Position: It's Time to Optimize LLMs for Self-Consistency

Despite ever-increasing sophistication in language model (LM) pre- and post-training pipelines, many important failures persist: models overcondition on user framing ("sycophancy"), exhibit incomplete logical generalization, and produce confident but incorrect responses. We argue that these failures arise from a modeling assumption permeating all aspects of the pipeline: that behavior can be specified and evaluated independently on single-output pairs. Many model failures are difficult, if not impossible, to detect without reasoning about relationships between a model's responses across inputs. In this position paper, we propose self-consistency as a framework for understanding these failures. We first observe that a wide variety of techniques designed to improve specific aspects of LM behavior-targeting properties as diverse as adversarial robustness and factual coherence-can be understood as special cases of a common "consistency optimization" procedure and addressed with a standard set of optimization tools. We next outline a set of new model properties that could be achieved by optimizing for consistency, and conclude with a discussion of what it would mean to develop generally consistent LMs, including the capabilities they would enable and the objections they raise.

Right in the Right Way: LM Training with Verifiable Rewards and Human Demonstrations

RL with verifiable rewards (RLVR) has emerged as a powerful paradigm for training LMs on tasks with well-defined success metrics, such as code generation and mathematical reasoning. However, current RLVR methods optimize only what can be objectively scored, often neglecting subjective, non-verifiable aspects of human-like outputs, such as style and structure. This limitation leads to well-documented failure modes such as diversity collapse, unnatural-sounding responses, and reward hacking. We propose an adversarial generator-discriminator framework that augments verifiable rewards with a learned signal from human demonstrations. A generator model is trained using RL to maximize both task accuracy and an adversarial reward derived from a discriminator. The discriminator, trained alongside the generator policy, learns to distinguish human-written outputs from model-generated ones. The discriminator serves as a learned proxy for the human output distribution, providing feedback on aspects of generation that are difficult to formalize as scalar rewards. Across diverse domains, including bug fixing and open-ended generation, our approach consistently improves non-verifiable properties while preserving the accuracy gains of RLVR. In bug fixing, our method produces solutions with significantly lower edit distance compared to RLVR baselines while matching end performance. In story generation, our method significantly improves win rate while producing stories that are diverse and more human-like. And in a simple reward hacking benchmark, our method nearly eliminates model misbehavior while maintaining high benchmark scores. Together, these results show that our approach bridges RL and SFT, offering a scalable path toward jointly optimizing the verifiable and non-verifiable properties of a task.

Vector Policy Optimization: Training for Diversity Improves Test-Time Search

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

Reaching Beyond the Mode: RL for Distributional Reasoning in Language Models

Given a question, a language model (LM) implicitly encodes a distribution over possible answers. In practice, post-training procedures for LMs often collapse this distribution onto a single dominant mode. While this is generally not a problem for benchmark-style evaluations that assume one correct answer, many real-world tasks inherently involve multiple valid answers or irreducible uncertainty. Examples include medical diagnosis, ambiguous question answering, and settings with incomplete information. In these cases, we would like LMs to generate multiple plausible hypotheses, ideally with confidence estimates for each one, and without computationally intensive repeated sampling to generate non-modal answers. This paper describes a multi-answer reinforcement learning approach for training LMs to perform distributional reasoning over multiple answers during inference. We modify the RL objective to enable models to explicitly generate multiple candidate answers in a single forward pass, internalizing aspects of inference-time search into the model's generative process. Across question-answering, medical diagnostic, and coding benchmarks, we observe improved diversity, coverage, and set-level calibration scores compared to single answer trained baselines. Models trained with our approach require fewer tokens to generate multiple answers than competing approaches. On coding tasks, they are also substantially more accurate. These results position multi-answer RL as a principled and compute-efficient alternative to inference-time scaling procedures such as best-of-k. Code and more information can be found at https://multi-answer-rl.github.io/.

Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or "hallucinate") in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score -- a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations -- outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

A System for Accurate Tracking and Video Recordings of Rodent Eye Movements using Convolutional Neural Networks for Biomedical Image Segmentation

Research in neuroscience and vision science relies heavily on careful measurements of animal subject's gaze direction. Rodents are the most widely studied animal subjects for such research because of their economic advantage and hardiness. Recently, video based eye trackers that use image processing techniques have become a popular option for gaze tracking because they are easy to use and are completely noninvasive. Although significant progress has been made in improving the accuracy and robustness of eye tracking algorithms, unfortunately, almost all of the techniques have focused on human eyes, which does not account for the unique characteristics of the rodent eye images, e.g., variability in eye parameters, abundance of surrounding hair, and their small size. To overcome these unique challenges, this work presents a flexible, robust, and highly accurate model for pupil and corneal reflection identification in rodent gaze determination that can be incrementally trained to account for variability in eye parameters encountered in the field. To the best of our knowledge, this is the first paper that demonstrates a highly accurate and practical biomedical image segmentation based convolutional neural network architecture for pupil and corneal reflection identification in eye images. This new method, in conjunction with our automated infrared videobased eye recording system, offers the state of the art technology in eye tracking for neuroscience and vision science research for rodents.

CoFrNets: Interpretable Neural Architecture Inspired by Continued Fractions

In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel neural architecture, CoFrNet, inspired by the form of continued fractions which are known to have many attractive properties in number theory, such as fast convergence of approximations to real numbers. We show that CoFrNets can be efficiently trained as well as interpreted leveraging their particular functional form. Moreover, we prove that such architectures are universal approximators based on a proof strategy that is different than the typical strategy used to prove universal approximation results for neural networks based on infinite width (or depth), which is likely to be of independent interest. We experiment on nonlinear synthetic functions and are able to accurately model as well as estimate feature attributions and even higher order terms in some cases, which is a testament to the representational power as well as interpretability of such architectures. To further showcase the power of CoFrNets, we experiment on seven real datasets spanning tabular, text and image modalities, and show that they are either comparable or significantly better than other interpretable models and multilayer perceptrons, sometimes approaching the accuracies of state-of-the-art models.

MedPAIR: Measuring Physicians and AI Relevance Alignment in Medical Question Answering

Large Language Models (LLMs) have demonstrated remarkable performance on various medical question-answering (QA) benchmarks, including standardized medical exams. However, correct answers alone do not ensure correct logic, and models may reach accurate conclusions through flawed processes. In this study, we introduce the MedPAIR (Medical Dataset Comparing Physicians and AI Relevance Estimation and Question Answering) dataset to evaluate how physician trainees and LLMs prioritize relevant information when answering QA questions. We obtain annotations on 1,300 QA pairs from 36 physician trainees, labeling each sentence within the question components for relevance. We compare these relevance estimates to those for LLMs, and further evaluate the impact of these "relevant" subsets on downstream task performance for both physician trainees and LLMs. We find that LLMs are frequently not aligned with the content relevance estimates of physician trainees. After filtering out physician trainee-labeled irrelevant sentences, accuracy improves for both the trainees and the LLMs. All LLM and physician trainee-labeled data are available at: http://medpair.csail.mit.edu/.

A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code and further information is available at https://probabilistic-inference-scaling.github.io.

Can AI Relate: Testing Large Language Model Response for Mental Health Support

Large language models (LLMs) are already being piloted for clinical use in hospital systems like NYU Langone, Dana-Farber and the NHS. A proposed deployment use case is psychotherapy, where a LLM-powered chatbot can treat a patient undergoing a mental health crisis. Deployment of LLMs for mental health response could hypothetically broaden access to psychotherapy and provide new possibilities for personalizing care. However, recent high-profile failures, like damaging dieting advice offered by the Tessa chatbot to patients with eating disorders, have led to doubt about their reliability in high-stakes and safety-critical settings. In this work, we develop an evaluation framework for determining whether LLM response is a viable and ethical path forward for the automation of mental health treatment. Using human evaluation with trained clinicians and automatic quality-of-care metrics grounded in psychology research, we compare the responses provided by peer-to-peer responders to those provided by a state-of-the-art LLM. We show that LLMs like GPT-4 use implicit and explicit cues to infer patient demographics like race. We then show that there are statistically significant discrepancies between patient subgroups: Responses to Black posters consistently have lower empathy than for any other demographic group (2%-13% lower than the control group). Promisingly, we do find that the manner in which responses are generated significantly impacts the quality of the response. We conclude by proposing safety guidelines for the potential deployment of LLMs for mental health response.