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TaoBench: Do Automated Theorem Prover LLMs Generalize Beyond MathLib?

arXiv:2603.12744v1 Announce Type: cross Abstract: Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.

Profiling of the mycobiome and metabolome: a comparative study of benign pulmonary nodules and lung adenocarcinoma

Front Cell Infect Microbiol. 2026 Feb 23;16:1732958. doi: 10.3389/fcimb.2026.1732958. eCollection 2026.

ABSTRACT

INTRODUCTION: Lung adenocarcinoma (LUAD), the most common subtype of non-small cell lung cancer, is a form of malignant pulmonary nodule that requires clinical differentiation from benign pulmonary nodules (BPN). The mechanisms underlying the development of LUAD are complex, and effective non-invasive methods for differentiating BPN from LUAD are lacking. This study aimed not only to distinguish BPN from LUAD using gut fungi and serum metabolites, but also to establish an integrated network of gut fungi-metabolite-cytokine interactions.

METHODS: Fecal and serum samples from individuals with BPN and patients with LUAD were subjected to internal transcribed spacer sequencing, ultra-performance liquid chromatography-tandem mass spectrometry, and multiplex Luminex assays to quantify gut fungi, metabolites, and cytokines, respectively.

RESULTS: A significant difference in gut fungal communities was observed between the BPN and LUAD groups. Multiple genera and species were more abundant in LUAD than in BPN. Docosapentaenoic acid n-6 (DPAn-6), indole-3-propionic acid (IPA), and interferon-γ-induced protein 10 (IP-10) were significantly elevated in the LUAD group. The integrated model established using a combination of gut fungi and metabolites demonstrated excellent performance in distinguishing BPN from LUAD. A network of interactions was established among differentially abundant gut fungi, serum metabolites, and cytokines.

CONCLUSION: Our study identifies a novel panel of fungal and metabolite biomarkers for differentiating between BPN and LUAD, and constructs a multi-omics network that provides new insights into investigating the mechanistic role of gut mycobiota dysbiosis in LUAD.

PMID:41809995 | PMC:PMC12968269 | DOI:10.3389/fcimb.2026.1732958

Evo: Autoregressive-Diffusion Large Language Models with Evolving Balance

arXiv:2603.06617v1 Announce Type: cross Abstract: We introduce \textbf{Evo}, a duality latent trajectory model that bridges autoregressive (AR) and diffusion-based language generation within a continuous evolutionary generative framework. Rather than treating AR decoding and diffusion generation as separate paradigms, Evo reconceptualizes text generation as a latent flow: each token is associated with a vector-valued embedding that evolves over a progression variable $t_i \in [0, 1]$, indicating its semantic maturity. Low $t_i$ values correspond to confident AR-like refinement, while high values invoke diffusion-style planning, allowing the model to adaptively balance AR and diffusion based on uncertainty. Theoretically, we show that both AR and diffusion models emerge as discretizations of a shared probability flow, and we derive Evo's training objective from a unified variational ELBO. The model is implemented as a time-conditioned Transformer governed by a shared vector field, trained end-to-end to jointly infer latent codes and their progression times. During decoding, Evo performs efficient, semantics-aware refinement, achieving high-quality outputs without sacrificing speed. Empirically, Evo 8B achieves state-of-the-art or highly competitive results on 15 diverse benchmarks, including reasoning (GSM8K, ARC-C), code generation (HumanEval, MBPP), and general language understanding, while maintaining fast inference speed. Our results demonstrate that Evo delivers a new paradigm for LLM design with strong generation quality, robust symbolic reasoning, and decoding efficiency.

Efficient Construction of Implicit Surface Models From a Single Image for Motion Generation

arXiv:2509.20681v2 Announce Type: replace-cross Abstract: Implicit representations have been widely applied in robotics for obstacle avoidance and path planning. In this paper, we explore the problem of constructing an implicit distance representation from a single image. Past methods for implicit surface reconstruction, such as NeuS and its variants generally require a large set of multi-view images as input, and require long training times. In this work, we propose Fast Image-to-Neural Surface (FINS), a lightweight framework that can reconstruct high-fidelity surfaces and SDF fields based on a single or a small set of images. FINS integrates a multi-resolution hash grid encoder with lightweight geometry and color heads, making the training via an approximate second-order optimizer highly efficient and capable of converging within a few seconds. Additionally, we achieve the construction of a neural surface requiring only a single RGB image, by leveraging pre-trained foundation models to estimate the geometry inherent in the image. Our experiments demonstrate that under the same conditions, our method outperforms state-of-the-art baselines in both convergence speed and accuracy on surface reconstruction and SDF field estimation. Moreover, we demonstrate the applicability of FINS for robot surface following tasks and show its scalability to a variety of benchmark datasets.

