arXiv subjects

Weijie J. Su

Publications and source records attributed to Weijie J. Su.

At least 37 records · Page 2Linked to original sources

arXiv2025

Debiasing Watermarks for Large Language Models via Maximal Coupling

Watermarking language models is essential for distinguishing between human and machine-generated text and thus maintaining the integrity and trustworthiness of digital communication. We present a novel green/red list watermarking approach that partitions the token set into ``green'' and ``red'' lists, subtly increasing the generation probability for green tokens. To correct token distribution bias, our method employs maximal coupling, using a uniform coin flip to decide whether to apply bias correction, with the result embedded as a pseudorandom watermark signal. Theoretical analysis confirms this approach's unbiased nature and robust detection capabilities. Experimental results show that it outperforms prior techniques by preserving text quality while maintaining high detectability, and it demonstrates resilience to targeted modifications aimed at improving text quality. This research provides a promising watermarking solution for language models, balancing effective detection with minimal impact on text quality.

stat.ML↗

arXiv2025

Precise High-Dimensional Asymptotics for Quantifying Heterogeneous Transfers

The problem of learning one task using samples from another task is central to transfer learning. In this paper, we focus on answering the following question: when does combining the samples from two related tasks perform better than learning with one target task alone? This question is motivated by an empirical phenomenon known as negative transfer, which has been observed in practice. While the transfer effect from one task to another depends on factors such as their sample sizes and the spectrum of their covariance matrices, precisely quantifying this dependence has remained a challenging problem. In order to compare a transfer learning estimator to single-task learning, one needs to compare the risks between the two estimators precisely. Further, the comparison depends on the distribution shifts between the two tasks. This paper applies recent developments of random matrix theory to tackle this challenge in a high-dimensional linear regression setting with two tasks. We show precise high-dimensional asymptotics for the bias and variance of a classical hard parameter sharing (HPS) estimator in the proportional limit, where the sample sizes of both tasks increase proportionally with dimension at fixed ratios. The precise asymptotics apply to various types of distribution shifts, including covariate shifts, model shifts, and combinations of both. We illustrate these results in a random-effects model to mathematically prove a phase transition from positive to negative transfer as the number of source task samples increases. One insight from the analysis is that a rebalanced HPS estimator, which downsizes the source task when the model shift is high, achieves the minimax optimal rate. The finding regarding phase transition also applies to multiple tasks when covariates are shared across tasks. Simulations validate the accuracy of the high-dimensional asymptotics for finite dimensions.

stat.ML↗

arXiv2025

Evaluating the Unseen Capabilities: How Many Theorems Do LLMs Know?

Accurate evaluation of large language models (LLMs) is crucial for understanding their capabilities and guiding their development. However, current evaluations often inconsistently reflect the actual capacities of these models. In this paper, we demonstrate that one of many contributing factors to this \textit{evaluation crisis} is the oversight of unseen knowledge -- information encoded by LLMs but not directly observed or not yet observed during evaluations. We introduce KnowSum, a statistical framework designed to provide a more comprehensive assessment by quantifying the unseen knowledge for a class of evaluation tasks. KnowSum estimates the unobserved portion by extrapolating from the appearance frequencies of observed knowledge instances. We demonstrate the effectiveness and utility of KnowSum across three critical applications: estimating total knowledge, evaluating information retrieval effectiveness, and measuring output diversity. Our experiments reveal that a substantial volume of knowledge is omitted when relying solely on observed LLM performance. Importantly, KnowSum yields significantly different comparative rankings for several common LLMs based on their internal knowledge.

cs.CL↗

arXiv2025

Fundamental Limits of Game-Theoretic LLM Alignment: Smith Consistency and Preference Matching

