The provided text introduces "e3," a new training methodology for Large Language Models (LLMs) designed to improve their reasoning capabilities and enable extrapolation of test-time compute. This means LLMs can continue to enhance performance even when given more processing time than they were trained on. The core of e3 lies in three key components: leveraging asymmetries in LLM competence, where models are better at verifying answers than generating them; utilizing negative gradients in reinforcement learning to encourage exploration and chain these asymmetric operations; and employing a coupled curriculum that aligns task difficulty with training budget to structure this exploration effectively. Experiments demonstrate that e3 significantly boosts performance on complex mathematical reasoning tasks like AIME and HMMT, outperforming other models within its size class and showing robust scaling with increased test-time compute.

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This academic paper explores length generalization transfer in Transformer language models, investigating their ability to extrapolate knowledge from shorter inputs to longer, unseen ones. The authors demonstrate that training a model on a related "auxiliary task" with longer inputs can significantly improve the generalization of a "main task" trained only on shorter examples, across diverse domains like arithmetic, string manipulation, and maze navigation. This transfer effect is also observed in pretrained language models, suggesting they develop reusable computational frameworks. Furthermore, the research provides mechanistic evidence that this transfer correlates with the shared use of attention heads between related tasks, indicating a compositional reuse of inductive structure.

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This paper investigates the underlying capabilities of large language models (LMs) by analyzing their performance on various benchmarks. The authors propose a novel Hierarchical Component Analysis (HCA) algorithm to uncover latent hierarchical structures within these capabilities. Through Principal Component Analysis (PCA), the study identifies that benchmark performance data exhibits an approximate low-rank structure, suggesting a limited number of core abilities. Furthermore, the research highlights heterogeneity in performance patterns across models fine-tuned from different base models, indicating the importance of considering the base model in evaluations. Finally, the work explores how these findings can improve the imputation of missing benchmark data and suggests that instruction following is causally linked to mathematical reasoning in LMs.

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This academic paper explores why large language models (LLMs) both generalize correctly and "hallucinate" incorrect information when fine-tuned with new facts. The authors propose that out-of-context reasoning (OCR) is the single underlying mechanism responsible for both phenomena. They demonstrate through experiments on five prominent LLMs that OCR drives generalization when concepts are causally related and hallucination when they are not. Furthermore, the research formalizes OCR as a synthetic factual recall task, revealing that a factorized model architecture in a one-layer transformer enables generalization by promoting an implicit bias during gradient descent that favors solutions minimizing the nuclear norm of combined matrices. Conversely, a non-factorized model fails to generalize, highlighting the critical role of matrix factorization in LLMs' ability to associate facts and implications, irrespective of causal links.

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The academic paper introduces GATE (Generative Augmentation for Treatment Effect estimation), a novel framework designed to improve the estimation of Conditional Average Treatment Effects (CATE), particularly when working with limited observational data. The core concept involves data augmentation, where synthetic counterfactual outcomes are generated using pre-trained generative models, specifically Large Language Models (LLMs). This augmentation strategy aims to address critical challenges in CATE estimation, such as data scarcity and covariate shift, by enriching the dataset with external knowledge from the LLMs. The authors demonstrate, through both theoretical analysis and empirical experiments, that LLM-based data augmentation significantly enhances the performance of various CATE models, especially in small-sample scenarios, by selectively generating outcomes in carefully chosen regions of the covariate space where the LLM's predictions are deemed reliable.

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This academic paper explores a novel approach to extracting numerical predictions from Large Language Models (LLMs) without relying on their computationally expensive autoregressive decoding process. The authors investigate whether LLM internal representations encode sufficient information to directly recover numerical values, including not only point estimates like the mean and median but also uncertainty measures like quantiles and confidence intervals. They demonstrate that magnitude-aware regression probes can accurately predict these numerical properties from frozen LLM embeddings across various scales and datasets. The research suggests that a significant portion of an LLM's numerical reasoning is embedded in its hidden states, paving the way for more efficient, sampling-free numerical prediction with uncertainty estimation in applications such as time series forecasting.

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This paper introduces Self-Adapting LLMs (SEAL), a novel framework enabling large language models to autonomously enhance their capabilities by generating and utilizing their own training data. Unlike static models, SEAL employs a reinforcement learning loop where the model produces "self-edits"—instructions for finetuning data and optimization—and is rewarded based on the performance of the updated model. Experiments demonstrate SEAL's effectiveness in knowledge incorporation and few-shot generalization, outperforming baselines and even synthetic data generated by larger models like GPT-4.1. The research also acknowledges limitations such as catastrophic forgetting and computational overhead, while envisioning future applications in continual learning and agentic systems.

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This paper investigates In-Context Learning (ICL) models, particularly those employing transformers, from a learning-to-learn perspective. The authors theoretically demonstrate that ICL models are expressive enough to emulate existing meta-learning algorithms, such as gradient-based, metric-based, and amortization-based approaches. Their findings suggest that ICL learns data-dependent optimal algorithms during pre-training, which, while powerful, can limit generalizability to out-of-distribution or novel tasks. To address this, the study proposes applying techniques from classical deep networks, like meta-level meta-learning and curriculum learning, to enhance ICL's domain adaptability and accelerate convergence during the pre-training phase.

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This academic paper investigates the suitability of large language models (LLMs) as substitutes for human participants in social science research. The authors examine LLMs' reasoning abilities using the "11-20 money request game," a test designed to evaluate strategic thinking. Their findings consistently show that LLMs generally fail to replicate human behavioral patterns, exhibiting less reasoning depth and inconsistent responses compared to human subjects. The study highlights several limitations of LLMs, including their reliance on probabilistic patterns rather than genuine understanding, sensitivity to subtle changes in prompts or language, and the potential for memorization of training data to be mistaken for true reasoning. Ultimately, the paper concludes that caution is essential when considering LLMs as human surrogates, suggesting they are currently better suited for generating novel ideas rather than simulating human behavior.

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This paper explores the ongoing debate surrounding AI's capacity for genuine reasoning, questioning whether current systems truly think or merely exhibit advanced pattern recognition. It defines AI reasoning as simulating human cognitive processes like deduction and problem-solving, distinguishing it from generative AI and pattern matching. The document highlights the historical evolution of AI approaches, from symbolic systems to neural networks, and the emergence of hybrid models. Critically, it presents evidence from Apple's "Illusion of Thinking" research suggesting current AI models fail at high-complexity problems, pointing to fundamental limitations in their logical processing. Finally, it discusses future directions like Neural-Symbolic AI and underscores the crucial ethical, legal, and governance implications of developing increasingly capable AI.