the optimal Lagrangian multiplier. Linear convergence rate for affine equality constrained problem is also obtained given appropriate conditions. Finally, numerical experiments on linear programming, $\ell_1$ minimization problem, and multi-block basis pursuit problem demonstrate the efficiency of our methods.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the pure state $v$-representability of density matrix embedding theory

Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are non-interacting pure-state $v$-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. In order to relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for 2D Hubbard and hydrogen model systems indicate that in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Riemannian Natural Gradient Methods

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By introducing the notion of Fisher information matrix in the manifold setting, we propose a novel Riemannian natural gradient method, which can be viewed as a natural extension of the natural gradient method from the Euclidean setting to the manifold setting. We establish the almost-sure global convergence of our proposed method under standard assumptions. Moreover, we show that if the loss function satisfies certain convexity and smoothness conditions and the input-output map satisfies a Riemannian Jacobian stability condition, then our proposed method enjoys a local linear -- or, under the Lipschitz continuity of the Riemannian Jacobian of the input-output map, even quadratic -- rate of convergence. We then prove that the Riemannian Jacobian stability condition will be satisfied by a two-layer fully connected neural network with batch normalization with high probability, provided that the width of the network is sufficiently large. This demonstrates the practical relevance of our convergence rate result. Numerical experiments on applications arising from machine learning demonstrate the advantages of the proposed method over state-of-the-art ones.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Joint Bandwidth Allocation and Path Selection in WANs with Path Cardinality Constraints

In this paper, we study a joint bandwidth allocation and path selection problem via solving a multi-objective minimization problem under the path cardinality constraints, namely MOPC. Our problem formulation captures various types of objectives including the proportional fairness, the total completion time, as well as the worst-case link utilization ratio. Such an optimization problem is very challenging since it is highly non-convex. Almost all existing works deal with such a problem using relaxation techniques to transform it to be a convex optimization problem. However, we provide a novel solution framework based on the classic alternating direction method of multipliers (ADMM) approach for solving this problem. Our proposed algorithm is simple and easy to be implemented. Each step of our algorithm consists of either finding the maximal root of a single-cubic equation which is guaranteed to have at least one positive solution or solving a one-dimensional convex subproblem in a fixed interval. Under some mild assumptions, we prove that any limiting point of the generated sequence under our proposed algorithm is a stationary point. Extensive numerical simulations are performed to demonstrate the advantages of our algorithm compared with various baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On the Analysis of Model-free Methods for the Linear Quadratic Regulator

Many reinforcement learning methods achieve great success in practice but lack theoretical foundation. In this paper, we study the convergence analysis on the problem of the Linear Quadratic Regulator (LQR). The global linear convergence properties and sample complexities are established for several popular algorithms such as the policy gradient algorithm, TD-learning and the actor-critic (AC) algorithm. Our results show that the actor-critic algorithm can reduce the sample complexity compared with the policy gradient algorithm. Although our analysis is still preliminary, it explains the benefit of AC algorithm in a certain sense.

0 citations0 reviewsNo code linkedOpen access