Search Results for author:
Found 15 papers, 14 papers with code
A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks
Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible.
The No Free Lunch Theorem, Kolmogorov Complexity, and the Role of Inductive Biases in Machine Learning
No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems.
PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization
While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works.
The Lie Derivative for Measuring Learned Equivariance
In order to better understand the role of equivariance in recent vision models, we introduce the Lie derivative, a method for measuring equivariance with strong mathematical foundations and minimal hyperparameters.
Deconstructing the Inductive Biases of Hamiltonian Neural Networks
Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases.
Residual Pathway Priors for Soft Equivariance Constraints
There is often a trade-off between building deep learning systems that are expressive enough to capture the nuances of the reality, and having the right inductive biases for efficient learning.
SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes
State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the covariance kernel.
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds.
Learning Invariances in Neural Networks from Training Data
Invariances to translations have imbued convolutional neural networks with powerful generalization properties.
Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics.
Learning Invariances in Neural Networks
Invariances to translations have imbued convolutional neural networks with powerful generalization properties.
Probabilistic Numeric Convolutional Neural Networks
Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods.
Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems.
Semi-Supervised Learning with Normalizing Flows
Normalizing flows transform a latent distribution through an invertible neural network for a flexible and pleasingly simple approach to generative modelling, while preserving an exact likelihood.
Semi-Supervised Image Classification
Semi-Supervised Text Classification
There Are Many Consistent Explanations of Unlabeled Data: Why You Should Average
Presently the most successful approaches to semi-supervised learning are based on consistency regularization, whereby a model is trained to be robust to small perturbations of its inputs and parameters.