Nash Learning from Human Feedback is a game-theoretic framework for aligning large language models (LLMs) with human preferences by modeling learning as a two-player zero-sum game. However, using raw preference as the payoff in the game highly limits the potential of the game-theoretic LLM alignment framework. In this paper, we systematically study using what choices of payoff based on the pairwise human preferences can yield desirable alignment properties. We establish necessary and sufficient conditions for Condorcet consistency, diversity through mixed strategies, and Smith consistency. These results provide a theoretical foundation for the robustness of game-theoretic LLM alignment. Further, we show the impossibility of preference matching -- i.e., no smooth and learnable mappings of pairwise preferences can guarantee a unique Nash equilibrium that matches a target policy, even under standard assumptions like the Bradley-Terry-Luce model. This result highlights the fundamental limitation of game-theoretic LLM alignment.

cs.GT↗

arXiv2025

Magnetic Preference Optimization: Achieving Last-iterate Convergence for Language Model Alignment

Self-play methods have demonstrated remarkable success in enhancing model capabilities across various domains. In the context of Reinforcement Learning from Human Feedback (RLHF), self-play not only boosts Large Language Model (LLM) performance but also overcomes the limitations of traditional Bradley-Terry (BT) model assumptions by finding the Nash equilibrium (NE) of a preference-based, two-player constant-sum game. However, existing methods either guarantee only average-iterate convergence, incurring high storage and inference costs, or converge to the NE of a regularized game, failing to accurately reflect true human preferences. In this paper, we introduce Magnetic Preference Optimization (MPO), a novel approach capable of achieving last-iterate convergence to the NE of the original game, effectively overcoming the limitations of existing methods. Building upon Magnetic Mirror Descent (MMD), MPO attains a linear convergence rate, making it particularly suitable for fine-tuning LLMs. To ensure our algorithm is both theoretically sound and practically viable, we present a simple yet effective implementation that adapts the theoretical insights to the RLHF setting. Empirical results demonstrate that MPO can significantly enhance the performance of LLMs, highlighting the potential of self-play methods in alignment.

cs.CL↗

arXiv2025

Tackling Copyright Issues in AI Image Generation Through Originality Estimation and Genericization

The rapid progress of generative AI technology has sparked significant copyright concerns, leading to numerous lawsuits filed against AI developers. Notably, generative AI's capacity for generating images of copyrighted characters has been well documented in the literature, and while various techniques for mitigating copyright issues have been studied, significant risks remain. Here, we propose a genericization method that modifies the outputs of a generative model to make them more generic and less likely to imitate distinctive features of copyrighted materials. To achieve this, we introduce a metric for quantifying the level of originality of data, estimated by drawing samples from a generative model, and applied in the genericization process. As a practical implementation, we introduce PREGen (Prompt Rewriting-Enhanced Genericization), which combines our genericization method with an existing mitigation technique. Compared to the existing method, PREGen reduces the likelihood of generating copyrighted characters by more than half when the names of copyrighted characters are used as the prompt. Additionally, while generative models can produce copyrighted characters even when their names are not directly mentioned in the prompt, PREGen almost entirely prevents the generation of such characters in these cases. Ultimately, this study advances computational approaches for quantifying and strengthening copyright protection, thereby providing practical methodologies to promote responsible generative AI development.

cs.LG↗

arXiv2025

Minimax Estimation for Personalized Federated Learning: An Alternative between FedAvg and Local Training?

A widely recognized difficulty in federated learning arises from the statistical heterogeneity among clients: local datasets often originate from distinct yet not entirely unrelated probability distributions, and personalization is, therefore, necessary to achieve optimal results from each individual's perspective. In this paper, we show how the excess risks of personalized federated learning using a smooth, strongly convex loss depend on data heterogeneity from a minimax point of view, with a focus on the FedAvg algorithm (McMahan et al., 2017) and pure local training (i.e., clients solve empirical risk minimization problems on their local datasets without any communication). Our main result reveals an approximate alternative between these two baseline algorithms for federated learning: the former algorithm is minimax rate optimal over a collection of instances when data heterogeneity is small, whereas the latter is minimax rate optimal when data heterogeneity is large, and the threshold is sharp up to a constant. As an implication, our results show that from a worst-case point of view, a dichotomous strategy that makes a choice between the two baseline algorithms is rate-optimal. Another implication is that the popular FedAvg following by local fine tuning strategy is also minimax optimal under additional regularity conditions. Our analysis relies on a new notion of algorithmic stability that takes into account the nature of federated learning.

