8 research outputs found
Practical Gauss-Newton Optimisation for Deep Learning
We present an efficient block-diagonal ap- proximation to the Gauss-Newton
matrix for feedforward neural networks. Our result- ing algorithm is
competitive against state- of-the-art first order optimisation methods, with
sometimes significant improvement in optimisation performance. Unlike
first-order methods, for which hyperparameter tuning of the optimisation
parameters is often a labo- rious process, our approach can provide good
performance even when used with default set- tings. A side result of our work
is that for piecewise linear transfer functions, the net- work objective
function can have no differ- entiable local maxima, which may partially explain
why such transfer functions facilitate effective optimisation.Comment: ICML 201
Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting
We introduce the Kronecker factored online Laplace approximation for
overcoming catastrophic forgetting in neural networks. The method is grounded
in a Bayesian online learning framework, where we recursively approximate the
posterior after every task with a Gaussian, leading to a quadratic penalty on
changes to the weights. The Laplace approximation requires calculating the
Hessian around a mode, which is typically intractable for modern architectures.
In order to make our method scalable, we leverage recent block-diagonal
Kronecker factored approximations to the curvature. Our algorithm achieves over
90% test accuracy across a sequence of 50 instantiations of the permuted MNIST
dataset, substantially outperforming related methods for overcoming
catastrophic forgetting.Comment: 13 pages, 6 figure
Scalable approximate inference methods for Bayesian deep learning
This thesis proposes multiple methods for approximate inference in deep Bayesian neural networks split across three parts.
The first part develops a scalable Laplace approximation based on a block- diagonal Kronecker factored approximation of the Hessian. This approximation accounts for parameter correlations – overcoming the overly restrictive independence assumption of diagonal methods – while avoiding the quadratic scaling in the num- ber of parameters of the full Laplace approximation. The chapter further extends the method to online learning where datasets are observed one at a time. As the experiments demonstrate, modelling correlations between the parameters leads to improved performance over the diagonal approximation in uncertainty estimation and continual learning, in particular in the latter setting the improvements can be substantial.
The second part explores two parameter-efficient approaches for variational inference in neural networks, one based on factorised binary distributions over the weights, one extending ideas from sparse Gaussian processes to neural network weight matrices. The former encounters similar underfitting issues as mean-field Gaussian approaches, which can be alleviated by a MAP-style method in a hierarchi- cal model. The latter, based on an extension of Matheron’s rule to matrix normal distributions, achieves comparable uncertainty estimation performance to ensembles with the accuracy of a deterministic network while using only 25% of the number of parameters of a single ResNet-50.
The third part introduces TyXe, a probabilistic programming library built on top of Pyro to facilitate turning PyTorch neural networks into Bayesian ones. In contrast to existing frameworks, TyXe avoids introducing a layer abstraction, allowing it to support arbitrary architectures. This is demonstrated in a range of applications, from image classification with torchvision ResNets over node labelling with DGL graph neural networks to incorporating uncertainty into neural radiance fields with PyTorch3d
Black-box Coreset Variational Inference
Recent advances in coreset methods have shown that a selection of
representative datapoints can replace massive volumes of data for Bayesian
inference, preserving the relevant statistical information and significantly
accelerating subsequent downstream tasks. Existing variational coreset
constructions rely on either selecting subsets of the observed datapoints, or
jointly performing approximate inference and optimizing pseudodata in the
observed space akin to inducing points methods in Gaussian Processes. So far,
both approaches are limited by complexities in evaluating their objectives for
general purpose models, and require generating samples from a typically
intractable posterior over the coreset throughout inference and testing. In
this work, we present a black-box variational inference framework for coresets
that overcomes these constraints and enables principled application of
variational coresets to intractable models, such as Bayesian neural networks.
We apply our techniques to supervised learning problems, and compare them with
existing approaches in the literature for data summarization and inference.Comment: NeurIPS 202
Addressing Catastrophic Forgetting in Few-Shot Problems
Neural networks are known to suffer from catastrophic forgetting when trained
on sequential datasets. While there have been numerous attempts to solve this
problem in large-scale supervised classification, little has been done to
overcome catastrophic forgetting in few-shot classification problems. We
demonstrate that the popular gradient-based model-agnostic meta-learning
algorithm (MAML) indeed suffers from catastrophic forgetting and introduce a
Bayesian online meta-learning framework that tackles this problem. Our
framework utilises Bayesian online learning and meta-learning along with
Laplace approximation and variational inference to overcome catastrophic
forgetting in few-shot classification problems. The experimental evaluations
demonstrate that our framework can effectively achieve this goal in comparison
with various baselines. As an additional utility, we also demonstrate
empirically that our framework is capable of meta-learning on sequentially
arriving few-shot tasks from a stationary task distribution.Comment: ICML 202
Gaussian mean field regularizes by limiting learned information
Variational inference with a factorized Gaussian posterior estimate is a widely-used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show how mean field inference improves generalization by limiting mutual information between learned parameters and the data through noise. We quantify a maximum capacity when the posterior variance is either fixed or learned and connect it to generalization error, even when the KL-divergence in the objective is scaled by a constant. Our experiments suggest that bounding information between parameters and data effectively regularizes neural networks on both supervised and unsupervised tasks