Daily Papers

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

We introduce a new framework for sample-efficient model evaluation that we call active testing. While approaches like active learning reduce the number of labels needed for model training, existing literature largely ignores the cost of labeling test data, typically unrealistically assuming large test sets for model evaluation. This creates a disconnect to real applications, where test labels are important and just as expensive, e.g. for optimizing hyperparameters. Active testing addresses this by carefully selecting the test points to label, ensuring model evaluation is sample-efficient. To this end, we derive theoretically-grounded and intuitive acquisition strategies that are specifically tailored to the goals of active testing, noting these are distinct to those of active learning. As actively selecting labels introduces a bias; we further show how to remove this bias while reducing the variance of the estimator at the same time. Active testing is easy to implement and can be applied to any supervised machine learning method. We demonstrate its effectiveness on models including WideResNets and Gaussian processes on datasets including Fashion-MNIST and CIFAR-100.

We propose a new learning paradigm called Deep Memory. It has the potential to completely revolutionize the Machine Learning field. Surprisingly, this paradigm has not been reinvented yet, unlike Deep Learning. At the core of this approach is the Learning By Heart principle, well studied in primary schools all over the world. Inspired by poem recitation, or by pi decimal memorization, we propose a concrete algorithm that mimics human behavior. We implement this paradigm on the task of generative modeling, and apply to images, natural language and even the pi decimals as long as one can print them as text. The proposed algorithm even generated this paper, in a one-shot learning setting. In carefully designed experiments, we show that the generated samples are indistinguishable from the training examples, as measured by any statistical tests or metrics.

Recently, test-time scaling has garnered significant attention from the research community, largely due to the substantial advancements of the o1 model released by OpenAI. By allocating more computational resources during the inference phase, large language models~(LLMs) can extensively explore the solution space by generating more thought tokens or diverse solutions, thereby producing more accurate responses. However, developing an o1-like reasoning approach is challenging, and researchers have been making various attempts to advance this open area of research. In this paper, we present a preliminary exploration into enhancing the reasoning abilities of LLMs through reward-guided tree search algorithms. This framework is implemented by integrating the policy model, reward model, and search algorithm. It is primarily constructed around a tree search algorithm, where the policy model navigates a dynamically expanding tree guided by a specially trained reward model. We thoroughly explore various design considerations necessary for implementing this framework and provide a detailed report of the technical aspects. To assess the effectiveness of our approach, we focus on mathematical reasoning tasks and conduct extensive evaluations on four challenging datasets, significantly enhancing the reasoning abilities of LLMs.

This paper investigates Reinforcement Learning (RL) on data without explicit labels for reasoning tasks in Large Language Models (LLMs). The core challenge of the problem is reward estimation during inference while not having access to ground-truth information. While this setting appears elusive, we find that common practices in Test-Time Scaling (TTS), such as majority voting, yield surprisingly effective rewards suitable for driving RL training. In this work, we introduce Test-Time Reinforcement Learning (TTRL), a novel method for training LLMs using RL on unlabeled data. TTRL enables self-evolution of LLMs by utilizing the priors in the pre-trained models. Our experiments demonstrate that TTRL consistently improves performance across a variety of tasks and models. Notably, TTRL boosts the pass@1 performance of Qwen-2.5-Math-7B by approximately 159% on the AIME 2024 with only unlabeled test data. Furthermore, although TTRL is only supervised by the Maj@N metric, TTRL has demonstrated performance to consistently surpass the upper limit of the initial model, and approach the performance of models trained directly on test data with ground-truth labels. Our experimental findings validate the general effectiveness of TTRL across various tasks, and highlight TTRL's potential for broader tasks and domains. GitHub: https://github.com/PRIME-RL/TTRL

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having limited diversity of symbols and rules, coupled with closed-ended answers. This paper proposes a method to leverage these shortcomings as useful features to a construct dynamic, counterfactual benchmark, which can be used to both reveal overfitting and measure true reasoning. We demonstrate this via MatheMagic, which generates math test instances with the interpretations of numbers and operators altered, yet has automatically verifiable answers. Test instances are randomly seeded and constructed at test time to evaluate a model's induction or deduction capability, offering stability, extensibility, comparability, and robustness to overfitting. Our experiments find that models solve deduction more easily than induction, but they revert to standard math. Further analysis reveals that math-adapted models fail to exhibit a general "skill" of reasoning, and fine-tuning on induction tasks generalizes poorly.

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the protection of user data, as individuals may not have given consent for their data to be used in training. To address this concern, recent studies introduce the concept of unlearnable examples, i.e., data instances that appear natural but are intentionally altered to prevent models from effectively learning from them. While existing methods demonstrate empirical effectiveness, they typically rely on heuristic trials and lack formal guarantees. Besides, when unlearnable examples are mixed with clean data, as is often the case in practice, their unlearnability disappears. In this work, we propose a novel approach to constructing unlearnable examples by systematically maximising the Bayes error, a measurement of irreducible classification error. We develop an optimisation-based approach and provide an efficient solution using projected gradient ascent. Our method provably increases the Bayes error and remains effective when the unlearning examples are mixed with clean samples. Experimental results across multiple datasets and model architectures are consistent with our theoretical analysis and show that our approach can restrict data learnability, effectively in practice.

With the scale capability of increasing training data, model size, and computational cost, video generation has achieved impressive results in digital creation, enabling users to express creativity across various domains. Recently, researchers in Large Language Models (LLMs) have expanded the scaling to test-time, which can significantly improve LLM performance by using more inference-time computation. Instead of scaling up video foundation models through expensive training costs, we explore the power of Test-Time Scaling (TTS) in video generation, aiming to answer the question: if a video generation model is allowed to use non-trivial amount of inference-time compute, how much can it improve generation quality given a challenging text prompt. In this work, we reinterpret the test-time scaling of video generation as a searching problem to sample better trajectories from Gaussian noise space to the target video distribution. Specifically, we build the search space with test-time verifiers to provide feedback and heuristic algorithms to guide searching process. Given a text prompt, we first explore an intuitive linear search strategy by increasing noise candidates at inference time. As full-step denoising all frames simultaneously requires heavy test-time computation costs, we further design a more efficient TTS method for video generation called Tree-of-Frames (ToF) that adaptively expands and prunes video branches in an autoregressive manner. Extensive experiments on text-conditioned video generation benchmarks demonstrate that increasing test-time compute consistently leads to significant improvements in the quality of videos. Project page: https://liuff19.github.io/Video-T1

Recent work on open domain question answering (QA) assumes strong supervision of the supporting evidence and/or assumes a blackbox information retrieval (IR) system to retrieve evidence candidates. We argue that both are suboptimal, since gold evidence is not always available, and QA is fundamentally different from IR. We show for the first time that it is possible to jointly learn the retriever and reader from question-answer string pairs and without any IR system. In this setting, evidence retrieval from all of Wikipedia is treated as a latent variable. Since this is impractical to learn from scratch, we pre-train the retriever with an Inverse Cloze Task. We evaluate on open versions of five QA datasets. On datasets where the questioner already knows the answer, a traditional IR system such as BM25 is sufficient. On datasets where a user is genuinely seeking an answer, we show that learned retrieval is crucial, outperforming BM25 by up to 19 points in exact match.

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

Test-time adaptation (TTA) addresses distribution shifts for streaming test data in unsupervised settings. Currently, most TTA methods can only deal with minor shifts and rely heavily on heuristic and empirical studies. To advance TTA under domain shifts, we propose the novel problem setting of active test-time adaptation (ATTA) that integrates active learning within the fully TTA setting. We provide a learning theory analysis, demonstrating that incorporating limited labeled test instances enhances overall performances across test domains with a theoretical guarantee. We also present a sample entropy balancing for implementing ATTA while avoiding catastrophic forgetting (CF). We introduce a simple yet effective ATTA algorithm, known as SimATTA, using real-time sample selection techniques. Extensive experimental results confirm consistency with our theoretical analyses and show that the proposed ATTA method yields substantial performance improvements over TTA methods while maintaining efficiency and shares similar effectiveness to the more demanding active domain adaptation (ADA) methods. Our code is available at https://github.com/divelab/ATTA

In this paper, we propose Test-Time Training, a general approach for improving the performance of predictive models when training and test data come from different distributions. We turn a single unlabeled test sample into a self-supervised learning problem, on which we update the model parameters before making a prediction. This also extends naturally to data in an online stream. Our simple approach leads to improvements on diverse image classification benchmarks aimed at evaluating robustness to distribution shifts.

Automatic evaluation with large language models, commonly known as LLM-as-a-judge, is now standard across reasoning and alignment tasks. Despite evaluating many samples in deployment, these evaluators typically (i) treat each case independently, missing the opportunity to accumulate experience, and (ii) rely on a single fixed prompt for all cases, neglecting the need for sample-specific evaluation criteria. We introduce Learning While Evaluating (LWE), a framework that allows evaluators to improve sequentially at inference time without requiring training or validation sets. LWE maintains an evolving meta-prompt that (i) produces sample-specific evaluation instructions and (ii) refines itself through self-generated feedback. Furthermore, we propose Selective LWE, which updates the meta-prompt only on self-inconsistent cases, focusing computation where it matters most. This selective approach retains the benefits of sequential learning while being far more cost-effective. Across two pairwise comparison benchmarks, Selective LWE outperforms strong baselines, empirically demonstrating that evaluators can improve during sequential testing with a simple selective update, learning most from the cases they struggle with.

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

Training state-of-the-art vision models has become prohibitively expensive for researchers and practitioners. For the sake of accessibility and resource reuse, it is important to focus on adapting these models to a variety of downstream scenarios. An interesting and practical paradigm is online test-time adaptation, according to which training data is inaccessible, no labelled data from the test distribution is available, and adaptation can only happen at test time and on a handful of samples. In this paper, we investigate how test-time adaptation methods fare for a number of pre-trained models on a variety of real-world scenarios, significantly extending the way they have been originally evaluated. We show that they perform well only in narrowly-defined experimental setups and sometimes fail catastrophically when their hyperparameters are not selected for the same scenario in which they are being tested. Motivated by the inherent uncertainty around the conditions that will ultimately be encountered at test time, we propose a particularly "conservative" approach, which addresses the problem with a Laplacian Adjusted Maximum-likelihood Estimation (LAME) objective. By adapting the model's output (not its parameters), and solving our objective with an efficient concave-convex procedure, our approach exhibits a much higher average accuracy across scenarios than existing methods, while being notably faster and have a much lower memory footprint. The code is available at https://github.com/fiveai/LAME.

