We demonstrate our framework's utility by proving and methods that are guaranteed to be defended against deception, given bounded sistent conclusions about performance. Our framework enables us to prove EHPO put forth a logical framework to capture its semantics and how it can lead to inconrigorous. We call this process epistemic hyperparameter optimization (EHPO), and deception, the process of drawing conclusions from HPO should be made more provide a theoretical complement to this prior work, arguing that, to avoid such the opposite. In short, the way we choose hyperparameters can deceive us. We yield the conclusion that J outperforms K, whereas searching another can entail research.

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks.

Supervised learning with deep models has tremendous potential for applications in materials science. Recently, graph neural networks have been used in this context, drawing direct inspiration from models for molecules. However, materials are typically much more structured than molecules, which is a feature that these models do not leverage. In this work, we introduce a class of models that are equivariant with respect to crystalline symmetry groups. We do this by defining a generalization of the message passing operations that can be used with more general permutation groups, or that can alternatively be seen as defining an expressive convolution operation on the crystal graph. Empirically, these models achieve competitive results with state-of-the-art on property prediction tasks.

The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam -- when treated as a function that maps initial conditions to optimized results -- is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.