arXiv subjects

Haishan Ye

Publications and source records attributed to Haishan Ye.

At least 37 records · Page 2Linked to original sources

arXiv2025

Numerical Sensitivity and Robustness: Exploring the Flaws of Mathematical Reasoning in Large Language Models

LLMs have made significant progress in the field of mathematical reasoning, but whether they have true the mathematical understanding ability is still controversial. To explore this issue, we propose a new perturbation framework to evaluate LLMs' reasoning ability in complex environments by injecting additional semantically irrelevant perturbation sentences and gradually increasing the perturbation intensity. At the same time, we use an additional perturbation method: core questioning instruction missing, to further analyze the LLMs' problem-solving mechanism. The experimental results show that LLMs perform stably when facing perturbation sentences without numbers, but there is also a robustness boundary. As the perturbation intensity increases, the performance exhibits varying degrees of decline; when facing perturbation sentences with numbers, the performance decreases more significantly, most open source models with smaller parameters decrease by nearly or even more than 10%, and further increasing with the enhancement of perturbation intensity, with the maximum decrease reaching 51.55%. Even the most advanced commercial LLMs have seen a 3%-10% performance drop. By analyzing the reasoning process of LLMs in detail, We find that models are more sensitive to perturbations with numerical information and are more likely to give incorrect answers when disturbed by irrelevant numerical information. The higher the perturbation intensity, the more obvious these defects are. At the same time, in the absence of core questioning instruction, models can still maintain an accuracy of 20%-40%, indicating that LLMs may rely on memory templates or pattern matching to complete the task, rather than logical reasoning. In general, our work reveals the shortcomings and limitations of current LLMs in their reasoning capabilities, which is of great significance for the further development of LLMs.

cs.AI↗

arXiv2025

MSCR: Exploring the Vulnerability of LLMs' Mathematical Reasoning Abilities Using Multi-Source Candidate Replacement

LLMs demonstrate performance comparable to human abilities in complex tasks such as mathematical reasoning, but their robustness in mathematical reasoning under minor input perturbations still lacks systematic investigation. Existing methods generally suffer from limited scalability, weak semantic preservation, and high costs. Therefore, we propose MSCR, an automated adversarial attack method based on multi-source candidate replacement. By combining three information sources including cosine similarity in the embedding space of LLMs, the WordNet dictionary, and contextual predictions from a masked language model, we generate for each word in the input question a set of semantically similar candidates, which are then filtered and substituted one by one to carry out the attack. We conduct large-scale experiments on LLMs using the GSM8K and MATH500 benchmarks. The results show that even a slight perturbation involving only a single word can significantly reduce the accuracy of all models, with the maximum drop reaching 49.89% on GSM8K and 35.40% on MATH500, while preserving the high semantic consistency of the perturbed questions. Further analysis reveals that perturbations not only lead to incorrect outputs but also substantially increase the average response length, which results in more redundant reasoning paths and higher computational resource consumption. These findings highlight the robustness deficiencies and efficiency bottlenecks of current LLMs in mathematical reasoning tasks.

cs.AI↗

arXiv2025

Frustratingly Easy Task-aware Pruning for Large Language Models

Pruning provides a practical solution to reduce the resources required to run large language models (LLMs) to benefit from their effective capabilities as well as control their cost for training and inference. Research on LLM pruning often ranks the importance of LLM parameters using their magnitudes and calibration-data activations and removes (or masks) the less important ones, accordingly reducing LLMs' size. However, these approaches primarily focus on preserving the LLM's ability to generate fluent sentences, while neglecting performance on specific domains and tasks. In this paper, we propose a simple yet effective pruning approach for LLMs that preserves task-specific capabilities while shrinking their parameter space. We first analyze how conventional pruning minimizes loss perturbation under general-domain calibration and extend this formulation by incorporating task-specific feature distributions into the importance computation of existing pruning algorithms. Thus, our framework computes separate importance scores using both general and task-specific calibration data, partitions parameters into shared and exclusive groups based on activation-norm differences, and then fuses their scores to guide the pruning process. This design enables our method to integrate seamlessly with various foundation pruning techniques and preserve the LLM's specialized abilities under compression. Experiments on widely used benchmarks demonstrate that our approach is effective and consistently outperforms the baselines with identical pruning ratios and different settings.

