Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive. We introduce Pythagoras-Prover, a compute-efficient open-source family of Lean theorem provers built for practical compute budgets. The family spans two generation paradigms: autoregressive models at 4B and 32B parameters, and a first proof-of-concept diffusion-based prover (4B) that iteratively refines Lean proofs at inference time. For training efficiency, we build a Lean-verified corpus stratified into easy, medium, and hard problems for curriculum SFT, so models acquire proof skills progressively from shorter, simpler proofs to longer, harder ones. During SFT, a dynamic proof-reasoning filtering scheme preserves informative proof traces while keeping each instance within an 8k-token context budget. We also introduce Augmented Lean Formalisation (ALF), which expands scarce verified corpora into variants of formal statements, populated via self-distillation for extra training signal without formally verifying every mutated instance. By perturbing known problems while preserving their formal character, ALF reduces reliance on any statement's surface form. Empirically, Pythagoras-Prover-4B surpasses DeepSeek-Prover-V2-671B at pass@32 on MiniF2F-Test (86.1% vs 82.4%) with ~167x fewer parameters, while Pythagoras-Prover-32B sets the open-source state of the art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems. We release MiniF2F-ALF, an ALF-mutated contamination-sensitive benchmark on which every evaluated model loses accuracy; here our 32B remains strongest and our 4B matches the prior state of the art, Goedel-Prover-V2-32B.

Structure from Reasoning, Numbers from Search: On-Premise Open LLMs as Structural Priors for Coupled MIMO Controller Tuning

Tuning controllers for strongly coupled multi-input multi-output (MIMO) industrial processes is hard: decentralized classical auto-tuning ignores loop interaction, and local numerical optimization from natural initializations stalls in the resulting non-convex cost landscape. We ask whether on-premise open-source large language models (LLMs), which keep data on-site and need no plant model, can help. On a single-loop CSTR, classical relay-feedback tuning (IAE 0.106, near the 0.102 optimum) beats an LLM tuner (0.162): for simple loops the LLM adds nothing. The picture inverts on a strongly coupled quadruple-tank with conflicting set-points, scored by a penalized cost J = IAE + lambda*TV(u) that rewards tracking without chattering actuators. There, naive relay tuning (J ~ 28.6) and naive LLM tuning (29.7) are no better than open loop (22.7), and a local optimizer from balanced starts fails in 10/10 runs. A scaffolded open LLM instead reasons about the coupling, proposes the counter-intuitive asymmetric structure, and reaches J ~ 16.9 +/- 0.2 from any start; refining it with a classical optimizer attains the smooth global optimum (J ~ 12.0, 10/10 vs. 0/10), which even applies a non-obvious negative integral correction decentralized tuning cannot. A global optimizer (differential evolution) also reaches this optimum, so the LLM is not the only route; its advantage is sample efficiency and interpretability: a usable controller in 18 evaluations (where the global optimizer is worse than open loop) plus a stated rationale. This edge grows with dimension, reaching ~6x fewer evaluations on a 3x3 plant. The behaviour generalizes across four open models, and on a benign plant the LLM offers no advantage, sharpening the boundary. We contribute a reproducible benchmark delimiting when open LLMs help in control tuning: not as optimizers, but as a sample-efficient, interpretable structural prior.

Multilingual Idioms in Sentences and Conversations Across High-, Medium-, and Low-Resource Languages

Idiomatic expressions pose a major challenge for multilingual NLP because their meanings shift between figurative and literal usage, often requiring context for accurate interpretation. Prior work has focused on high-resource languages typically evaluates isolated idiom-meaning questions, overlooking realistic discourse. We introduce MIDI, a multilingual idiom dataset spanning 3 high-, 3 medium-, and 12 low-resource languages, curated by native speakers. Unlike previous datasets, MIDI provides idioms embedded in both sentence-level and conversational contexts, capturing both literal and figurative readings. Benchmarking state-of-the-art models shows that idiom comprehension degrades in low-resource languages and that, in all resource tiers, literal interpretations are substantially harder than figurative ones. Conversational context improves performance but does not eliminate these disparities. Through controlled tests and interventions on hidden representations, we further separate memorization from reasoning, exposing core limitations of current models.