stat.ML↗

arXiv2025

HiGrad: Uncertainty Quantification for Online Learning and Stochastic Approximation

Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known about the statistical inferential properties of SGD-based predictions. Taking a fully inferential viewpoint, this paper introduces a novel procedure termed HiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with SGD. The HiGrad procedure begins by performing SGD updates for a while and then splits the single thread into several threads, and this procedure hierarchically operates in this fashion along each thread. With predictions provided by multiple threads in place, a $t$-based confidence interval is constructed by decorrelating predictions using covariance structures given by a Donsker-style extension of the Ruppert--Polyak averaging scheme, which is a technical contribution of independent interest. Under certain regularity conditions, the HiGrad confidence interval is shown to attain asymptotically exact coverage probability. Finally, the performance of HiGrad is evaluated through extensive simulation studies and a real data example. An R package \texttt{higrad} has been developed to implement the method.

stat.ML↗

arXiv2025

An Overview of Large Language Models for Statisticians

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has primarily been driven by advances in computational power and deep learning architectures, emerging problems -- in areas such as uncertainty quantification, decision-making, causal inference, and distribution shift -- require a deeper engagement with the field of statistics. This paper explores potential areas where statisticians can make important contributions to the development of LLMs, particularly those that aim to engender trustworthiness and transparency for human users. Thus, we focus on issues such as uncertainty quantification, interpretability, fairness, privacy, watermarking and model adaptation. We also consider possible roles for LLMs in statistical analysis. By bridging AI and statistics, we aim to foster a deeper collaboration that advances both the theoretical foundations and practical applications of LLMs, ultimately shaping their role in addressing complex societal challenges.

stat.ML↗

arXiv2025

Towards Rationality in Language and Multimodal Agents: A Survey

This work discusses how to build more rational language and multimodal agents and what criteria define rationality in intelligent systems. Rationality is the quality of being guided by reason, characterized by decision-making that aligns with evidence and logical principles. It plays a crucial role in reliable problem-solving by ensuring well-grounded and consistent solutions. Despite their progress, large language models (LLMs) often fall short of rationality due to their bounded knowledge space and inconsistent outputs. In response, recent efforts have shifted toward developing multimodal and multi-agent systems, as well as integrating modules like external tools, programming codes, symbolic reasoners, utility function, and conformal risk controls rather than relying solely on a single LLM for decision-making. This paper surveys state-of-the-art advancements in language and multimodal agents, assesses their role in enhancing rationality, and outlines open challenges and future research directions. We maintain an open repository at https://github.com/bowen-upenn/Agent_Rationality.

cs.AI↗

arXiv2025

Isotonic Mechanism for Exponential Family Estimation in Machine Learning Peer Review

In 2023, the International Conference on Machine Learning (ICML) required authors with multiple submissions to rank their submissions based on perceived quality. In this paper, we aim to employ these author-specified rankings to enhance peer review in machine learning and artificial intelligence conferences by extending the Isotonic Mechanism to exponential family distributions. This mechanism generates adjusted scores that closely align with the original scores while adhering to author-specified rankings. Despite its applicability to a broad spectrum of exponential family distributions, implementing this mechanism does not require knowledge of the specific distribution form. We demonstrate that an author is incentivized to provide accurate rankings when her utility takes the form of a convex additive function of the adjusted review scores. For a certain subclass of exponential family distributions, we prove that the author reports truthfully only if the question involves only pairwise comparisons between her submissions, thus indicating the optimality of ranking in truthful information elicitation. Moreover, we show that the adjusted scores improve dramatically the estimation accuracy compared to the original scores and achieve nearly minimax optimality when the ground-truth scores have bounded total variation. We conclude with a numerical analysis of the ICML 2023 ranking data, showing substantial estimation gains in approximating a proxy ground-truth quality of the papers using the Isotonic Mechanism.