cs.CL↗

arXiv2025

A Unified Zeroth-Order Optimization Framework via Oblivious Randomized Sketching

We propose a new framework for analyzing zeroth-order optimization (ZOO) from the perspective of \emph{oblivious randomized sketching}.In this framework, commonly used gradient estimators in ZOO-such as finite difference (FD) and random finite difference (RFD)-are unified through a general sketch-based formulation. By introducing the concept of oblivious randomized sketching, we show that properly chosen sketch matrices can significantly reduce the high variance of RFD estimates and enable \emph{high-probability} convergence guarantees of ZOO, which are rarely available in existing RFD analyses. \noindent We instantiate the framework on convex quadratic objectives and derive a query complexity of $\tilde{\mathcal{O}}(\mathrm{tr}(A)/L \cdot L/μ\log\frac{1}ε)$ to achieve a $ε$-suboptimal solution, where $A$ is the Hessian, $L$ is the largest eigenvalue of $A$, and $μ$ denotes the strong convexity parameter. This complexity can be substantially smaller than the standard query complexity of ${\cO}(d\cdot L/μ\log\frac{1}ε)$ that is linearly dependent on problem dimensionality, especially when $A$ has rapidly decaying eigenvalues. These advantages naturally extend to more general settings, including strongly convex and Hessian-aware optimization. \noindent Overall, this work offers a novel sketch-based perspective on ZOO that explains why and when RFD-type methods can achieve \emph{weakly dimension-independent} convergence in general smooth problems, providing both theoretical foundations and practical implications for ZOO.

math.OC↗

arXiv2025

Can a One-Point Feedback Zeroth-order Algorithm Achieve Linear Dimension Dependent Sample Complexity?

We revisit the one-point feedback zeroth-order (ZO) optimization problem, a classical setting in derivative-free optimization where only a single noisy function evaluation is available per query. Compared to their two-point counterparts, existing one-point feedback ZO algorithms typically suffer from poor dimension dependence in their sample complexities -- often quadratic or worse -- even for convex problems. This gap has led to the open question of whether one-point feedback ZO algorithms can match the optimal \emph{linear} dimension dependence achieved by two-point methods. In this work, we answer this question \emph{affirmatively}.

math.OC↗

arXiv2025

PPFL: A Personalized Federated Learning Framework for Heterogeneous Population

Personalization aims to characterize individual preferences and is widely applied across many fields. However, conventional personalized methods operate in a centralized manner, potentially exposing raw data when pooling individual information. In this paper, with privacy considerations, we develop a flexible and interpretable personalized framework within the paradigm of federated learning, called \texttt{PPFL} (Population Personalized Federated Learning). By leveraging ``canonical models" to capture fundamental characteristics of a heterogeneous population and employing ``membership vectors" to reveal clients' preferences, \texttt{PPFL} models heterogeneity as clients' varying preferences for these characteristics. This approach provides substantial insights into client characteristics, which are lacking in existing Personalized Federated Learning (PFL) methods. Furthermore, we explore the relationship between \texttt{PPFL} and three main branches of PFL methods: clustered FL, multi-task PFL, and decoupling PFL, and demonstrate the advantages of \texttt{PPFL}. To solve \texttt{PPFL} (a non-convex optimization problem with linear constraints), we propose a novel random block coordinate descent algorithm and establish its convergence properties. We conduct experiments on both pathological and practical data sets, and the results validate the effectiveness of \texttt{PPFL}.

cs.LG↗

arXiv2025

FZOO: Fast Zeroth-Order Optimizer for Fine-Tuning Large Language Models towards Adam-Scale Speed

