Relative gradient optimization of the Jacobian term in unsupervised deep learning
arXiv:2006.15090
Abstract
Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution, which can typically be written as a product of its marginals -- thus drawing a connection with the field of nonlinear independent component analysis. Deep density models have been widely used for this task, but their maximum likelihood based training requires estimating the log-determinant of the Jacobian and is computationally expensive, thus imposing a trade-off between computation and expressive power. In this work, we propose a new approach for exact training of such neural networks. Based on relative gradients, we exploit the matrix structure of neural network parameters to compute updates efficiently even in high-dimensional spaces; the computational cost of the training is quadratic in the input size, in contrast with the cubic scaling of naive approaches. This allows fast training with objective functions involving the log-determinant of the Jacobian, without imposing constraints on its structure, in stark contrast to autoregressive normalizing flows.
References in corpus (13)
- NICE: Non-linear Independent Components Estimation
- Variational Inference with Normalizing Flows
- Normalizing Flows: An Introduction and Review of Current Methods
- An Introduction to Convolutional Neural Networks
- Density estimation using Real NVP
- The Reversible Residual Network: Backpropagation Without Storing Activations
- Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA
- FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
- Improving Variational Auto-Encoders using Householder Flow
- High-Dimensional Probability Estimation with Deep Density Models
- i-RevNet: Deep Invertible Networks
- Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning
- Neural Networks with Cheap Differential Operators