Specifically, we train GPT -3, an autoregressive language model with 175 billion parameters, 10x more than any previous non-sparse language model, and test its performance in the few-shot setting.

Reinforcement Learning, particularly through policy gradient methods, has played a central role in enabling reasoning capabilities of Large Language Models. However, the optimization stability of policy gradients in this setting remains understudied. As a result, existing implementations often resort to conservative hyperparameter choices to ensure stability, which requires more training samples and increases computational costs. Hence, developing models for reliably tracking the underlying optimization dynamics and leveraging them into training enables more sample-efficient regimes and further unleashes scalable post-training. We address this gap by formalizing the stochastic optimization problem of policy gradients with explicit consideration of second-order geometry. We propose a tractable computational framework that tracks and leverages curvature information during policy updates. We further employ this framework to design interventions in the optimization process through data selection. The resultant algorithm, Curvature-Aware Policy Optimization (CAPO), identifies samples that contribute to unstable updates and masks them out. Theoretically, we establish monotonic improvement guarantees under realistic assumptions. On standard math reasoning benchmarks, we empirically show that CAPO ensures stable updates under aggressive learning regimes where baselines catastrophically fail. With minimal intervention (rejecting fewer than 8% of tokens), CAPO achieves up to 30x improvement in sample efficiency over standard GRPO for LLM reasoning.

The emergence of in-context learning (ICL) in large language models (LLMs) remains poorly understood despite its consistent effectiveness, enabling models to adapt to new tasks from only a handful of examples. To clarify and improve these capabilities, we characterize how the statistical properties of the pretraining distribution (e.g., tail behavior, coverage) shape ICL on numerical tasks. We develop a theoretical framework that unifies task selection and generalization, extending and sharpening earlier results, and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize Bayesian posterior consistency and concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. We then empirically study how ICL performance varies with the pretraining distribution on challenging tasks such as stochastic differential equations and stochastic processes with memory. Together, these findings suggest that controlling key statistical properties of the pretraining distribution is essential for building ICL-capable and reliable LLMs.

State-of-the-art machine learning often follows a two-stage process: $(i)$~pre-training on large, general-purpose datasets; $(ii)$~fine-tuning on task-specific data. In fine-tuning, selecting training examples that closely reflect the target distribution is crucial. However, it is often the case that only a few samples are available from the target distribution. Existing data selection methods treat these target samples as a validation set and estimate the effect of adding or removing a single sample from the training pool by performing inference on the validation set. We propose a simpler and faster alternative that inverts the usual role of train and validation: we perform inference on the training pool before and after fine-tuning on the validation set. We then select samples whose predictions change the most. Our key insight is that the training samples most affected by fine-tuning on a small validation set tend to be the most beneficial for reducing test loss on the target distribution. Experiments on instruction tuning and named entity recognition tasks show that, in most cases, our method achieves lower test log-loss than state-of-the-art approaches. We support our findings with theoretical analysis.

We introduce \textbf{Directed Information $γ$-covering}, a simple but general framework for redundancy-aware context engineering. Directed information (DI), a causal analogue of mutual information, measures asymmetric predictiveness between chunks. If $\operatorname{DI}_{i \to j} \ge H(C_j) - γ$, then $C_i$ suffices to represent $C_j$ up to $γ$ bits. Building on this criterion, we formulate context selection as a $γ$-cover problem and propose a greedy algorithm with provable guarantees: it preserves query information within bounded slack, inherits $(1+\ln n)$ and $(1-1/e)$ approximations from submodular set cover, and enforces a diversity margin. Importantly, building the $γ$-cover is \emph{query-agnostic}: it incurs no online cost and can be computed once offline and amortized across all queries. Experiments on HotpotQA show that $γ$-covering consistently improves over BM25, a competitive baseline, and provides clear advantages in hard-decision regimes such as context compression and single-slot prompt selection. These results establish DI $γ$-covering as a principled, self-organizing backbone for modern LLM pipelines.

Although LLMs have achieved remarkable performance, the inherent stochasticity of their reasoning process and varying conclusions present significant challenges. Majority voting or Best-of-N with external verification models has been explored to find the most promising solution among multiple LLM outputs. However, these approaches have certain limitations, such as limited applicability or the cost of an additional training step. To address this problem, we propose a novel and effective framework that Recycles Few-shot examples to verify LLM outputs (ReFeri). Our key idea is to additionally utilize the given few-shot examples to evaluate the candidate outputs of the target query, not only using them to generate outputs as the conventional few-shot prompting setup. Specifically, ReFeri evaluates the generated outputs by combining two different scores, designed motivated from Bayes' rule, and subsequently selects the candidate that is both confidently determined and contextually coherent through a few additional LLM inferences. Experiments with three different LLMs and across seven diverse tasks demonstrate that our framework significantly improves the accuracy of LLMs-achieving an average gain of 4.8%-through effective response selection, without additional training.