Fine-tuning large language models (LLMs) often faces GPU memory bottlenecks: the backward pass of first-order optimizers like Adam increases memory usage to more than 10 times the inference level (e.g., 633 GB for OPT-30B). Zeroth-order (ZO) optimizers avoid this cost by estimating gradients only from forward passes, yet existing methods like MeZO usually require many more steps to converge. Can this trade-off between speed and memory in ZO be fundamentally improved? Normalized-SGD demonstrates strong empirical performance with greater memory efficiency than Adam. In light of this, we introduce FZOO, a Fast Zeroth-Order Optimizer toward Adam-Scale Speed. FZOO reduces the total forward passes needed for convergence by employing batched one-sided estimates that adapt step sizes based on the standard deviation of batch losses. It also accelerates per-batch computation through the use of Rademacher random vector perturbations coupled with CUDA's parallel processing. Extensive experiments on diverse models, including RoBERTa-large, OPT (350M-66B), Phi-2, and Llama3, across 11 tasks validate FZOO's effectiveness. On average, FZOO outperforms MeZO by 3 percent in accuracy while requiring 3 times fewer forward passes. For RoBERTa-large, FZOO achieves average improvements of 5.6 percent in accuracy and an 18 times reduction in forward passes compared to MeZO, achieving convergence speeds comparable to Adam. We also provide theoretical analysis proving FZOO's formal equivalence to a normalized-SGD update rule and its convergence guarantees. FZOO integrates smoothly into PEFT techniques, enabling even larger memory savings. Overall, our results make single-GPU, high-speed, full-parameter fine-tuning practical and point toward future work on memory-efficient pre-training.

cs.LG↗

arXiv2025

Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles

We study the problem of estimating the diagonal of an implicitly given matrix $\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \ub^\top \Ab \ub$. Based on this query oracle, we propose a stochastic diagonal estimation method with random variable $\ub$ drawn from the standard Gaussian distribution. We provide the element-wise and norm-wise sample complexities of the proposed method. Our numerical experiments on different types and dimensions matrices demonstrate the effectiveness of our method and validate the tightness of theoretical results.

math.NA↗

arXiv2025

Privacy Leaks by Adversaries: Adversarial Iterations for Membership Inference Attack

Membership inference attack (MIA) has become one of the most widely used and effective methods for evaluating the privacy risks of machine learning models. These attacks aim to determine whether a specific sample is part of the model's training set by analyzing the model's output. While traditional membership inference attacks focus on leveraging the model's posterior output, such as confidence on the target sample, we propose IMIA, a novel attack strategy that utilizes the process of generating adversarial samples to infer membership. We propose to infer the member properties of the target sample using the number of iterations required to generate its adversarial sample. We conduct experiments across multiple models and datasets, and our results demonstrate that the number of iterations for generating an adversarial sample is a reliable feature for membership inference, achieving strong performance both in black-box and white-box attack scenarios. This work provides a new perspective for evaluating model privacy and highlights the potential of adversarial example-based features for privacy leakage assessment.

cs.CR↗

arXiv2025

Breaking the Prompt Wall (I): A Real-World Case Study of Attacking ChatGPT via Lightweight Prompt Injection

This report presents a real-world case study demonstrating how prompt injection can attack large language model platforms such as ChatGPT according to a proposed injection framework. By providing three real-world examples, we show how adversarial prompts can be injected via user inputs, web-based retrieval, and system-level agent instructions. These attacks, though lightweight and low-cost, can cause persistent and misleading behaviors in LLM outputs. Our case study reveals that even commercial-grade LLMs remain vulnerable to subtle manipulations that bypass safety filters and influence user decisions. \textbf{More importantly, we stress that this report is not intended as an attack guide, but as a technical alert. As ethical researchers, we aim to raise awareness and call upon developers, especially those at OpenAI, to treat prompt-level security as a critical design priority.

cs.CR↗

arXiv2025

Second-Order Fine-Tuning without Pain for LLMs:A Hessian Informed Zeroth-Order Optimizer

Fine-tuning large language models (LLMs) with classic first-order optimizers entails prohibitive GPU memory due to the backpropagation process. Recent works have turned to zeroth-order optimizers for fine-tuning, which save substantial memory by using two forward passes. However, these optimizers are plagued by the heterogeneity of parameter curvatures across different dimensions. In this work, we propose HiZOO, a diagonal Hessian informed zeroth-order optimizer which is the first work to leverage the diagonal Hessian to enhance zeroth-order optimizer for fine-tuning LLMs. What's more, HiZOO avoids the expensive memory cost and only increases one forward pass per step. Extensive experiments on various models (350M~66B parameters) indicate that HiZOO improves model convergence, significantly reducing training steps and effectively enhancing model accuracy. Moreover, we visualize the optimization trajectories of HiZOO on test functions, illustrating its effectiveness in handling heterogeneous curvatures. Lastly, we provide theoretical proofs of convergence for HiZOO. Code is publicly available at https://anonymous.4open.science/r/HiZOO27F8.

