Modeling correlations in spontaneous activity of visual cortex with centered Gaussian-binary deep Boltzmann machines
Authors: nan wang, Laurenz Wiskott, Dirk Jancke
ICLR 2014

Abstract: Spontaneous cortical activity -- the ongoing cortical activities in absence of sensory input -- are considered to play a vital role in many aspects of both normal brain functions and mental dysfunctions. We present a centered Gaussian-binary deep Boltzmann machine (GDBM) for modeling the activity in visual cortex and relate the random sampling in DBMs to the spontaneous cortical activity. After training on natural image patches, the proposed model is able to learn the filters similar to the receptive fields of simple cells in V1. Furthermore, we show that the samples collected from random sampling in the centered GDBMs encompass similar activity patterns as found in the spontaneous cortical activity of the visual cortex. Specifically, filters having the same orientation preference tend to be active together during random sampling. Our work demonstrates the homeostasis learned by the centered GDBM and its potential for modeling visual cortical activity. Besides, the results support the hypothesis that the homeostatic mechanism exists in the cortex.


Peer review:
[Review]:
This paper revisits on a simulated model learned from data, previous work by Kenet et al. 2003 in the journal Nature, on the statistics of spontaneous neural activities in the visual cortex, in particular, their correlations to orientation maps. The authors first learn to model image patches in an unsupervised fashion. In a second step, the spontaneous hidden activities produced by the learned model are recorded and compared to the ones observed by Kenet et al. 2003.

The authors build on the centered deep Boltzmann machines, adapting them to real-valued Gaussian-like inputs. An important aspect of the solution learned by a DBM is the amount of sparsity. Authors do not use an explicit sparse penalty, but biases are shown in Algorithm 1 to be initialized to -4, suggesting that sparsity is still important.

Activation patterns produced by the proposed model are shown to be similar to measurements by Kenet et al. 2003 on real neural activity. The use of an unconstrained Gibbs sampler to compute spontaneous activities is questionable, as to my understanding, input should be deactivated. A more powerful result would be to show similar activation patterns when the input units are explicitly constrained to be inactive. Conditional DBMs might be useful in this regard.