arXiv subjects

Fangzhao Zhang

Publications and source records attributed to Fangzhao Zhang.

12 recordsLinked to original sources

arXiv2026

TERMS-Bench: Diagnosing LLM Negotiation Agents Beyond Deal Rate

Negotiation is a central mechanism of economic exchange, shaping markets, procurement, labor agreements, and resource allocation. It is also a canonical testbed for agentic language models, requiring multi-turn interaction under hidden preferences, strategic communication, and binding constraints. These properties make negotiation hard to evaluate: unlike math or code, it has no intrinsic verifier. Existing LLM negotiation evaluations rely on LLM-vs.-LLM interaction or aggregate outcomes such as deal rate, leaving failures opaque. We introduce Terms-Bench, short for Testbed for Economic Reasoning in Multi-turn Strategy, a Bayesian-game framework that makes the environment itself the verifier by specifying the counterpart's latent type, policy, and payoff structure. We instantiate it in bilateral price negotiation, where the counterpart's private state and simulator policy are hidden from the agent but observable to the evaluator. This turns the counterpart from a black-box opponent into a diagnostic instrument, enabling agent-attributable failure analysis and oracle-reference optimality gaps. Evaluating 13 LLM agents spanning frontier systems from major providers, Terms-Bench turns negotiation evaluation from aggregate ranking into actionable diagnosis: where agents fail, why they fail, and what to strengthen. Empirically, frontier models saturate deal rate yet diverge in surplus extraction, cue use, belief calibration, and compliance, revealing agent-specific bargaining bottlenecks masked by prior benchmarks.

cs.GT↗

arXiv2026

Optimizer-Induced Mode Connectivity: From AdamW to Muon

Mode connectivity has been widely studied, yet the role of the optimizer remains underexplored. We revisit it through optimizer-induced implicit regularization, asking how connectivity behaves when restricted to solutions constrained by a given optimizer. For two-layer ReLU networks, we show that solutions from a single optimizer -- AdamW, Muon, or others in the Lion-$\mathcal{K}$ family -- form a connected set at sufficiently large width, a result not implied by prior work. We then characterize how optimizer-induced regions interact: at large width two different regions can be disjoint or overlap depending on regularization, while in our small-width example AdamW and Muon converge to disconnected zero-loss components separated by a provable loss barrier. Empirically, in GPT-2 pretraining, we observe same-optimizer paths preserve each model's spectrum while cross-optimizer paths traverse a smooth transition. Our results reveal optimizer-dependent structure beyond classical mode connectivity literature.

cs.AI↗

arXiv2026

Learning When to Trust LLM Priors: A Validated Framework for Semantic Prior Integration

Large language models (LLMs) encode rich semantic knowledge that can be useful for supervised learning, but their outputs are unreliable as statistical priors: they may be noisy, misspecified, or hallucinated. Existing LLM-informed learning methods either trust such signals directly, leaving predictions vulnerable to unreliable LLM guidance, or restrict semantic integration to a single model class. We introduce Statsformer, a validated framework for learning when to trust LLM-derived semantic priors in supervised statistical learning. Statsformer maps LLM-derived feature scores into a family of learner-specific prior-injection mechanisms across a heterogeneous library of linear and nonlinear predictors. It then uses out-of-fold validation to adaptively calibrate the influence of each prior-informed learner, allowing useful semantic information to improve prediction while attenuating weak, misspecified, or adversarial priors. This yields a guardrailed statistical learning system with an oracle-style guarantee: up to statistical error, the final predictor performs no worse than the best convex combination of its in-library candidates, including prior-free learners. Across diverse prediction tasks, informative LLM priors improve performance, while unreliable priors are automatically downweighted. These results position Statsformer as a reliability-oriented approach to LLM-informed statistical learning: rather than trusting LLM knowledge directly, it validates semantic priors against data before allowing them to influence the final predictor.

stat.ML↗

arXiv2025

AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?

Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (Jimenez et al., 2024) and mathematics (Glazer et al., 2024). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTune benchmark consists of 154 coding tasks collected from domain experts and a framework for validating and timing LM-synthesized solution code, which is compared to reference implementations from popular open-source packages. In addition, we develop a baseline LM agent, AlgoTuner, and evaluate its performance across a suite of frontier models. AlgoTuner uses a simple, budgeted loop that edits code, compiles and runs it, profiles performance, verifies correctness on tests, and selects the fastest valid version. AlgoTuner achieves an average 1.72x speedup against our reference solvers, which use libraries such as SciPy, sk-learn and CVXPY. However, we find that current models fail to discover algorithmic innovations, instead preferring surface-level optimizations. We hope that AlgoTune catalyzes the development of LM agents exhibiting creative problem solving beyond state-of-the-art human performance.

cs.SE↗

arXiv2025

Active Learning of Deep Neural Networks via Gradient-Free Cutting Planes

Active learning methods aim to improve sample complexity in machine learning. In this work, we investigate an active learning scheme via a novel gradient-free cutting-plane training method for ReLU networks of arbitrary depth and develop a convergence theory. We demonstrate, for the first time, that cutting-plane algorithms, traditionally used in linear models, can be extended to deep neural networks despite their nonconvexity and nonlinear decision boundaries. Moreover, this training method induces the first deep active learning scheme known to achieve convergence guarantees, revealing a geometric contraction rate of the feasible set. We exemplify the effectiveness of our proposed active learning method against popular deep active learning baselines via both synthetic data experiments and sentimental classification task on real datasets.

