Multi-agent collaborative perception could significantly upgrade the perception performance by enabling agents to share complementary information with each other through communication. It inevitably results in a fundamental trade-off between perception performance and communication bandwidth. To tackle this bottleneck issue, we propose a spatial confidence map, which reflects the spatial heterogeneity of perceptual information. It empowers agents to only share spatially sparse, yet perceptually critical information, contributing to where to communicate. Based on this novel spatial confidence map, we propose Where2comm, a communication-efficient collaborative perception framework. Where2comm has two distinct advantages: i) it considers pragmatic compression and uses less communication to achieve higher perception performance by focusing on perceptually critical areas; and ii) it can handle varying communication bandwidth by dynamically adjusting spatial areas involved in communication. To evaluate Where2comm, we consider 3D object detection in both real-world and simulation scenarios with two modalities (camera/LiDAR) and two agent types (cars/drones) on four datasets: OPV2V, V2X-Sim, DAIR-V2X, and our original CoPerception-UAVs. Where2comm consistently outperforms previous methods; for example, it achieves more than 100,000 lower communication volume and still outperforms DiscoNet and V2X-ViT on OPV2V.

A.1 Linear mappings between zand x Usually, we have data x PRNˆD1 and latent representation z PRNˆD2 with N the number of neurons, D1 the dimensionality of the data, D2 the dimensionality of the latent space and, usually, D1 " D2. In cases where a method mdoes only produce some latent representation zm, we fit a reconstruction ˆxm "Wzm with a least squares projection W "pzTmzmq 1zTmx. In cases where a method mdoes only produce some reconstruction ˆxm, we produce a simple latent representation zm by extracting the first D2 columns of the left singular vectors U from the singular value decomposition x"USVT. Both of these projections are fitted on the training data, then fixed and also used on the validation and test data. We used three datasets, where the first two (dataset A [2] n=8417 cells; B [54] n=4600) are two-photon recordings of mouse retinal bipolar cell (BC) responses to the chirp stimuli (local and full-field, see [2] for details).

We propose a new approach to automated theorem proving where an AlphaZerostyle agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to generate tasks of suitable relevance and difficulty for the learner. This allows leveraging minimal amounts of domain knowledge to tackle problems for which training data is unavailable or hard to synthesize. As a specific illustration, we consider loop invariant synthesis for imperative programs and use neural networks to refine both the teacher and solver strategies.