In this section, we provide a short overview of the definitions relevant to the context of our work. The symmetry of an object is a transformation that leaves some of its properties unchanged.

Strong mixed-integer programming formulations for trained neural networks.

In this supplementary material we provide additional details about: Video (with audio) for qualitative illustration of our task and qualitative evaluation of our model predictions (Sec. Evaluation of the impact of the query source location on our model's prediction quality for a fixed receiver (Sec. Moreover, we qualitatively demonstrate our model's prediction quality by comparing the predictions with the ground truths, both at the RIR level and in terms of perceptual similarity when the RIRs are convolved with real-world monaural sounds, like speech and music. We also analyze common failure cases for our model (Sec. Please use headphones to hear the spatial audio correctly.

Additionally, we show generalization performance of our proposed method across differentvisualdomains. Withthegiven problemcategory(task),asubsetforlearning can be sampled (via domain episode module in Figure 4 in main text). Here, by replacingclass with task, K-shot andN-task reasoning framework can be defined. Here, we show analogical learning with the existing meta learning framework for fast adaptation fromthesourcedomain tothetargetdomain.

Network pruning is a commonly used measure to alleviate the storage and computational burden of deep neural networks. However, the fundamental limit of network pruning is still lacking. To close the gap, in this work we'll take a first-principles approach, i.e. we'll directly impose the sparsity constraint on the loss function and leverage the framework of statistical dimension in convex geometry, thus enabling us to characterize the sharp phase transition point, which can be regarded as the fundamental limit of the pruning ratio. Through this limit, we're able to identify two key factors that determine the pruning ratio limit, namely, weight magnitude and network sharpness .