arXiv subjects

Noah D. Goodman

Publications and source records attributed to Noah D. Goodman.

At least 19 recordsLinked to original sources

arXiv2026

QuasiMoTTo: Quasi-Monte Carlo Test-Time Scaling

Scaling inference compute, by generating many parallel attempts per problem, is a costly but reliable lever for improving language model capabilities. By default these attempts are generated independently, wasting inference compute on redundant solutions. This waste seems unavoidable. After all, independence is what makes parallel sampling trivial to scale. However, this tradeoff is not fundamental: there is a rich design space of samplers that generate correlated but exact samples entirely in parallel. We explore this design space as an avenue for improving sample efficiency in scaling inference compute and reinforcement learning (RL). Concretely, we introduce QuasiMoTTo, which uses correlated samples as a drop-in replacement for i.i.d. samples. To generate these samples, QuasiMoTTo uses a reparameterization of autoregressive sampling as inverse-CDF sampling and draws the underlying uniforms with quasi-Monte Carlo (QMC); because QMC spreads the uniforms out more evenly than i.i.d., the resulting samples cover the output space with far less redundancy. Even though the batch is correlated, each sample is marginally distributed according to the language model, so we can use the batch for policy-gradient training. Our empirical analysis focuses on understanding how efficiently QuasiMoTTo can turn compute into performance. To evaluate correlated samplers, whose dependence breaks standard pass@k estimators, we first develop an unbiased bootstrap estimator. Across four reasoning benchmarks, QuasiMoTTo matches i.i.d. pass@k accuracy with 25-47% fewer samples. Strikingly, QuasiMoTTo often saturates an upper bound on pass@k that holds for any marginal-preserving sampler. We also apply QuasiMoTTo to policy-gradient RL (GRPO) where it matches i.i.d. performance with 50% fewer training steps. These gains come from higher coverage, which yields a stronger learning signal per batch.

cs.LG↗

arXiv2026

auto-psych: Automating the science of mind using agent-driven theory discovery and experimentation

AI-based scientific automation is increasingly possible by using agents to generate hypotheses, design experiments, and analyze data. Data collection is a major bottleneck in this pipeline, however. Psychology, and computational cognitive science in particular, is well-positioned to benefit from AI experimentation because theories are often represented as code and crowdsourcing platforms enable programmatic human data collection at scale. Here, we apply automated discovery techniques to the project of generating theories in computational cognitive science, with an agent-based system collecting human data independently through crowdsourced survey experiments. As a testbed, we use a classic case study from cognitive psychology: judging which sequences of coin flips seem subjectively more random. Our system, auto-psych, uses nested agent-based discovery loops to generate explanatory theories of human behavior. The inner loop conjectures, fits, and critiques probabilistic cognitive models; the outer loop designs experiments to test these models, launches them online, and analyzes the data. This system can quickly and reliably recover ground-truth theories from synthetic data via systematic experimentation, but the nested structure is critical to model performance. Further, in three independent sequences of human experiments, the system finds theories that fit the data better than theories generated from the scientific literature. This work thus demonstrates the feasibility of automated data collection and theory discovery in computational cognitive science.

cs.AI↗

arXiv2026

CORE: Contrastive Reflection Enables Rapid Improvements in Reasoning

Language models can use verifiable rewards to improve at a wide variety of reasoning tasks. However, both parametric (e.g. RLVR) and non-parametric (e.g. prompt optimization) approaches to doing so typically require hundreds of training samples and thousands of model rollouts, making them expensive in the best case and intractable in the worst. To address this challenge, we introduce Contrastive Reflection (CORE), a non-parametric learning algorithm that compares past reasoning traces to generate insights: short natural-language descriptions of reasoning strategies and constraints that capture differences between successful and unsuccessful problem attempts. Across four reasoning tasks, we demonstrate that CORE enables more rapid improvement than both parametric (GRPO) and non-parametric (GEPA, episodic RAG, and MemRL) methods, while using fewer rollouts. Under fixed rollout budgets with as few as five training samples, CORE achieves the strongest performance in most task-data regimes. Finally, we highlight how CORE is substantially more context-efficient than non-parametric baselines, requiring fewer prompt tokens while storing learned knowledge as compact, interpretable natural-language insights. Our results therefore suggest that distilling contrasts between successful and unsuccessful reasoning traces into abstract and useful insights can provide a more efficient and interpretable route to model self-improvement than weight updates, prompt optimization, or direct reuse of stored reasoning traces.

