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]:
In this paper the authors train a DBM model on natural image patches, conduct a pseudo-physiology experiment on the model, and show that the spontaneous correlation structure of the model resembles that in a V1 experiment.

The claimed results of the paper are:
+ Receptive fields that resemble V1 and V2 (only a qualitative statement is made)
+ Correlation structure that resembles spontaneous activity

My biggest concern relates to the question, 'Why are any of these results unexpected?'  The V1 and V2 receptive field results have been previously reported (ad nauseam for V1), and are not the focus of the paper, so I will ignore these.  The correlation structure also appears to be a result entirely expected by the model construction.  Isn't it the case that the DBM should be capturing statistical relationships in natural images and that co-linearity (and feature non-orthogonality, or high inner product) is a well known property of natural scene statistics?  Taking the results at face value, why is this model unique to the finding, or what does this teach me about the brain, or about the model?

Another concern, is that the main result in Figure 3 is not very convincing.  Is there any statistical test to show the difference between the distributions in 3a?  Why is the uncorrelated noise distribution the proper control?  For Figure 3b, the max (solid blue line) looks pretty close to the relative occurrence line (solid red line), while the neural data seems to have larger divergence in these two measures.  What is the important characteristic of this curve?  Is there anything surprising about it?  It peaks at 0 and 90, just like the neural data, but what makes this model unique to capturing this phenomena?

Some of the most interesting statements in the paper are given in the footnotes or stated as ongoing work.  For example, I find it most interesting that certain models show the observed behavior, while others do not (footnote 6).  In fact, I would have preferred to see the entire paper revolve around this finding.  Far too many papers of this type propose one and only one model to account for the data.  The advancement of this type of work requires the comparison of models and the invalidation of models.  Also, your title seems to indicate that a 'centered Gaussian-binary DBM' is necessary to fit the findings.

I am very confused about your use of the term 'homeostatic'.  You seem to refer to homeostatic as the condition where you sample from your model with the input unclamped.  However, in biology homeostasis is the regulation of variables (or machinery) such that some state is held fixed.  I thought that homeostasis in your model would be more related to learning, i.e. weight updates.

Why, in your model, isn't the spontaneous activity condition a situation where the input is black (or all zeros)?  Isn't this the 'stimulus' condition that resembles the experiment?  How should we model closing the eyes, going into a pitch black room, or severing the input from retina to LGN (or LGN to V1)?

Why did you use mean-field to approximate the response to the stimuli?  This means for one condition you run mean-field and the other you run sampling.  It seems that this just introduces discrepancy between the conditions.

A note on exposition, I would prefer less detail on already published models and training algorithms, e.g. section 2.1 and Algorithm 1. and more detail on the experiment that you ran (sampling procedure, and explaining better the background of Figure 3b).