Logical reasoning is needed in a wide range of NLP tasks. Can a BERT model be trained end-to-end to solve logical reasoning problems presented in natural language? We attempt to answer this question in a confined problem space where there exists a set of parameters that perfectly simulates logical reasoning. We make observations that seem to contradict each other: BERT attains near-perfect accuracy on in-distribution test examples while failing to generalize to other data distributions over the exact same problem space. Our study provides an explanation for this paradox: instead of learning to emulate the correct reasoning function, BERT has in fact learned statistical features that inherently exist in logical reasoning problems. We also show that it is infeasible to jointly remove statistical features from data, illustrating the difficulty of learning to reason in general. Our result naturally extends to other neural models and unveils the fundamental difference between learning to reason and learning to achieve high performance on NLP benchmarks using statistical features.
On the Paradox of Learning to Reason from Data
Logical reasoning is needed in a wide range of NLP tasks. Can a BERT model be trained end-to-end to solve logical reasoning problems presented in natural language? We attempt to answer this...
Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.
Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.
Cognitive Episodes in LLM Reasoning Traces Enable Interpretable Human Item Difficulty Prediction
Predicting item difficulty is a central challenge in educational assessment, where accurate estimates are critical for fairness and effective test construction. Existing methods are either expensive to scale or limited in predictive power, even with recent Large Language Model(LLM) related methods. Meanwhile, Large Reasoning Models (LRMs) expose detailed reasoning traces that resemble human problem solving, creating new opportunities for difficulty modeling. We propose a new perspective that treats item difficulty as an observable consequence of problem-solving burden. Building on this formulation, we introduce a structured framework that converts LRM reasoning traces into sentence-level episode sequences using a cognitively grounded taxonomy and then derives compact process features for downstream prediction, which is named Epi2Diff (Episode to Difficulty). This produces a structured process-based representation of each assessment item. Across four real-world human difficulty datasets, our method consistently outperforms various methods, including fine-tuning small encoder-only language models, LLM In-Context Learning, and LLM Supervised Finetuning with full parameters or LoRA. Epi2Diff delivers an 8.0% relative gain in classification and a 24.4% reduction in RMSE for regression against strong baselines. We also find that harder items are associated with more effortful and iterative reasoning dynamics. Moreover, our method not only predicts the difficulty value, but it also provides a new perspective on the explanation of the predicted difficulty based on the episode transition of LRM responses. These results suggest that structured reasoning dynamics are both predictive and interpretable, and provide a new lens for understanding the utility of LRMs in educational measurement.
Climbing towards NLU: On Meaning, Form, and Understanding in the Age of Data
The success of the large neural language models on many NLP tasks is exciting. However, we find that these successes sometimes lead to hype in which these models are being described as “understanding” language or capturing “meaning”. In this position paper, we argue that a system trained only on form has a priori no way to learn meaning. In keeping with the ACL 2020 theme of “Taking Stock of Where We've Been and Where We're Going”, we argue that a clear understanding of the distinction between form and meaning will help guide the field towards better science around natural language understanding.
Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning
As large language models (LLMs) continue to advance, many existing benchmarks designed to evaluate their reasoning capabilities are becoming saturated. Therefore, we present the Putnam-AXIOM Original benchmark consisting of 236 mathematical problems from the William Lowell Putnam Mathematical Competition, along with detailed step-by-step solutions. To preserve the Putnam-AXIOM benchmark's validity and mitigate potential data contamination, we created the Putnam-AXIOM Variation benchmark with functional variations of 52 problems. By programmatically altering problem elements like variables and constants, we can generate unlimited novel, equally challenging problems not found online. We see that almost all models have significantly lower accuracy in the variations than the original problems. Our results reveal that OpenAI's o1-preview, the best performing model, achieves merely 41.95\% accuracy on the Putnam-AXIOM Original but experiences around a 30\% reduction in accuracy on the variations' dataset when compared to corresponding original problems.
Rethinking the Multilingual Reasoning Gap with Layer Swap
Recent reasoning Large Language Models produce a chain-of-thought (CoT) predominantly in English, even when prompted in non-English languages. Prior work suggests that forcing the CoT to remain in the input language (\emph{native reasoning}) substantially degrades performance relative to allowing the model to reason in English before answering in the input language (\emph{English-pivoted reasoning}). However, most studies of this native reasoning gap rely on inference-time interventions or limited native-language training data. We revisit this comparison at a larger scale and under comparable supervision. We construct long multilingual reasoning datasets across six languages (English, French, German, Spanish, Chinese and Swahili); fine-tune specialists in both native and English-pivoted regimes on top of \texttt{Qwen/Qwen3-8B-Base}, and evaluate across mathematics, science, general knowledge, and code. In this setting, the average native reasoning gap shrinks to 1.9--3.5\% across the five non-English languages, considerably smaller than previously reported. Weight-space analysis of the native specialists reveals aligned fine-tuning updates in the middle layers and divergence in the outer layers. This points to a largely language-agnostic reasoning core surrounded by language-specific layers. Exploiting this structure, we introduce a Layer Swap: transferring the English specialist's stronger reasoning mid-layers into each native specialist, closing most of the native reasoning gap across the five non-English languages while preserving CoT in the target language. We release all models and datasets.
