arXiv subjects

Stefanie Jegelka

Publications and source records attributed to Stefanie Jegelka.

At least 37 records · Page 2Linked to original sources

arXiv2026

Fairness Aware Reward Optimization

Demographic skews in human preference data propagate systematic unfairness through reward models into aligned LLMs. We introduce Fairness Aware Reward Optimization (Faro), an in-processing framework that trains reward models under demographic parity, equalized odds, or counterfactual fairness constraints. We provide the first theoretical analysis of reward-level fairness in LLM alignment, establishing: (i) provable fairness certificates for Faro-trained rewards with controllable slack; a (ii) formal characterization of the accuracy-fairness trade-off induced by KL-regularized fine-tuning, proving fairness transfers from reward to policy; and the (iii) existence of a non-empty Pareto frontier. Unlike pre- and post-processing methods, Faro ensures reward models are simultaneously ordinal (ranking correctly), cardinal (calibrated), and fair. Across multiple LLMs and benchmarks, Faro significantly reduces bias and harmful generations while maintaining or improving model quality.

cs.LG↗

arXiv2026

ReasonCACHE: Teaching LLMs To Reason Without Weight Updates

Can Large language models (LLMs) learn to reason without any weight update and only through in-context learning (ICL)? ICL is strikingly sample-efficient, often learning from only a handful of demonstrations, but complex reasoning tasks typically demand many training examples to learn from. However, naively scaling ICL by adding more demonstrations breaks down at this scale: attention costs grow quadratically, performance saturates or degrades with longer contexts, and the approach remains a shallow form of learning. Due to these limitations, practitioners predominantly rely on in-weight learning (IWL) to induce reasoning. In this work, we show that by using Prefix Tuning, LLMs can learn to reason without overloading the context window and without any weight updates. We introduce $\textbf{ReasonCACHE}$, an instantiation of this mechanism that distills demonstrations into a fixed key-value cache. Empirically, across challenging reasoning benchmarks, including GPQA-Diamond, ReasonCACHE outperforms standard ICL and matches or surpasses IWL approaches. Further, it achieves this all while being more efficient across three key axes: data, inference cost, and trainable parameters. We also theoretically prove that ReasonCACHE can be strictly more expressive than low-rank weight update since the latter ties expressivity to input rank, whereas ReasonCACHE bypasses this constraint by directly injecting key-values into the attention mechanism. Together, our findings identify ReasonCACHE as a middle path between in-context and in-weight learning, providing a scalable algorithm for learning reasoning skills beyond the context window without modifying parameters. Our project page: https://reasoncache.github.io/

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arXiv2026

Geometric Algorithms for Neural Combinatorial Optimization with Constraints

Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete constraints. We design an end-to-end differentiable framework that enables us to solve discrete constrained optimization problems with neural networks. Concretely, we leverage algorithmic techniques from the literature on convex geometry and Carathéodory's theorem to decompose neural network outputs into convex combinations of polytope corners that correspond to feasible sets. This decomposition-based approach enables self-supervised training but also ensures efficient quality-preserving rounding of the neural net output into feasible solutions. Extensive experiments in cardinality-constrained optimization show that our approach can consistently outperform neural baselines. We further provide worked-out examples of how our method can be applied beyond cardinality-constrained problems to a diverse set of combinatorial optimization tasks, including finding independent sets in graphs, and solving matroid-constrained problems.

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arXiv2025

Learning Linear Attention in Polynomial Time

Previous research has explored the computational expressivity of Transformer models in simulating Boolean circuits or Turing machines. However, the learnability of these simulators from observational data has remained an open question. Our study addresses this gap by providing the first polynomial-time learnability results (specifically strong, agnostic PAC learning) for single-layer Transformers with linear attention. We show that linear attention may be viewed as a linear predictor in a suitably defined RKHS. As a consequence, the problem of learning any linear transformer may be converted into the problem of learning an ordinary linear predictor in an expanded feature space, and any such predictor may be converted back into a multiheaded linear transformer. Moving to generalization, we show how to efficiently identify training datasets for which every empirical risk minimizer is equivalent (up to trivial symmetries) to the linear Transformer that generated the data, thereby guaranteeing the learned model will correctly generalize across all inputs. Finally, we provide examples of computations expressible via linear attention and therefore polynomial-time learnable, including associative memories, finite automata, and a class of Universal Turing Machine (UTMs) with polynomially bounded computation histories. We empirically validate our theoretical findings on three tasks: learning random linear attention networks, key--value associations, and learning to execute finite automata. Our findings bridge a critical gap between theoretical expressivity and learnability of Transformers, and show that flexible and general models of computation are efficiently learnable.

