Large language model (LLM)-based reasoning systems have recently achieved gold medallevel performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported.To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites.We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor.Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions.We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models.We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.

To keep pace with the increasing velocity of large language models (LLM) development, model output evaluation has transitioned away from time-consuming human evaluation to automatic evaluation, where LLMs themselves are tasked with assessing and critiquing other model outputs.LLM-as-judge models are a class of generative evaluators that excel in evaluating relatively simple domains, like chat quality, but struggle in reasoning intensive domains where model responses contain more substantive and challenging content.To remedy existing judge shortcomings, we explore training judges with reinforcement learning (RL).We make three key contributions: (1) We propose the Equivalent Initial State Group Relative Policy Optimization (EIS-GRPO) algorithm, which allows us to train our judge to be robust to positional biases that arise in more complex evaluation settings.(2) We introduce ReasoningJudgeBench, a benchmark that evaluates judges in diverse reasoning settings not covered by prior work.(3) We train Judge for Reasoning (J4R), a 7B judge trained with EIS-GRPO that outperforms GPT-4o and the next best small judge by 6.7% and 9%, matching or exceeding the performance of larger GRPOtrained judges on both JudgeBench and Rea-soningJudgeBench.

The large language model (LLM)-as-judge paradigm has been used to meet the demand for a cheap, reliable, and fast evaluation of model outputs during AI system development and post-deployment monitoring. While judge models—LLMs finetuned to specialize in assessing and critiquing model outputs—have been touted as general purpose evaluators, they are typically evaluated only on non-contextual scenarios, such as instruction following. The omission of contextual settings—those where external information is used as context to generate an output—is surprising given the increasing prevalence of retrieval-augmented generation (RAG) and summarization use cases. Contextual assessment is uniquely challenging, as evaluation often depends on practitioner priorities, leading to conditional evaluation criteria (e.g., comparing responses based on factuality and then considering completeness if they are equally factual). To address the gap, we propose ContextualJudgeBench, a judge benchmark with 2,000 challenging response pairs across eight splits inspired by real-world contextual evaluation scenarios. We build our benchmark with a multi-pronged data construction pipeline that leverages both existing human annotations and model-based perturbations. Our comprehensive study across 11 judge models and 7 general purpose models, reveals that the contextual information and assessment criteria present a significant challenge to even state-of-the-art models. For example, o1, the best-performing model, barely reaches 55% consistent accuracy.

To meet the increasing need for timely and accurate evaluation of large language model (LLM) responses, training LLM-as-judges to evaluate and critique other model responses has emerged as a popular paradigm.However, existing judge models are largely trained with supervised finetuning (SFT) on small data scales to perform limited types of evaluation tasks, fundamentally limiting generalization.To meet the need for strong, generalized judge models, we explore training foundational judge models at large data scales (680K) with direct preference optimization (DPO).Using four training tasks, we form three types of DPO preference pairs targeting different aspects of evaluation: Generating meaningful critiques, making accurate judgements, and understanding what comprises good and bad responses.To demonstrate the effectiveness of our method, we train judge models of three sizes: 8B parameters, 12B, and 70B, and evaluate on a comprehensive suite of 13 benchmarks (7 pairwise, 4 single rating, and 2 classification).Our models achieve the best aggregate performance, with even our 8B model outperforming GPT-4o in pairwise benchmarks.Further analysis shows that our judge models produce factual and actionable critiques and serve as strong foundational judges for continued finetuning.

Scaling test-time computation, or affording a generator large language model (LLM) extra compute during inference, typically employs the help of external non-generative evaluators (i.e., reward models). Concurrently, LLM-judges, models trained to generate evaluations and critiques (explanations) in natural language, are becoming increasingly popular in automatic evaluation. Despite judge empirical successes, their effectiveness as evaluators in test-time scaling settings is largely unknown. In this paper, we introduce the Judge Evaluation for Test-Time Scaling (JETTS) benchmark, which evaluates judge performance in three domains (math reasoning, code generation, and instruction following) under three task settings: response reranking, step-level beam search, and critique-based response refinement. We evaluate 10 different judge models (7B-70B parameters) for 8 different base generator models (6.7B-72B parameters). Our benchmark shows that while judges are competitive with outcome reward models in reranking, they are consistently worse than process reward models in beam search procedures. Furthermore, though unique to LLM-judges, their natural language critiques are currently ineffective in guiding the generator towards better responses.

We study the problem of zero-shot exercise retrieval in the context of online language learning, to give learners the ability to explicitly request personalized exercises via natural language. Using real-world data collected from language learners, we observe that vector similarity approaches poorly capture the relationship between exercise content and the language that learners use to express what they want to learn. This semantic gap between queries and content dramatically reduces the effectiveness of general-purpose retrieval models pretrained on large scale information retrieval datasets like MS MARCO [2]. We leverage the generative capabilities of large language models to bridge the gap by synthesizing hypothetical exercises based on the learner’s input, which are then used to search for relevant exercises. Our approach, which we call mHyER, overcomes three challenges: (1) lack of relevance labels for training, (2) unrestricted learner input content, and (3) low semantic similarity between input and retrieval candidates. mHyER outperforms several strong baselines on two novel benchmarks created from crowdsourced data and publicly available data.