cs.LG↗

arXiv2025

An Enhanced Zeroth-Order Stochastic Frank-Wolfe Framework for Constrained Finite-Sum Optimization

We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance reduction framework that effectively reduces the gradient approximation variance induced by zeroth-order oracles and the stochastic sampling variance from finite-sum objectives. By leveraging this framework, our algorithm achieves significant improvements in query efficiency, making it particularly well-suited for high-dimensional optimization tasks. Specifically, for convex objectives, the algorithm achieves a query complexity of O(d \sqrt{n}/ε) to find an epsilon-suboptimal solution, where d is the dimensionality and n is the number of functions in the finite-sum objective. For non-convex objectives, it achieves a query complexity of O(d^{3/2}\sqrt{n}/ε^2 ) without requiring the computation ofd partial derivatives at each iteration. These complexities are the best known among zeroth-order stochastic Frank-Wolfe algorithms that avoid explicit gradient calculations. Empirical experiments on convex and non-convex machine learning tasks, including sparse logistic regression, robust classification, and adversarial attacks on deep networks, validate the computational efficiency and scalability of our approach. Our algorithm demonstrates superior performance in both convergence rate and query complexity compared to existing methods.

cs.LG↗

arXiv2025

On the Complexity of Decentralized Smooth Nonconvex Finite-Sum Optimization

We study the decentralized optimization problem $\min_{{\bf x}\in{\mathbb R}^d} f({\bf x})\triangleq \frac{1}{m}\sum_{i=1}^m f_i({\bf x})$, where the local function on the $i$-th agent has the form of $f_i({\bf x})\triangleq \frac{1}{n}\sum_{j=1}^n f_{i,j}({\bf x})$ and every individual $f_{i,j}$ is smooth but possibly nonconvex. We propose a stochastic algorithm called DEcentralized probAbilistic Recursive gradiEnt deScenT (DEAREST) method, which achieves an $ε$-stationary point at each agent with the communication rounds of $\tilde{\mathcal O}(Lε^{-2}/\sqrtγ\,)$, the computation rounds of $\tilde{\mathcal O}(n+(L+\min\{nL, \sqrt{n/m}\bar L\})ε^{-2})$, and the local incremental first-oracle calls of ${\mathcal O}(mn + {\min\{mnL, \sqrt{mn}\bar L\}}{ε^{-2}})$, where $L$ is the smoothness parameter of the objective function, $\bar L$ is the mean-squared smoothness parameter of all individual functions, and $γ$ is the spectral gap of the mixing matrix associated with the network. We then establish the lower bounds to show that the proposed method is near-optimal. Notice that the smoothness parameters $L$ and $\bar L$ used in our algorithm design and analysis are global, leading to sharper complexity bounds than existing results that depend on the local smoothness. We further extend DEAREST to solve the decentralized finite-sum optimization problem under the Polyak-Łojasiewicz condition, also achieving the near-optimal complexity bounds.

math.OC↗

arXiv2024

Optimal Decentralized Composite Optimization for Convex Functions

In this paper, we focus on the decentralized composite optimization for convex functions. Because of advantages such as robust to the network and no communication bottle-neck in the central server, the decentralized optimization has attracted much research attention in signal processing, control, and optimization communities. Many optimal algorithms have been proposed for the objective function is smooth and (strongly)-convex in the past years. However, it is still an open question whether one can design an optimal algorithm when there is a non-smooth regularization term. In this paper, we fill the gap between smooth decentralized optimization and decentralized composite optimization and propose the first algorithm which can achieve both the optimal computation and communication complexities. Our experiments also validate the effectiveness and efficiency of our algorithm both in computation and communication.