This work investigates large language models (LLMs) as teachable agents for learning by teaching (LBT). LBT with teachable agents helps learners identify their knowledge gaps and discover new knowledge. However, teachable agents require expensive programming of subject-specific knowledge. While LLMs as teachable agents can reduce the cost, LLMs' over-competence as tutees discourages learners from teaching. We propose a prompting pipeline that restrains LLMs' competence and makes them initiate "why" and "how" questions for effective knowledge-building. We combined these techniques into TeachYou, an LBT environment for algorithm learning, and AlgoBo, an LLM-based tutee chatbot that can simulate misconceptions and unawareness prescribed in its knowledge state. Our technical evaluation confirmed that our prompting pipeline can effectively configure AlgoBo's problem-solving performance. Through a between-subject study with 40 algorithm novices, we also observed that AlgoBo's questions led to knowledge-dense conversations (effect size=0.73). Lastly, we discuss design implications, cost-efficiency, and personalization of LLM-based teachable agents.

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

Discovering novel concepts in unlabelled datasets and in a continuous manner is an important desideratum of lifelong learners. In the literature such problems have been partially addressed under very restricted settings, where novel classes are learned by jointly accessing a related labelled set (e.g., NCD) or by leveraging only a supervisedly pre-trained model (e.g., class-iNCD). In this work we challenge the status quo in class-iNCD and propose a learning paradigm where class discovery occurs continuously and truly unsupervisedly, without needing any related labelled set. In detail, we propose to exploit the richer priors from strong self-supervised pre-trained models (PTM). To this end, we propose simple baselines, composed of a frozen PTM backbone and a learnable linear classifier, that are not only simple to implement but also resilient under longer learning scenarios. We conduct extensive empirical evaluation on a multitude of benchmarks and show the effectiveness of our proposed baselines when compared with sophisticated state-of-the-art methods. The code is open source.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

Large language models (LLMs) currently dominate the field of natural language processing (NLP), representing the state-of-the-art across a diverse array of tasks. Developing a model of this nature, from training to inference, requires making numerous decisions which define a combinatorial search problem. For example, selecting the optimal pre-trained LLM, prompt, or hyperparameters to attain the best performance for a task often requires evaluating multiple candidates on an entire test set. This exhaustive evaluation can be time-consuming and costly, as both inference and metric computation with LLMs are resource-intensive. In this paper, we address the challenge of identifying the best method within a limited budget for evaluating methods on test examples. By leveraging the well-studied multi-armed bandit framework, which sequentially selects the next method-example pair to evaluate, our approach, combining multi-armed bandit algorithms with low-rank factorization, significantly reduces the required resources. Experiments show that our algorithms can identify the top-performing method using only 5-15\% of the typically needed resources, resulting in an 85-95\% reduction in cost.

In recent years, large pre-trained language models (LLMs) have demonstrated the ability to follow instructions and perform novel tasks from a few examples. The possibility to parameterise an LLM through such in-context examples widens their capability at a much lower cost than finetuning. We extend this line of reasoning and present a method which further expands the capabilities of an LLM by embedding it within an algorithm or program. To demonstrate the benefits of this approach, we present an illustrative example of evidence-supported question-answering. We obtain a 6.4\% improvement over the chain of thought baseline through a more algorithmic approach without any finetuning. Furthermore, we highlight recent work from this perspective and discuss the advantages and disadvantages in comparison to the standard approaches.

In-context learning (ICL), the ability of large language models to perform novel tasks by conditioning on a prompt with a few task examples, requires these examples to be informative about the test instance. The standard approach of independently ranking and selecting the most similar examples selects redundant examples while omitting important information. In this work, we show that BERTScore-Recall (BSR) selects better examples that demonstrate more of the salient aspects, e.g. reasoning patterns, of the test input. We further extend BSR and many standard metrics to easily optimizable set-level metrics, giving still better coverage of those salient aspects. On 15 datasets spanning 6 tasks and with 7 diverse LLMs, we show that (1) BSR is the superior metric for in-context example selection across the board, and (2) for compositional tasks, set selection using Set-BSR outperforms independent ranking by up to 17 points on average and, despite being training-free, surpasses methods that leverage task or LLM-specific training.

One long-term goal of machine learning research is to produce methods that are applicable to reasoning and natural language, in particular building an intelligent dialogue agent. To measure progress towards that goal, we argue for the usefulness of a set of proxy tasks that evaluate reading comprehension via question answering. Our tasks measure understanding in several ways: whether a system is able to answer questions via chaining facts, simple induction, deduction and many more. The tasks are designed to be prerequisites for any system that aims to be capable of conversing with a human. We believe many existing learning systems can currently not solve them, and hence our aim is to classify these tasks into skill sets, so that researchers can identify (and then rectify) the failings of their systems. We also extend and improve the recently introduced Memory Networks model, and show it is able to solve some, but not all, of the tasks.

Large language models are trained on vast amounts of internet data, prompting concerns and speculation that they have memorized public benchmarks. Going from speculation to proof of contamination is challenging, as the pretraining data used by proprietary models are often not publicly accessible. We show that it is possible to provide provable guarantees of test set contamination in language models without access to pretraining data or model weights. Our approach leverages the fact that when there is no data contamination, all orderings of an exchangeable benchmark should be equally likely. In contrast, the tendency for language models to memorize example order means that a contaminated language model will find certain canonical orderings to be much more likely than others. Our test flags potential contamination whenever the likelihood of a canonically ordered benchmark dataset is significantly higher than the likelihood after shuffling the examples. We demonstrate that our procedure is sensitive enough to reliably prove test set contamination in challenging situations, including models as small as 1.4 billion parameters, on small test sets of only 1000 examples, and datasets that appear only a few times in the pretraining corpus. Using our test, we audit five popular publicly accessible language models for test set contamination and find little evidence for pervasive contamination.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Questions of fair use of copyright-protected content to train Large Language Models (LLMs) are being very actively debated. Document-level inference has been proposed as a new task: inferring from black-box access to the trained model whether a piece of content has been seen during training. SOTA methods however rely on naturally occurring memorization of (part of) the content. While very effective against models that memorize a lot, we hypothesize--and later confirm--that they will not work against models that do not naturally memorize, e.g. medium-size 1B models. We here propose to use copyright traps, the inclusion of fictitious entries in original content, to detect the use of copyrighted materials in LLMs with a focus on models where memorization does not naturally occur. We carefully design an experimental setup, randomly inserting traps into original content (books) and train a 1.3B LLM. We first validate that the use of content in our target model would be undetectable using existing methods. We then show, contrary to intuition, that even medium-length trap sentences repeated a significant number of times (100) are not detectable using existing methods. However, we show that longer sequences repeated a large number of times can be reliably detected (AUC=0.75) and used as copyright traps. We further improve these results by studying how the number of times a sequence is seen improves detectability, how sequences with higher perplexity tend to be memorized more, and how taking context into account further improves detectability.

We describe a new class of learning models called memory networks. Memory networks reason with inference components combined with a long-term memory component; they learn how to use these jointly. The long-term memory can be read and written to, with the goal of using it for prediction. We investigate these models in the context of question answering (QA) where the long-term memory effectively acts as a (dynamic) knowledge base, and the output is a textual response. We evaluate them on a large-scale QA task, and a smaller, but more complex, toy task generated from a simulated world. In the latter, we show the reasoning power of such models by chaining multiple supporting sentences to answer questions that require understanding the intension of verbs.

Recent empirical studies have explored the idea of continuing to train a model at test-time for a given task, known as test-time training (TTT), and have found it to yield significant performance improvements. However, there is limited understanding of why and when TTT is effective. Earlier explanations mostly focused on the observation that TTT may help when applied to out-of-distribution adaptation or used with privileged data. However, the growing scale of foundation models with most test data being in-distribution questions these explanations. We instead posit that foundation models remain globally underparameterized, with TTT providing a mechanism for specialization after generalization, focusing capacity on concepts relevant to the test task. Specifically, under the linear representation hypothesis, we propose a model in which TTT achieves a substantially smaller in-distribution test error than global training. We empirically validate our model's key assumptions by training a sparse autoencoder on ImageNet, showing that semantically related data points are explained by only a few shared concepts. Finally, we perform scaling studies across image and language tasks that confirm the practical implications of our model, identifying the regimes where specialization is most effective.

This work studies the general principles of improving the learning of language models (LMs), which aims at reducing the necessary training steps for achieving superior performance. Specifically, we present a theory for the optimal learning of LMs. We first propose an objective that optimizes LM learning by maximizing the data compression ratio in an "LM-training-as-lossless-compression" view. Then, we derive a theorem, named Learning Law, to reveal the properties of the dynamics in the optimal learning process under our objective. The theorem is then validated by experiments on a linear classification and a real-world language modeling task. Finally, we empirically verify that the optimal learning of LMs essentially stems from the improvement of the coefficients in the scaling law of LMs, indicating great promise and significance for designing practical learning acceleration methods. Our code can be found at https://aka.ms/LearningLaw.

