QED-Nano: Teaching a Tiny Model to Prove Hard Theorems

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math? In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages: (1) supervised fine-tuning to imbue good proof-writing styles by distilling from DeepSeek-Math-V2, (2) reinforcement learning (RL) with rubric-based rewards, and (3) expanding RL with a reasoning cache, which decomposes long proofs into iterative summarize-and-refine cycles and enables stronger test-time reasoning. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost. To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

Generalizable Audio-Visual Navigation via Binaural Difference Attention and Action Transition Prediction

In Audio-Visual Navigation (AVN), agents must locate sound sources in unseen 3D environments using visual and auditory cues. However, existing methods often struggle with generalization in unseen scenarios, as they tend to overfit to semantic sound features and specific training environments. To address these challenges, we propose the \textbf{Binaural Difference Attention with Action Transition Prediction (BDATP)} framework, which jointly optimizes perception and policy. Specifically, the \textbf{Binaural Difference Attention (BDA)} module explicitly models interaural differences to enhance spatial orientation, reducing reliance on semantic categories. Simultaneously, the \textbf{Action Transition Prediction (ATP)} task introduces an auxiliary action prediction objective as a regularization term, mitigating environment-specific overfitting. Extensive experiments on the Replica and Matterport3D datasets demonstrate that BDATP can be seamlessly integrated into various mainstream baselines, yielding consistent and significant performance gains. Notably, our framework achieves state-of-the-art Success Rates across most settings, with a remarkable absolute improvement of up to 21.6 percentage points in Replica dataset for unheard sounds. These results underscore BDATP's superior generalization capability and its robustness across diverse navigation architectures.

Evaluating the Formal Reasoning Capabilities of Large Language Models through Chomsky Hierarchy

The formal reasoning capabilities of LLMs are crucial for advancing automated software engineering. However, existing benchmarks for LLMs lack systematic evaluation based on computation and complexity, leaving a critical gap in understanding their formal reasoning capabilities. Therefore, it is still unknown whether SOTA LLMs can grasp the structured, hierarchical complexity of formal languages as defined by Computation Theory. To address this, we introduce ChomskyBench, a benchmark for systematically evaluating LLMs through the lens of Chomsky Hierarchy. Unlike prior work that uses vectorized classification for neural networks, ChomskyBench is the first to combine full Chomsky Hierarchy coverage, process-trace evaluation via natural language, and deterministic symbolic verifiability. ChomskyBench is composed of a comprehensive suite of language recognition and generation tasks designed to test capabilities at each level. Extensive experiments indicate a clear performance stratification that correlates with the hierarchy's levels of complexity. Our analysis reveals a direct relationship where increasing task difficulty substantially impacts both inference length and performance. Furthermore, we find that while larger models and advanced inference methods offer notable relative gains, they face severe efficiency barriers: achieving practical reliability would require prohibitive computational costs, revealing that current limitations stem from inefficiency rather than absolute capability bounds. A time complexity analysis further indicates that LLMs are significantly less efficient than traditional algorithmic programs for these formal tasks. These results delineate the practical limits of current LLMs, highlight the indispensability of traditional software tools, and provide insights to guide the development of future LLMs with more powerful formal reasoning capabilities.

Mitigating the ID-OOD Tradeoff in Open-Set Test-Time Adaptation

Open-set test-time adaptation (OSTTA) addresses the challenge of adapting models to new environments where out-of-distribution (OOD) samples coexist with in-distribution (ID) samples affected by distribution shifts. In such settings, covariate shift-for example, changes in weather conditions such as snow-can alter ID samples, reducing model reliability. Consequently, models must not only correctly classify covariate-shifted ID (csID) samples but also effectively reject covariate-shifted OOD (csOOD) samples. Entropy minimization is a common strategy in test-time adaptation to maintain ID performance under distribution shifts, while entropy maximization is widely applied to enhance OOD detection. Several studies have sought to combine these objectives to tackle the challenges of OSTTA. However, the intrinsic conflict between entropy minimization and maximization inevitably leads to a trade-off between csID classification and csOOD detection. In this paper, we first analyze the limitations of entropy maximization in OSTTA and then introduce an angular loss to regulate feature norm magnitudes, along with a feature-norm loss to suppress csOOD logits, thereby improving OOD detection. These objectives form ROSETTA, a $\underline{r}$obust $\underline{o}$pen-$\underline{se}$t $\underline{t}$est-$\underline{t}$ime $\underline{a}$daptation. Our method achieves strong OOD detection while maintaining high ID classification performance on CIFAR-10-C, CIFAR-100-C, Tiny-ImageNet-C and ImageNet-C. Furthermore, experiments on the Cityscapes validate the method's effectiveness in real-world semantic segmentation, and results on the HAC dataset demonstrate its applicability across different open-set TTA setups.

ComBench: A Repo-level Real-world Benchmark for Compilation Error Repair

Compilation errors pose pervasive and critical challenges in software development, significantly hindering productivity. Therefore, Automated Compilation Error Repair (ACER) techniques are proposed to mitigate these issues. Despite recent advancements in ACER, its real-world performance remains poorly evaluated. This can be largely attributed to the limitations of existing benchmarks, \ie decontextualized single-file data, lack of authentic source diversity, and biased local task modeling that ignores crucial repository-level complexities. To bridge this critical gap, we propose ComBench, the first repository-level, reproducible real-world benchmark for C/C++ compilation error repair. ComBench is constructed through a novel, automated framework that systematically mines real-world failures from the GitHub CI histories of large-scale open-source projects. Our framework contributes techniques for the high-precision identification of ground-truth repair patches from complex version histories and a high-fidelity mechanism for reproducing the original, ephemeral build environments. To ensure data quality, all samples in ComBench are execution-verified -- guaranteeing reproducible failures and build success with ground-truth patches. Using ComBench, we conduct a comprehensive evaluation of 12 modern LLMs under both direct and agent-based repair settings. Our experiments reveal a significant gap between a model's ability to achieve syntactic correctness (a 73% success rate for GPT-5) and its ability to ensure semantic correctness (only 41% of its patches are valid). We also find that different models exhibit distinct specializations for different error types. ComBench provides a robust and realistic platform to guide the future development of ACER techniques capable of addressing the complexities of modern software development.

