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Publications
Towards Understanding Generalization via Analytical Learning Theory
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this the… (see more)ory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.
Achieving machine intelligence requires a smooth integration of perception and reasoning, yet models developed to date tend to specialize in… (see more) one or the other; sophisticated manipulation of symbols acquired from rich perceptual spaces has so far proved elusive. Consider a visual arithmetic task, where the goal is to carry out simple arithmetical algorithms on digits presented under natural conditions (e.g. hand-written, placed randomly). We propose a two-tiered architecture for tackling this problem. The lower tier consists of a heterogeneous collection of information processing modules, which can include pre-trained deep neural networks for locating and extracting characters from the image, as well as modules performing symbolic transformations on the representations extracted by perception. The higher tier consists of a controller, trained using reinforcement learning, which coordinates the modules in order to solve the high-level task. For instance, the controller may learn in what contexts to execute the perceptual networks and what symbolic transformations to apply to their outputs. The resulting model is able to solve a variety of tasks in the visual arithmetic domain, and has several advantages over standard, architecturally homogeneous feedforward networks including improved sample efficiency.
In this work we explore how gene-gene interaction graphs can be used as a prior for the representation of a model to construct features base… (see more)d on known interactions between genes. Most existing machine learning work on graphs focuses on building models when data is confined to a graph structure. In this work we focus on using the information from a graph to build better representations in our models. We use the percolate task, determining if a path exists across a grid for a set of node values, as a proxy for gene pathways. We create variants of the percolate task to explore where existing methods fail. We test the limits of existing methods in order to determine what can be improved when applying these methods to a real task. This leads us to propose new methods based on Graph Convolutional Networks (GCN) that use pooling and dropout to deal with noise in the graph prior.
We propose a method for modelling groups of face images from the same identity. The model is trained to infer a distribution over the latent… (see more) space for identity given a small set of “training data”. One can then sample images using that latent representation to produce images of the same identity. We demonstrate that the model extracts disentangled factors for identity factors and image-specific vectors. We also perform generative classification over identities to assess its feasibility for few-shot face recognition.