cs.LG↗

arXiv2025

Solving Large Multicommodity Network Flow Problems on GPUs

We consider the all-pairs multicommodity network flow problem on a network with capacitated edges. The usual treatment keeps track of a separate flow for each source-destination pair on each edge; we rely on a more efficient formulation in which flows with the same destination are aggregated, reducing the number of variables by a factor equal to the size of the network. Problems with hundreds of nodes, with a total number of variables on the order of a million, can be solved using standard generic interior-point methods on CPUs; we focus on GPU-compatible algorithms that can solve such problems much faster, and in addition scale to much larger problems, with up to a billion variables. Our method relies on the primal-dual hybrid gradient algorithm, and exploits several specific features of the problem for efficient GPU computation. Numerical experiments show that our primal-dual multicommodity network flow method accelerates state of the art generic commercial solvers by $100\times$ to $1000\times$, and scales to problems that are much larger. We provide an open source implementation of our method.

math.OC↗

arXiv2024

Spectral Adapter: Fine-Tuning in Spectral Space

Recent developments in Parameter-Efficient Fine-Tuning (PEFT) methods for pretrained deep neural networks have captured widespread interest. In this work, we study the enhancement of current PEFT methods by incorporating the spectral information of pretrained weight matrices into the fine-tuning procedure. We investigate two spectral adaptation mechanisms, namely additive tuning and orthogonal rotation of the top singular vectors, both are done via first carrying out Singular Value Decomposition (SVD) of pretrained weights and then fine-tuning the top spectral space. We provide a theoretical analysis of spectral fine-tuning and show that our approach improves the rank capacity of low-rank adapters given a fixed trainable parameter budget. We show through extensive experiments that the proposed fine-tuning model enables better parameter efficiency and tuning performance as well as benefits multi-adapter fusion.

cs.LG↗

arXiv2024

Newton Meets Marchenko-Pastur: Massively Parallel Second-Order Optimization with Hessian Sketching and Debiasing

Motivated by recent advances in serverless cloud computing, in particular the "function as a service" (FaaS) model, we consider the problem of minimizing a convex function in a massively parallel fashion, where communication between workers is limited. Focusing on the case of a twice-differentiable objective subject to an L2 penalty, we propose a scheme where the central node (server) effectively runs a Newton method, offloading its high per-iteration cost -- stemming from the need to invert the Hessian -- to the workers. In our solution, workers produce independently coarse but low-bias estimates of the inverse Hessian, using an adaptive sketching scheme. The server then averages the descent directions produced by the workers, yielding a good approximation for the exact Newton step. The main component of our adaptive sketching scheme is a low-complexity procedure for selecting the sketching dimension, an issue that was left largely unaddressed in the existing literature on Hessian sketching for distributed optimization. Our solution is based on ideas from asymptotic random matrix theory, specifically the Marchenko-Pastur law. For Gaussian sketching matrices, we derive non asymptotic guarantees for our algorithm which are essentially dimension-free. Lastly, when the objective is self-concordant, we provide convergence guarantees for the approximate Newton's method with noisy Hessians, which may be of independent interest beyond the setting considered in this paper.

math.OC↗

arXiv2024

Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models

Low-Rank Adaptation (LoRA) emerges as a popular parameter-efficient fine-tuning (PEFT) method, which proposes to freeze pretrained model weights and update an additive low-rank trainable matrix. In this work, we study the enhancement of LoRA training by introducing an $r \times r$ preconditioner in each gradient step where $r$ is the LoRA rank. We theoretically verify that the proposed preconditioner stabilizes feature learning with LoRA under infinite-width NN setting. Empirically, the implementation of this new preconditioner requires a small change to existing optimizer code and creates virtually minuscule storage and runtime overhead. Our experimental results with both large language models and text-to-image diffusion models show that with this new preconditioner, the convergence and reliability of SGD and AdamW can be significantly enhanced. Moreover, the training process becomes much more robust to hyperparameter choices such as learning rate. The new preconditioner can be derived from a novel Riemannian metric in low-rank matrix field. Code can be accessed at https://github.com/pilancilab/Riemannian_Preconditioned_LoRA.

cs.LG↗

arXiv2024

Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization

Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In this study, we present a theoretical framework to analyze two-layer neural network-based diffusion models by reframing score matching and denoising score matching as convex optimization. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Although most analyses of diffusion models operate in the asymptotic setting or rely on approximations, we characterize the exact predicted score function and establish convergence results for neural network-based diffusion models with finite data. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.

cs.LG↗

arXiv2024

Optimal Shrinkage for Distributed Second-Order Optimization

In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and characterize its non-asymptotic convergence rate in the isotropic case. We apply this estimator to bias correction of Newton steps in distributed second-order optimization algorithms, as well as randomized sketching based methods. We examine the bias present in the naive averaging-based distributed Newton's method using analytical expressions and contrast it with our proposed bias-free approach. Our approach leads to significant improvements in convergence rate compared to standard baselines and recent proposals, as shown through experiments on both real and synthetic datasets.

math.OC↗

arXiv2023

Implementation of an Oracle-Structured Bundle Method for Distributed Optimization

We consider the problem of minimizing a function that is a sum of convex agent functions plus a convex common public function that couples them. The agent functions can only be accessed via a subgradient oracle; the public function is assumed to be structured and expressible in a domain specific language (DSL) for convex optimization. We focus on the case when the evaluation of the agent oracles can require significant effort, which justifies the use of solution methods that carry out significant computation in each iteration. To solve this problem we integrate multiple known techniques (or adaptations of known techniques) for bundle-type algorithms, obtaining a method which has a number of practical advantages over other methods that are compatible with our access methods, such as proximal subgradient methods. First, it is reliable, and works well across a number of applications. Second, it has very few parameters that need to be tuned, and works well with sensible default values. Third, it typically produces a reasonable approximate solution in just a few tens of iterations. This paper is accompanied by an open-source implementation of the proposed solver, available at \url{https://github.com/cvxgrp/OSBDO}.

math.OC↗