2023-02-07-thakur23a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Does Geometric Structure in Convolutional Filter Space Provide Filter Redundancy Information?	This paper aims to study the geometrical structure present in a CNN filter space for investigating redundancy or importance of an individual filter. In particular, this paper analyses the convolutional layer filter space using simplical geometry to establish a relation between filter relevance and their location on the simplex. Convex combination of extremal points of a simplex can span the entire volume of the simplex. As a result, these points are inherently the most relevant components. Based on this principle, we hypothesise a notion that filters lying near these extremal points of a simplex modelling the filter space are least redundant filters and vice-versa. We validate this positional relevance hypothesis by successfully employing it for data-independent filter ranking and artificial filter fabrication in trained convolutional neural networks. The empirical analysis on different CNN architectures such as ResNet-50 and VGG-16 provide strong evidence in favour of the postulated positional relevance hypothesis.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	thakur23a	0	Does Geometric Structure in Convolutional Filter Space Provide Filter Redundancy Information?	111	121	111-121	111	false	Thakur, Anshul and Abrol, Vinayak and Sharma, Pulkit	given family Anshul Thakur given family Vinayak Abrol given family Pulkit Sharma	2023-02-07		Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations	197	inproceedings	date-parts 2023 2 7	https://proceedings.mlr.press/v197/thakur23a/thakur23a.pdf