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arXiv2025

LANPO: Bootstrapping Language and Numerical Feedback for Reinforcement Learning in LLMs

Reinforcement learning in large language models (LLMs) often relies on scalar rewards, a practice that discards valuable textual rationale buried in the rollouts, forcing the model to explore \textit{de novo} with each attempt and hindering sample efficiency. While LLMs can uniquely learn from language feedback provided in-context, naively integrating on-line experiences into RL training presents a paradox: feedback from the same problem risks information leakage and memorization, while feedback from different problems often leads to behavior collapse due to irrelevant context. To resolve this tension, we propose \textbf{Language-And-Numerical Policy Optimization (LANPO)}, a framework that cleanly separates the roles of feedback: language guides exploration, while numerical rewards drive optimization. LANPO builds a dynamic experience pool from past trials and introduces two principles to ensure feedback is effective: \emph{Reward-Agnostic Reflection} for safe intra-sample self-correction and \emph{Relevant Abstraction} to distill generalizable lessons from inter-sample experiences. Across mathematical reasoning benchmarks, LANPO enables 7B and 14B models to significantly outperform strong baselines trained with GRPO in test accuracy. Our work provides a robust method for integrating historical experiences into the LLM RL loop, creating more effective and data-efficient learning agents.

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arXiv2025

Learning Diffusion Models with Flexible Representation Guidance

Diffusion models can be improved with additional guidance towards more effective representations of input. Indeed, prior empirical work has already shown that aligning internal representations of the diffusion model with those of pre-trained models improves generation quality. In this paper, we present a systematic framework for incorporating representation guidance into diffusion models. We provide alternative decompositions of denoising models along with their associated training criteria, where the decompositions determine when and how the auxiliary representations are incorporated. Guided by our theoretical insights, we introduce two new strategies for enhancing representation alignment in diffusion models. First, we pair examples with target representations either derived from themselves or arisen from different synthetic modalities, and subsequently learn a joint model over the multimodal pairs. Second, we design an optimal training curriculum that balances representation learning and data generation. Our experiments across image, protein sequence, and molecule generation tasks demonstrate superior performance as well as accelerated training. In particular, on the class-conditional ImageNet $256\times 256$ benchmark, our guidance results in $23.3$ times faster training than the original SiT-XL as well as four times speedup over the state-of-the-art method REPA. The code is available at https://github.com/ChenyuWang-Monica/REED.

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arXiv2025

Better Together: Leveraging Unpaired Multimodal Data for Stronger Unimodal Models

Traditional multimodal learners find unified representations for tasks like visual question answering, but rely heavily on paired datasets. However, an overlooked yet potentially powerful question is: can one leverage auxiliary unpaired multimodal data to directly enhance representation learning in a target modality? We introduce UML: Unpaired Multimodal Learner, a modality-agnostic training paradigm in which a single model alternately processes inputs from different modalities while sharing parameters across them. This design exploits the assumption that different modalities are projections of a shared underlying reality, allowing the model to benefit from cross-modal structure without requiring explicit pairs. Theoretically, under linear data-generating assumptions, we show that unpaired auxiliary data can yield representations strictly more informative about the data-generating process than unimodal training. Empirically, we show that using unpaired data from auxiliary modalities -- such as text, audio, or images -- consistently improves downstream performance across diverse unimodal targets such as image and audio. Our project page: https://unpaired-multimodal.github.io/

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arXiv2025

Generalization, Expressivity, and Universality of Graph Neural Networks on Attributed Graphs