cs.AI↗

arXiv2026

Measuring Progress Toward AGI: A Cognitive Framework

Despite widespread discussion of AGI, there is no clear framework for measuring progress toward it. This ambiguity fuels subjective claims, makes it difficult to track progress, and risks hindering responsible governance. As a starting point to address this gap, we present a framework for understanding system capabilities in relation to human cognitive abilities. Drawing from decades of research in psychology, neuroscience, and cognitive science, we introduce a Cognitive Taxonomy that deconstructs general intelligence into 10 key cognitive faculties. We then propose a rigorous evaluation protocol in which a system's performance is measured across a suite of targeted, held-out cognitive tasks, generating a 'cognitive profile' that can be used to understand a system's strengths and weaknesses. We hope this framework will provide a practical roadmap and an initial step toward more rigorous, empirical evaluation of AGI.

cs.AI↗

arXiv2026

Neural Garbage Collection: Learning to Forget while Learning to Reason

Chain-of-thought reasoning has driven striking advances in language model capability, yet every reasoning step grows the KV cache, creating a bottleneck to scaling this paradigm further. Current approaches manage these constraints on the model's behalf using hand-designed criteria. A more scalable approach would let end-to-end learning subsume this design choice entirely, following a broader pattern in deep learning. After all, if a model can learn to reason, why can't it learn to forget? We introduce Neural Garbage Collection (NGC), in which a language model learns to forget while learning to reason, trained end-to-end from outcome-based task reward alone. As the model reasons, it periodically pauses, decides which KV cache entries to evict, and continues to reason conditioned on the remaining cache. By treating tokens in a chain-of-thought and cache-eviction decisions as discrete actions sampled from the language model, we can use reinforcement learning to jointly optimize how the model reasons and how it manages its own memory: what the model evicts shapes what it remembers, what it remembers shapes its reasoning, and the correctness of that reasoning determines its reward. Crucially, the model learns this behavior entirely from a single learning signal - the outcome-based task reward - without supervised fine-tuning or proxy objectives. On Countdown, AMC, and AIME tasks, NGC maintains strong accuracy relative to the full-cache upper bound at 2-3x peak KV cache size compression and substantially outperforms eviction baselines. Our results are a first step towards a broader vision where end-to-end optimization drives both capability and efficiency in language models.

cs.LG↗

arXiv2026

GIANTS: Generative Insight Anticipation from Scientific Literature

Scientific breakthroughs often emerge from synthesizing prior ideas into novel contributions. While language models (LMs) show promise in scientific discovery, their ability to perform this targeted, literature-grounded synthesis remains underexplored. We introduce insight anticipation, a generation task in which a model predicts a downstream paper's core insight from its foundational parent papers. To evaluate this capability, we develop GiantsBench, a benchmark of 17k examples across eight scientific domains, where each example consists of a set of parent papers paired with the core insight of a downstream paper. We evaluate models using an LM judge that scores similarity between generated and ground-truth insights, and show that these similarity scores correlate with expert human ratings. Finally, we present GIANTS-4B, an LM trained via reinforcement learning (RL) to optimize insight anticipation using these similarity scores as a proxy reward. Despite its smaller open-source architecture, GIANTS-4B outperforms proprietary baselines and generalizes to unseen domains, achieving a 34% relative improvement in similarity score over gemini-3-pro. Human evaluations further show that GIANTS-4B produces insights that are more conceptually clear than those of the base model. In addition, SciJudge-30B, a third-party model trained to compare research abstracts by likely citation impact, predicts that insights generated by GIANTS-4B are more likely to lead to higher citations, preferring them over the base model in 68% of pairwise comparisons. We release our code, benchmark, and model to support future research in automated scientific discovery.