math.OC↗

arXiv2024

Double Variance Reduction: A Smoothing Trick for Composite Optimization Problems without First-Order Gradient

Variance reduction techniques are designed to decrease the sampling variance, thereby accelerating convergence rates of first-order (FO) and zeroth-order (ZO) optimization methods. However, in composite optimization problems, ZO methods encounter an additional variance called the coordinate-wise variance, which stems from the random gradient estimation. To reduce this variance, prior works require estimating all partial derivatives, essentially approximating FO information. This approach demands O(d) function evaluations (d is the dimension size), which incurs substantial computational costs and is prohibitive in high-dimensional scenarios. This paper proposes the Zeroth-order Proximal Double Variance Reduction (ZPDVR) method, which utilizes the averaging trick to reduce both sampling and coordinate-wise variances. Compared to prior methods, ZPDVR relies solely on random gradient estimates, calls the stochastic zeroth-order oracle (SZO) in expectation $\mathcal{O}(1)$ times per iteration, and achieves the optimal $\mathcal{O}(d(n + κ)\log (\frac{1}ε))$ SZO query complexity in the strongly convex and smooth setting, where $κ$ represents the condition number and $ε$ is the desired accuracy. Empirical results validate ZPDVR's linear convergence and demonstrate its superior performance over other related methods.

cs.LG↗

arXiv2024

Near-Optimal Distributed Minimax Optimization under the Second-Order Similarity

This paper considers the distributed convex-concave minimax optimization under the second-order similarity. We propose stochastic variance-reduced optimistic gradient sliding (SVOGS) method, which takes the advantage of the finite-sum structure in the objective by involving the mini-batch client sampling and variance reduction. We prove SVOGS can achieve the $\varepsilon$-duality gap within communication rounds of ${\mathcal O}(δD^2/\varepsilon)$, communication complexity of ${\mathcal O}(n+\sqrt{n}δD^2/\varepsilon)$, and local gradient calls of $\tilde{\mathcal O}(n+(\sqrt{n}δ+L)D^2/\varepsilon\log(1/\varepsilon))$, where $n$ is the number of nodes, $δ$ is the degree of the second-order similarity, $L$ is the smoothness parameter and $D$ is the diameter of the constraint set. We can verify that all of above complexity (nearly) matches the corresponding lower bounds. For the specific $μ$-strongly-convex-$μ$-strongly-convex case, our algorithm has the upper bounds on communication rounds, communication complexity, and local gradient calls of $\mathcal O(δ/μ\log(1/\varepsilon))$, ${\mathcal O}((n+\sqrt{n}δ/μ)\log(1/\varepsilon))$, and $\tilde{\mathcal O}(n+(\sqrt{n}δ+L)/μ)\log(1/\varepsilon))$ respectively, which are also nearly tight. Furthermore, we conduct the numerical experiments to show the empirical advantages of proposed method.

math.OC↗

arXiv2024

An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization

This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the $ε$-stationary points. Concretely, it requires $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(κ^2 ε^{-2})$ communication rounds, where $κ$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods.

cs.LG↗

arXiv2024

Anderson Acceleration Without Restart: A Novel Method with $n$-Step Super Quadratic Convergence Rate

In this paper, we propose a novel Anderson's acceleration method to solve nonlinear equations, which does \emph{not} require a restart strategy to achieve numerical stability. We propose the greedy and random versions of our algorithm. Specifically, the greedy version selects the direction to maximize a certain measure of progress for approximating the current Jacobian matrix. In contrast, the random version chooses the random Gaussian vector as the direction to update the approximate Jacobian. Furthermore, our algorithm, including both greedy and random versions, has an $n$-step super quadratic convergence rate, where $n$ is the dimension of the objective problem. For example, the explicit convergence rate of the random version can be presented as $ \norm{\vx_{k+n+1} - \vx_*} / \norm{\vx_k- \vx_*}^2 = \cO\left(\left(1-\frac{1}{n}\right)^{kn}\right)$ for any $k\geq 0$ where $\vx_*$ is the optimum of the objective problem. This kind of convergence rate is new to Anderson's acceleration and quasi-Newton methods. The experiments also validate the fast convergence rate of our algorithm.

math.OC↗