We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained expressivity of GNNs. Namely, GNNs are both Lipschitz continuous with respect to our pseudometrics and can separate attributed graphs that are distant in the metric. Moreover, we prove that the space of all attributed graphs is relatively compact with respect to our metrics. Based on these properties, we prove a universal approximation theorem for GNNs and generalization bounds for GNNs on any data distribution of attributed graphs. The proposed metrics compute the similarity between the structures of attributed graphs via a hierarchical optimal transport between computation trees. Our work extends and unites previous approaches which either derived theory only for graphs with no attributes, derived compact metrics under which GNNs are continuous but without separation power, or derived metrics under which GNNs are continuous and separate points but the space of graphs is not relatively compact, which prevents universal approximation and generalization analysis.

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arXiv2025

G1: Teaching LLMs to Reason on Graphs with Reinforcement Learning

Although Large Language Models (LLMs) have demonstrated remarkable progress, their proficiency in graph-related tasks remains notably limited, hindering the development of truly general-purpose models. Previous attempts, including pretraining graph foundation models or employing supervised fine-tuning, often face challenges such as the scarcity of large-scale, universally represented graph data. We introduce G1, a simple yet effective approach demonstrating that Reinforcement Learning (RL) on synthetic graph-theoretic tasks can significantly scale LLMs' graph reasoning abilities. To enable RL training, we curate Erdõs, the largest graph reasoning dataset to date comprising 50 diverse graph-theoretic tasks of varying difficulty levels, 100k training data and 5k test data, all drived from real-world graphs. With RL on Erdõs, G1 obtains substantial improvements in graph reasoning, where our finetuned 3B model even outperforms Qwen2.5-72B-Instruct (24x size). RL-trained models also show strong zero-shot generalization to unseen tasks, domains, and graph encoding schemes, including other graph-theoretic benchmarks as well as real-world node classification and link prediction tasks, without compromising general reasoning abilities. Our findings offer an efficient, scalable path for building strong graph reasoners by finetuning LLMs with RL on graph-theoretic tasks, which combines the strengths of pretrained LLM capabilities with abundant, automatically generated synthetic data, suggesting that LLMs possess graph understanding abilities that RL can elicit successfully. Our implementation is open-sourced at https://github.com/PKU-ML/G1, with models and datasets hosted on Hugging Face collections https://huggingface.co/collections/PKU-ML/g1-683d659e992794fc99618cf2 for broader accessibility.

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arXiv2025

On the Emergence of Position Bias in Transformers

Recent studies have revealed various manifestations of position bias in transformer architectures, from the "lost-in-the-middle" phenomenon to attention sinks, yet a comprehensive theoretical understanding of how attention masks and positional encodings shape these biases remains elusive. This paper presents a graph-theoretic framework for analyzing position bias in multi-layer attention. Modeling attention masks as directed graphs, we quantify how tokens interact with contextual information based on their sequential positions. We uncover two key insights: First, causal masking inherently biases attention toward earlier positions, as tokens in deeper layers attend to increasingly more contextualized representations of earlier tokens. Second, we characterize the competing effects of the causal mask and relative positional encodings, such as the decay mask and rotary positional encoding (RoPE): while both mechanisms introduce distance-based decay within individual attention maps, their aggregate effect across multiple attention layers$\unicode{x2013}$coupled with the causal mask$\unicode{x2013}$leads to a trade-off between the long-term decay effects and the cumulative importance of early sequence positions. Through controlled numerical experiments, we not only validate our theoretical findings but also reproduce position biases observed in real-world LLMs. Our framework offers a principled foundation for understanding positional biases in transformers, shedding light on the complex interplay of attention mechanism components and guiding more informed architectural design.

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arXiv2025

What is Wrong with Perplexity for Long-context Language Modeling?