Reinforcement Learning with Robust Rubric Rewards

While Reinforcement Learning with Verifiable Rewards (RLVR) is effective for deterministically checkable tasks, many vision-language tasks are partially verifiable, demanding multi-criteria supervision (e.g., perceptual details, reasoning steps, and constraints). Rubrics provide a natural interface for this fine-grained supervision, but their effectiveness depends on the execution accuracy during online RL. We propose Reinforcement Learning with Robust Rubric Rewards ($\text{RLR}^3$), extending RLVR from task-level verification to criterion-level verification. $\text{RLR}^3$ routes instance-specific rubrics through two execution paths: an LLM-as-an-extractor paired with a deterministic verifier, or an LLM-as-a-Judge for non-verifiable criteria. To ensure faithful scoring, $\text{RLR}^3$ introduce a minimal exposure strategy that masks ground truths from extractors and images from judges. Furthermore, $\text{RLR}^3$ employs hierarchical aggregation to prioritize essential criteria over additional criteria, and mitigates score saturation within rollout groups. Evaluated on Qwen3-VL-30B-A3B across 15 benchmarks, $\text{RLR}^3$ consistently outperforms RLVR, yielding a 4.7-point improvement over the base model and exceeding the official instruct-to-thinking model gap. Controlled audits confirm our deterministic verification and minimal exposure significantly reduce exploitable false positives.

Visual Preference Optimization with Rubric Rewards

The effectiveness of Direct Preference Optimization (DPO) depends on preference data that reflect the quality differences that matter in multimodal tasks. Existing pipelines often rely on off-policy perturbations or coarse outcome-based signals, which are not well suited to fine-grained visual reasoning. We propose rDPO, a preference optimization framework based on instance-specific rubrics. For each image-instruction pair, we create a checklist-style rubric of essential and additional criteria to score responses from any possible policies. The instruction-rubric pool is built offline and reused during the construction of on-policy data. On public reward modeling benchmarks, rubric-based prompting massively improves a 30B-A3B judge and brings it close to GPT-5.4. On public downstream benchmarks, rubric-based filtering raises the macro average to 82.69, whereas outcome-based filtering drops it to 75.82 from 81.14. When evaluating scalability on a comprehensive benchmark, rDPO achieves 61.01, markedly outperforming the style-constrained baseline (52.36) and surpassing the 59.48 base model. Together, these results show that visual preference optimization benefits from combining on-policy data construction with instance-specific criterion-level feedback.

Controllable Reasoning Models Are Private Thinkers

AI agents powered by reasoning models require access to sensitive user data. However, their reasoning traces are difficult to control, which can result in the unintended leakage of private information to external parties. We propose training models to follow instructions not only in the final answer, but also in reasoning traces, potentially under different constraints. We hypothesize that improving their instruction following abilities in the reasoning traces can improve their privacy-preservation skills. To demonstrate this, we fine-tune models on a new instruction-following dataset with explicit restrictions on reasoning traces. We further introduce a generation strategy that decouples reasoning and answer generation using separate LoRA adapters. We evaluate our approach on six models from two model families, ranging from 1.7B to 14B parameters, across two instruction-following benchmarks and two privacy benchmarks. Our method yields substantial improvements, achieving gains of up to 20.9 points in instruction-following performance and up to 51.9 percentage points on privacy benchmarks. These improvements, however, can come at the cost of task utility, due to the trade-off between reasoning performance and instruction-following abilities. Overall, our results show that improving instruction-following behavior in reasoning models can significantly enhance privacy, suggesting a promising direction for the development of future privacy-aware agents. Our code and data are available at https://github.com/UKPLab/arxiv2026-controllable-reasoning-models

SimuScene: Training and Benchmarking Code Generation to Simulate Physical Scenarios

Large language models (LLMs) have been extensively studied for tasks like math competitions, complex coding, and scientific reasoning, yet their ability to accurately represent and simulate physical scenarios via code remains underexplored. We propose SimuScene, the first systematic study that trains and evaluates LLMs on simulating physical scenarios across five physics domains and 52 physical concepts. We build an automatic pipeline to collect data, with human verification to ensure quality. The final dataset contains 7,659 physical scenarios with 334 human-verified examples as the test set. We evaluated 10 contemporary LLMs and found that even the strongest model achieves only a 21.5% pass rate, demonstrating the difficulty of the task. Finally, we introduce a reinforcement learning pipeline with visual rewards that uses a vision-language model as a judge to train textual models. Experiments show that training with our data improves physical simulation via code while substantially enhancing general code generation performance.

