2023-02-07-wang23a.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
On the level sets and invariance of neural tuning landscapes	Visual representations can be defined as the activations of neuronal populations in response to images. The activation of a neuron as a function over all image space has been described as a "tuning landscape". As a function over a high-dimensional space, what is the structure of this landscape? In this study, we characterize tuning landscapes through the lens of level sets and Morse theory. A recent study measured the in vivo two-dimensional tuning maps of neurons in different brain regions. Here, we developed a statistically reliable signature for these maps based on the change of topology in level sets. We found this topological signature changed progressively throughout the cortical hierarchy, with similar trends found for units in convolutional neural networks (CNNs). Further, we analyzed the geometry of level sets on the tuning landscapes of CNN units. We advanced the hypothesis that higher-order units can be locally regarded as isotropic radial basis functions, but not globally. This shows the power of level sets as a conceptual tool to understand neuronal activations over image space.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	wang23a	0	On the level sets and invariance of neural tuning landscapes	278	300	278-300	278	false	Wang, Binxu and Ponce, Carlos R.	given family Binxu Wang given family Carlos R. Ponce	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/wang23a/wang23a.pdf