cs.CL↗

arXiv2026

Human-like Affective Cognition in Foundation Models

Understanding emotions is fundamental to human interaction and experience. Humans easily infer emotions from situations or facial expressions, situations from emotions, and do a variety of other affective cognition. How adept is modern AI at these inferences? We introduce an evaluation framework for testing affective cognition in foundation models. Starting from psychological theory, we generate 1,280 diverse scenarios exploring relationships between appraisals, emotions, expressions, and outcomes. We evaluate the abilities of foundation models (GPT-4, Claude-3, Gemini-1.5-Pro) and humans (N = 567) across carefully selected conditions. Our results show foundation models tend to agree with human intuitions, matching or exceeding interparticipant agreement. In some conditions, models are ``superhuman'' -- they better predict modal human judgements than the average human. All models benefit from chain-of-thought reasoning. This suggests foundation models have acquired a human-like understanding of emotions and their influence on beliefs and behavior.

cs.CL↗

arXiv2026

Endless Terminals: Scaling RL Environments for Terminal Agents

Environments are the bottleneck for self-improving agents. Current terminal benchmarks were built for evaluation, not training; reinforcement learning requires a scalable pipeline, not just a dataset. We introduce Endless Terminals, a fully autonomous pipeline that procedurally generates terminal-use tasks without human annotation. The pipeline has four stages: generating diverse task descriptions, building and validating containerized environments, producing completion tests, and filtering for solvability. From this pipeline we obtain 3255 tasks spanning file operations, log management, data processing, scripting, and database operations. We train agents using vanilla PPO with binary episode level rewards and a minimal interaction loop: no retrieval, multi-agent coordination, or specialized tools. Despite this simplicity, models trained on Endless Terminals show substantial gains: on our held-out dev set, Llama-3.2-3B improves from 4.0% to 18.2%, Qwen2.5-7B from 10.7% to 53.3%, and Qwen3-8B-openthinker-sft from 42.6% to 59.0%. These improvements transfer to human-curated benchmarks: models trained on Endless Terminals show substantial gains on held out human curated benchmarks: on TerminalBench 2.0, Llama-3.2-3B improves from 0.0% to 2.2%, Qwen2.5-7B from 2.2% to 3.4%, and Qwen3-8B-openthinker-sft from 1.1% to 6.7%, in each case outperforming alternative approaches including models with more complex agentic scaffolds. These results demonstrate that simple RL succeeds when environments scale.

cs.LG↗

arXiv2026

Learning to Simulate Human Dialogue

To predict what someone will say is to model how they think. We study this through next-turn dialogue prediction: given a conversation, predict the next utterance produced by a person. We compare learning approaches along two dimensions: (1) whether the model is allowed to think before responding, and (2) how learning is rewarded either through an LLM-as-a-judge that scores semantic similarity and information completeness relative to the ground-truth response, or by directly maximizing the log-probability of the true human dialogue. We find that optimizing for judge-based rewards indeed increases judge scores throughout training, however it decreases the likelihood assigned to ground truth human responses and decreases the win rate when human judges choose the most human-like response among a real and synthetic option. This failure is amplified when the model is allowed to think before answering. In contrast, by directly maximizing the log-probability of observed human responses, the model learns to better predict what people actually say, improving on both log-probability and win rate evaluations. Treating chain-of-thought as a latent variable, we derive a lower bound on the log-probability. Optimizing this objective yields the best results on all our evaluations. These results suggest that thinking helps primarily when trained with a distribution-matching objective grounded in real human dialogue, and that scaling this approach to broader conversational data may produce models with a more nuanced understanding of human behavior.

cs.CL↗

arXiv2025

Lossy communication constrains iterated learning

Humans' distinctive role in the world can largely be attributed to our capacity for iterated learning, a process by which knowledge is expanded and refined over generations. A range of theories seek to explain why humans are so adept at iterated learning, many positing substantial evolutionary discontinuities in communication or cognition. Is it necessary to posit large differences in abilities between humans and other species, or could small differences in communication ability produce large differences in what a species can learn over generations? We investigate this question through a formal model based on information theory. We manipulate how much information individual learners can send each other and observe the effect on iterated learning performance. Incremental changes to the channel rate can lead to dramatic, non-linear changes to the eventual performance of the population. We complement this model with a theoretical result that describes how individual lossy communications constrain the global performance of iterated learning. Our results demonstrate that incremental, quantitative changes to communication abilities could be sufficient to explain large differences in what can be learned over many generations.

