Agent systems based on Large Language Models (LLMs) are increasingly deployed for autonomous tasks, yet existing evaluations mostly focus on task success rather than whether agents know when to abstain. This gap poses real risks: under ambiguity, conflicting constraints, or tool failures, agents may execute unintended and irreversible actions. To close this gap, we present the first systematic evaluation framework for agentic abstention: the ability to recognize when not to act. At its core, AgentAbstain is a paired-task benchmark that defines 8 abstention categories spanning pre-execution reasoning and runtime discovery, with 263 paired tasks across 42 executable sandbox environments, each pairing a should-act task with a should-abstain variant produced by a controlled perturbation to the instruction, tool, or environment state. Scaling such paired evaluations poses two practical challenges: manually authoring diverse tasks is expensive, and static benchmarks risk data contamination as models evolve. To address both, we propose AbstainGen, a fully automated pipeline that synthesizes sandbox environments and generates paired tasks end-to-end, validated by deterministic replay and semantic LLM judges. Its scalable design enables on-demand regeneration of fresh task instances, and human validation rates 96% of generated tasks as well-designed. Evaluating 17 frontier LLMs across 4 agent harnesses, the best model (Gemini 3.1 Pro) achieves only 59.5% paired accuracy (correct on both the act and abstain sides of each paired task). More importantly, abstention capability is largely independent of general task-solving capability, indicating that scaling task-solving alone will not close this gap. We identify failure modes such as Post-hoc Abstention, in which agents execute irreversible actions before recognizing abstention triggers. For instance, an agent may cancel a flight reservation before noticing contradictory rebooking instructions, leaving the user stranded. These findings underscore the need for rigorous abstention evaluation to develop more trustworthy LLM agents.

Reliable hypothesis testing is the foundation of many empirical scientific claims. Large language model (LLM) agents are increasingly used to automate this process, as they can inspect datasets, generate code, and produce analyses end-to-end. However, we show that they frequently make subtle inferential errors that lead to incorrect conclusions despite correctly executed analyses. Existing benchmarks fail to capture this failure mode, as they rarely assess whether a reported p-value is statistically valid given the assumptions underlying the data. We address this gap by building P-Bench, a benchmark comprising 425 open-ended, realistic hypothesis-testing tasks spanning economics, biology, and medicine. Each task requires an agent to select a statistical method, compute a p-value, and draw a conclusion given only a scientific hypothesis and a dataset. We further introduce Fisher-R1, an open-weight LLM agent trained for rigorous hypothesis testing using synthetic tasks and reinforcement learning. On P-Bench, Fisher-R1-14B substantially improves over its backbone and outperforms strong proprietary and open-source baselines, including GPT-5.4 and DeepSeek-V4-Pro, achieving a 21% average relative improvement in single-trial success over DeepSeek-V4-Pro, with gains up to 26% on the most challenging tasks. Our results demonstrate that current LLM agents lack reliable statistical reasoning for hypothesis testing and that reinforcement learning on tasks with verified statistical reward substantially improves reliability.

LLM agents that execute multi-step tool calls must satisfy two objectives simultaneously: completing the user's task (utility) and conforming to domain policies and correctness constraints (safety). These objectives are in tension -- blocking an unsafe action prevents a violation but can leave the agent stranded with no principled way to recover. Existing approaches sacrifice one objective for the other. We introduce Soteria, a framework that reconciles safety and utility through verified hierarchical planning and runtime enforcement of specifications. Before execution, the agent generates a structured plan that is formally verified against the specifications prior to any tool invocation. During execution, the verified plan serves dual roles: it ensures that the agent takes specification-conformant trajectories and provides guidance when unsafe actions are blocked. Across multiple benchmarks covering a diverse range of tool-use tasks, Soteria achieves perfect specification conformance while improving utility by up to $5\times$ over existing guardrail approaches, demonstrating that safety and utility need not be traded off.

In the past year, custom and unreleased math reasoning models reached gold medal performance on the International Mathematical Olympiad (IMO). Similar performance was then reported using large-scale inference on publicly available models but at prohibitive costs (e.g., 3000 per problem). In this work, we present an inference pipeline that attains best-in-class performance on IMO-style math problems at an average inference cost orders of magnitude below competing methods while using only general-purpose off-the-shelf models. Our method relies on insights about grader failure in solver-grader pipelines, which we call the Cognitive Well (iterative refinement converging to a wrong solution that the solver as well as the pipeline's internal grader consider to be basically correct). Our pipeline addresses these failure modes through conjecture extraction, wherein candidate lemmas are isolated from generated solutions and independently verified alongside their negations in a fresh environment (context detachment). On IMO-ProofBench Advanced (PB-Adv), our pipeline achieves 67.1\% performance using Gemini 3.0 Pro with an average cost per question of $\sim$ \$31. This surpasses the performance of the DeepThink IMO gold-winning model, and more than doubles the success rate of the next best publicly accessible pipeline, all at a fraction of the cost.