Using Summary Layers to Probe Neural Network Behaviour
No framework exists that can explain and predict the generalisation ability of deep neural networks in general circumstances. In fact, this question has not been answered for some of the least complicated of neural network architectures: fully-connected feedforward networks with rectified linear activations and a limited number of hidden layers. For such an architecture, we show how adding a summary layer to the network makes it more amenable to analysis, and allows us to define the conditions that are required to guarantee that a set of samples will all be classified correctly. This process does not describe the generalisation behaviour of these networks, but produces a number of metrics that are useful for probing their learning and generalisation behaviour. We support the analytical conclusions with empirical results, both to confirm that the mathematical guarantees hold in practice, and to demonstrate the use of the analysis process.
Copyright (c) 2020 Marelie Hattingh Davel
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Copyright of all work published here subsists in the authors. While SACJ retains right of first publication, subsequent re-publication is expressly permitted provided the original SACJ publication is acknowledged and cited, according to the terms detailed below. If plagiarism is detected during review, a paper may be summarily rejected and will not be accepted unless even minor infringements are corrected. Should plagiarism be detected after a paper is published, the Editor reserves the right to withdraw a paper from publication. We expect authors to be honest in representing work as their own, and to respect the time and effort our reviewers put in without an undue burden of policing plagiarism, and hence take violations seriously. SACJ applies the Creative Commons Attribution NonCommercial 4.0 License (CC BY-NC 4.0) to all papers published in this journal. Authors who publish with SACJ agree to the following:
- Authors retain copyright and grant SACJ right of first publication. The work is additionally licensed under a Creative Commons Attribution Non-Commercial License that requires others who share the work to acknowledge the work’s authorship and initial publication in SACJ. Should anyone else wish to make commercial use of the work, SACJ cedes the right to the author to negotiate terms and does not expect to be paid any royalties.
- Authors may enter into additional arrangements for non-exclusive distribution of the SACJ-published version of the work (e.g., post it to a repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are required to refrain from posting their work online prior to completion of reviews so as not to compromise double-blind reviewing or confuse plagiarism checks.