Asymmetric physics enables efficient learning in quadrupedal robot swarms

Animal collectives navigate cluttered environments through local coordination, yet robot swarms still struggle to reproduce this capability in the physical world. End-to-end learning offers a route to such coordination, but scaling it to embodied swarms remains difficult: standard sampling-based reinforcement learning becomes inefficient when visual perception, dense robot-robot interaction, and contact-rich locomotion must be learned together. Here we show that asymmetric physics enables efficient end-to-end learning of vision-based, decentralized control in large swarms of quadrupedal robots. During training, quadrupeds interact in shared environments, where a high-fidelity, non-differentiable simulator generates realistic motion and contact dynamics, and differentiable surrogate models provide gradients for navigation and locomotion policies. This separation enables up to 512 quadrupeds to learn coordinated navigation policies in obstacle-rich environments. At deployment, each robot acts from a single forward-facing depth camera, without explicit communication, centralized planning, or global maps. The policies generalize across forests, bridges, enclosures, narrow passages, and mazes, and zero-shot transfer to six physical quadrupeds across five real-world scenarios. The resulting swarms exhibit predictive avoidance, right-side yielding, pausing before bottlenecks, and wall following, showing that asymmetric physics enables efficient training of scalable decentralized control policies for quadrupedal robot swarms.

BasisFormer: Attention-based Time Series Forecasting with Learnable and Interpretable Basis

Bases have become an integral part of modern deep learning-based models for time series forecasting due to their ability to act as feature extractors or future references. To be effective, a basis must be tailored to the specific set of time series data and exhibit distinct correlation with each time series within the set. However, current state-of-the-art methods are limited in their ability to satisfy both of these requirements simultaneously. To address this challenge, we propose BasisFormer, an end-to-end time series forecasting architecture that leverages learnable and interpretable bases. This architecture comprises three components: First, we acquire bases through adaptive self-supervised learning, which treats the historical and future sections of the time series as two distinct views and employs contrastive learning. Next, we design a Coef module that calculates the similarity coefficients between the time series and bases in the historical view via bidirectional cross-attention. Finally, we present a Forecast module that selects and consolidates the bases in the future view based on the similarity coefficients, resulting in accurate future predictions. Through extensive experiments on six datasets, we demonstrate that BasisFormer outperforms previous state-of-the-art methods by 11.04\% and 15.78\% respectively for univariate and multivariate forecasting tasks. Code is available at: \url{https://github.com/nzl5116190/Basisformer}