arXiv:2604.03789v1 Announce Type: cross Abstract: Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework for tackling research-level mathematical problems that integrates natural language reasoning with formal verification, enabling end-to-end problem solving with minimal human intervention. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas mimics the workflow of human mathematicians by combining reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with our formal theorem search engine LeanSearch, translates informal arguments into formalized Lean 4 projects through structured task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we automatically resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent is capable of autonomously filling nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, substantially reduce human effort, and offer a concrete instantiation of human-AI collaborative mathematical research.

arXiv:2603.24239v2 Announce Type: replace-cross Abstract: Dynamism is common in AI computation, e.g., the dynamic tensor shapes and the dynamic control flows in models. Due to the long compilation time, existing runtime compilation damages the model efficiency, while the offline compilers either suffer from the long compilation time and device memory footprint to cover all the possible execution instances of a dynamic model, or sacrifice optimization opportunities for usability. In this paper, we rethink the feasibility of runtime compilation for dynamic models and identify that the key for it to work is to speed up the compilation or hide the compilation overhead. To do this, we propose a real-time compiler, DVM. In DVM, we design a runtime operator compiler based on a bytecode virtual machine to perform effective and efficient compilation for each dynamic operator instance given its input. Specifically, instead of compiling programs into machine code, we encode the operator program into bytecode on the CPU and decode the bytecode into virtual instructions for direct execution on the NPU. Based on the runtime operator compiler, we further propose an operator fuser, which performs symbol-deduction-based fusion on static graphs and runtime fusion on dynamic graphs. Both pattern- and stacking-based fusion are supported to increase fusion opportunities. Evaluation on operators, subgraphs, and models shows that, compared with TorchInductor, PyTorch-eager and MindSpore-graph-O0, we are up to 11.77$\times$ better in terms of the operator/model efficiency and up to 5 orders of magnitude faster in terms of the maximum compilation time.

arXiv:2603.24176v2 Announce Type: replace-cross Abstract: Capturing dynamic spatiotemporal neural activity is essential for understanding large-scale brain mechanisms. Functional magnetic resonance imaging (fMRI) provides high-resolution cortical representations that form a strong basis for characterizing fine-grained brain activity patterns. The high acquisition cost of fMRI limits large-scale applications, therefore making high-quality fMRI reconstruction a crucial task. Electroencephalography (EEG) offers millisecond-level temporal cues that complement fMRI. Leveraging this complementarity, we present an EEG-conditioned framework for reconstructing dynamic fMRI as continuous neural sequences with high spatial fidelity and strong temporal coherence at the cortical-vertex level. To address sampling irregularities common in real fMRI acquisitions, we incorporate a null-space intermediate-frame reconstruction, enabling measurement-consistent completion of arbitrary intermediate frames and improving sequence continuity and practical applicability. Experiments on the CineBrain dataset demonstrate superior voxel-wise reconstruction quality and robust temporal consistency across whole-brain and functionally specific regions. The reconstructed fMRI also preserves essential functional information, supporting downstream visual decoding tasks. This work provides a new pathway for estimating high-resolution fMRI dynamics from EEG and advances multimodal neuroimaging toward more dynamic brain activity modeling.

arXiv:2511.02872v4 Announce Type: replace-cross Abstract: Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth, breadth, and abstraction of modern mathematical research. To bridge this gap, we introduce FATE (Formal Algebra Theorem Evaluation), a new benchmark series in formal algebra designed to chart a course toward advanced mathematical reasoning. We present two new components, FATE-H and FATE-X, each with 100 problems in abstract and commutative algebra. The FATE series spans a difficulty spectrum from undergraduate exercises to problems exceeding PhD qualifying exams. Notably, FATE-X is the first formal benchmark to surpass both PhD-level exam difficulty and the coverage of the Mathlib library. Our evaluations of state-of-the-art LLM provers on this new benchmark reveal a stark performance gap compared to contest math: the best model achieves only 3% (pass@64) accuracy on FATE-H and 0% on FATE-X. Our two-stage evaluation reveals that models' natural-language reasoning is notably more accurate than their ability to formalize this reasoning. We systematically classify the common errors that arise during this formalization process. Furthermore, a comparative study shows that a specialized prover can exhibit less effective reflection than general-purpose models, reducing its accuracy at the natural-language stage. We believe FATE provides a robust and challenging benchmark that establishes essential checkpoints on the path toward research-level formal mathematical reasoning.