Open-ended algorithms aim to learn new, interesting behaviors forever. That requires a vast environment search space, but there are thus infinitely many possible tasks. Even after filtering for tasks the current agent can learn (i.e., learning progress), countless learnable yet uninteresting tasks remain (e.g., minor variations of previously learned tasks). An Achilles Heel of open-endedness research is the inability to quantify (and thus prioritize) tasks that are not just learnable, but also interesting (e.g., worthwhile and novel). We propose solving this problem by Open-endedness via Models of human Notions of Interestingness (OMNI). The insight is that we can utilize foundation models (FMs) as a model of interestingness (MoI), because they already internalize human concepts of interestingness from training on vast amounts of human-generated data, where humans naturally write about what they find interesting or boring. We show that FM-based MoIs improve open-ended learning by focusing on tasks that are both learnable and interesting, outperforming baselines based on uniform task sampling or learning progress alone. This approach has the potential to dramatically advance the ability to intelligently select which tasks to focus on next (i.e., auto-curricula), and could be seen as AI selecting its own next task to learn, facilitating self-improving AI and AI-Generating Algorithms. Project website at https://www.jennyzhangzt.com/omni/

Multiple choice question answering (MCQA) is popular for LLM evaluation due to its simplicity and human-like testing, but we argue for its reform. We first reveal flaws in MCQA's format, as it struggles to: 1) test generation/subjectivity; 2) match LLM use cases; and 3) fully test knowledge. We instead advocate for generative formats based on human testing-where LLMs construct and explain answers-better capturing user needs and knowledge while remaining easy to score. We then show even when MCQA is a useful format, its datasets suffer from: leakage; unanswerability; shortcuts; and saturation. In each issue, we give fixes from education, like rubrics to guide MCQ writing; scoring methods to bridle guessing; and Item Response Theory to build harder MCQs. Lastly, we discuss LLM errors in MCQA-robustness, biases, and unfaithful explanations-showing how our prior solutions better measure or address these issues. While we do not need to desert MCQA, we encourage more efforts in refining the task based on educational testing, advancing evaluations.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which can then be robustly generalized to novel scenarios. Recent work has evaluated large language models (LLMs) on inductive reasoning tasks by directly prompting them yielding "in context learning." This can work well for straightforward inductive tasks, but performs very poorly on more complex tasks such as the Abstraction and Reasoning Corpus (ARC). In this work, we propose to improve the inductive reasoning ability of LLMs by generating explicit hypotheses at multiple levels of abstraction: we prompt the LLM to propose multiple abstract hypotheses about the problem, in natural language, then implement the natural language hypotheses as concrete Python programs. These programs can be directly verified by running on the observed examples and generalized to novel inputs. Because of the prohibitive cost of generation with state-of-the-art LLMs, we consider a middle step to filter the set of hypotheses that will be implemented into programs: we either ask the LLM to summarize into a smaller set of hypotheses, or ask human annotators to select a subset of the hypotheses. We verify our pipeline's effectiveness on the ARC visual inductive reasoning benchmark, its variant 1D-ARC, and string transformation dataset SyGuS. On a random 40-problem subset of ARC, our automated pipeline using LLM summaries achieves 27.5% accuracy, significantly outperforming the direct prompting baseline (accuracy of 12.5%). With the minimal human input of selecting from LLM-generated candidates, the performance is boosted to 37.5%. (And we argue this is a lower bound on the performance of our approach without filtering.) Our ablation studies show that abstract hypothesis generation and concrete program representations are both beneficial for LLMs to perform inductive reasoning tasks.

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.

The remarkable performance of the o1 model in complex reasoning demonstrates that test-time computing scaling can further unlock the model's potential, enabling powerful System-2 thinking. However, there is still a lack of comprehensive surveys for test-time computing scaling. We trace the concept of test-time computing back to System-1 models. In System-1 models, test-time computing addresses distribution shifts and improves robustness and generalization through parameter updating, input modification, representation editing, and output calibration. In System-2 models, it enhances the model's reasoning ability to solve complex problems through repeated sampling, self-correction, and tree search. We organize this survey according to the trend of System-1 to System-2 thinking, highlighting the key role of test-time computing in the transition from System-1 models to weak System-2 models, and then to strong System-2 models. We also point out a few possible future directions.

While large language models have shown impressive capabilities across a wide range of domains, they still encounter significant challenges in reasoning tasks that require gathering evidence over multiple turns and drawing logical conclusions. These challenges present significant obstacles for LLM chat user interfaces, which rely on multi-turn interactions to facilitate effective collaboration. This limitation leads to real-world issues; for example, service chatbots must gather necessary information from customers over multiple turns to diagnose and resolve problems effectively. Despite the multi-turn nature of many real-world LLM use cases, most existing benchmarks rely on carefully curated single-turn tests, which often blur the line between memorization and genuine reasoning. To address this, we introduce the Wason Inductive Logic Test (WILT), a simple yet challenging multi-turn reasoning benchmark designed to resist memorization. WILT is inspired by the Wason 2-4-6 task, where participants must infer a boolean function involving three variables (e.g., x < y < z) by proposing test cases (such as (2, 4, 6)). In WILT, each test starts from a clean slate, with only the initial instructions provided, preventing models from relying on pre-learned responses. Over several turns, models must interact with the environment by suggesting test cases to narrow the possible hypotheses and ultimately infer the hidden function based on the outcomes. Our findings reveal that LLMs struggle with this task, exhibiting distinct strengths and weaknesses: some are better at narrowing down the hypothesis space by proposing valuable test cases, while others are more adept at deducing the hidden function from observed cases. Despite these variations, the best-performing model achieves only 28% accuracy, highlighting a significant gap in LLM performance on complex multi-turn reasoning tasks.

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

Test-time computing approaches, which leverage additional computational resources during inference, have been proven effective in enhancing large language model performance. This work introduces a novel, linearly scaling approach, TestNUC, that improves test-time predictions by leveraging the local consistency of neighboring unlabeled data-it classifies an input instance by considering not only the model's prediction on that instance but also on neighboring unlabeled instances. We evaluate TestNUC across eight diverse datasets, spanning intent classification, topic mining, domain discovery, and emotion detection, demonstrating its consistent superiority over baseline methods such as standard prompting and self-consistency. Furthermore, TestNUC can be seamlessly integrated with existing test-time computing approaches, substantially boosting their performance. Our analysis reveals that TestNUC scales effectively with increasing amounts of unlabeled data and performs robustly across different embedding models, making it practical for real-world applications. Our code is available at https://github.com/HenryPengZou/TestNUC.

In this technical report, we introduce OpenR, an open-source framework designed to integrate key components for enhancing the reasoning capabilities of large language models (LLMs). OpenR unifies data acquisition, reinforcement learning training (both online and offline), and non-autoregressive decoding into a cohesive software platform. Our goal is to establish an open-source platform and community to accelerate the development of LLM reasoning. Inspired by the success of OpenAI's o1 model, which demonstrated improved reasoning abilities through step-by-step reasoning and reinforcement learning, OpenR integrates test-time compute, reinforcement learning, and process supervision to improve reasoning in LLMs. Our work is the first to provide an open-source framework that explores the core techniques of OpenAI's o1 model with reinforcement learning, achieving advanced reasoning capabilities beyond traditional autoregressive methods. We demonstrate the efficacy of OpenR by evaluating it on the MATH dataset, utilising publicly available data and search methods. Our initial experiments confirm substantial gains, with relative improvements in reasoning and performance driven by test-time computation and reinforcement learning through process reward models. The OpenR framework, including code, models, and datasets, is accessible at https://openreasoner.github.io.

Evaluation of reasoning language models gained importance after it was observed that they can combine their existing capabilities into novel traces of intermediate steps before task completion and that the traces can sometimes help them to generalize better than past models. As reasoning becomes the next scaling dimension of large language models, careful study of their capabilities in critical tasks is needed. We show that better performance is not always caused by test-time algorithmic improvements or model sizes but also by using impactful benchmarks as curricula for learning. We call this benchmark-driven selection of AI and show its effects on DeepSeek-R1 using our sequential decision-making problem from Humanity's Last Exam. Steering development of AI by impactful benchmarks trades evaluation for learning and makes novelty of test tasks key for measuring generalization capabilities of reasoning models. Consequently, some benchmarks could be seen as curricula for training rather than unseen test sets.

Humans are good at learning on the job: We learn how to solve the tasks we face as we go along. Can a model do the same? We propose an agent that assembles a task-specific curriculum, called test-time curriculum (TTC-RL), and applies reinforcement learning to continue training the model for its target task. The test-time curriculum avoids time-consuming human curation of datasets by automatically selecting the most task-relevant data from a large pool of available training data. Our experiments demonstrate that reinforcement learning on a test-time curriculum consistently improves the model on its target tasks, across a variety of evaluations and models. Notably, on challenging math and coding benchmarks, TTC-RL improves the pass@1 of Qwen3-8B by approximately 1.8x on AIME25 and 2.1x on CodeElo. Moreover, we find that TTC-RL significantly raises the performance ceiling compared to the initial model, increasing pass@8 on AIME25 from 40% to 62% and on CodeElo from 28% to 43%. Our findings show the potential of test-time curricula in extending the test-time scaling paradigm to continual training on thousands of task-relevant experiences during test-time.

We investigate the predictability of large language model (LLM) capabilities: given records of past experiments using different model families, numbers of parameters, tasks, and numbers of in-context examples, can we accurately predict LLM performance on new experiment configurations? Answering this question has practical implications for LLM users (e.g., deciding which models to try), developers (e.g., prioritizing evaluation on representative tasks), and the research community (e.g., identifying hard-to-predict capabilities that warrant further investigation). We study the performance prediction problem on experiment records from BIG-bench. On a random train-test split, an MLP-based predictor achieves an R^2 score greater than 95%, indicating the presence of learnable patterns within the experiment records. We then formulate the problem of searching for "small-bench," an informative subset of BIG-bench tasks from which the performance on the full set can be maximally recovered. We find a subset as informative as BIG-bench Hard for evaluating new model families, while being 3times smaller. Additionally, we find competitive subsets by clustering task representations learned by our MLP-based predictor and selecting tasks close to cluster centroids, highlighting the importance of task diversity in constructing "small-bench."

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Large Language Models (LLMs) can comply with harmful instructions, raising serious safety concerns despite their impressive capabilities. Recent work has leveraged probing-based approaches to study the separability of malicious and benign inputs in LLMs' internal representations, and researchers have proposed using such probing methods for safety detection. We systematically re-examine this paradigm. Motivated by poor out-of-distribution performance, we hypothesize that probes learn superficial patterns rather than semantic harmfulness. Through controlled experiments, we confirm this hypothesis and identify the specific patterns learned: instructional patterns and trigger words. Our investigation follows a systematic approach, progressing from demonstrating comparable performance of simple n-gram methods, to controlled experiments with semantically cleaned datasets, to detailed analysis of pattern dependencies. These results reveal a false sense of security around current probing-based approaches and highlight the need to redesign both models and evaluation protocols, for which we provide further discussions in the hope of suggesting responsible further research in this direction. We have open-sourced the project at https://github.com/WangCheng0116/Why-Probe-Fails.

