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End-to-end visuomotor policies trained using behavior cloning have shown a remarkable ability to generate complex, multi-modal low-level robot behaviors. However, at deployment time, these policies still struggle to act reliably when faced with out-of-distribution (OOD) visuals induced by objects, backgrounds, or environment changes. Prior works in interactive imitation learning solicit corrective expert demonstrations under the OOD conditions -- but this can be costly and inefficient. We observe that task success under OOD conditions does not always warrant novel robot behaviors. In-distribution (ID) behaviors can directly be transferred to OOD conditions that share functional similarities with ID conditions. For example, behaviors trained to interact with in-distribution (ID) pens can apply to interacting with a visually-OOD pencil. The key challenge lies in disambiguating which ID observations functionally correspond to the OOD observation for the task at hand. We propose that an expert can provide this OOD-to-ID functional correspondence. Thus, instead of collecting new demonstrations and re-training at every OOD encounter, our method: (1) detects the need for feedback by first checking if current observations are OOD and then identifying whether the most similar training observations show divergent behaviors, (2) solicits functional correspondence feedback to disambiguate between those behaviors, and (3) intervenes on the OOD observations with the functionally corresponding ID observations to perform deployment-time generalization. We validate our method across diverse real-world robotic manipulation tasks with a Franka Panda robotic manipulator. Our results show that test-time functional correspondences can improve the generalization of a vision-based diffusion policy to OOD objects and environment conditions with low feedback. 

Given a compact Kähler manifold , due to the work of Darvas–Di Nezza–Lu, the space of singularity types of ω-psh functions admits a natural pseudo-metric that is complete in the presence of positive mass. When restricted to model singularity types, this pseudo-metric is a bona fide metric. In case of the projective space, there is a known one-to-one correspondence between toric model singularity types and convex bodies inside the unit simplex. Hence in this case it is natural to compare the metric to the classical Hausdorff metric. We provide precise Hölder bounds, showing that their induced topologies are the same. More generally, we introduce a quasi-metric on the space of compact convex sets inside an arbitrary convex body G, with in case G is the unit simplex. We prove optimal Hölder bounds comparing with the Hausdorff metric. Our analysis shows that the Hölder exponents differ depending on the geometry of G, with the worst exponents in case G is a polytope, and the best in case G has boundary. 

Teachers today have increasing access to professional learning communities (PLCs) through a rapidly expanding menu of online professional development offerings. While a valued opportunity for growth, online PLCs can limit opportunities for co-teaching, pedagogical practice, and experiential learning. This paper examines a teacher professional development program implemented in 2022, where 14 middle school teachers joined either an online or an in-person version of a summer practicum in which PLCs were fostered. In both versions of the PD, teachers worked in small teams of co-teachers to learn and practice teaching middle school students about Artificial Intelligence (AI), a topic in which teachers were non-experts. Findings from qualitative analysis of teacher interviews suggest affordances and barriers to teacher learning online as compared to in-person PLCs. The paper offers recommendations for online PLC structure and co-teaching to enhance teacher learning. 

Teachers today have increasing access to professional learning communities (PLCs) through a rapidly expanding menu of online professional development offerings. While a valued opportunity for growth, online PLCs can limit opportunities for co-teaching, pedagogical practice, and experiential learning. This paper examines a teacher professional development program implemented in 2022, where 14 middle school teachers joined either an online or an in-person version of a summer practicum in which PLCs were fostered. In both versions of the PD, teachers worked in small teams of co-teachers to learn and practice teaching middle school students about Artificial Intelligence (AI), a topic in which teachers were non-experts. Findings from qualitative analysis of teacher interviews suggest affordances and barriers to teacher learning online as compared to in-person PLCs. The paper offers recommendations for online PLC structure and co-teaching to enhance teacher learning.