math.ST↗

arXiv2024

A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation and Blackwell's Theorem

Differential privacy is widely considered the formal privacy for privacy-preserving data analysis due to its robust and rigorous guarantees, with increasingly broad adoption in public services, academia, and industry. Despite originating in the cryptographic context, in this review paper we argue that, fundamentally, differential privacy can be considered a \textit{pure} statistical concept. By leveraging David Blackwell's informativeness theorem, our focus is to demonstrate based on prior work that all definitions of differential privacy can be formally motivated from a hypothesis testing perspective, thereby showing that hypothesis testing is not merely convenient but also the right language for reasoning about differential privacy. This insight leads to the definition of $f$-differential privacy, which extends other differential privacy definitions through a representation theorem. We review techniques that render $f$-differential privacy a unified framework for analyzing privacy bounds in data analysis and machine learning. Applications of this differential privacy definition to private deep learning, private convex optimization, shuffled mechanisms, and U.S.\ Census data are discussed to highlight the benefits of analyzing privacy bounds under this framework compared to existing alternatives.

math.ST↗

arXiv2024

Neural Collapse Meets Differential Privacy: Curious Behaviors of NoisyGD with Near-perfect Representation Learning

A recent study by De et al. (2022) has reported that large-scale representation learning through pre-training on a public dataset significantly enhances differentially private (DP) learning in downstream tasks, despite the high dimensionality of the feature space. To theoretically explain this phenomenon, we consider the setting of a layer-peeled model in representation learning, which results in interesting phenomena related to learned features in deep learning and transfer learning, known as Neural Collapse (NC). Within the framework of NC, we establish an error bound indicating that the misclassification error is independent of dimension when the distance between actual features and the ideal ones is smaller than a threshold. Additionally, the quality of the features in the last layer is empirically evaluated under different pre-trained models within the framework of NC, showing that a more powerful transformer leads to a better feature representation. Furthermore, we reveal that DP fine-tuning is less robust compared to fine-tuning without DP, particularly in the presence of perturbations. These observations are supported by both theoretical analyses and experimental evaluation. Moreover, to enhance the robustness of DP fine-tuning, we suggest several strategies, such as feature normalization or employing dimension reduction methods like Principal Component Analysis (PCA). Empirically, we demonstrate a significant improvement in testing accuracy by conducting PCA on the last-layer features.

cs.LG↗

arXiv2024

A Peek into Token Bias: Large Language Models Are Not Yet Genuine Reasoners

This study introduces a hypothesis-testing framework to assess whether large language models (LLMs) possess genuine reasoning abilities or primarily depend on token bias. We go beyond evaluating LLMs on accuracy; rather, we aim to investigate their token bias in solving logical reasoning tasks. Specifically, we develop carefully controlled synthetic datasets, featuring conjunction fallacy and syllogistic problems. Our framework outlines a list of hypotheses where token biases are readily identifiable, with all null hypotheses assuming genuine reasoning capabilities of LLMs. The findings in this study suggest, with statistical guarantee, that most LLMs still struggle with logical reasoning. While they may perform well on classic problems, their success largely depends on recognizing superficial patterns with strong token bias, thereby raising concerns about their actual reasoning and generalization abilities. Codes and data are open-sourced at https://github.com/bowen-upenn/llm_token_bias.

