苹果公司

Imitation learning for manipulation has a well-known data scarcity problem. Unlike natural language and 2D computer vision, there is no Internet-scale corpus of data for dexterous manipulation. One appealing option is egocentric human video, a passively scalable data source. However, existing large-scale datasets such as Ego4D do not have native hand pose annotations and do not focus on object manipulation. To this end, we use Apple Vision Pro to collect EgoDex: the largest and most diverse dataset of dexterous human manipulation to date. EgoDex has 829 hours of egocentric video with paired 3D hand and finger tracking data collected at the time of recording, where multiple calibrated cameras and on-device SLAM can be used to precisely track the pose of every joint of each hand. The dataset covers a wide range of diverse manipulation behaviors with everyday household objects in 194 different tabletop tasks ranging from tying shoelaces to folding laundry. Furthermore, we train and systematically evaluate imitation learning policies for hand trajectory prediction on the dataset, introducing metrics and benchmarks for measuring progress in this increasingly important area. By releasing this large-scale dataset, we hope to push the frontier of robotics, computer vision, and foundation models. EgoDex is publicly available for download at https://github.com/apple/ml-egodex.

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial redundancy, which limits the efficiency of LRMs. In this paper, we investigate RL-based approaches to promote reasoning efficiency. Specifically, we first present a unified framework that formulates various efficient reasoning methods through the lens of length-based reward shaping. Building on this perspective, we propose a novel **L**ength-b**A**sed **S**t**E**p **R**eward shaping method (LASER), which employs a step function as the reward based on target length. LASER surpasses previous methods, achieving a superior trade-off between performance and efficiency. Next, we further extend LASER based on two key intuitions: (1) The reasoning behavior of the model evolves dynamically during training, necessitating reward specifications that are also adaptive and dynamic; (2) Rather than uniformly encouraging shorter or longer chains of thought (CoT), we posit that length-based reward shaping should be difficulty-aware i.e., it should penalize lengthy CoTs more for easy queries. This approach is expected to facilitate a combination of fast and slow thinking, leading to a better overall tradeoff. The resulting method is termed LASER-D (**D**ynamic and **D**ifficulty-aware). Experiments on five open-weight models from 1.5B to 32B demonstrate that our approach significantly enhances both reasoning performance and response length efficiency. For instance, LASER-D achieves a **5.3** improvement on AIME2024 while reducing token usage by **64**%. Further analysis reveals that our RL-based compression produces more concise reasoning patterns with less redundant ``self-reflections''. All resources (Models, Code, Data) are available at https://github.com/hkust-nlp/Laser.

Recent advances in multimodal models have demonstrated remarkable text-guided image editing capabilities, with systems like GPT-4o and Nano-Banana setting new benchmarks. However, the research community's progress remains constrained by the absence of large-scale, high-quality, and openly accessible datasets built from real images. We introduce Pico-Banana-400K, a comprehensive 400K-image dataset for instruction-based image editing. Our dataset is constructed by leveraging Nano-Banana to generate diverse edit pairs from real photographs in the OpenImages collection. What distinguishes Pico-Banana-400K from previous synthetic datasets is our systematic approach to quality and diversity. We employ a fine-grained image editing taxonomy to ensure comprehensive coverage of edit types while maintaining precise content preservation and instruction faithfulness through MLLM-based quality scoring and careful curation. Beyond single turn editing, Pico-Banana-400K enables research into complex editing scenarios. The dataset includes three specialized subsets: (1) a 72K-example multi-turn collection for studying sequential editing, reasoning, and planning across consecutive modifications; (2) a 56K-example preference subset for alignment research and reward model training; and (3) paired long-short editing instructions for developing instruction rewriting and summarization capabilities. By providing this large-scale, high-quality, and task-rich resource, Pico-Banana-400K establishes a robust foundation for training and benchmarking the next generation of text-guided image editing models.

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated verification with complete accuracy, motivating recent efforts to build specialized prover LLMs that generate verifiable proofs in formal languages. However, a significant gap remains: current prover LLMs solve substantially fewer problems than general-purpose LLMs operating in natural language. We introduce Hilbert, an agentic framework that bridges this gap by combining the complementary strengths of informal reasoning and formal verification. Our system orchestrates four components: an informal LLM that excels at mathematical reasoning, a specialized prover LLM optimized for Lean 4 tactics, a formal verifier, and a semantic theorem retriever. Given a problem that the prover is unable to solve, Hilbert employs recursive decomposition to split the problem into subgoals that it solves with the prover or reasoner LLM. It leverages verifier feedback to refine incorrect proofs as necessary. Experimental results demonstrate that Hilbert, substantially outperforms existing approaches on key benchmarks, achieving 99.2\% on miniF2F, 6.6\% points above the best publicly available method. Hilbert achieves the \textbf{strongest known result} from a publicly available model on PutnamBench. It solves 462/660 problems (70.0\%), outperforming proprietary approaches like SeedProver (50.4\%) and achieving a 422\% improvement over the best publicly available baseline. Thus, Hilbert effectively narrows the gap between informal reasoning and formal proof generation. Code is available at ~\url{https://github.com/Rose-STL-Lab/ml-hilbert}.

Can a large language model (LLM) improve at code generation using only its own raw outputs, without a verifier, a teacher model, or reinforcement learning? We answer in the affirmative with simple self-distillation (SSD): sample solutions from the model with certain temperature and truncation configurations, then fine-tune on those samples with standard supervised fine-tuning. SSD improves Qwen3-30B-Instruct from 42.4