Please go to https://arxiv.org/abs/2409.00119 for the newest version.

F or developing mathematical reasoning models, why are open-source models not used in place of closed-source models?

Following the wide-spread adoption of machine learning models in real-world applications, the phenomenon of performativity, i.e. model-dependent shifts in the test distribution, becomes increasingly prevalent. Unfortunately, since models are usually trained solely based on samples from the original (unshifted) distribution, this performative shift may lead to decreased test-time performance. In this paper, we study the question of whether and when performative binary classification problems are learnable, via the lens of the classic PAC (Probably Approximately Correct) learning framework. We motivate several performative scenarios, accounting in particular for linear shifts in the label distribution, as well as for more general changes in both the labels and the features. We construct a performative empirical risk function, which depends only on data from the original distribution and on the type performative effect, and is yet an unbiased estimate of the true risk of a classifier on the shifted distribution. Minimizing this notion of performative risk allows us to show that any PAC-learnable hypothesis space in the standard binary classification setting remains PAC-learnable for the considered performative scenarios. We also conduct an extensive experimental evaluation of our performative risk minimization method and showcase benefits on synthetic and real data.

Adaptive testing and sequential estimation problems have recently gained substantial attention due to their foundational role in modern artificial intelligence and interactive systems. Prominent applications include online preference learning, where systems dynamically adapt to user feedback to refine personalized recommendations, and reinforcement learning from human feedback (RLHF), which aims to align AI agents with human values by adaptively querying users. In these contexts, the main focus is to efficiently extract maximal information from human responses, which are inherently stochastic and limited in quantity. Among various types of such problems, this work particularly considers a fundamental yet illustrative case involving stochastic binary responses. Here, a decision-maker sequentially selects questions of varying difficulty from a continuous pool to pose to a candidate and aims to efficiently estimate the candidate's ability (represented by an unknown continuous parameter) by utilizing the binary feedback (e.g., correct/incorrect) collected, which depends probabilistically on the candidate's ability and the question's difficulty. This setup is arguably the simplest scenario that captures the essence of continuous parameter estimation under uncertainty, making it an ideal benchmark for developing fundamental theoretical insights and practical algorithms. Variants of this fundamental adaptive estimation problem have been studied in several communities.

Large language models (LLMs) are highly sensitive to subtle changes in prompt phrasing, posing challenges for reliable auditing. Prior methods often apply unconstrained prompt paraphrasing, which risk missing linguistic and demographic factors that shape authentic user interactions. We introduce AUGMENT (Automated User-Grounded Modeling and Evaluation of Natural Language Transformations), a framework for generating controlled paraphrases, grounded in user behaviors. AUGMENT leverages linguistically informed rules and enforces quality through checks on instruction adherence, semantic similarity, and realism, ensuring paraphrases are both reliable and meaningful for auditing. Through case studies on the BBQ and MMLU datasets, we show that controlled paraphrases uncover systematic weaknesses that remain obscured under unconstrained variation. These results highlight the value of the AUGMENT framework for reliable auditing.

This paper explores a multimodal co-training framework designed to enhance model generalization in situations where labeled data is limited and distribution shifts occur. We thoroughly examine the theoretical foundations of this framework, deriving conditions under which the use of unlabeled data and the promotion of agreement between classifiers for different modalities lead to significant improvements in generalization. We also present a convergence analysis that confirms the effectiveness of iterative co-training in reducing classification errors. In addition, we establish a novel generalization bound that, for the first time in a multimodal co-training context, decomposes and quantifies the distinct advantages gained from leveraging unlabeled multimodal data, promoting inter-view agreement, and maintaining conditional view independence. Our findings highlight the practical benefits of multimodal co-training as a structured approach to developing data-efficient and robust AI systems that can effectively generalize in dynamic, real-world environments. The theoretical foundations are examined in dialogue with, and in advance of, established co-training principles.

Humans often use visual aids, for example diagrams or sketches, when solving complex problems. Training multimodal models to do the same, known as Visual Chain of Thought (Visual CoT), is challenging due to: (1) poor off-the-shelf visual CoT performance, which hinders reinforcement learning, and (2) the lack of high-quality visual CoT training data. We introduce $\textbf{Zebra-CoT}$, a diverse large-scale dataset with 182,384 samples, containing logically coherent interleaved text-image reasoning traces. We focus on four categories of tasks where sketching or visual reasoning is especially natural, spanning scientific questions such as geometry, physics, and algorithms; 2D visual reasoning tasks like visual search and jigsaw puzzles; 3D reasoning tasks including 3D multi-hop inference, embodied and robot planning; visual logic problems and strategic games like chess. Fine-tuning the Anole-7B model on the Zebra-CoT training corpus results in an improvement of +12% in our test-set accuracy and yields up to +13% performance gain on standard VLM benchmark evaluations. Fine-tuning Bagel-7B yields a model that generates high-quality interleaved visual reasoning chains, underscoring Zebra-CoT's effectiveness for developing multimodal reasoning abilities. We open-source our dataset and models to support development and evaluation of visual CoT.