arXiv:2602.14473v1 Announce Type: cross Abstract: Quadruped robots are employed in various scenarios in building construction. However, autonomous stair climbing across different indoor staircases remains a major challenge for robot dogs to complete building construction tasks. In this project, we employed a two-stage end-to-end deep reinforcement learning (RL) approach to optimize a robot's performance on U-shaped stairs. The training robot-dog modality, Unitree Go2, was first trained to climb stairs on Isaac Lab's pyramid-stair terrain, and then to climb a U-shaped indoor staircase using the learned policies. This project explores end-to-end RL methods that enable robot dogs to autonomously climb stairs. The results showed (1) the successful goal reached for robot dogs climbing U-shaped stairs with a stall penalty, and (2) the transferability from the policy trained on U-shaped stairs to deployment on straight, L-shaped, and spiral stair terrains, and transferability from other stair models to deployment on U-shaped terrain.

arXiv:2602.14872v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RL for transformers on compositional reasoning tasks. Our theory characterizes how the effectiveness of RLVR is governed by the smoothness of the difficulty spectrum. When data contains abrupt discontinuities in difficulty, learning undergoes grokking-type phase transitions, producing prolonged plateaus before progress recurs. In contrast, a smooth difficulty spectrum leads to a relay effect: persistent gradient signals on easier problems elevate the model's capabilities to the point where harder ones become tractable, resulting in steady and continuous improvement. Our theory explains how RLVR can improve performance at the edge of competence, and suggests that appropriately designed data mixtures can yield scalable gains. As a technical contribution, our analysis develops and adapts tools from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via synthetic experiments.