#01Jul 17, 2026
cs.LG
Understanding Reasoning from Pretraining to Post-Training
Jingyan Shen, Ang Li, Salman Rahman and 4 more
Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it. As a result, two basic questions remain open: (1) how do pretraining choices (model size, data) shape the returns to RL compute, and (2) what does RL actually do to the model? These questions are difficult to study in the standard LLM setting: pretraining corpora are vast and uncontrolled, making it hard to attribute behaviors to pretraining versus RL, and systematic compute sweeps across both stages are prohibitively expensive. To address these challenges, we use chess as a controlled testbed for studying reasoning across the full pretraining-to-post-training pipeline. We follow the standard LLM training pipeline by pretraining language models from 5M to 1B parameters on human chess games, supervised fine-tuning on synthetic reasoning traces, and running RL on chess puzzles with verifiable rewards. Using this framework, we find that the post-RL performance at given RL compute level is well-predicted from the pretraining loss, and slope of the RL reward curves improves approximately linearly with the pretraining tokens. Beyond scaling, we find that RL does not simply sharpen the SFT policy: on easy puzzles it amplifies correct moves the SFT policy already preferred, while on hard puzzles it surfaces correct moves that were nearly absent under SFT. We further test whether our findings transfer beyond chess by training a 1B language model on math-domain text, where the same predictive pattern emerges: longer-pretrained checkpoints reach higher post-RL performance and improve faster under RL. In sum, we provide a quantitative account of the pretraining-to-RL interface and a controlled testbed for studying the science of reasoning across the full pretraining-to-post-training pipeline.
#02Jul 17, 2026
cs.LG
When Model Merging Rivals Joint Multi-Task Reinforcement Learning: A Task-Vector Geometry Analysis
S. Aaron McClendon
Model merging is promoted as a substitute for joint multi-task training, yet in the reinforcement-learning setting this substitution is essentially never tested against the baseline it claims to replace: methods merge independently released agents precisely because a joint model is unavailable. We build the missing comparison. Training difficulty-1 and difficulty-2 Qwen3-8B specialists on the AppWorld agent benchmark with LOOP, we merge them (TIES, RAM+) and pit the result against a jointly trained model on the same data. On task-goal completion, merging matches joint RL -- and every merge variant is statistically indistinguishable. To explain why merge method does not matter here, we measure the geometry of the specialists' task vectors, which carries no task-sampling noise: they are near-orthogonal (cosine 0.06 - 0.10) despite ~65% support overlap, a small, shared direction that grows over training and that we calibrate against a random-init floor and a same-run ceiling to confirm it reflects learning, not the low-rank parameterization. Because direction and support are decoupled, support and sign-based merging (RAM, TIES) collapse to near-uniform averaging. We release all code and statistics.
#03Jul 17, 2026
eess.SY
Pick-to-Learn Calibration of an MPC Policy for an Origin-to-Destination Flight Problem
Marco C. Campi, Simone Garatti
This paper illustrates the Pick-to-Learn methodology applied to the calibration of a Model Predictive Control policy. While developed around a specific example, the presentation is meant to highlight a methodology of broad applicability. The example concerns an aircraft traveling from an origin point to a destination point in the presence of uncertain crosswinds and a low-connectivity zone that should be avoided. The MPC policy is parameterized by two hyperparameters, which are selected from data by the P2L procedure. Starting from a dataset of 400 wind realizations, also called scenarios, P2L identifies a final compression set containing only two informative scenarios. The resulting MPC policy avoids the low-connectivity zone on all available scenarios and, according to the P2L theory, satisfies a probabilistic risk bound of $4.8\%$ at confidence level $1-10^{-5}$, where the risk is the probability of entering the low-connectivity zone in a future flight under a new wind realization not included in the sample.
#04Jul 17, 2026
cs.AI
CRAFT: Clustering Rubrics to Diagnose Weak LLM Capabilities and Generate Targeted Fine-Tuning Data
Vipul Gupta, Zihao Wang, Razvan-Gabriel Dumitru and 3 more
Evaluations should do more than measure a models current performance. They should tell us what to fix for the next model iteration and provide a way to generate targeted post training data. Most evaluation pipelines identify weak examples, topics, or categories, but they leave the underlying capability failure implicit: they say where a model fails, not why. We introduce CRAFT, a method that converts any rubric based evaluation dataset into a model specific diagnosis of weak capabilities. CRAFT treats each grading criterion as a capability probe: it extracts a capability description from every prompt rubric pair, clusters these descriptions into a hierarchical capability tree, scores the target model at every node, and selects low performing nodes dynamically across tree levels, at the granularity where each failure is clearest. The selected weak capabilities then direct the generation of targeted supervised finetuning data. Holding the data generation, finetuning, and evaluation setup fixed, we compare CRAFT against prompt level EvalTree clustering and untargeted random generation on four open source models, two professional domains (finance and legal), and 13 held out benchmarks disjoint from the diagnostic data. CRAFT achieves the strongest finance domain average for all four models under repeated temperature decoding; on legal domain, it is strongest for three of four models and remains within the decoding variance bands of the best baseline on the fourth. Diagnosing weaknesses at the level of rubric criteria, rather than prompts or categories, thus yields both a sharper picture of what a model cannot do and measurably better models after finetuning on that diagnosis.
#05Jul 17, 2026
cs.LG
A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing
Owen Lockwood, Jérémy Béjanin, Joost Bus and 4 more
To address the escalating energy and latency demands of machine-learning workloads, we introduce a blueprint for an energy-efficient and fast thermodynamic computing stack that leverages stochastic analog processes in physical hardware. In this work, we focus on energy-based thermodynamic computing where the stochastic process is well described by Langevin dynamics with tunable energy potentials. The implementation of such potentials in physical hardware enables us to generate and sample from basic parameterized energy-based models. We demonstrate how to construct and train popular classes of machine learning models based on these hardware-native energy-based models, using the framework of probabilistic graphical models. We analyze the runtime and energy consumption of different models in this thermodynamic paradigm based on theoretical considerations and numerical studies. As a preliminary experimental realization of such hardware, we present our stochastic analog superconducting circuits driven by thermal noise. Together, these results outline a path toward energy-efficient thermodynamic hardware for probabilistic machine learning.