cs.SI↗

arXiv2025

From Next-Token to Mathematics: The Learning Dynamics of Mathematical Reasoning in Language Models

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical reasoning abilities of several open-weight LLMs develop during pre-training and post-training. To this end, we construct MathCAMPS, a synthetic dataset of novel mathematical reasoning problems grounded in 44 fine-grained skills taken from the Common Core curriculum from K to 8th grades. In one experiment, we show that mathematical skills are learned during pre-training in an order that measurably correlates with the human-designed curriculum, even though training data are randomly ordered. We also show a detailed analysis of which mathematical abilities benefit from instruction tuning, a widely used post-training method and, in contrast, which skills suffer. Our work paves the way for an empirical understanding of LLM training dynamics in relation to reasoning.

cs.AI↗

arXiv2025

BoxingGym: Benchmarking Progress in Automated Experimental Design and Model Discovery

Understanding the world and explaining it with scientific theories is a central aspiration of artificial intelligence research. Proposing theories, designing experiments to test them, and then revising them based on data are fundamental to scientific discovery. Despite the significant promise of LLM-based scientific agents, no benchmarks systematically test LLM's ability to propose scientific models, collect experimental data, and revise them in light of new data. We introduce BoxingGym, a benchmark with 10 environments for systematically evaluating both experimental design (e.g. collecting data to test a scientific theory) and model discovery (e.g. proposing and revising scientific theories). To enable tractable and quantitative evaluation, we implement each environment as a generative probabilistic model with which a scientific agent can run interactive experiments. These probabilistic models are drawn from various real-world scientific domains ranging from psychology to ecology. To quantitatively evaluate a scientific agent's ability to collect informative experimental data, we compute the expected information gain (EIG), an information-theoretic quantity which measures how much an experiment reduces uncertainty about the parameters of a generative model. A good scientific theory is a concise and predictive explanation. Therefore, to quantitatively evaluate model discovery, we ask a scientific agent to explain their model and then assess whether this explanation enables another scientific agent to make reliable predictions about this environment. In addition to this explanation-based evaluation, we compute standard model evaluation metrics such as prediction errors. We find that current LLMs, such as GPT-4o, struggle with both experimental design and model discovery. We find that augmenting the LLM-based agent with an explicit statistical model does not reliably improve these results.

cs.LG↗

arXiv2025

Bayesian scaling laws for in-context learning

In-context learning (ICL) is a powerful technique for getting language models to perform complex tasks with no training updates. Prior work has established strong correlations between the number of in-context examples provided and the accuracy of the model's predictions. In this paper, we seek to explain this correlation by showing that ICL approximates a Bayesian learner. This perspective gives rise to a novel Bayesian scaling law for ICL. In experiments with \mbox{GPT-2} models of different sizes, our scaling law matches existing scaling laws in accuracy while also offering interpretable terms for task priors, learning efficiency, and per-example probabilities. To illustrate the analytic power that such interpretable scaling laws provide, we report on controlled synthetic dataset experiments designed to inform real-world studies of safety alignment. In our experimental protocol, we use SFT or DPO to suppress an unwanted existing model capability and then use ICL to try to bring that capability back (many-shot jailbreaking). We then study ICL on real-world instruction-tuned LLMs using capabilities benchmarks as well as a new many-shot jailbreaking dataset. In all cases, Bayesian scaling laws accurately predict the conditions under which ICL will cause suppressed behaviors to reemerge, which sheds light on the ineffectiveness of post-training at increasing LLM safety.

