Frontier reasoning models are produced by posttraining base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power distribution, elicits comparable reasoning without additional training, curated datasets, or verifiers. However, making this method practical requires efficiently sampling from the power distribution. A sampler needs to "mix" to the power distribution, which necessitates moving between modes of the target distribution; intuitively, e.g., trying different reasoning strategies. The samplers proposed in prior works repeatedly select a "cut" position in the current reasoning trace uniformly at random and resample the suffix from that position onward. However, reasoning traces typically contain a few consequential decisions (e.g., the choice of proof strategy or algorithm), and we observe that a uniformly chosen cut tends to rewrite local details rather than revisit decision points. We introduce an algorithm (Entropy-Cut Metropolis-Hastings) that uses the base model's next-token entropy as a proxy to identify key decision points and resample from those positions. We empirically verify that entropy jumps are a useful proxy for decision points and, in a stylized model of reasoning, prove that our method's mixing time scales with the number of decisions in a trace rather than with the number of tokens, which can be much larger. Across MATH500, HumanEval, GPQA Diamond, and AIME26, our method consistently improves over baselines and RL-trained models.

We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer, allowing deferral rates to be adjusted without retraining. For KL-based ideal distributions, our deferral rules recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior -- which incorporates the expert's performance -- depending on if the ideal distributions are joint or marginal distributions. Experimentally, our approach is competitive compared to common baselines and more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio learning between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples -- including those with low likelihood under the base model -- which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens -- those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

Training large language models (LLMs) such as GPT-5 and Qwen-3 (Singh et al., 2025; Yang et al., 2025) on massive text corpora aims at capturing the underlying distribution of natural language. Yet, it remains challenging for the trained model to extrapolate to out-of-distribution or out-of-domain settings beyond the support of its training data. The literature has seen the development of various data perturbation techniques, such as synonym replacement, random insertion, deletion, and swap, that modify training instances into semantically similar variants to effectively expose LLMs to a broader range of inputs and improve their ability to generalize beyond the training data (Feng et al., 2019, 2020; Li et al., 2024; Cen et al., 2026). However, their approach remains grounded in the discrete, word-level augmentation procedures mentioned previously, which may restrict its adaptivity across diverse domains. While discrete perturbations are simple to use, they could be too coarse and hard to refine due to the complexity of natural language (Park et al., 2022; Li et al., 2023). Meanwhile, fixed perturbations apply the same transformations to the data regardless of the contexts, thus failing to generalize appropriately (Ismailov and Asanova, 2025).

LLM-as-a-Judge evaluation has become a standard tool for assessing base model performance. However, characterizing performance via the naive estimator, i.e., raw judge outputs, is systematically biased. Recent work has proposed estimators to correct this bias, but their reliability depends critically on judge quality and, for model comparisons, on calibration stability. Sharing calibration across compared models is practically attractive but can introduce severe bias, including cases where the comparison estimate points in the wrong direction with high apparent confidence. We study these failure modes through analytical results, simulations over judge quality ($J$) and cross-model calibration instability ($ΔJ$), and a real-data MMLU-Pro case study with sign reversal. We propose $J$ and $ΔJ$ as diagnostics for when corrected estimates, especially shared-calibration comparisons, are likely unreliable, and provide reporting guidance for LaaJ evaluation.

Language models can generate harmful and biased outputs and exhibit undesirable behavior according to a given cultural context. We propose a Process for Adapting Language Models to Society (PALMS) with ValuesTargeted Datasets, an iterative process to significantly change model behavior by crafting and fine-tuning on a dataset that reflects a predetermined set of target values. We evaluate our process using three metrics: quantitative metrics with human evaluations that score output adherence to a target value, toxicity scoring on outputs; and qualitative metrics analyzing the most common word associated with a given social category. Through each iteration, we add additional training dataset examples based on observed shortcomings from evaluations. PALMS performs significantly better on all metrics compared to baseline and control models for a broad range of GPT-3 language model sizes without compromising capability integrity. We find that the effectiveness of PALMS increases with model size. We show that significantly adjusting language model behavior is feasible with a small, hand-curated dataset.

Pseudo labeling (PL) is a wide-applied strategy to enlarge the labeled dataset by self-annotating the potential samples during the training process. Several works have shown that it can improve the graph learning model performance in general. However, we notice that the incorrect labels can be fatal to the graph training process. Inappropriate PL may result in the performance degrading, especially on graph data where the noise can propagate. Surprisingly, the corresponding error is seldom theoretically analyzed in the literature.