Gregory W. Benton

Gregory W. Benton, Wesley J. Maddox, Sanae Lotfi et al.

With a better understanding of the loss surfaces for multilayer networks, we can build more robust and accurate training procedures. Recently it was discovered that independently trained SGD solutions can be connected along one-dimensional paths of near-constant training loss. In this paper, we show that there are mode-connecting simplicial complexes that form multi-dimensional manifolds of low loss, connecting many independently trained models. Inspired by this discovery, we show how to efficiently build simplicial complexes for fast ensembling, outperforming independently trained deep ensembles in accuracy, calibration, and robustness to dataset shift. Notably, our approach only requires a few training epochs to discover a low-loss simplex, starting from a pre-trained solution. Code is available at https://github.com/g-benton/loss-surface-simplexes.

Marc Finzi, Gregory Benton, Andrew Gordon Wilson

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. We introduce Residual Pathway Priors (RPPs) as a method for converting hard architectural constraints into soft priors, guiding models towards structured solutions, while retaining the ability to capture additional complexity. Using RPPs, we construct neural network priors with inductive biases for equivariances, but without limiting flexibility. We show that RPPs are resilient to approximate or misspecified symmetries, and are as effective as fully constrained models even when symmetries are exact. We showcase the broad applicability of RPPs with dynamical systems, tabular data, and reinforcement learning. In Mujoco locomotion tasks, where contact forces and directional rewards violate strict equivariance assumptions, the RPP outperforms baseline model-free RL agents, and also improves the learned transition models for model-based RL.

Gregory Benton, Marc Finzi, Pavel Izmailov et al.

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to a given symmetry group. We show how to \emph{learn} invariances and equivariances by parameterizing a distribution over augmentations and optimizing the training loss simultaneously with respect to the network parameters and augmentation parameters. With this simple procedure we can recover the correct set and extent of invariances on image classification, regression, segmentation, and molecular property prediction from a large space of augmentations, on training data alone.

Wesley J. Maddox, Gregory Benton, Andrew Gordon Wilson

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good generalization performance. Moreover, when we measure generalization as a function of parameters, we see double descent behaviour, where the test error decreases, increases, and then again decreases. We show that many of these properties become understandable when viewed through the lens of effective dimensionality, which measures the dimensionality of the parameter space determined by the data. We relate effective dimensionality to posterior contraction in Bayesian deep learning, model selection, width-depth tradeoffs, double descent, and functional diversity in loss surfaces, leading to a richer understanding of the interplay between parameters and functions in deep models. We also show that effective dimensionality compares favourably to alternative norm- and flatness- based generalization measures.

Gregory W. Benton, Wesley J. Maddox, Jayson P. Salkey et al.

Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop functional kernel learning (FKL) to directly infer functional posteriors over kernels. In particular, we place a transformed Gaussian process over a spectral density, to induce a non-parametric distribution over kernel functions. The resulting approach enables learning of rich representations, with support for any stationary kernel, uncertainty over the values of the kernel, and an interpretable specification of a prior directly over kernels, without requiring sophisticated initialization or manual intervention. We perform inference through elliptical slice sampling, which is especially well suited to marginalizing posteriors with the strongly correlated priors typical to function space modelling. We develop our approach for non-uniform, large-scale, multi-task, and multidimensional data, and show promising performance in a wide range of settings, including interpolation, extrapolation, and kernel recovery experiments.