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Which Frequencies do CNNs Need? Emergent Bottleneck Structure in Feature Learning
We describe the emergence of a Convolution Bottleneck (CBN) structure in CNNs, where the network uses its first few layers to transform the input representation into a representation that is supported only along a few frequencies and channels, before using the last few layers to map back to the outputs.
Stochastic contextual bandits with graph feedback: from independence number to MAS number
Interestingly, $\beta_M(G)$ interpolates between $\alpha(G)$ (the independence number of the graph) and $\mathsf{m}(G)$ (the maximum acyclic subgraph (MAS) number of the graph) as the number of contexts $M$ varies.
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes
Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in limited settings only.
Active operator inference for learning low-dimensional dynamical-system models from noisy data
Furthermore, the connection between operator inference and projection-based model reduction enables bounding the mean-squared errors of predictions made with the learned models with respect to traditional reduced models.