Large language models (LLMs) have shown impressive capabilities in real-world applications. The capability of in-context learning (ICL) allows us to adapt an LLM to downstream tasks by including input-label exemplars in the prompt without model fine-tuning. However, the quality of these exemplars in the prompt greatly impacts performance, highlighting the need for an effective automated exemplar selection method. Recent studies have explored retrieval-based approaches to select exemplars tailored to individual test queries, which can be undesirable due to extra test-time computation and an increased risk of data exposure. Moreover, existing methods fail to adequately account for the impact of exemplar ordering on the performance. On the other hand, the impact of the instruction, another essential component in the prompt given to the LLM, is often overlooked in existing exemplar selection methods. To address these challenges, we propose a novel method named EASE, which leverages the hidden embedding from a pre-trained language model to represent ordered sets of exemplars and uses a neural bandit algorithm to optimize the sets of exemplars while accounting for exemplar ordering. Our EASE can efficiently find an ordered set of exemplars that performs well for all test queries from a given task, thereby eliminating test-time computation. Importantly, EASE can be readily extended to jointly optimize both the exemplars and the instruction. Through extensive empirical evaluations (including novel tasks), we demonstrate the superiority of EASE over existing methods, and reveal practical insights about the impact of exemplar selection on ICL, which may be of independent interest. Our code is available at https://github.com/ZhaoxuanWu/EASE-Prompt-Optimization.

Augmenting large language models (LLMs) with external retrieval has become a standard method to address their inherent knowledge cutoff limitations. However, traditional retrieval-augmented generation methods employ static, pre-inference retrieval strategies, making them inadequate for complex tasks involving ambiguous, multi-step, or evolving information needs. Recent advances in test-time scaling techniques have demonstrated significant potential in enabling LLMs to dynamically interact with external tools, motivating the shift toward adaptive inference-time retrieval. Inspired by Information Foraging Theory (IFT), we propose InForage, a reinforcement learning framework that formalizes retrieval-augmented reasoning as a dynamic information-seeking process. Unlike existing approaches, InForage explicitly rewards intermediate retrieval quality, encouraging LLMs to iteratively gather and integrate information through adaptive search behaviors. To facilitate training, we construct a human-guided dataset capturing iterative search and reasoning trajectories for complex, real-world web tasks. Extensive evaluations across general question answering, multi-hop reasoning tasks, and a newly developed real-time web QA dataset demonstrate InForage's superior performance over baseline methods. These results highlight InForage's effectiveness in building robust, adaptive, and efficient reasoning agents.

Program synthesis methods aim to automatically generate programs restricted to a language that can explain a given specification of input-output pairs. While purely symbolic approaches suffer from a combinatorial search space, recent methods leverage neural networks to learn distributions over program structures to narrow this search space significantly, enabling more efficient search. However, for challenging problems, it remains difficult to train models to perform program synthesis in one shot, making test-time search essential. Most neural methods lack structured search mechanisms during inference, relying instead on stochastic sampling or gradient updates, which can be inefficient. In this work, we propose the Latent Program Network (LPN), a general algorithm for program induction that learns a distribution over latent programs in a continuous space, enabling efficient search and test-time adaptation. We explore how to train these networks to optimize for test-time computation and demonstrate the use of gradient-based search both during training and at test time. We evaluate LPN on ARC-AGI, a program synthesis benchmark that evaluates performance by generalizing programs to new inputs rather than explaining the underlying specification. We show that LPN can generalize beyond its training distribution and adapt to unseen tasks by utilizing test-time computation, outperforming algorithms without test-time adaptation mechanisms.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves extensive sampling at inference time guided by an external LLM verifier, resulting in a two-player system. Despite external guidance, the effectiveness of this system demonstrates the potential of a single LLM to tackle complex tasks. Thus, we pose a new research problem: Can we internalize the searching capabilities to fundamentally enhance the reasoning abilities of a single LLM? This work explores an orthogonal direction focusing on post-training LLMs for autoregressive searching (i.e., an extended reasoning process with self-reflection and self-exploration of new strategies). To achieve this, we propose the Chain-of-Action-Thought (COAT) reasoning and a two-stage training paradigm: 1) a small-scale format tuning stage to internalize the COAT reasoning format and 2) a large-scale self-improvement stage leveraging reinforcement learning. Our approach results in Satori, a 7B LLM trained on open-source models and data. Extensive empirical evaluations demonstrate that Satori achieves state-of-the-art performance on mathematical reasoning benchmarks while exhibits strong generalization to out-of-domain tasks. Code, data, and models will be fully open-sourced.

In this paper, I introduce the retrieval problem, a simple reasoning task that can be solved only by transformers with a minimum number of layers. The task has an adjustable difficulty that can further increase the required number of layers to any arbitrary value. I demonstrate that large language models can solve the task under different prompting formulations without any fine-tuning. To understand how transformers solve the retrieval problem, I train several transformers on a minimal formulation. I find that successful learning occurs only under the presence of an implicit curriculum. I uncover the learned mechanisms by studying the attention maps in the trained transformers. I also study the training process, uncovering that attention heads always emerge in a specific sequence.

Supervised Fine-Tuning (SFT) serves as a crucial phase in aligning Large Language Models (LLMs) to specific task prerequisites. The selection of fine-tuning data profoundly influences the model's performance, whose principle is traditionally grounded in data quality and distribution. In this paper, we introduce a new dimension in SFT data selection: learnability. This new dimension is motivated by the intuition that SFT unlocks capabilities acquired by a LLM during the pretraining phase. Given that different pretrained models have disparate capabilities, the SFT data appropriate for one may not suit another. Thus, we introduce the term learnability to define the suitability of data for effective learning by the model. We present the Loss Based SFT Data Selection (LoBaSS) method, utilizing data learnability as the principal criterion for the selection SFT data. This method provides a nuanced approach, allowing the alignment of data selection with inherent model capabilities, ensuring optimal compatibility and learning efficiency. In experimental comparisons involving 7B and 13B models, our LoBaSS method is able to surpass full-data fine-tuning at merely 6% of the total training data. When employing 16.7% of the data, LoBaSS harmonizes the model's capabilities across conversational and mathematical domains, proving its efficacy and adaptability.

We introduce LADDER (Learning through Autonomous Difficulty-Driven Example Recursion), a framework which enables Large Language Models to autonomously improve their problem-solving capabilities through self-guided learning by recursively generating and solving progressively simpler variants of complex problems. Unlike prior approaches that require curated datasets or human feedback, LADDER leverages a model's own capabilities to generate easier question variants. We demonstrate LADDER's effectiveness in the subject of mathematical integration, improving Llama 3.2 3B's accuracy from 1% to 82% on undergraduate-level problems and enabling Qwen2.5 7B Deepseek-R1 Distilled to achieve 73% on the MIT Integration Bee qualifying examination. We also introduce TTRL (Test-Time Reinforcement Learning), where we perform reinforcement learning on variants of test problems at inference time. TTRL enables Qwen2.5 7B Deepseek-R1 Distilled to achieve a state-of-the-art score of 90% on the MIT Integration Bee qualifying examination, surpassing OpenAI o1's performance. These results show how self-directed strategic learning can achieve significant capability improvements without relying on architectural scaling or human supervision.

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called "data-copying," was proposed by Meehan et. al. (2020). We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect data-copying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

We present an empirical evaluation of various outputs generated by nine of the most widely-available large language models (LLMs). Our analysis is done with off-the-shelf, readily-available tools. We find a correlation between percentage of memorized text, percentage of unique text, and overall output quality, when measured with respect to output pathologies such as counterfactual and logically-flawed statements, and general failures like not staying on topic. Overall, 80.0% of the outputs evaluated contained memorized data, but outputs containing the most memorized content were also more likely to be considered of high quality. We discuss and evaluate mitigation strategies, showing that, in the models evaluated, the rate of memorized text being output is reduced. We conclude with a discussion on potential implications around what it means to learn, to memorize, and to evaluate quality text.

O1/R1 style large reasoning models (LRMs) signal a substantial leap forward over conventional instruction-following LLMs. By applying test-time scaling to generate extended reasoning paths, they establish many SOTAs across a wide range of complex reasoning tasks. However, recent studies show that LRMs are prone to suffer from overthinking -- the tendency to overcomplicate simple problems, leading to excessive strategy switching and long, convoluted reasoning traces that hinder their interpretability. To mitigate this issue, we conduct a systematic investigation into the reasoning efficiency of a broad set of LRMs and uncover a common dilemma: the difficulty in balancing multiple generation objectives such as correctness and brevity. Based on this discovery, we propose a test-time scaling method, EDIT (Efficient Dynamic Inference Trimming), which efficiently guides LRMs to identify the shortest correct reasoning paths at test time. EDIT employs constraint-guided generation while jointly tracking length and answer distributions under varying constraints, allowing it to select responses that strike an optimal balance between conciseness and correctness. Extensive experiments across diverse models and datasets show that EDIT substantially enhance the reasoning efficiency, producing compact yet informative outputs that improve readability and user experience.

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.

With the increasing numbers of publicly available models, there are probably pretrained, online models for most tasks users require. However, current model search methods are rudimentary, essentially a text-based search in the documentation, thus users cannot find the relevant models. This paper presents ProbeLog, a method for retrieving classification models that can recognize a target concept, such as "Dog", without access to model metadata or training data. Differently from previous probing methods, ProbeLog computes a descriptor for each output dimension (logit) of each model, by observing its responses on a fixed set of inputs (probes). Our method supports both logit-based retrieval ("find more logits like this") and zero-shot, text-based retrieval ("find all logits corresponding to dogs"). As probing-based representations require multiple costly feedforward passes through the model, we develop a method, based on collaborative filtering, that reduces the cost of encoding repositories by 3x. We demonstrate that ProbeLog achieves high retrieval accuracy, both in real-world and fine-grained search tasks and is scalable to full-size repositories.

