We also demonstrate its effectiveness in generating robotic tasks.

This gap hinders accurate sensory grounding in real-world scenarios.

Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or value function scores) that potentially lead to suboptimal or even distracting sub-goals, preventing us from finding longer proofs. To address this challenge, we propose POETRY (PrOvE Theorems RecursivelY), which proves theorems in a recursive, level-by-level manner in the Isabelle theorem prover. Unlike previous step-by-step methods, POETRY searches for a verifiable sketch of the proof at each level and focuses on solving the current level's theorem or conjecture. Detailed proofs of intermediate conjectures within the sketch are temporarily replaced by a placeholder tactic called sorry, deferring their proofs to subsequent levels. This approach allows the theorem to be tackled incrementally by outlining the overall theorem at the first level and then solving the intermediate conjectures at deeper levels. Experiments are conducted on the miniF2F and PISA datasets and significant performance gains are observed in our POETRY approach over state-of-the-art methods. POETRY on miniF2F achieves an average proving success rate improvement of 5. 1% . Moreover, we observe a substantial increase in the maximum proof length found by POETRY, from 10 to 26 .

In this paper, we take an inspiration from human perception and explore a compositional approach for egocentric video representation.

"I have high cortisol but low ACTH on a dexamethasone suppression test.

Large language models (LLMs) are considered a crucial technology for advancing intelligent education since they exhibit the potential for an in-depth understanding of teaching scenarios and providing students with personalized guidance. Nonetheless, current LLM-based application in personalized teaching predominantly follows a "Question-Answering" paradigm, where students are passively provided with answers and explanations. In this paper, we propose SocraticLM, which achieves a Socratic "Thought-Provoking" teaching paradigm that fulfills the role of a real classroom teacher in actively engaging students in the thought

We consider model selection for online supervised learning.

Prod is a seminal algorithm in full-information online learning, which has been conjectured to be fundamentally sub-optimal for multi-armed bandits.