Eliciting Reasoning in Language Models with Cognitive Tools
The recent advent of reasoning models like OpenAI's o1 was met with excited speculation by the AI community about the mechanisms underlying these capabilities in closed models, followed by a rush of replication efforts, particularly from the open source community. These speculations were largely settled by the demonstration from DeepSeek-R1 that chains-of-thought and reinforcement learning (RL) can effectively replicate reasoning on top of base LLMs. However, it remains valuable to explore alternative methods for theoretically eliciting reasoning that could help elucidate the underlying mechanisms, as well as providing additional methods that may offer complementary benefits. Here, we build on the long-standing literature in cognitive psychology and cognitive architectures, which postulates that reasoning arises from the orchestrated, sequential execution of a set of modular, predetermined cognitive operations. Crucially, we implement this key idea within a modern agentic tool-calling framework. In particular, we endow an LLM with a small set of "cognitive tools" encapsulating specific reasoning operations, each executed by the LLM itself. Surprisingly, this simple strategy results in considerable gains in performance on standard mathematical reasoning benchmarks compared to base LLMs, for both closed and open-weight models. For instance, providing our "cognitive tools" to GPT-4.1 increases its pass@1 performance on AIME2024 from 32% to 53%, even surpassing the performance of o1-preview. In addition to its practical implications, this demonstration contributes to the debate regarding the role of post-training methods in eliciting reasoning in LLMs versus the role of inherent capabilities acquired during pre-training, and whether post-training merely uncovers these latent abilities.
Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer
Transfer learning, where a model is first pre-trained on a data-rich task before being fine-tuned on a downstream task, has emerged as a powerful technique in natural language processing (NLP). The effectiveness of transfer learning has given rise to a diversity of approaches, methodology, and practice. In this paper, we explore the landscape of transfer learning techniques for NLP by introducing a unified framework that converts all text-based language problems into a text-to-text format. Our systematic study compares pre-training objectives, architectures, unlabeled data sets, transfer approaches, and other factors on dozens of language understanding tasks. By combining the insights from our exploration with scale and our new “Colossal Clean Crawled Corpus”, we achieve state-of-the-art results on many benchmarks covering summarization, question answering, text classification, and more. To facilitate future work on transfer learning for NLP, we release our data set, pre-trained models, and code.
Performative Thinking? The Brittle Correlation Between CoT Length and Problem Complexity
Intermediate token generation (ITG), where a model produces output before the solution, has been proposed as a method to improve the performance of language models on reasoning tasks. While these reasoning traces or Chain of Thoughts (CoTs) are correlated with performance gains, the mechanisms underlying them remain unclear. A prevailing assumption in the community has been to anthropomorphize these tokens as "thinking", treating longer traces as evidence of higher problem-adaptive computation. In this work, we critically examine whether intermediate token sequence length reflects or correlates with problem difficulty. To do so, we train transformer models from scratch on derivational traces of the A* search algorithm, where the number of operations required to solve a maze problem provides a precise and verifiable measure of problem complexity. We first evaluate the models on trivial free-space problems, finding that even for the simplest tasks, they often produce excessively long reasoning traces and sometimes fail to generate a solution. We then systematically evaluate the model on out-of-distribution problems and find that the intermediate token length and ground truth A* trace length only loosely correlate. We notice that the few cases where correlation appears are those where the problems are closer to the training distribution, suggesting that the effect arises from approximate recall rather than genuine problem-adaptive computation. This suggests that the inherent computational complexity of the problem instance is not a significant factor, but rather its distributional distance from the training data. These results challenge the assumption that intermediate trace generation is adaptive to problem difficulty and caution against interpreting longer sequences in systems like R1 as automatically indicative of "thinking effort".