Recent Continual Learning (CL) methods have combined pretrained Transformers with prompt tuning, a parameter-efficient fine-tuning (PEFT) technique. We argue that the choice of prompt tuning in prior works was an undefended and unablated decision, which has been uncritically adopted by subsequent research, but warrants further research to understand its implications. In this paper, we conduct this research and find that the choice of prompt tuning as a PEFT method hurts the overall performance of the CL system. To illustrate this, we replace prompt tuning with LoRA in two state-of-the-art continual learning methods: Learning to Prompt and S-Prompts. These variants consistently achieve higher accuracy across a wide range of domain-incremental and class-incremental benchmarks, while being competitive in inference speed. Our work highlights a crucial argument: unexamined choices can hinder progress in the field, and rigorous ablations, such as the PEFT method, are required to drive meaningful adoption of CL techniques in real-world applications.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

We consider the problem of Recognizing Textual Entailment within an Information Retrieval context, where we must simultaneously determine the relevancy as well as degree of entailment for individual pieces of evidence to determine a yes/no answer to a binary natural language question. We compare several variants of neural networks for sentence embeddings in a setting of decision-making based on evidence of varying relevance. We propose a basic model to integrate evidence for entailment, show that joint training of the sentence embeddings to model relevance and entailment is feasible even with no explicit per-evidence supervision, and show the importance of evaluating strong baselines. We also demonstrate the benefit of carrying over text comprehension model trained on an unrelated task for our small datasets. Our research is motivated primarily by a new open dataset we introduce, consisting of binary questions and news-based evidence snippets. We also apply the proposed relevance-entailment model on a similar task of ranking multiple-choice test answers, evaluating it on a preliminary dataset of school test questions as well as the standard MCTest dataset, where we improve the neural model state-of-art.

As enthusiasm for scaling computation (data and parameters) in the pretraining era gradually diminished, test-time scaling (TTS), also referred to as ``test-time computing'' has emerged as a prominent research focus. Recent studies demonstrate that TTS can further elicit the problem-solving capabilities of large language models (LLMs), enabling significant breakthroughs not only in specialized reasoning tasks, such as mathematics and coding, but also in general tasks like open-ended Q&A. However, despite the explosion of recent efforts in this area, there remains an urgent need for a comprehensive survey offering a systemic understanding. To fill this gap, we propose a unified, multidimensional framework structured along four core dimensions of TTS research: what to scale, how to scale, where to scale, and how well to scale. Building upon this taxonomy, we conduct an extensive review of methods, application scenarios, and assessment aspects, and present an organized decomposition that highlights the unique functional roles of individual techniques within the broader TTS landscape. From this analysis, we distill the major developmental trajectories of TTS to date and offer hands-on guidelines for practical deployment. Furthermore, we identify several open challenges and offer insights into promising future directions, including further scaling, clarifying the functional essence of techniques, generalizing to more tasks, and more attributions.

Existing datasets that contain boolean questions, such as BoolQ and TYDI QA , provide the user with a YES/NO response to the question. However, a one word response is not sufficient for an explainable system. We promote explainability by releasing a new set of annotations marking the evidence in existing TyDi QA and BoolQ datasets. We show that our annotations can be used to train a model that extracts improved evidence spans compared to models that rely on existing resources. We confirm our findings with a user study which shows that our extracted evidence spans enhance the user experience. We also provide further insight into the challenges of answering boolean questions, such as passages containing conflicting YES and NO answers, and varying degrees of relevance of the predicted evidence.

Current large language models (LLMs) often struggle to produce accurate responses on the first attempt for complex reasoning tasks like code generation. Prior research tackles this challenge by generating multiple candidate solutions and validating them with LLM-generated unit tests. The execution results of unit tests serve as reward signals to identify correct solutions. As LLMs always confidently make mistakes, these unit tests are not reliable, thereby diminishing the quality of reward signals. Motivated by the observation that scaling the number of solutions improves LLM performance, we explore the impact of scaling unit tests to enhance reward signal quality. Our pioneer experiment reveals a positive correlation between the number of unit tests and reward signal quality, with greater benefits observed in more challenging problems. Based on these insights, we propose CodeRM-8B, a lightweight yet effective unit test generator that enables efficient and high-quality unit test scaling. Additionally, we implement a dynamic scaling mechanism that adapts the number of unit tests based on problem difficulty, further improving efficiency. Experimental results show that our approach significantly improves performance across various models on three benchmarks (e.g., with gains of 18.43% for Llama3-8B and 3.42% for GPT-4o-mini on HumanEval Plus).

In this paper, we propose a method to partially mimic natural intelligence for the problem of lifelong learning representations that are compatible. We take the perspective of a learning agent that is interested in recognizing object instances in an open dynamic universe in a way in which any update to its internal feature representation does not render the features in the gallery unusable for visual search. We refer to this learning problem as Compatible Lifelong Learning Representations (CL2R) as it considers compatible representation learning within the lifelong learning paradigm. We identify stationarity as the property that the feature representation is required to hold to achieve compatibility and propose a novel training procedure that encourages local and global stationarity on the learned representation. Due to stationarity, the statistical properties of the learned features do not change over time, making them interoperable with previously learned features. Extensive experiments on standard benchmark datasets show that our CL2R training procedure outperforms alternative baselines and state-of-the-art methods. We also provide novel metrics to specifically evaluate compatible representation learning under catastrophic forgetting in various sequential learning tasks. Code at https://github.com/NiccoBiondi/CompatibleLifelongRepresentation.

Large language models (LLMs) hold great potential for many natural language applications but risk generating incorrect or toxic content. To probe when an LLM generates unwanted content, the current paradigm is to recruit a red team of human testers to design input prompts (i.e., test cases) that elicit undesirable responses from LLMs. However, relying solely on human testers is expensive and time-consuming. Recent works automate red teaming by training a separate red team LLM with reinforcement learning (RL) to generate test cases that maximize the chance of eliciting undesirable responses from the target LLM. However, current RL methods are only able to generate a small number of effective test cases resulting in a low coverage of the span of prompts that elicit undesirable responses from the target LLM. To overcome this limitation, we draw a connection between the problem of increasing the coverage of generated test cases and the well-studied approach of curiosity-driven exploration that optimizes for novelty. Our method of curiosity-driven red teaming (CRT) achieves greater coverage of test cases while mantaining or increasing their effectiveness compared to existing methods. Our method, CRT successfully provokes toxic responses from LLaMA2 model that has been heavily fine-tuned using human preferences to avoid toxic outputs. Code is available at https://github.com/Improbable-AI/curiosity_redteam

When do machine learning systems fail to generalize, and what mechanisms could improve their generalization? Here, we draw inspiration from cognitive science to argue that one weakness of machine learning systems is their failure to exhibit latent learning -- learning information that is not relevant to the task at hand, but that might be useful in a future task. We show how this perspective links failures ranging from the reversal curse in language modeling to new findings on agent-based navigation. We then highlight how cognitive science points to episodic memory as a potential part of the solution to these issues. Correspondingly, we show that a system with an oracle retrieval mechanism can use learning experiences more flexibly to generalize better across many of these challenges. We also identify some of the essential components for effectively using retrieval, including the importance of within-example in-context learning for acquiring the ability to use information across retrieved examples. In summary, our results illustrate one possible contributor to the relative data inefficiency of current machine learning systems compared to natural intelligence, and help to understand how retrieval methods can complement parametric learning to improve generalization.

We present STARC (Structured Annotations for Reading Comprehension), a new annotation framework for assessing reading comprehension with multiple choice questions. Our framework introduces a principled structure for the answer choices and ties them to textual span annotations. The framework is implemented in OneStopQA, a new high-quality dataset for evaluation and analysis of reading comprehension in English. We use this dataset to demonstrate that STARC can be leveraged for a key new application for the development of SAT-like reading comprehension materials: automatic annotation quality probing via span ablation experiments. We further show that it enables in-depth analyses and comparisons between machine and human reading comprehension behavior, including error distributions and guessing ability. Our experiments also reveal that the standard multiple choice dataset in NLP, RACE, is limited in its ability to measure reading comprehension. 47% of its questions can be guessed by machines without accessing the passage, and 18% are unanimously judged by humans as not having a unique correct answer. OneStopQA provides an alternative test set for reading comprehension which alleviates these shortcomings and has a substantially higher human ceiling performance.

We propose a new shared task for tactical data-to-text generation in the domain of source code libraries. Specifically, we focus on text generation of function descriptions from example software projects. Data is drawn from existing resources used for studying the related problem of semantic parser induction (Richardson and Kuhn, 2017b; Richardson and Kuhn, 2017a), and spans a wide variety of both natural languages and programming languages. In this paper, we describe these existing resources, which will serve as training and development data for the task, and discuss plans for building new independent test sets.

Knowledge probing assesses to which degree a language model (LM) has successfully learned relational knowledge during pre-training. Probing is an inexpensive way to compare LMs of different sizes and training configurations. However, previous approaches rely on the objective function used in pre-training LMs and are thus applicable only to masked or causal LMs. As a result, comparing different types of LMs becomes impossible. To address this, we propose an approach that uses an LM's inherent ability to estimate the log-likelihood of any given textual statement. We carefully design an evaluation dataset of 7,731 instances (40,916 in a larger variant) from which we produce alternative statements for each relational fact, one of which is correct. We then evaluate whether an LM correctly assigns the highest log-likelihood to the correct statement. Our experimental evaluation of 22 common LMs shows that our proposed framework, BEAR, can effectively probe for knowledge across different LM types. We release the BEAR datasets and an open-source framework that implements the probing approach to the research community to facilitate the evaluation and development of LMs.

As large language models (LLMs) become increasingly versatile, numerous large scale benchmarks have been developed to thoroughly assess their capabilities. These benchmarks typically consist of diverse datasets and prompts to evaluate different aspects of LLM performance. However, comprehensive evaluations on hundreds or thousands of prompts incur tremendous costs in terms of computation, money, and time. In this work, we investigate strategies to improve evaluation efficiency by selecting a subset of examples from each benchmark using a learned policy. Our approach models the dependencies across test examples, allowing accurate prediction of the evaluation outcomes for the remaining examples based on the outcomes of the selected ones. Consequently, we only need to acquire the actual evaluation outcomes for the selected subset. We rigorously explore various subset selection policies and introduce a novel RL-based policy that leverages the captured dependencies. Empirical results demonstrate that our approach significantly reduces the number of evaluation prompts required while maintaining accurate performance estimates compared to previous methods.