Handling long-context inputs is crucial for large language models (LLMs) in tasks such as extended conversations, document summarization, and many-shot in-context learning. While recent approaches have extended the context windows of LLMs and employed perplexity (PPL) as a standard evaluation metric, PPL has proven unreliable for assessing long-context capabilities. The underlying cause of this limitation has remained unclear. In this work, we provide a comprehensive explanation for this issue. We find that PPL overlooks key tokens, which are essential for long-context understanding, by averaging across all tokens and thereby obscuring the true performance of models in long-context scenarios. To address this, we propose \textbf{LongPPL}, a novel metric that focuses on key tokens by employing a long-short context contrastive method to identify them. Our experiments demonstrate that LongPPL strongly correlates with performance on various long-context benchmarks (e.g., Pearson correlation of -0.96), significantly outperforming traditional PPL in predictive accuracy. Additionally, we introduce \textbf{LongCE} (Long-context Cross-Entropy) loss, a re-weighting strategy for fine-tuning that prioritizes key tokens, leading to consistent improvements across diverse benchmarks. In summary, these contributions offer deeper insights into the limitations of PPL and present effective solutions for accurately evaluating and enhancing the long-context capabilities of LLMs. Code is available at https://github.com/PKU-ML/LongPPL.

cs.CL↗

arXiv2025

When More is Less: Understanding Chain-of-Thought Length in LLMs

Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on combined evidence from real-world observations, controlled experiments, and theoretical analysis, we demonstrate that task accuracy typically follows an inverted U-shaped curve with CoT length, where performance initially improves but eventually decreases as the number of CoT steps increases. With controlled experiments, we further uncover the scaling behaviors of the optimal CoT length: it increases with task difficulty but decreases with model capability, exposing an inherent simplicity bias where more capable models favor shorter, more efficient CoT reasoning. This bias is also evident in Reinforcement Learning (RL) training, where models gravitate towards shorter CoTs as their accuracy improves. To have a deep understanding of these dynamics, we establish a simple theoretical model that formally proves these phenomena, including the optimal length's scaling laws and the emergence of simplicity bias during RL. Guided by this framework, we demonstrate significant practical benefits from training with optimally-lengthed CoTs and employing length-aware filtering at inference. These findings offer both a principled understanding of the "overthinking" phenomenon and multiple practical guidelines for CoT calibration, enabling LLMs to achieve optimal reasoning performance with adaptive CoTs tailored to task complexity and model capability.

cs.AI↗

arXiv2025

Beyond Matryoshka: Revisiting Sparse Coding for Adaptive Representation

Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive embedding lengths, but it requires full model retraining and suffers from noticeable performance degradations at short lengths. In this paper, we show that sparse coding offers a compelling alternative for achieving adaptive representation with minimal overhead and higher fidelity. We propose Contrastive Sparse Representation (CSR), a method that sparsifies pre-trained embeddings into a high-dimensional but selectively activated feature space. By leveraging lightweight autoencoding and task-aware contrastive objectives, CSR preserves semantic quality while allowing flexible, cost-effective inference at different sparsity levels. Extensive experiments on image, text, and multimodal benchmarks demonstrate that CSR consistently outperforms MRL in terms of both accuracy and retrieval speed-often by large margins-while also cutting training time to a fraction of that required by MRL. Our results establish sparse coding as a powerful paradigm for adaptive representation learning in real-world applications where efficiency and fidelity are both paramount. Code is available at https://github.com/neilwen987/CSR_Adaptive_Rep

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arXiv2025

Higher-Order Graphon Neural Networks: Approximation and Cut Distance

Graph limit models, like graphons for limits of dense graphs, have recently been used to study size transferability of graph neural networks (GNNs). While most literature focuses on message passing GNNs (MPNNs), in this work we attend to the more powerful higher-order GNNs. First, we extend the $k$-WL test for graphons (Böker, 2023) to the graphon-signal space and introduce signal-weighted homomorphism densities as a key tool. As an exemplary focus, we generalize Invariant Graph Networks (IGNs) to graphons, proposing Invariant Graphon Networks (IWNs) defined via a subset of the IGN basis corresponding to bounded linear operators. Even with this restricted basis, we show that IWNs of order $k$ are at least as powerful as the $k$-WL test, and we establish universal approximation results for graphon-signals in $L^p$ distances. This significantly extends the prior work of Cai & Wang (2022), showing that IWNs--a subset of their IGN-small--retain effectively the same expressivity as the full IGN basis in the limit. In contrast to their approach, our blueprint of IWNs also aligns better with the geometry of graphon space, for example facilitating comparability to MPNNs. We highlight that, while typical higher-order GNNs are discontinuous w.r.t. cut distance--which causes their lack of convergence and is inherently tied to the definition of $k$-WL--transferability remains achievable.