Performative Thinking? The Brittle Correlation Between CoT Length and Problem Complexity
Intermediate token generation (ITG), where a model produces output before the solution, has been proposed as a method to improve the performance of language models on reasoning tasks. While these reasoning traces or Chain of Thoughts (CoTs) are correlated with performance gains, the mechanisms underlying them remain unclear. A prevailing assumption in the community has been to anthropomorphize these tokens as "thinking", treating longer traces as evidence of higher problem-adaptive computation. In this work, we critically examine whether intermediate token sequence length reflects or correlates with problem difficulty. To do so, we train transformer models from scratch on derivational traces of the A* search algorithm, where the number of operations required to solve a maze problem provides a precise and verifiable measure of problem complexity. We first evaluate the models on trivial free-space problems, finding that even for the simplest tasks, they often produce excessively long reasoning traces and sometimes fail to generate a solution. We then systematically evaluate the model on out-of-distribution problems and find that the intermediate token length and ground truth A* trace length only loosely correlate. We notice that the few cases where correlation appears are those where the problems are closer to the training distribution, suggesting that the effect arises from approximate recall rather than genuine problem-adaptive computation. This suggests that the inherent computational complexity of the problem instance is not a significant factor, but rather its distributional distance from the training data. These results challenge the assumption that intermediate trace generation is adaptive to problem difficulty and caution against interpreting longer sequences in systems like R1 as automatically indicative of "thinking effort".
Measuring short-form factuality in large language models
We present SimpleQA, a benchmark that evaluates the ability of language models to answer short, fact-seeking questions. We prioritized two properties in designing this eval. First, SimpleQA is challenging, as it is adversarially collected against GPT-4 responses. Second, responses are easy to grade, because questions are created such that there exists only a single, indisputable answer. Each answer in SimpleQA is graded as either correct, incorrect, or not attempted. A model with ideal behavior would get as many questions correct as possible while not attempting the questions for which it is not confident it knows the correct answer. SimpleQA is a simple, targeted evaluation for whether models "know what they know," and our hope is that this benchmark will remain relevant for the next few generations of frontier models. SimpleQA can be found at https://github.com/openai/simple-evals.
Measuring short-form factuality in large language models
We present SimpleQA, a benchmark that evaluates the ability of language models to answer short, fact-seeking questions. We prioritized two properties in designing this eval. First, SimpleQA is challenging, as it is adversarially collected against GPT-4 responses. Second, responses are easy to grade, because questions are created such that there exists only a single, indisputable answer. Each answer in SimpleQA is graded as either correct, incorrect, or not attempted. A model with ideal behavior would get as many questions correct as possible while not attempting the questions for which it is not confident it knows the correct answer. SimpleQA is a simple, targeted evaluation for whether models "know what they know," and our hope is that this benchmark will remain relevant for the next few generations of frontier models. SimpleQA can be found at https://github.com/openai/simple-evals.
The LLM Reasoning Debate Heats Up
Three recent papers examine the robustness of reasoning and problem-solving in large language models
Do Large Language Models Perform the Way People Expect? Measuring the Human Generalization Function
What makes large language models (LLMs) impressive is also what makes them hard to evaluate: their diversity of uses. To evaluate these models, we must understand the purposes they will be used for. We consider a setting where these deployment decisions are made by people, and in particular, people's beliefs about where an LLM will perform well. We model such beliefs as the consequence of a human generalization function: having seen what an LLM gets right or wrong, people generalize to where else it might succeed. We collect a dataset of 19K examples of how humans make generalizations across 79 tasks from the MMLU and BIG-Bench benchmarks. We show that the human generalization function can be predicted using NLP methods: people have consistent structured ways to generalize. We then evaluate LLM alignment with the human generalization function. Our results show that -- especially for cases where the cost of mistakes is high -- more capable models (e.g. GPT-4) can do worse on the instances people choose to use them for, exactly because they are not aligned with the human generalization function.
ICML Poster Learning syntax without semantics: Disentangled tiny language models
Language models acquire syntax and world knowledge together, entangling the two in ways that limit efficiency and controllability. We show that syntax can be learned while suppressing semantic plausibility and world‑knowledge cues, yielding more efficient and controllable models. We train tiny LMs on grammatical nonsense — syntactically well-formed text with semantic content ablated via constrained relexicalization (SAMBAL). Models trained on this data perform comparably to standard pretraining on syntactic benchmarks (BLiMP, SyntaxGym) while scoring at chance on world knowledge probes (EWoK). On targeted grammar-plausibility conflict probes, content-neutral models prefer grammaticality where standard models prefer plausibility, and their representations show more syntactic vs lexical alignment. On efficiency, disentanglement yields substantial sample and parameter gains: in low‑resource regimes, a 5M‑parameter model matches a 30M‑parameter baseline at the same data budget. On controllability, content-neutral models adapt rapidly to a new domain with minimal exposure, suggesting the feasibility of modular post‑hoc knowledge specialization.