Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization (GRPO) divides by this number, GRPO Done Right (Dr. GRPO) drops the division, and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) discards the groups where it is zero. Each is presented as its own fix, yet this paper proves they are three settings of one dial. That dial is not cosmetic: for right-or-wrong rewards, the disagreement is exactly the size of the training update, the group-standard-deviation identity. A split group teaches the most, while a unanimous group teaches nothing and falls silent. The same result says which problems deserve the most weight and how many tries each one needs. This paper confirms the intuition on a large real difficulty dataset (Big-Math) and in a controlled training run. What looks like a harmless normalization step is the dial that decides where learning happens and how strongly.

Solving and learning partial differential equations (PDEs) lies at the core of physicsinformed machine learning. Traditional numerical methods, such as finite difference and finite element approaches, are rooted in domain-specific techniques and often lack scalability. Recent advances have introduced neural networks and Gaussian processes (GPs) as flexible tools for automating PDE solving and incorporating physical knowledge into learning frameworks. While GPs offer tractable predictive distributions and a principled probabilistic foundation, they may be suboptimal in capturing complex behaviors such as sharp transitions or non-smooth dynamics. To address this limitation, we propose the use of the q-exponential process (Q-EP), a recently developed generalization of GPs designed to better handle data with abrupt changes and to more accurately model derivative information. We advocate for Q-EP as a superior alternative to GPs in solving PDEs and associated inverse problems. Leveraging sparse variational inference, our method enables principled uncertainty quantification - a capability not naturally afforded by neural network-based approaches. Through a series of experiments, including the Eikonal equation, Burgers' equation, and an inverse Darcy flow problem, we demonstrate that the variational Q-EP method consistently yields more accurate solutions while providing meaningful uncertainty estimates.

Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the reproducibility of LLM performance is fragile: changing system configuration, such as evaluation batch size, GPU count, and GPU version, can introduce significant differences in the generated responses. This issue is especially pronounced in reasoning models, where minor rounding differences in early tokens can cascade into divergent chains of thought, ultimately affecting accuracy. For instance, under bfloat16 precision with greedy decoding, a reasoning model like DeepSeek-R1-Distill-Qwen-7B can exhibit up to 9% variation in accuracy and 9,000 tokens difference in response length due to differences in GPU count, type, and evaluation batch size.

Diffusion Transformers (DiTs) have demonstrated strong performance in generative modeling, particularly in image synthesis, making them a compelling choice for molecular conformer generation. However, applying DiTs to molecules introduces novel challenges, such as integrating discrete molecular graph information with continuous 3D geometry, handling Euclidean symmetries, and designing conditioning mechanisms that generalize across molecules of varying sizes and structures. We propose DiTMC, a framework that adapts DiTs to address these challenges through a modular architecture that separates the processing of 3D coordinates from conditioning on atomic connectivity. To this end, we introduce two complementary graph-based conditioning strategies that integrate seamlessly with the DiT architecture. These are combined with different attention mechanisms, including both standard non-equivariant and SO(3)-equivariant formulations, enabling flexible control over the trade-off between between accuracy and computational efficiency. Experiments on standard conformer generation benchmarks (GEOMQM9, -DRUGS, -XL) demonstrate that DiTMC achieves state-of-the-art precision and physical validity. Our results highlight how architectural choices and symmetry priors affect sample quality and efficiency, suggesting promising directions for large-scale generative modeling of molecular structures.

In-context learning (ICL) enables large language models to perform few-shot learning by conditioning on labeled examples in the prompt. Despite its flexibility, ICL suffers from instability - especially as prompt length increases with more demonstrations. To address this, we treat ICL as a source of weak supervision and propose a parameter-efficient method that disentangles demonstration-induced latent shifts from those of the query. An ICL-based teacher generates pseudo-labels on unlabeled queries, while a student predicts them using only the query input, updating a lightweight adapter.