cs.CL↗

arXiv2024

An Economic Solution to Copyright Challenges of Generative AI

Generative artificial intelligence (AI) systems are trained on large data corpora to generate new pieces of text, images, videos, and other media. There is growing concern that such systems may infringe on the copyright interests of training data contributors. To address the copyright challenges of generative AI, we propose a framework that compensates copyright owners proportionally to their contributions to the creation of AI-generated content. The metric for contributions is quantitatively determined by leveraging the probabilistic nature of modern generative AI models and using techniques from cooperative game theory in economics. This framework enables a platform where AI developers benefit from access to high-quality training data, thus improving model performance. Meanwhile, copyright owners receive fair compensation, driving the continued provision of relevant data for generative model training. Experiments demonstrate that our framework successfully identifies the most relevant data sources used in artwork generation, ensuring a fair and interpretable distribution of revenues among copyright owners.

cs.LG↗

arXiv2024

Envisioning Future Deep Learning Theories: Some Basic Concepts and Characteristics

To advance deep learning methodologies in the next decade, a theoretical framework for reasoning about modern neural networks is needed. While efforts are increasing toward demystifying why deep learning is so effective, a comprehensive picture remains lacking, suggesting that a better theory is possible. We argue that a future deep learning theory should inherit three characteristics: a \textit{hierarchically} structured network architecture, parameters \textit{iteratively} optimized using stochastic gradient-based methods, and information from the data that evolves \textit{compressively}. As an instantiation, we integrate these characteristics into a graphical model called \textit{neurashed}. This model effectively explains some common empirical patterns in deep learning. In particular, neurashed enables insights into implicit regularization, information bottleneck, and local elasticity. Finally, we discuss how neurashed can guide the development of deep learning theories.

cs.LG↗

arXiv2024

Bridging the Gap: Rademacher Complexity in Robust and Standard Generalization

Training Deep Neural Networks (DNNs) with adversarial examples often results in poor generalization to test-time adversarial data. This paper investigates this issue, known as adversarially robust generalization, through the lens of Rademacher complexity. Building upon the studies by Khim and Loh (2018); Yin et al. (2019), numerous works have been dedicated to this problem, yet achieving a satisfactory bound remains an elusive goal. Existing works on DNNs either apply to a surrogate loss instead of the robust loss or yield bounds that are notably looser compared to their standard counterparts. In the latter case, the bounds have a higher dependency on the width $m$ of the DNNs or the dimension $d$ of the data, with an extra factor of at least $\mathcal{O}(\sqrt{m})$ or $\mathcal{O}(\sqrt{d})$. This paper presents upper bounds for adversarial Rademacher complexity of DNNs that match the best-known upper bounds in standard settings, as established in the work of Bartlett et al. (2017), with the dependency on width and dimension being $\mathcal{O}(\ln(dm))$. The central challenge addressed is calculating the covering number of adversarial function classes. We aim to construct a new cover that possesses two properties: 1) compatibility with adversarial examples, and 2) precision comparable to covers used in standard settings. To this end, we introduce a new variant of covering number called the \emph{uniform covering number}, specifically designed and proven to reconcile these two properties. Consequently, our method effectively bridges the gap between Rademacher complexity in robust and standard generalization.

stat.ML↗

arXiv2024

Robust Inference Under Heteroskedasticity via the Hadamard Estimator

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units (i.e., heteroskedasticity) for statistical inference in linear regression. We leverage the Hadamard estimator, which is unbiased for the variances of ordinary least-squares regression. This is in contrast to the popular White's sandwich estimator, which can be substantially biased in high dimensions. We propose to estimate the signal strength, noise level, signal-to-noise ratio, and mean squared error via the Hadamard estimator. We develop a new degrees of freedom adjustment that gives more accurate confidence intervals than variants of White's sandwich estimator. Moreover, we provide conditions ensuring the estimator is well-defined, by studying a new random matrix ensemble in which the entries of a random orthogonal projection matrix are squared. We also show approximate normality, using the second-order Poincare inequality. Our work provides improved statistical theory and methods for linear regression in high dimensions.

math.ST↗