We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce FERMAT, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through FERMAT: automatically scoring the interestingness of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even stateof-the-art PRMs can be poorly calibrated. Specifically, they tend to overestimate the success probability that a partial reasoning step will lead to a correct final answer, particularly when smaller LLMs are used to complete the reasoning trajectory. To address this, we present a calibration approach--performed via quantile regression-- that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the compute budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective IAS, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Out-of-tree kernel patches are essential for adapting the Linux kernel to new hardware or enabling specific functionalities. Maintaining and updating these patches across different kernel versions demands significant effort from experienced engineers. Large language models (LLMs) have shown remarkable progress across various domains, suggesting their potential for automating out-of-tree kernel patch migration. However, our findings reveal that LLMs, while promising, struggle with incomplete code context understanding and inaccurate migration point identification. In this work, we propose MIGGPT, a framework that employs a novel code fingerprint structure to retain code snippet information and incorporates three meticulously designed modules to improve the migration accuracy and efficiency of out-of-tree kernel patches. Furthermore, we establish a robust benchmark using real-world out-of-tree kernel patch projects to evaluate LLM capabilities. Evaluations show that MIGGPT significantly outperforms the direct application of vanilla LLMs, achieving an average completion rate of 74.07%

Large language model (LLM) decoding suffers from high latency due to fragmented execution across operators and heavy reliance on off-chip memory for data exchange and reduction. This execution model limits opportunities for fusion and incurs significant memory traffic and kernel launch overhead. While modern architectures such as NVIDIA Hopper provide distributed shared memory and low-latency intra-cluster interconnects, they expose only low-level data movement instructions, lacking structured abstractions for collective on-chip communication. To bridge this software-hardware gap, we introduce two cluster-level communication primitives, ClusterReduce and ClusterGather, which abstract common communication patterns and enable structured, high-speed data exchange and reduction between thread blocks within a cluster, allowing intermediate results to be on-chip without involving off-chip memory. Building on these abstractions, we design ClusterFusion, an execution framework that schedules communication and computation jointly to expand operator fusion scope by composing decoding stages such as QKVProjection, Attention, and Output Projection into a single fused kernels. Evaluations on H100 GPUs show that ClusterFusion outperforms state-of-the-art inference frameworks by 1.61 on average in end-to-end latency across different models and configurations.

Reinforcement fine-tuning (RFT) is essential for enhancing the reasoning and generalization capabilities of large language models, but its success heavily relies on the quality of the training data. While data selection has been extensively studied in supervised learning, its role in reinforcement learning, particularly during the RFT stage, remains largely underexplored. In this work, we introduce RFT-Inf, the first influence estimator designed for data in reinforcement learning. RFT-Inf quantifies the importance of each training example by measuring how its removal affects the final training reward, offering a direct estimate of its contribution to model learning. To ensure scalability, we propose a first-order approximation of the RFT-Inf score by backtracking through the optimization process and applying temporal differentiation to the sample-wise influence term, along with a first-order Taylor approximation to adjacent time steps. This yields a lightweight, gradient-based estimator that evaluates the alignment between an individual sample's gradient and the average gradient direction of all training samples, where a higher degree of alignment implies greater training utility. Extensive experiments demonstrate that RFT-Inf consistently improves reward performance and accelerates convergence in reinforcement fine-tuning.

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation-based approaches underpin many state-of-the-art likelihood estimation models, yet they often face slow convergence and limited theoretical understanding. In this paper, we derive a tighter likelihood bound for noise-driven models to improve both the accuracy and efficiency of maximum likelihood learning. Our key insight extends the classical Kullback-Leibler (KL) divergence-Fisher information relationship to arbitrary noise perturbations, going beyond the Gaussian assumption and enabling structured noise distributions. This formulation allows flexible use of randomized noise distributions that naturally account for sensor artifacts, quantization effects, and data distribution smoothing, while remaining compatible with standard diffusion training. Treating the diffusion process as a Gaussian channel, we further express the mismatched entropy between data and model, showing that the proposed objective upper-bounds the negative log-likelihood (NLL). In experiments, our models achieve competitive NLL on CIFAR-10 and state-of-the-art results on ImageNet across multiple resolutions, all without data augmentation, and the framework extends naturally to discrete data.

Unrolledpolynomials. Recently, diagonal alternatives have shown to reach a similar level of

Robust policy evaluation for non-rectangular uncertainty set is generally NP-hard, even in approximation. Consequently, existing approaches suffer from either exponential iteration complexity or significant accuracy gaps. Interestingly, we identify a powerful class of Lp-bounded uncertainty sets that avoid these complexity barriers due to their structural simplicity. We further show that this class can be decomposed into infinitely many sa-rectangular Lp-bounded sets and leverage its structural properties to derive a novel dual formulation for Lp robust Markov Decision Processes (MDPs). This formulation reveals key insights into the adversary's strategy and leads to the first polynomial-time robust policy evaluation algorithm for L1-normed non-rectangular robust MDPs.

Multilingual reasoning remains a significant challenge for large language models (LLMs), with performance disproportionately favoring high-resource languages. Drawing inspiration from cognitive neuroscience, which suggests that human reasoning functions largely independently of language processing, we hypothesize that LLMs similarly encode reasoning and language as separable components that can be disentangled to enhance multilingual reasoning. To evaluate this, we perform a causal intervention by ablating language-specific representations at inference time. Experiments on 10 open-weight LLMs spanning 11 typologically diverse languages show that this language-specific ablation consistently boosts multilingual reasoning performance. Layer-wise analyses further confirm that language and reasoning representations can be effectively disentangled throughout the model, yielding improved multilingual reasoning capabilities, while preserving top-layer language features remains essential for maintaining linguistic fidelity. Compared to post-training methods such as supervised fine-tuning or reinforcement learning, our training-free language-reasoning disentanglement achieves comparable or superior results with minimal computational overhead. These findings shed light on the internal mechanisms underlying multilingual reasoning in LLMs and suggest a lightweight and interpretable strategy for improving cross-lingual generalization.

"Caught in a landslide, no escape from reality" summarizes the state of the research in AI offense: an attack might work on paper but does not necessarily in practice. In the last 5 years, we have seen the rise of latency attacks against computer vision systems. Most of them targeted 2D object detection, especially its Non-MaxSuppression (NMS) block, via adversarial images. However, we uncovered that, when tested in realistic deployment settings, the NMS latency attacks, accepted to top conferences, have very limited negative effects. In this paper, we define an evaluation framework (EVADE) to assess the practicality of attacks, and apply it to state-of-the-art NMS latency attacks.