A.1 Behavioral Task A male nonhuman primate (NHP, Macaca mulatta), Monkey N (age 7 at the beginning of the dataset, age 11 at the end), was trained to perform a trial-based, two degree-of-freedom (DOF) dexterous finger movement task, shown in Figure 1. During all sessions, Monkey N sat in a primate chair (Crist Instruments, Hagerstown, MA) in a shielded chamber, with his arms fixed at his sides and flexed 90 degrees at the elbow, resting on a table. The left hand was positioned securely in a manipulandum, which used bend sensors (FS-L-0073-103-ST, Spectra Symbol, Salt Lake City, UT) to measure the flexion of two finger groups, index (IDX) and middle-ring-small (MRS). At the beginning of each experimental session (and as needed throughout a session), these flexion sensors were calibrated such that a reading of 1 indicated full flexion of a finger group and a reading of 0 indicated full extension. These readings were used to update the positions of the corresponding finger groups of a virtual hand presented on a screen in front of Monkey N. Bend sensor values were sampled at 1000 Hz. Updates to the virtual hand were limited to the refresh rate of the monitor (120 Hz). The task itself involved trial-based target acquisitions. At the beginning of each trial, two color-coded spherical targets, one for each DOF, were placed on the screen, covering 15% of the full arc of motion (see Figure 1A). Monkey N then acquired the targets by moving his fingers to the correct positions and holding his position for 750 ms.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach hasnot yet led to comparable fidelity. There are several key obstacles: (i) the datalikelihood term is usually intractable; (ii) learned generative models cannot be directly conditioned on the distorted observations, leading to conflicting objectives between data likelihood and prior; and (iii) the reconstructions can deviate from theobserved data.

In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to approximate the value function. Leveraging a continuous-time version of the dynamic programming principle, we derive two different training objectives based on the Hamilton-Jacobi-Bellman equation, ensuring that the networks capture the underlying stochastic dynamics. Empirical evaluations on different problems illustrate the accuracy and scalability of our approach, demonstrating its effectiveness in solving complex high-dimensional stochastic control tasks. Code is available at https://github.com/jdupret97/

Top-kdecoding is a widely used method for sampling from LLMs: at each token, only the largest k next-token-probabilities are kept, and the next token is sampled after renormalizing them to sum to unity. Top-kand other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-k decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-k decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We introduce Bregman decoders obtained by minimizing a separable Bregman divergence (for both the primal and dual cases) with a sparsity-inducing ℓ0-regularization; in particular, these decoders are adaptive in the sense that the sparsity parameter k is chosen depending on the underlying token distribution. Despite the combinatorial nature of the sparse Bregman objective, we show how to optimize it efficiently for a large class of divergences. We prove that (i) the optimal decoding strategies are greedy, and further that (ii) the objective is discretely convex in k, such that the optimal k can be identified in logarithmic time. We note that standard top-k decoding arises as a special case for the KL divergence, and construct new decoding strategies with substantially different behaviors (e.g., non-linearly up-weighting larger probabilities after renormalization).

Estimating the Kullback-Leibler (KL) divergence between language models has many applications, e.g., reinforcement learning from human feedback (RLHF), interpretability, and knowledge distillation. However, computing the exact KL divergence between two arbitrary language models is intractable. Thus, practitioners often resort to sampling-based estimators. While it is easy to fashion a simple Monte Carlo (MC) estimator that provides an unbiased estimate of the KL divergence between language models, this estimator notoriously suffers from high variance and can even result in a negative estimate of the KL divergence, a non-negative quantity. In this paper, we introduce a Rao-Blackwellized estimator that is unbiased and provably has variance less than or equal to that of the standard Monte Carlo estimator. In an empirical study on sentiment-controlled fine-tuning, we show that our estimator provides more stable KL estimates and reduces variance substantially. Additionally, we derive an analogous Rao-Blackwellized estimator of the gradient of the KL divergence, which leads to more stable training and produces models that more frequently appear on the Pareto frontier of reward vs. KL compared to the ones trained with the MC estimator of the gradient.