PERMA: Benchmarking Personalized Memory Agents via Event-Driven Preference and Realistic Task Environments

Empowering large language models with long-term memory is crucial for building agents that adapt to users' evolving needs. However, prior evaluations typically interleave preference-related dialogues with irrelevant conversations, reducing the task to needle-in-a-haystack retrieval while ignoring relationships between events that drive the evolution of user preferences. Such settings overlook a fundamental characteristic of real-world personalization: preferences emerge gradually and accumulate across interactions within noisy contexts. To bridge this gap, we introduce PERMA, a benchmark designed to evaluate persona consistency over time beyond static preference recall. Additionally, we incorporate (1) text variability and (2) linguistic alignment to simulate erratic user inputs and individual idiolects in real-world data. PERMA consists of temporally ordered interaction events spanning multiple sessions and domains, with preference-related queries inserted over time. We design both multiple-choice and interactive tasks to probe the model's understanding of persona along the interaction timeline. Experiments demonstrate that by linking related interactions, advanced memory systems can extract more precise preferences and reduce token consumption, outperforming traditional semantic retrieval of raw dialogues. Nevertheless, they still struggle to maintain a coherent persona across temporal depth and cross-domain interference, highlighting the need for more robust personalized memory management in agents. Our code and data are open-sourced at https://github.com/PolarisLiu1/PERMA.

I3DM: Implicit 3D-aware Memory Retrieval and Injection for Consistent Video Scene Generation

Despite remarkable progress in video generation, maintaining long-term scene consistency upon revisiting previously explored areas remains challenging. Existing solutions rely either on explicitly constructing 3D geometry, which suffers from error accumulation and scale ambiguity, or on naive camera Field-of-View (FoV) retrieval, which typically fails under complex occlusions. To overcome these limitations, we propose I3DM, a novel implicit 3D-aware memory mechanism for consistent video scene generation that bypasses explicit 3D reconstruction. At the core of our approach is a 3D-aware memory retrieval strategy, which leverages the intermediate features of a pre-trained Feed-Forward Novel View Synthesis (FF-NVS) model to score view relevance, enabling robust retrieval even in highly occluded scenarios. Furthermore, to fully utilize the retrieved historical frames, we introduce a 3D-aligned memory injection module. This module implicitly warps historical content to the target view and adaptively conditions the generation on reliable warping regions, leading to improved revisit consistency and accurate camera control. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches, achieving superior revisit consistency, generation fidelity, and camera control precision.

LoopRPT: Reinforcement Pre-Training for Looped Language Models

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering a promising alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on the Ouro architecture across multiple model scales. Results demonstrate that LoopRPT consistently improves per-step representation quality, achieving Pareto dominance in accuracy-computation trade-offs. Notably, significant gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

To See is Not to Master: Teaching LLMs to Use Private Libraries for Code Generation

Large Language Models (LLMs) have shown strong potential for code generation, yet they remain limited in private-library-oriented code generation, where the goal is to generate code using APIs from private libraries. Existing approaches mainly rely on retrieving private-library API documentation and injecting relevant knowledge into the context at inference time. However, our study shows that this is insufficient: even given accurate required knowledge, LLMs still struggle to invoke private-library APIs effectively. To address this limitation, we propose PriCoder, an approach that teaches LLMs to invoke private-library APIs through automatically synthesized data. Specifically, PriCoder models private-library data synthesis as the construction of a graph, and alternates between two graph operators: (1) Progressive Graph Evolution, which improves data diversity by progressively synthesizing more diverse training samples from basic ones, and (2) Multidimensional Graph Pruning, which improves data quality through a rigorous filtering pipeline. To support rigorous evaluation, we construct two new benchmarks based on recently released libraries that are unfamiliar to the tested models. Experiments on three mainstream LLMs show that PriCoder substantially improves private-library-oriented code generation, yielding gains of over 20% in pass@1 in many settings, while causing negligible impact on general code generation capability. Our code and benchmarks are publicly available at https://github.com/eniacode/PriCoder.

A Skill-augmented Agentic Framework and Benchmark for Multi-Video Understanding

Multimodal Large Language Models have achieved strong performance in single-video understanding, yet their ability to reason across multiple videos remains limited. Existing approaches typically concatenate multiple videos into a single input and perform direct inference, which introduces training-inference mismatch, information loss from frame compression, and a lack of explicit cross-video coordination. Meanwhile, current multi-video benchmarks primarily emphasize event-level comparison, leaving identity-level matching, fine-grained discrimination, and structured multi-step reasoning underexplored. To address these gaps, we introduce MVX-Bench, a Multi-Video Cross-Dimension Benchmark that reformulates 11 classical computer vision tasks into a unified multi-video question-answering framework, comprising 1,442 questions over 4,255 videos from diverse real-world datasets. We further propose SAMA, a Skill-Augmented Agentic Framework for Multi-Video Understanding, which integrates visual tools, task-specific skills, and a conflict-aware verification mechanism to enable iterative and structured reasoning. Experimental results show that SAMA outperforms strong open-source baselines and GPT on MVX-Bench, and ablations validate the effectiveness of skill design and conflict resolution.