Can Large Language Models Reinvent Foundational Algorithms?

LLMs have shown strong potential to advance scientific discovery. Whether they possess the capacity for foundational innovation, however, remains an open question. In this work, we focus on a prerequisite for foundational innovation: can LLMs reinvent foundational algorithms in computer science? Our \textit{Unlearn-and-Reinvent} pipeline applies LLM unlearning to remove a specific foundational algorithm, such as Dijkstra's or Euclid's algorithm, from an LLM's pretrained knowledge, and then tests whether the model can reinvent it in a controlled environment. To enable effective unlearning, we adopt a GRPO-based, on-policy unlearning method. Across 10 target algorithms, 3 strong open-weight models, and 3 hint levels, our experiments demonstrate that (1) the strongest model Qwen3-4B-Thinking-2507 successfully reinvents 50% of the algorithms with no hint, 70% at hint level 1, and 90% at hint level 2; (2) a few high-level hints can enhance the reinvention success rate, but even step-by-step hints fail for those complicated algorithms; and (3) test-time reinforcement learning enables successful reinvention for the Strassen algorithm at hint level 2. Through analyses of output trajectories and ablation studies, we find that generative verifier in the reinvention phase plays a critical role in sustaining models' reasoning strength, helping to avoid the ``thought collapse'' phenomenon. These findings offer insights into both the potential and current limits of LLMs' innovative thinking.

Mastering Agile Tasks with Limited Trials

Embodied robots nowadays can already handle many real-world manipulation tasks. However, certain other real-world tasks (e.g., shooting a basketball into a hoop) are highly agile and require high execution precision, presenting additional challenges for methods primarily designed for quasi-static manipulation tasks. This leads to increased efforts in costly data collection, laborious reward design, or complex motion planning. Such tasks, however, are far less challenging for humans. Say a novice basketball player typically needs only $\sim$10 attempts to make their first successful shot, by roughly imitating a motion prior and then iteratively adjusting their motion based on the past outcomes. Inspired by this human learning paradigm, we propose the Adaptive Diffusion Action Plannin (ADAP) algorithm, a simple & scalable approach which iteratively refines its action plan by few real-world trials within a learned prior motion pattern, until reaching a specific goal. Experiments demonstrated that ADAP can learn and accomplish a wide range of goal-conditioned agile dynamic tasks with human-level precision and efficiency directly in real-world, such as throwing a basketball into the hoop in fewer than 10 trials. Project website:https://adap-robotics.github.io/ .

Data Scaling Laws in Imitation Learning for Robotic Manipulation

Data scaling has revolutionized fields like natural language processing and computer vision, providing models with remarkable generalization capabilities. In this paper, we investigate whether similar data scaling laws exist in robotics, particularly in robotic manipulation, and whether appropriate data scaling can yield single-task robot policies that can be deployed zero-shot for any object within the same category in any environment. To this end, we conduct a comprehensive empirical study on data scaling in imitation learning. By collecting data across numerous environments and objects, we study how a policy's generalization performance changes with the number of training environments, objects, and demonstrations. Throughout our research, we collect over 40,000 demonstrations and execute more than 15,000 real-world robot rollouts under a rigorous evaluation protocol. Our findings reveal several intriguing results: the generalization performance of the policy follows a roughly power-law relationship with the number of environments and objects. The diversity of environments and objects is far more important than the absolute number of demonstrations; once the number of demonstrations per environment or object reaches a certain threshold, additional demonstrations have minimal effect. Based on these insights, we propose an efficient data collection strategy. With four data collectors working for one afternoon, we collect sufficient data to enable the policies for two tasks to achieve approximately 90% success rates in novel environments with unseen objects.