The New Movie Is Sparking a Right-Wing Backlash. Emily Wilson's 2017 translation of Homer's epic--the first by a woman--was called a woke "abomination" by online reactionaries. Christopher Nolan's film is facing similar critiques. Who'd have thought Helen of Troy would cause so much trouble? Earlier this year, certain quarters of the internet spun out at news that Kenyan-Mexican Oscar-winning actress Lupita Nyong'o was rumored to appear as the impossibly beautiful Spartan noble Helen--whose face, it was later written, launched a thousand ships--in Christopher Nolan's forthcoming Hollywood Homeric epic, The Odyssey The confirmation of her casting in May kicked off another wave of conniption fits.

Large language models (LLMs) have recently transformed from text-based assistants to autonomous agents capable of planning, reasoning, and iteratively improving their actions. While numerical reward signals and verifiers can effectively rank candidate actions, they often provide limited contextual guidance.

Multi-agent debate improves the reliability of large language models (LLMs) through iterative peer critiques. However, fixed topologies often introduce persistent positional biases, amplify unreliable agents, and cause high sensitivity to role assignments. We introduce \textit{Permutation-Equivariant Adaptive Routing Multi-Agent Debate (PEAR)}, an inference-time protocol that dynamically reconfigures communication roles and sparse topologies across consecutive debate rounds. By strategically switching agent-to-role assignments based on evolving agent states, PEAR prevents any agent from permanently occupying a privileged network position or distributes influence more evenly across the debate. We theoretically characterize PEAR as an equivariant sparse router: it preserves accuracy under agent relabeling while reducing routing complexity and improving generalization. Comprehensive empirical evaluations across four reasoning benchmarks and six diverse LLM backbones demonstrate PEAR significantly improves average accuracy over the strongest debate baselines. The code is at https://github.com/EVIEHub/PEAR.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce SelfPlay Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, SPC can guide the test-time search of diverse LLMs and significantly improve their mathematical reasoning performance on MATH500 and AIME2024, surpassing those guided by state-of-the-art process reward models.

Large language models (LLMs) for code are typically trained to align with natural language instructions to closely follow their intentions and requirements. However, in many practical scenarios, it becomes increasingly challenging for these models to navigate the intricate boundary between helpfulness and safety, especially against highly complex yet potentially malicious instructions. In this work, we introduce INDICT: a new framework that empowers LLMs with Internal Dialogues of Critiques for both safety and helpfulness guidance. The internal dialogue is a dual cooperative system between a safety-driven critic and a helpfulness-driven critic. Each critic provides analysis against the given task and corresponding generated response, equipped with external knowledge queried through relevant code snippets and tools like web search and code interpreter. We engage the dual critic system in both code generation stage as well as code execution stage, providing preemptive and post-hoc guidance respectively to LLMs. We evaluated INDICT on 8 diverse tasks across 8 programming languages from 5 benchmarks, using LLMs from 7B to 70B parameters. We observed that our approach can provide an advanced level of critiques of both safety and helpfulness analysis, significantly improving the quality of output codes (+10% absolute improvements in all models).

Critique ability, i.e., the capability of Large Language Models (LLMs) to identify