Bee: A High-Quality Corpus and Full-Stack Suite to Unlock Advanced Fully Open MLLMs

arXiv:2510.13795v4 Announce Type: replace-cross Abstract: Fully open multimodal large language models (MLLMs) currently lag behind proprietary counterparts, primarily due to a significant gap in data quality for supervised fine-tuning (SFT). Existing open-source datasets are often plagued by widespread noise and a critical deficit in complex reasoning data, such as Chain-of-Thought (CoT), which hinders the development of advanced model capabilities. Addressing these challenges, our work makes three primary contributions. First, we introduce Honey-Data-15M, a new SFT dataset comprising approximately 15 million QA pairs, processed through multiple cleaning techniques and enhanced with a novel dual-level (short and long) CoT enrichment strategy. Second, we introduce HoneyPipe, the data curation pipeline, and its underlying framework DataStudio, providing the community with a transparent and adaptable methodology for data curation that moves beyond static dataset releases. Finally, to validate our dataset and pipeline, we train Bee-8B, an 8B model on Honey-Data-15M. Experiments show that Bee-8B establishes a new state-of-the-art (SOTA) for fully open MLLMs, achieving performance that is competitive with, and in some cases surpasses, recent semi-open models such as InternVL3.5-8B. Our work delivers to the community a suite of foundational resources, including: the Honey-Data-15M corpus; the full-stack suite comprising HoneyPipe and DataStudio; training recipes; an evaluation harness; and the model weights. This effort demonstrates that a principled focus on data quality is a key pathway to developing fully open MLLMs that are highly competitive with their semi-open counterparts.

PRAM-R: A Perception-Reasoning-Action-Memory Framework with LLM-Guided Modality Routing for Adaptive Autonomous Driving

arXiv:2603.04222v1 Announce Type: cross Abstract: Multimodal perception enables robust autonomous driving but incurs unnecessary computational cost when all sensors remain active. This paper presents PRAM-R, a unified Perception-Reasoning-Action-Memory framework with LLM-Guided Modality Routing for adaptive autonomous driving. PRAM-R adopts an asynchronous dual-loop design: a fast reactive loop for perception and control, and a slow deliberative loop for reasoning-driven modality selection and memory updates. An LLM router selects and weights modalities using environmental context and sensor diagnostics, while a hierarchical memory module preserves temporal consistency and supports long-term adaptation. We conduct a two-stage evaluation: (1) synthetic stress tests for stability analysis and (2) real-world validation on the nuScenes dataset. Synthetic stress tests confirm 87.2% reduction in routing oscillations via hysteresis-based stabilization. Real-world validation on nuScenes shows 6.22% modality reduction with 20% memory recall while maintaining comparable trajectory accuracy to full-modality baselines in complex urban scenarios. Our work demonstrates that LLM-augmented architectures with hierarchical memory achieve efficient, adaptive multimodal perception in autonomous driving.

FUSAR-GPT : A Spatiotemporal Feature-Embedded and Two-Stage Decoupled Visual Language Model for SAR Imagery

arXiv:2602.19190v1 Announce Type: cross Abstract: Research on the intelligent interpretation of all-weather, all-time Synthetic Aperture Radar (SAR) is crucial for advancing remote sensing applications. In recent years, although Visual Language Models (VLMs) have demonstrated strong open-world understanding capabilities on RGB images, their performance is severely limited when directly applied to the SAR field due to the complexity of the imaging mechanism, sensitivity to scattering features, and the scarcity of high-quality text corpora. To systematically address this issue, we constructed the inaugural SAR Image-Text-AlphaEarth feature triplet dataset and developed FUSAR-GPT, a VLM specifically for SAR. FUSAR-GPT innovatively introduces a geospatial baseline model as a 'world knowledge' prior and embeds multi-source remote-sensing temporal features into the model's visual backbone via 'spatiotemporal anchors', enabling dynamic compensation for the sparse representation of targets in SAR images. Furthermore, we designed a two-stage SFT strategy to decouple the knowledge injection and task execution of large models. The spatiotemporal feature embedding and the two-stage decoupling paradigm enable FUSAR-GPT to achieve state-of-the-art performance across several typical remote sensing visual-language benchmark tests, significantly outperforming mainstream baseline models by over 12%.

On Predictability of Reinforcement Learning Dynamics for Large Language Models

arXiv:2510.00553v3 Announce Type: replace-cross Abstract: Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 8 LLMs and 7 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5 speedup while retaining \textgreater 96\% of reasoning performance without extra modules or hyperparameter tuning. This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.

Train Less, Learn More: Adaptive Efficient Rollout Optimization for Group-Based Reinforcement Learning

arXiv:2602.14338v1 Announce Type: cross Abstract: Reinforcement learning (RL) plays a central role in large language model (LLM) post-training. Among existing approaches, Group Relative Policy Optimization (GRPO) is widely used, especially for RL with verifiable rewards (RLVR) fine-tuning. In GRPO, each query prompts the LLM to generate a group of rollouts with a fixed group size $N$. When all rollouts in a group share the same outcome, either all correct or all incorrect, the group-normalized advantages become zero, yielding no gradient signal and wasting fine-tuning compute. We introduce Adaptive Efficient Rollout Optimization (AERO), an enhancement of GRPO. AERO uses an adaptive rollout strategy, applies selective rejection to strategically prune rollouts, and maintains a Bayesian posterior to prevent zero-advantage dead zones. Across three model configurations (Qwen2.5-Math-1.5B, Qwen2.5-7B, and Qwen2.5-7B-Instruct), AERO improves compute efficiency without sacrificing performance. Under the same total rollout budget, AERO reduces total training compute by about 48% while shortening wall-clock time per step by about 45% on average. Despite the substantial reduction in compute, AERO matches or improves Pass@8 and Avg@8 over GRPO, demonstrating a practical, scalable, and compute-efficient strategy for RL-based LLM alignment.
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