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arXiv2025

Survey on Generalization Theory for Graph Neural Networks

Message-passing graph neural networks (MPNNs) have emerged as the leading approach for machine learning on graphs, attracting significant attention in recent years. While a large set of works explored the expressivity of MPNNs, i.e., their ability to separate graphs and approximate functions over them, comparatively less attention has been directed toward investigating their generalization abilities, i.e., making meaningful predictions beyond the training data. Here, we systematically review the existing literature on the generalization abilities of MPNNs. We analyze the strengths and limitations of various studies in these domains, providing insights into their methodologies and findings. Furthermore, we identify potential avenues for future research, aiming to deepen our understanding of the generalization abilities of MPNNs.

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arXiv2025

An Information Criterion for Controlled Disentanglement of Multimodal Data

Multimodal representation learning seeks to relate and decompose information inherent in multiple modalities. By disentangling modality-specific information from information that is shared across modalities, we can improve interpretability and robustness and enable downstream tasks such as the generation of counterfactual outcomes. Separating the two types of information is challenging since they are often deeply entangled in many real-world applications. We propose Disentangled Self-Supervised Learning (DisentangledSSL), a novel self-supervised approach for learning disentangled representations. We present a comprehensive analysis of the optimality of each disentangled representation, particularly focusing on the scenario not covered in prior work where the so-called Minimum Necessary Information (MNI) point is not attainable. We demonstrate that DisentangledSSL successfully learns shared and modality-specific features on multiple synthetic and real-world datasets and consistently outperforms baselines on various downstream tasks, including prediction tasks for vision-language data, as well as molecule-phenotype retrieval tasks for biological data. The code is available at https://github.com/uhlerlab/DisentangledSSL.

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arXiv2025

Learning with Exact Invariances in Polynomial Time

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either fail to provide a polynomial-time solution or are not applicable in the kernel setting. However, with oracle access to the geometric properties of the input space, we propose a polynomial-time algorithm that learns a classifier with \emph{exact} invariances. Moreover, our approach achieves the same excess population risk (or generalization error) as the original kernel regression problem. To the best of our knowledge, this is the first polynomial-time algorithm to achieve exact (not approximate) invariances in this context. Our proof leverages tools from differential geometry, spectral theory, and optimization. A key result in our development is a new reformulation of the problem of learning under invariances as optimizing an infinite number of linearly constrained convex quadratic programs, which may be of independent interest.

cs.LG↗

arXiv2025

Subsampling Graphs with GNN Performance Guarantees

How can we subsample graph data so that a graph neural network (GNN) trained on the subsample achieves performance comparable to training on the full dataset? This question is of fundamental interest, as smaller datasets reduce labeling costs, storage requirements, and computational resources needed for training. Selecting an effective subset is challenging: a poorly chosen subsample can severely degrade model performance, and empirically testing multiple subsets for quality obviates the benefits of subsampling. Therefore, it is critical that subsampling comes with guarantees on model performance. In this work, we introduce new subsampling methods for graph datasets that leverage the Tree Mover's Distance to reduce both the number of graphs and the size of individual graphs. To our knowledge, our approach is the first that is supported by rigorous theoretical guarantees: we prove that training a GNN on the subsampled data results in a bounded increase in loss compared to training on the full dataset. Unlike existing methods, our approach is both model-agnostic, requiring minimal assumptions about the GNN architecture, and label-agnostic, eliminating the need to label the full training set. This enables subsampling early in the model development pipeline (before data annotation, model selection, and hyperparameter tuning) reducing costs and resources needed for storage, labeling, and training. We validate our theoretical results with experiments showing that our approach outperforms existing subsampling methods across multiple datasets.

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