In this work, we carry out a data archaeology to infer books that are known to ChatGPT and GPT-4 using a name cloze membership inference query. We find that OpenAI models have memorized a wide collection of copyrighted materials, and that the degree of memorization is tied to the frequency with which passages of those books appear on the web. The ability of these models to memorize an unknown set of books complicates assessments of measurement validity for cultural analytics by contaminating test data; we show that models perform much better on memorized books than on non-memorized books for downstream tasks. We argue that this supports a case for open models whose training data is known.

We demonstrate that LLMs may learn indicators of document usefulness and modulate their updates accordingly. We introduce random strings ("tags") as indicators of usefulness in a synthetic fine-tuning dataset. Fine-tuning on this dataset leads to implicit meta-learning (IML): in further fine-tuning, the model updates to make more use of text that is tagged as useful. We perform a thorough empirical investigation of this phenomenon, finding (among other things) that (i) it occurs in both pretrained LLMs and those trained from scratch, as well as on a vision task, and (ii) larger models and smaller batch sizes tend to give more IML. We also use probing to examine how IML changes the way models store knowledge in their parameters. Finally, we reflect on what our results might imply about capabilities, risks, and controllability of future AI systems. Our code can be found at https://github.com/krasheninnikov/internalization.

Large language models (LLMs) and multimodal LLMs (MLLMs) excel at chain-of-thought reasoning but face distribution shift at test-time and a lack of verifiable supervision. Recent test-time reinforcement learning (TTRL) methods derive label-free pseudo-rewards from self-consistency voting over sampled trajectories, yet they often collapse: the majority-vote reward prevails, responses shorten, and Pass@1 declines. We trace this to uniform sequence updates in which most tokens are low-entropy followers, while a small high-entropy subset determines the reasoning branches. Thus we propose SPINE, a token-selective test-time reinforcement learning framework that (i) updates only forking tokens, the high-entropy branch points identified from forward-pass statistics, and (ii) applies an entropy-band regularizer at those tokens to sustain exploration when entropy is too low and to suppress noisy supervision when it is too high. SPINE plugs into GRPO-style objectives, optionally with a KL anchor, and requires no labels or reward models. Across ten benchmarks spanning multimodal VQA, general and expert QA, mathematical reasoning, and medical QA, SPINE consistently improves Pass@1 over TTRL while avoiding response-length collapse and yielding more stable training dynamics on both LLM and MLLM backbones. These results indicate that aligning updates with chain-of-thought branch points is a simple and label-free mechanism for stable and effective test-time adaptation in reasoning models. Code is available at https://github.com/JianghaoWu/SPINE.

Large language models are able to perform a task by conditioning on a few input-output demonstrations - a paradigm known as in-context learning. We show that language models can explicitly infer an underlying task from a few demonstrations by prompting them to generate a natural language instruction that fits the examples. To explore this ability, we introduce the instruction induction challenge, compile a dataset consisting of 24 tasks, and define a novel evaluation metric based on executing the generated instruction. We discover that, to a large extent, the ability to generate instructions does indeed emerge when using a model that is both large enough and aligned to follow instructions; InstructGPT achieves 65.7% of human performance in our execution-based metric, while the original GPT-3 model reaches only 9.8% of human performance. This surprising result suggests that instruction induction might be a viable learning paradigm in and of itself, where instead of fitting a set of latent continuous parameters to the data, one searches for the best description in the natural language hypothesis space.

Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and scalable tools for fine-grained analysis. Existing benchmarks and datasets often lack the necessary variable control for multi-dimensional, systematic analysis and training, or have narrow problem types and formats. To address these limitations, we introduce SATQuest, a systematic verifier designed to evaluate and enhance logical reasoning in LLMs by generating diverse, Satisfiability-based logical reasoning problems directly from Conjunctive Normal Form (CNF) instances. SATQuest structures these problems along three orthogonal dimensions: instance scale, problem type, and question format, employing randomized, SAT-based problem generation and objective answer verification via PySAT. This design mitigates memorization issues, allows for nuanced insights into reasoning performance, and enables effective reinforcement fine-tuning. Our extensive evaluation of various LLMs using SATQuest identified significant limitations in their logical reasoning, particularly in generalizing beyond familiar mathematical formats. Furthermore, we show that reinforcement fine-tuning with SATQuest rewards substantially improves targeted task performance and generalizes to more complex instances, while highlighting remaining challenges in cross-format adaptation. Through these demonstrations, we showcase SATQuest's potential as a foundational tool and a valuable starting point for advancing LLM logical reasoning.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

The instruction learning paradigm -- where a model learns to perform new tasks from task descriptions alone -- has become popular in general-purpose model research. The capabilities of large transformer models as instruction learners, however, remain poorly understood. We use a controlled synthetic environment to characterize such capabilities. Specifically, we use the task of deciding whether a given string matches a regular expression (viewed as an instruction) to identify properties of tasks, instructions, and instances that make instruction learning challenging. For instance, we find that our model, a fine-tuned T5-based text2text transformer, struggles with large regular languages, suggesting that less precise instructions are challenging for models. Additionally, instruction executions that require tracking longer contexts of prior steps are also more difficult. We use our findings to systematically construct a challenging instruction learning dataset, which we call Hard RegSet. Fine-tuning on Hard RegSet, our large transformer learns to correctly interpret only 65.6% of test instructions (with at least 90% accuracy), and 11%-24% of the instructions in out-of-distribution generalization settings. We propose Hard RegSet as a challenging instruction learning task, and a controlled environment for studying instruction learning.

Large language models (LLMs) are revolutionizing education, with LLM-based agents playing a key role in simulating student behavior. A major challenge in student simulation is modeling the diverse learning patterns of students at various cognitive levels. However, current LLMs, typically trained as ``helpful assistants'', target at generating perfect responses. As a result, they struggle to simulate students with diverse cognitive abilities, as they often produce overly advanced answers, missing the natural imperfections that characterize student learning and resulting in unrealistic simulations. To address this issue, we propose a training-free framework for student simulation. We begin by constructing a cognitive prototype for each student using a knowledge graph, which captures their understanding of concepts from past learning records. This prototype is then mapped to new tasks to predict student performance. Next, we simulate student solutions based on these predictions and iteratively refine them using a beam search method to better replicate realistic mistakes. To validate our approach, we construct the Student\_100 dataset, consisting of 100 students working on Python programming and 5,000 learning records. Experimental results show that our method consistently outperforms baseline models, achieving 100% improvement in simulation accuracy.

Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1 exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1 with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1.

Interestingly, LLMs yet struggle with some basic tasks that humans find trivial to handle, e.g., counting the number of character r's in the word "strawberry". There are several popular conjectures (e.g., tokenization, architecture and training data) regarding the reason for deficiency of LLMs in simple word-based counting problems, sharing the similar belief that such failure stems from model pretraining hence probably inevitable during deployment. In this paper, we carefully design multiple evaluation settings to investigate validity of prevalent conjectures. Meanwhile, we measure transferability of advanced mathematical and coding reasoning capabilities from specialized LLMs to simple counting tasks. Although specialized LLMs suffer from counting problems as well, we find conjectures about inherent deficiency of LLMs invalid and further seek opportunities to elicit knowledge and capabilities from LLMs that are beneficial to counting tasks. Compared with strategies such as finetuning and in-context learning that are commonly adopted to enhance performance on new or challenging tasks, we show that engaging reasoning is the most robust and efficient way to help LLMs better perceive tasks with more accurate responses. We hope our conjecture validation design could provide insights into the study of future critical failure modes of LLMs. Based on challenges in transferring advanced capabilities to much simpler tasks, we call for more attention to model capability acquisition and evaluation. We also highlight the importance of cultivating consciousness of "reasoning before responding" during model pretraining.

Reasoning ability, a core component of human intelligence, continues to pose a significant challenge for Large Language Models (LLMs) in the pursuit of AGI. Although model performance has improved under the training scaling law, significant challenges remain, particularly with respect to training algorithms, such as catastrophic forgetting, and the limited availability of novel training data. As an alternative, test-time scaling enhances reasoning performance by increasing test-time computation without parameter updating. Unlike prior methods in this paradigm focused on token space, we propose leveraging latent space for more effective reasoning and better adherence to the test-time scaling law. We introduce LatentSeek, a novel framework that enhances LLM reasoning through Test-Time Instance-level Adaptation (TTIA) within the model's latent space. Specifically, LatentSeek leverages policy gradient to iteratively update latent representations, guided by self-generated reward signals. LatentSeek is evaluated on a range of reasoning benchmarks, including GSM8K, MATH-500, and AIME2024, across multiple LLM architectures. Results show that LatentSeek consistently outperforms strong baselines, such as Chain-of-Thought prompting and fine-tuning-based methods. Furthermore, our analysis demonstrates that LatentSeek is highly efficient, typically converging within a few iterations for problems of average complexity, while also benefiting from additional iterations, thereby highlighting the potential of test-time scaling in the latent space. These findings position LatentSeek as a lightweight, scalable, and effective solution for enhancing the reasoning capabilities of LLMs.

A machine learning system can score well on a given test set by relying on heuristics that are effective for frequent example types but break down in more challenging cases. We study this issue within natural language inference (NLI), the task of determining whether one sentence entails another. We hypothesize that statistical NLI models may adopt three fallible syntactic heuristics: the lexical overlap heuristic, the subsequence heuristic, and the constituent heuristic. To determine whether models have adopted these heuristics, we introduce a controlled evaluation set called HANS (Heuristic Analysis for NLI Systems), which contains many examples where the heuristics fail. We find that models trained on MNLI, including BERT, a state-of-the-art model, perform very poorly on HANS, suggesting that they have indeed adopted these heuristics. We conclude that there is substantial room for improvement in NLI systems, and that the HANS dataset can motivate and measure progress in this area

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Recent work has demonstrated that controlled pretraining experiments are a powerful tool for understanding learning, reasoning, and memorization in large language models (LLMs). However, the computational cost of pretraining presents a significant constraint. To overcome this constraint, we propose to conduct multiple pretraining experiments simultaneously during a single training run. We demonstrate the feasibility of this approach by conducting ten experiments during the training of a 1.5B parameter model on 210B tokens. Although we only train a single model, we can replicate the results from multiple previous works on data contamination, poisoning, and memorization. We also conduct novel investigations into knowledge acquisition, mathematical reasoning, and watermarking. For example, we dynamically update the training data until the model acquires a particular piece of knowledge. Remarkably, the influence of the ten experiments on the model's training dynamics and overall performance is minimal. However, interactions between different experiments may act as a potential confounder in our approach. We propose to test for interactions with continual pretraining experiments, finding them to be negligible in our setup. Overall, our findings suggest that performing multiple pretraining experiments in a single training run can enable rigorous scientific experimentation with large models on a compute budget.