cs.CL↗

arXiv2025

Emergent Symbol-like Number Variables in Artificial Neural Networks

What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of methods to understand how well we can interpret them through the lens of interpretable Symbolic Algorithms (SAs) -- precise programs describable by rules and typed, mutable variables. We use autoregressive GRUs, LSTMs, and Transformers trained on tasks where the correct tokens depend on numeric information only latent in the task structure. We show through multiple causal and theoretical methods that we can interpret raw NN activity through the lens of simplified SAs when we frame the activity in terms of neural subspaces rather than individual neurons. Using Distributed Alignment Search (DAS), we find that, depending on network architecture, dimensionality, and task specifications, alignments with SA's can be very high, or they can be only approximate, or fail altogether. We extend our analytic toolkit to address the failure cases by expanding the DAS framework to a broader class of alignment functions that more flexibly capture NN activity in terms of interpretable variables from SAs, and we provide theoretic and empirical explorations of Linear Alignment Functions (LAFs) in contrast to the preexisting Orthogonal Alignment Functions (OAFs). Through analyses of specific cases we confirm the usefulness of causal interventions on neural subspaces for NN interpretability, and we show that recurrent models can develop graded, symbol-like number variables in their neural activity. We further show that shallow Transformers learn very different solutions than recurrent networks, and we prove that such models must use anti-Markovian solutions -- solutions that do not rely on cumulative, Markovian hidden states -- in the absence of sufficient attention layers.

cs.LG↗

arXiv2025

Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs

Test-time inference has emerged as a powerful paradigm for enabling language models to ``think'' longer and more carefully about complex challenges, much like skilled human experts. While reinforcement learning (RL) can drive self-improvement in language models on verifiable tasks, some models exhibit substantial gains while others quickly plateau. For instance, we find that Qwen-2.5-3B far exceeds Llama-3.2-3B under identical RL training for the game of Countdown. This discrepancy raises a critical question: what intrinsic properties enable effective self-improvement? We introduce a framework to investigate this question by analyzing four key cognitive behaviors -- verification, backtracking, subgoal setting, and backward chaining -- that both expert human problem solvers and successful language models employ. Our study reveals that Qwen naturally exhibits these reasoning behaviors, whereas Llama initially lacks them. In systematic experimentation with controlled behavioral datasets, we find that priming Llama with examples containing these reasoning behaviors enables substantial improvements during RL, matching or exceeding Qwen's performance. Importantly, the presence of reasoning behaviors, rather than correctness of answers, proves to be the critical factor -- models primed with incorrect solutions containing proper reasoning patterns achieve comparable performance to those trained on correct solutions. Finally, leveraging continued pretraining with OpenWebMath data, filtered to amplify reasoning behaviors, enables the Llama model to match Qwen's self-improvement trajectory. Our findings establish a fundamental relationship between initial reasoning behaviors and the capacity for improvement, explaining why some language models effectively utilize additional computation while others plateau.

cs.CL↗

arXiv2025

In-Context Learning Strategies Emerge Rationally

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

cs.LG↗

arXiv2025

Non-literal Understanding of Number Words by Language Models

Humans naturally interpret numbers non-literally, effortlessly combining context, world knowledge, and speaker intent. We investigate whether large language models (LLMs) interpret numbers similarly, focusing on hyperbole and pragmatic halo effects. Through systematic comparison with human data and computational models of pragmatic reasoning, we find that LLMs diverge from human interpretation in striking ways. By decomposing pragmatic reasoning into testable components, grounded in the Rational Speech Act framework, we pinpoint where LLM processing diverges from human cognition -- not in prior knowledge, but in reasoning with it. This insight leads us to develop a targeted solution -- chain-of-thought prompting inspired by an RSA model makes LLMs' interpretations more human-like. Our work demonstrates how computational cognitive models can both diagnose AI-human differences and guide development of more human-like language understanding capabilities.

cs.CL↗

arXiv2025

Scaling up the think-aloud method

The think-aloud method, where participants voice their thoughts as they solve a task, is a valuable source of rich data about human reasoning processes. Yet, it has declined in popularity in contemporary cognitive science, largely because labor-intensive transcription and annotation preclude large sample sizes. Here, we develop methods to automate the transcription and annotation of verbal reports of reasoning using natural language processing tools, allowing for large-scale analysis of think-aloud data. In our study, 640 participants thought aloud while playing the Game of 24, a mathematical reasoning task. We automatically transcribed the recordings and coded the transcripts as search graphs, finding moderate inter-rater reliability with humans. We analyze these graphs and characterize consistency and variation in human reasoning traces. Our work demonstrates the value of think-aloud data at scale and serves as a proof of concept for the automated analysis of verbal reports.

cs.CL↗