Recent work leverages the expressive power of generative adversarial networks (GANs) to generate labeled synthetic datasets. These dataset generation methods often require new annotations of synthetic images, which forces practitioners to seek out annotators, curate a set of synthetic images, and ensure the quality of generated labels. We introduce the HandsOff framework, a technique capable of producing an unlimited number of synthetic images and corresponding labels after being trained on less than 50 preexisting labeled images. Our framework avoids the practical drawbacks of prior work by unifying the field of GAN inversion with dataset generation. We generate datasets with rich pixel-wise labels in multiple challenging domains such as faces, cars, full-body human poses, and urban driving scenes. Our method achieves state-of-the-art performance in semantic segmentation, keypoint detection, and depth estimation compared to prior dataset generation approaches and transfer learning baselines. We additionally showcase its ability to address broad challenges in model development which stem from fixed, hand-annotated datasets, such as the long-tail problem in semantic segmentation. Project page: austinxu87.github.io/handsoff.

We introduce a new type of query mechanism for collecting human feedback, called the perceptual adjustment query (PAQ). Being both informative and cognitively lightweight, the PAQ adopts an inverted measurement scheme, and combines advantages from both cardinal and ordinal queries. We showcase the PAQ in the metric learning problem, where we collect PAQ measurements to learn an unknown Mahalanobis distance. This gives rise to a high-dimensional, low-rank matrix estimation problem to which standard matrix estimators cannot be applied. Consequently, we develop a two-stage estimator for metric learning from PAQs, and provide sample complexity guarantees for this estimator. We present numerical simulations demonstrating the performance of the estimator and its notable properties.

Active learning is commonly used to train label-efficient models by adaptively selecting the most informative queries. However, most active learning strategies are designed to either learn a representation of the data (e.g., embedding or metric learning) or perform well on a task (e.g., classification) on the data. However, many machine learning tasks involve a combination of both representation learning and a task-specific goal. Motivated by this, we propose a novel unified query framework that can be applied to any problem in which a key component is learning a representation of the data that reflects similarity. Our approach builds on similarity or nearest neighbor (NN) queries which seek to select samples that result in improved embeddings. The queries consist of a reference and a set of objects, with an oracle selecting the object most similar (i.e., nearest) to the reference. In order to reduce the number of solicited queries, they are chosen adaptively according to an information theoretic criterion. We demonstrate the effectiveness of the proposed strategy on two tasks - active metric learning and active classification - using a variety of synthetic and real world datasets. In particular, we demonstrate that actively selected NN queries outperform recently developed active triplet selection methods in a deep metric learning setting. Further, we show that in classification, actively selecting class labels can be reformulated as a process of selecting the most informative NN query, allowing direct application of our method.

A common problem in recommendation systems is to learn a model of user preferences based only on comparisons of the relative attractiveness of different items. We consider this problem in the context of an ideal point model of user preference, where each user can be represented as a point in a low-dimensional space together with a set of items. In this model, the closer an item is to a user’s ideal point, the more that user prefers the item. When an embedding of items is known a priori, the problem of localizing a user’s ideal point from comparisons amongst items is well studied. However, relatively little work exists on learning embeddings for new items based only on such comparisons. In this paper, we consider the problem of embedding a set of items using paired comparisons from a set of known users. Specifically, we present a novel convex lifted method of learning the embedding representation p1,…,pn∈ Rnof n items given noisy responses of the form "user ukprefers item pito item pj" for an arbitrary set of users {uk} in Rd. We provide a range of simulations that validate the efficacy of our approach.

A popular model of preference in the context of recommendation systems is the so-called ideal point model. In this model, a user is represented as a vector u together with a collection of items x1 ... xN in a common low-dimensional space. The vector u represents the user's "ideal point," or the ideal combination of features that represents a hypothesized most preferred item. The underlying assumption in this model is that a smaller distance between u and an item xj indicates a stronger preference for xj. In the vast majority of the existing work on learning ideal point models, the underlying distance has been assumed to be Euclidean. However, this eliminates any possibility of interactions between features and a user's underlying preferences. In this paper, we consider the problem of learning an ideal point representation of a user's preferences when the distance metric is an unknown Mahalanobis metric. Specifically, we present a novel approach to estimate the user's ideal point u and the Mahalanobis metric from paired comparisons of the form "item xi is preferred to item xj.'' This can be viewed as a special case of a more general metric learning problem where the location of some points are unknown a priori. We conduct extensive experiments on synthetic and real-world datasets to exhibit the effectiveness of our algorithm.