Reliably determining the performance of Retrieval-Augmented Generation (RAG) systems depends on comprehensive test questions. While a proliferation of evaluation frameworks for LLM-powered applications exists, current practices lack a systematic method to ensure these test sets adequately cover the underlying knowledge base, leaving developers with significant blind spots. To address this, we present a novel, applied methodology to quantify the semantic coverage of RAG test questions against their underlying documents. Our approach leverages existing technologies, including vector embeddings and clustering algorithms, to create a practical framework for validating test comprehensiveness. Our methodology embeds document chunks and test questions into a unified vector space, enabling the calculation of multiple coverage metrics: basic proximity, content-weighted coverage, and multi-topic question coverage. Furthermore, we incorporate outlier detection to filter irrelevant questions, allowing for the refinement of test sets. Experimental evidence from two distinct use cases demonstrates that our framework effectively quantifies test coverage, identifies specific content areas with inadequate representation, and provides concrete recommendations for generating new, high-value test questions. This work provides RAG developers with essential tools to build more robust test suites, thereby improving system reliability and extending to applications such as identifying misaligned documents.

Developing full-stack web applications is complex and time-intensive, demanding proficiency across diverse technologies and frameworks. Although recent advances in multimodal large language models (MLLMs) enable automated webpage generation from visual inputs, current solutions remain limited to front-end tasks and fail to deliver fully functional applications. In this work, we introduce TDDev, the first test-driven development (TDD)-enabled LLM-agent framework for end-to-end full-stack web application generation. Given a natural language description or design image, TDDev automatically derives executable test cases, generates front-end and back-end code, simulates user interactions, and iteratively refines the implementation until all requirements are satisfied. Our framework addresses key challenges in full-stack automation, including underspecified user requirements, complex interdependencies among multiple files, and the need for both functional correctness and visual fidelity. Through extensive experiments on diverse application scenarios, TDDev achieves a 14.4% improvement on overall accuracy compared to state-of-the-art baselines, demonstrating its effectiveness in producing reliable, high-quality web applications without requiring manual intervention.

Large language models (LLMs) are increasingly entrusted with high-stakes decisions that affect human welfare. However, the principles and values that guide these models when distributing scarce societal resources remain largely unexamined. To address this, we introduce the Social Welfare Function (SWF) Benchmark, a dynamic simulation environment where an LLM acts as a sovereign allocator, distributing tasks to a heterogeneous community of recipients. The benchmark is designed to create a persistent trade-off between maximizing collective efficiency (measured by Return on Investment) and ensuring distributive fairness (measured by the Gini coefficient). We evaluate 20 state-of-the-art LLMs and present the first leaderboard for social welfare allocation. Our findings reveal three key insights: (i) A model's general conversational ability, as measured by popular leaderboards, is a poor predictor of its allocation skill. (ii) Most LLMs exhibit a strong default utilitarian orientation, prioritizing group productivity at the expense of severe inequality. (iii) Allocation strategies are highly vulnerable, easily perturbed by output-length constraints and social-influence framing. These results highlight the risks of deploying current LLMs as societal decision-makers and underscore the need for specialized benchmarks and targeted alignment for AI governance.

LLMs cannot reliably recognize their parametric knowledge boundaries and often hallucinate answers to outside-of-boundary questions. In contrast, humans recognize their limitations and can either seek external help for such questions or abstain. In this paper, we introduce MASH (Modeling Abstention via Selective Help-seeking), a training framework that readily extracts abstentions from LLMs. Our key idea is that any external help-seeking by an LLM, i.e. search tool use, can serve as a proxy for abstention if the external help (search) is appropriately penalized while simultaneously rewarding answer accuracy. MASH operationalizes this idea using reinforcement learning with a pay-per-search reward. We run experiments on three knowledge-intensive QA datasets. Our results show that MASH substantially improves upon the selective help-seeking performance of prior efficient search approaches; on multi-hop datasets, MASH improves answer accuracy by 7.6%. Furthermore, MASH demonstrates strong off-the-shelf abstention -- it can distinguish between unanswerable/answerable questions and selectively generate responses for answerable questions -- showcasing behavior analogous to specialized abstention approaches. We emphasize that contrary to prior abstention methods, MASH does not require pre-determining knowledge boundaries to construct training data. Instead, MASH's abstentions are a by-product of training for the auxiliary selective help-seeking task. Overall, we show that MASH training effectively aligns search tool use with parametric knowledge, which can be successfully leveraged for making abstention decisions.