Thomas Mach, Michele Rinelli, Raf Vandebril et al.
Periodic CMV matrices are unitary matrices that can be specified by $O(n)$ data. Their eigenvalues can be computed by standard methods, storing them as conventional matrices (using $O(n^{2})$ data) in $O(n^{3})$ time. Here a fast method that computes the eigenvalues in $O(n^{2})$ time (using $O(n)$ data) is presented.
Vanya Cohen, Jason Xinyu Liu, Raymond Mooney et al.
With large language models, robots can understand language more flexibly and more capable than ever before. This survey reviews and situates recent literature into a spectrum with two poles: 1) mapping between language and some manually defined formal representation of meaning, and 2) mapping between language and high-dimensional vector spaces that translate directly to low-level robot policy. Using a formal representation allows the meaning of the language to be precisely represented, limits the size of the learning problem, and leads to a framework for interpretability and formal safety guarantees. Methods that embed language and perceptual data into high-dimensional spaces avoid this manually specified symbolic structure and thus have the potential to be more general when fed enough data but require more data and computing to train. We discuss the benefits and tradeoffs of each approach and finish by providing directions for future work that achieves the best of both worlds.
Vidullan Surendran, Neehar Peri, David Watkins
Handheld data collection systems, such as the Universal Manipulation Interface (UMI), enable scalable data collection across diverse environments but only capture observed actions rather than the desired actions executed by a robot controller. In contrast, teleoperation captures desired actions directly, but is prohibitively time-consuming to collect. We revisit this trade-off through the lens of action validity across task phases. We observe that handheld trajectories provide valid supervision in tolerant, free-space phases, but lack dynamic feasibility in contact-sensitive phases, where tracking observed trajectories at high stiffness produces large, unsafe contact forces. We study the interaction between these two supervision types for contact-rich manipulation and find that training policies that combine handheld data with a small number of targeted teleoperated demonstrations provide an efficient hybrid strategy. Specifically, rather than teleoperating the entire task, we only collect partial teleoperated demonstrations for task segments where base handheld policies fail. However, naively mixing handheld and teleoperated phase-specific data yields worse performance than training on handheld data alone. To address this mismatch between observed and desired supervision, we propose Bi-modal Routing for Imitation Data via Gated Experts (BRIDGE), a mixture of diffusion policy experts that routes between specialist task phase heads conditioned on the current robot state. Notably, our approach enables task-phase specific use of desired actions during contact sensitive segments and improves success rates over handheld-only baselines by up to 36.7% across three contact-rich manipulation tasks.