Recent instruction-finetuned large language models (LMs) have achieved notable performances in various tasks, such as question-answering (QA). However, despite their ability to memorize a vast amount of general knowledge across diverse tasks, they might be suboptimal on specific tasks due to their limited capacity to transfer and adapt knowledge to target tasks. Moreover, further finetuning LMs with labeled datasets is often infeasible due to their absence, but it is also questionable if we can transfer smaller LMs having limited knowledge only with unlabeled test data. In this work, we show and investigate the capabilities of smaller self-adaptive LMs, only with unlabeled test data. In particular, we first stochastically generate multiple answers, and then ensemble them while filtering out low-quality samples to mitigate noise from inaccurate labels. Our proposed self-adaption strategy demonstrates significant performance improvements on benchmark QA datasets with higher robustness across diverse prompts, enabling LMs to stay stable. Code is available at: https://github.com/starsuzi/T-SAS.

Amid the expanding use of pre-training data, the phenomenon of benchmark dataset leakage has become increasingly prominent, exacerbated by opaque training processes and the often undisclosed inclusion of supervised data in contemporary Large Language Models (LLMs). This issue skews benchmark effectiveness and fosters potentially unfair comparisons, impeding the field's healthy development. To address this, we introduce a detection pipeline utilizing Perplexity and N-gram accuracy, two simple and scalable metrics that gauge a model's prediction precision on benchmark, to identify potential data leakages. By analyzing 31 LLMs under the context of mathematical reasoning, we reveal substantial instances of training even test set misuse, resulting in potentially unfair comparisons. These findings prompt us to offer several recommendations regarding model documentation, benchmark setup, and future evaluations. Notably, we propose the "Benchmark Transparency Card" to encourage clear documentation of benchmark utilization, promoting transparency and healthy developments of LLMs. we have made our leaderboard, pipeline implementation, and model predictions publicly available, fostering future research.

Language models typically need to be trained or finetuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this work, we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate kNN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. On benchmarks including code and mathematics, we find that the model is capable of making use of newly defined functions and theorems during test time.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

The rapid advancement of large language models (LLMs) demands robust, unbiased, and scalable evaluation methods. However, human annotations are costly to scale, model-based evaluations are susceptible to stylistic biases, and target-answer-based benchmarks are vulnerable to data contamination and cheating. To address these limitations, we propose StructTest, a novel benchmark that evaluates LLMs on their ability to follow compositional instructions and generate structured outputs, providing an unbiased, cost-effective, and difficult-to-cheat evaluation framework. Assessments are conducted deterministically using a rule-based evaluator, which can be easily extended to new tasks and datasets. By testing structured outputs across diverse domains including Summarization, Code, HTML, and Math, and evaluating 17 popular LLMs, we demonstrate that StructTest remains challenging even for top-performing models like Deepseek-V3/R1 and GPT-4o, establishing it as a robust proxy for measuring reasoning capabilities. We believe StructTest offers a critical and complementary approach to achieving objective and comprehensive model evaluation.

The focus of recent meta-learning research has been on the development of learning algorithms that can quickly adapt to test time tasks with limited data and low computational cost. Few-shot learning is widely used as one of the standard benchmarks in meta-learning. In this work, we show that a simple baseline: learning a supervised or self-supervised representation on the meta-training set, followed by training a linear classifier on top of this representation, outperforms state-of-the-art few-shot learning methods. An additional boost can be achieved through the use of self-distillation. This demonstrates that using a good learned embedding model can be more effective than sophisticated meta-learning algorithms. We believe that our findings motivate a rethinking of few-shot image classification benchmarks and the associated role of meta-learning algorithms. Code is available at: http://github.com/WangYueFt/rfs/.

Long-context reasoning requires accurately identifying relevant information in extensive, noisy input contexts. Previous research shows that using test-time learning to encode context directly into model parameters can effectively enable reasoning over noisy information. However, meta-learning methods for enabling test-time learning are prohibitively memory-intensive, preventing their application to long context settings. In this work, we propose PERK (Parameter Efficient Reasoning over Knowledge), a scalable approach for learning to encode long input contexts using gradient updates to a lightweight model adapter at test time. Specifically, PERK employs two nested optimization loops in a meta-training phase. The inner loop rapidly encodes contexts into a low-rank adapter (LoRA) that serves as a parameter-efficient memory module for the base model. Concurrently, the outer loop learns to use the updated adapter to accurately recall and reason over relevant information from the encoded long context. Our evaluations on several long-context reasoning tasks show that PERK significantly outperforms the standard prompt-based long-context baseline, achieving average absolute performance gains of up to 90% for smaller models (GPT-2) and up to 27% for our largest evaluated model, Qwen-2.5-0.5B. In general, PERK is more robust to reasoning complexity, length extrapolation, and the locations of relevant information in contexts. Finally, we show that while PERK is memory-intensive during training, it scales more efficiently at inference time than prompt-based long-context inference.

Context: Test-driven development (TDD) is a widely employed software development practice that involves developing test cases based on requirements prior to writing the code. Although various methods for automated test case generation have been proposed, they are not specifically tailored for TDD, where requirements instead of code serve as input. Objective: In this paper, we introduce a text-to-testcase generation approach based on a large language model (GPT-3.5) that is fine-tuned on our curated dataset with an effective prompt design. Method: Our approach involves enhancing the capabilities of basic GPT-3.5 for text-to-testcase generation task that is fine-tuned on our curated dataset with an effective prompting design. We evaluated the effectiveness of our approach using a span of five large-scale open-source software projects. Results: Our approach generated 7k test cases for open source projects, achieving 78.5% syntactic correctness, 67.09% requirement alignment, and 61.7% code coverage, which substantially outperforms all other LLMs (basic GPT-3.5, Bloom, and CodeT5). In addition, our ablation study demonstrates the substantial performance improvement of the fine-tuning and prompting components of the GPT-3.5 model. Conclusions: These findings lead us to conclude that fine-tuning and prompting should be considered in the future when building a language model for the text-to-testcase generation task

Competitive programming, due to its high reasoning difficulty and precise correctness feedback, has become a key task for both training and evaluating the reasoning capabilities of large language models (LLMs). However, while a large amount of public problem data, such as problem statements and solutions, is available, the test cases of these problems are often difficult to obtain. Therefore, test case generation is a necessary task for building large-scale datasets, and the quality of the test cases directly determines the accuracy of the evaluation. In this paper, we introduce an LLM-based agent system that creates high-quality test cases for competitive programming problems. We apply this system to the CodeContests dataset and propose a new version with improved test cases, named CodeContests+. We evaluated the quality of test cases in CodeContestsPlus. First, we used 1.72 million submissions with pass/fail labels to examine the accuracy of these test cases in evaluation. The results indicated that CodeContests+ achieves significantly higher accuracy than CodeContests, particularly with a notably higher True Positive Rate (TPR). Subsequently, our experiments in LLM Reinforcement Learning (RL) further confirmed that improvements in test case quality yield considerable advantages for RL.

Recent advancements in language modeling have enabled the translation of natural language into code, and the use of execution feedback to improve code generation. However, these methods often rely heavily on pre-existing test cases, which may not always be available or comprehensive. In this work, we propose a novel approach that concurrently trains a code generation model and a test generation model, utilizing execution feedback to refine and enhance the performance of both. We introduce two strategies for test and code data augmentation and a new scoring function for code and test ranking. We experiment on the APPS dataset and demonstrate that our approach can effectively generate and augment test cases, filter and synthesize correct code solutions, and rank the quality of generated code and tests. The results demonstrate that our models, when iteratively trained with an increasing number of test cases and code solutions, outperform those trained on the original dataset.

We introduce transductive program synthesis, a new formulation of the program synthesis task that explicitly leverages test inputs during synthesis. While prior approaches to program synthesis--whether based on natural language descriptions or input-output examples--typically aim to generalize from training examples, they often struggle with robustness, especially in real-world settings where training examples are limited and test inputs involve various edge cases. To address this, we propose a novel framework that improves robustness by treating synthesis as an active learning over a finite hypothesis class defined by programs' outputs. We use an LLM to predict outputs for selected test inputs and eliminate inconsistent hypotheses, where the inputs are chosen via a greedy maximin algorithm to minimize the number of LLM queries required. We evaluate our approach on four benchmarks: Playgol, MBPP+, 1D-ARC, and programmatic world modeling on MiniGrid. We demonstrate that our method significantly improves program synthesis in both accuracy and efficiency. We release our code at https://github.com/klee972/SYNTRA.

Recent advancements in Large Language Models (LLMs) have created new opportunities to enhance performance on complex reasoning tasks by leveraging test-time computation. However, conventional approaches such as repeated sampling with majority voting or reward model scoring, often face diminishing returns as test-time compute scales, in addition to requiring costly task-specific reward model training. In this paper, we present Self-Enhanced Test-Time Scaling (SETS), a novel method that leverages the self-verification and self-correction capabilities of recent advanced LLMs to overcome these limitations. SETS integrates sampling, self-verification, and self-correction into a unified framework, enabling efficient and scalable test-time computation for improved capabilities at complex tasks. Through extensive experiments on challenging planning and reasoning benchmarks, compared to the alternatives, we demonstrate that SETS achieves significant performance improvements and more favorable test-time scaling laws.