Neural Theorem Proving for Verification Conditions: A Real-World Benchmark

Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem Provers (ATPs) cannot prove, leading to a critical need for extensive manual proofs that burden practical application. While Neural Theorem Proving (NTP) has achieved significant success in mathematical competitions, demonstrating the potential of machine learning approaches to formal reasoning, its application to program verification--particularly VC proving--remains largely unexplored. Despite existing work on annotation synthesis and verification-related theorem proving, no benchmark has specifically targeted this fundamental bottleneck: automated VC proving. This work introduces Neural Theorem Proving for Verification Conditions (NTP4VC), presenting the first real-world multi-language benchmark for this task. From real-world projects such as Linux and Contiki-OS kernel, our benchmark leverages industrial pipelines (Why3 and Frama-C) to generate semantically equivalent test cases across formal languages of Isabelle, Lean, and Rocq. We evaluate large language models (LLMs), both general-purpose and those fine-tuned for theorem proving, on NTP4VC. Results indicate that although LLMs show promise in VC proving, significant challenges remain for program verification, highlighting a large gap and opportunity for future research.

TorchTraceAP: A New Benchmark Dataset for Detecting Performance Anti-Patterns in Computer Vision Models

Identifying and addressing performance anti-patterns in machine learning (ML) models is critical for efficient training and inference, but it typically demands deep expertise spanning system infrastructure, ML models and kernel development. While large tech companies rely on dedicated ML infrastructure engineers to analyze torch traces and benchmarks, such resource-intensive workflows are largely inaccessible to computer vision researchers in general. Among the challenges, pinpointing problematic trace segments within lengthy execution traces remains the most time-consuming task, and is difficult to automate with current ML models, including LLMs. In this work, we present the first benchmark dataset specifically designed to evaluate and improve ML models' ability to detect anti patterns in traces. Our dataset contains over 600 PyTorch traces from diverse computer vision models classification, detection, segmentation, and generation collected across multiple hardware platforms. We also propose a novel iterative approach: a lightweight ML model first detects trace segments with anti patterns, followed by a large language model (LLM) for fine grained classification and targeted feedback. Experimental results demonstrate that our method significantly outperforms unsupervised clustering and rule based statistical techniques for detecting anti pattern regions. Our method also effectively compensates LLM's limited context length and reasoning inefficiencies.

LLMBisect: Breaking Barriers in Bug Bisection with A Comparative Analysis Pipeline

Bug bisection has been an important security task that aims to understand the range of software versions impacted by a bug, i.e., identifying the commit that introduced the bug. However, traditional patch-based bisection methods are faced with several significant barriers: For example, they assume that the bug-inducing commit (BIC) and the patch commit modify the same functions, which is not always true. They often rely solely on code changes, while the commit message frequently contains a wealth of vulnerability-related information. They are also based on simple heuristics (e.g., assuming the BIC initializes lines deleted in the patch) and lack any logical analysis of the vulnerability. In this paper, we make the observation that Large Language Models (LLMs) are well-positioned to break the barriers of existing solutions, e.g., comprehend both textual data and code in patches and commits. Unlike previous BIC identification approaches, which yield poor results, we propose a comprehensive multi-stage pipeline that leverages LLMs to: (1) fully utilize patch information, (2) compare multiple candidate commits in context, and (3) progressively narrow down the candidates through a series of down-selection steps. In our evaluation, we demonstrate that our approach achieves significantly better accuracy than the state-of-the-art solution by more than 38\%. Our results further confirm that the comprehensive multi-stage pipeline is essential, as it improves accuracy by 60\% over a baseline LLM-based bisection method.