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves 94.21% of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves 92.04 % of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

Instruction-following is a fundamental capability of language models, requiring the model to recognize even the most subtle requirements in the instructions and accurately reflect them in its output. Such an ability is well-suited for and often optimized by preference learning. However, existing methods often directly sample multiple independent responses from the model when creating preference pairs. Such practice can introduce content variations irrelevant to whether the instruction is precisely followed (e.g., different expressions about the same semantic), interfering with the goal of teaching models to recognize the key differences that lead to improved instruction following. In light of this, we introduce SPaR, a self-play framework integrating tree-search self-refinement to yield valid and comparable preference pairs free from distractions. By playing against itself, an LLM employs a tree-search strategy to refine its previous responses with respect to the instruction while minimizing unnecessary variations. Our experiments show that a LLaMA3-8B model, trained over three iterations guided by SPaR, surpasses GPT-4-Turbo on the IFEval benchmark without losing general capabilities. Furthermore, SPaR demonstrates promising scalability and transferability, greatly enhancing models like GLM-4-9B and LLaMA3-70B. We also identify how inference scaling in tree search would impact model performance. Our code and data are publicly available at https://github.com/thu-coai/SPaR.

Neural Conversational QA tasks like ShARC require systems to answer questions based on the contents of a given passage. On studying recent state-of-the-art models on the ShARCQA task, we found indications that the models learn spurious clues/patterns in the dataset. Furthermore, we show that a heuristic-based program designed to exploit these patterns can have performance comparable to that of the neural models. In this paper we share our findings about four types of patterns found in the ShARC corpus and describe how neural models exploit them. Motivated by the aforementioned findings, we create and share a modified dataset that has fewer spurious patterns, consequently allowing models to learn better.

Recent years have witnessed a surge in the number of large language models (LLMs), yet efficiently managing and utilizing these vast resources remains a significant challenge. In this work, we explore how to learn compact representations of LLM abilities that can facilitate downstream tasks, such as model routing and performance prediction on new benchmarks. We frame this problem as estimating the probability that a given model will correctly answer a specific query. Inspired by the item response theory (IRT) in psychometrics, we model this probability as a function of three key factors: (i) the model's multi-skill ability vector, (2) the query's discrimination vector that separates models of differing skills, and (3) the query's difficulty scalar. To learn these parameters jointly, we introduce a Mixture-of-Experts (MoE) network that couples model- and query-level embeddings. Extensive experiments demonstrate that our approach leads to state-of-the-art performance in both model routing and benchmark accuracy prediction. Moreover, analysis validates that the learned parameters encode meaningful, interpretable information about model capabilities and query characteristics.

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Tree search has become as a representative framework for test-time reasoning with large language models (LLMs), exemplified by methods such as Tree-of-Thought and Monte Carlo Tree Search that explore multiple reasoning paths. However, it remains difficult to provide instant and reliable quantitative assessments of intermediate reasoning step quality, and extensive path exploration is computationally costly. To address this, we propose Mutual Information Tree Search (MITS), a novel framework that guides reasoning with information-theoretic principles. MITS introduces an effective scoring function based on pointwise mutual information (PMI), which enables step-wise evaluation of reasoning paths and search tree expansion via beam search without expensive look-ahead simulations, achieving superior reasoning performances while maintaining computational efficiency. The framework is complemented by an entropy-based dynamic sampling strategy that adaptively allocates computational resources to uncertain reasoning steps where exploration is most beneficial. For final prediction, MITS employs a weighted voting scheme that combines PMI scores with prediction consensus. Through comprehensive experiments on diverse reasoning benchmarks, MITS consistently surpasses baseline methods, establishing a principled and efficient framework for LLM reasoning.

Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on benchmarking practices that lack transparency, robustness, or statistical grounding. In this work, we conduct a comprehensive empirical study and find that current mathematical reasoning benchmarks are highly sensitive to subtle implementation choices - including decoding parameters, random seeds, prompt formatting, and even hardware and software-framework configurations. Performance gains reported in recent studies frequently hinge on unclear comparisons or unreported sources of variance. To address these issues, we propose a standardized evaluation framework with clearly defined best practices and reporting standards. Using this framework, we reassess recent methods and find that reinforcement learning (RL) approaches yield only modest improvements - far below prior claims - and are prone to overfitting, especially on small-scale benchmarks like AIME24. In contrast, supervised finetuning (SFT) methods show consistently stronger generalization. To foster reproducibility, we release all code, prompts, and model outputs, for reasoning benchmarks, establishing more rigorous foundations for future work.

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

Test-time scaling has emerged as a powerful technique for enhancing the reasoning capabilities of large language models. However, its effectiveness in medical reasoning remains uncertain, as the medical domain fundamentally differs from mathematical tasks in terms of knowledge representation and decision-making processes. In this paper, we provide the first comprehensive investigation of test-time scaling for medical reasoning and present m1, a simple yet effective approach that increases a model's medical reasoning capability at inference. Our evaluation across diverse medical tasks demonstrates that test-time scaling consistently enhances medical reasoning, enabling lightweight fine-tuned models under 10B parameters to establish new state-of-the-art performance, while our 32B model rivals previous 70B-scale medical LLMs. However, we identify an optimal reasoning token budget of approximately 4K, beyond which performance may degrade due to overthinking. Budget forcing, which extends test-time computation through iterative prompts, helps models double-check answers but does not necessarily improve the overall medical QA performance and, in some cases, even introduces errors into previously correct responses. Our case-by-case analysis identifies insufficient medical knowledge as a key bottleneck that prevents further performance gains through test-time scaling. We find that increasing data scale, improving data quality, and expanding model capacity consistently enhance medical knowledge grounding, enabling continued performance improvements, particularly on challenging medical benchmarks where smaller models reach saturation. These findings underscore fundamental differences between medical and mathematical reasoning in LLMs, highlighting that enriched medical knowledge, other than increased reasoning depth alone, is essential for realizing the benefits of test-time scaling.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Meta-learning researchers face two fundamental issues in their empirical work: prototyping and reproducibility. Researchers are prone to make mistakes when prototyping new algorithms and tasks because modern meta-learning methods rely on unconventional functionalities of machine learning frameworks. In turn, reproducing existing results becomes a tedious endeavour -- a situation exacerbated by the lack of standardized implementations and benchmarks. As a result, researchers spend inordinate amounts of time on implementing software rather than understanding and developing new ideas. This manuscript introduces learn2learn, a library for meta-learning research focused on solving those prototyping and reproducibility issues. learn2learn provides low-level routines common across a wide-range of meta-learning techniques (e.g. meta-descent, meta-reinforcement learning, few-shot learning), and builds standardized interfaces to algorithms and benchmarks on top of them. In releasing learn2learn under a free and open source license, we hope to foster a community around standardized software for meta-learning research.

Most positive and unlabeled data is subject to selection biases. The labeled examples can, for example, be selected from the positive set because they are easier to obtain or more obviously positive. This paper investigates how learning can be ena BHbled in this setting. We propose and theoretically analyze an empirical-risk-based method for incorporating the labeling mechanism. Additionally, we investigate under which assumptions learning is possible when the labeling mechanism is not fully understood and propose a practical method to enable this. Our empirical analysis supports the theoretical results and shows that taking into account the possibility of a selection bias, even when the labeling mechanism is unknown, improves the trained classifiers.

Unit testing is a core practice in programming, enabling systematic evaluation of programs produced by human developers or large language models (LLMs). Given the challenges in writing comprehensive unit tests, LLMs have been employed to automate test generation, yet methods for training LLMs to produce high-quality tests remain underexplored. In this work, we propose UTRL, a novel reinforcement learning framework that trains an LLM to generate high-quality unit tests given a programming instruction. Our key idea is to iteratively train two LLMs, the unit test generator and the code generator, in an adversarial manner via reinforcement learning. The unit test generator is trained to maximize a discrimination reward, which reflects its ability to produce tests that expose faults in the code generator's solutions, and the code generator is trained to maximize a code reward, which reflects its ability to produce solutions that pass the unit tests generated by the test generator. In our experiments, we demonstrate that unit tests generated by Qwen3-4B trained via UTRL show higher quality compared to unit tests generated by the same model trained via supervised fine-tuning on human-written ground-truth unit tests, yielding code evaluations that more closely align with those induced by the ground-truth tests. Moreover, Qwen3-4B trained with UTRL outperforms frontier models such as GPT-4.1 in generating high-quality unit tests, highlighting the effectiveness of UTRL in training LLMs for this task.

Test-time prompt tuning enhances zero-shot generalization of vision-language models but tends to ignore the relatedness among test samples during inference. Online test-time prompt tuning provides a simple way to leverage the information in previous test samples, albeit with the risk of prompt collapse due to error accumulation. To enhance test-time prompt tuning, we propose DynaPrompt, short for dynamic test-time prompt tuning, exploiting relevant data distribution information while reducing error accumulation. Built on an online prompt buffer, DynaPrompt adaptively selects and optimizes the relevant prompts for each test sample during tuning. Specifically, we introduce a dynamic prompt selection strategy based on two metrics: prediction entropy and probability difference. For unseen test data information, we develop dynamic prompt appending, which allows the buffer to append new prompts and delete the inactive ones. By doing so, the prompts are optimized to exploit beneficial information on specific test data, while alleviating error accumulation. Experiments on fourteen datasets demonstrate the effectiveness of dynamic test-time prompt tuning.

A central notion in practical and theoretical machine learning is that of a weak learner, classifiers that achieve better-than-random performance (on any given distribution over data), even by a small margin. Such weak learners form the practical basis for canonical machine learning methods such as boosting. In this work, we illustrate that prompt-based large language models can operate effectively as said weak learners. Specifically, we illustrate the use of a large language model (LLM) as a weak learner in a boosting algorithm applied to tabular data. We show that by providing (properly sampled according to the distribution of interest) text descriptions of tabular data samples, LLMs can produce a summary of the samples that serves as a template for classification and achieves the aim of acting as a weak learner on this task. We incorporate these models into a boosting approach, which in some settings can leverage the knowledge within the LLM to outperform traditional tree-based boosting. The model outperforms both few-shot learning and occasionally even more involved fine-tuning procedures, particularly for tasks involving small numbers of data points. The results illustrate the potential for prompt-based LLMs to function not just as few-shot learners themselves, but as components of larger machine learning pipelines.