Paper:
Similar to a convolutional neural network (CNN), the mammalian retina encodes visual information into several dozen nonlinear feature maps, each formed by one ganglion cell type that tiles the visual space in an approximately shift-equivariant manner. Whether such organization into distinct cell types is maintained at the level of cortical image processing is an open question. Predictive models building upon convolutional features have been shown to provide state-of-the-art performance, and have recently been extended to include rotation equivariance in order to account for the orientation selectivity of V1 neurons. However, generally no direct correspondence between CNN feature maps and groups of individual neurons emerges in these models, thus rendering it an open question whether V1 neurons form distinct functional clusters. Here we build upon the rotation-equivariant representation of a CNN-based V1 model and propose a methodology for clustering the representations of neurons in this model to find functional cell types independent of preferred orientations of the neurons. We apply this method to a dataset of 6000 neurons and visualize the preferred stimuli of the resulting clusters. Our results highlight the range of non-linear computations in mouse V1.

Review:
In this study, the authors develop a method to cluster cells in primary visual cortex (V1) based on the cells' responses to natural images. The method consists in three steps: 
- fit a rotation-equivariant convolutional neural network model to V1 cells (previously described in Ecker et al. 2019)
- align all cells by choosing the rotation for each cell that minimizes overall distance between cells in feature space, so that the clustering is mostly blind to the orientation of the filters.
- cluster the cells using a Gaussian mixture model (GMM).
Although I find this article mostly well-written and the topic important, I cannot recommend acceptance because (1) the study does not make a significant contribution to our understanding of V1, (2) the main innovation in ML presented (alignment method) is quite specific and will thus not likely be of interest for the general audience of ICLR:
(1) An important question in visual neuroscience is whether V1 cells form discrete functional clusters as opposed to a continuum. Another related question is whether these functional clusters correspond to distinct cell types characterized by specific wiring patterns, gene expression and/or morphology.
The analyses performed do not answer any of these two questions:
- the clustering model (GMM model) is not compared statistically to other models that would assume a continuous structure in the data (e.g. cells form a sparse continuous manifold in feature space). Although clusters do appear in the t-SNE visualization, this visualization does not provide statistical evidence that cells indeed form distinct clusters.
- The correspondence of the proposed clusters to cell types with specific wiring patterns, gene expression and/or morphology is not established. To establish this correspondence would require further experiments, as acknowledged by the authors: "To systematically classify the V1 functional cell types, these proposals need to be subsequently examined based on a variety of biological criteria reflecting the different properties of the neurons and the prior knowledge about the experiment".
(2) The alignment method, which consists in rotating the cells in feature space so that orientation is not a factor for subsequent clustering, is quite specific to the problem studied and likely not of interest for the general ICLR audience.
Additional feedback:
- Title: ROTATION-INVARIANT CLUSTERING OF FUNCTIONAL CELL TYPES IN PRIMARY VISUAL CORTEX 
=> "functional cell types" is not adequate here, since the article does not establish the existence of functional cell types. Could be replaced with "cell responses".
- Abstract: We apply this method to a dataset of 6000 neurons and provide evidence that discrete functional cell types may exist in V1.
=> this sentence is misleading, since no evidence for functional clusters is provided.
- "Thus, the network has learned an internal representation that allows constructing very similar functions in multiple ways"
=> To avoid the caveat of redundant features, the authors could try to add a dimensionality bottleneck on feature space before readout.
- "Small values of β incur a small cost for poor reconstructions resulting in small optimised values of T and over-smoothed aligned readouts."
=> A simulated annealing procedure (progressive increase of T during learning) could potentially allow the use of larger β values here (i.e. less distortion of the filter).
- The alignment procedure could lead to the emergence of spurious structure in the clustering. It would be important to control for this potential artifact by running the procedure on an unstructured synthetic dataset.
- It is possible that the MEIs within clusters look more similar than they actually are, since the cells are fitted from the same common bank of features. It would be useful but maybe difficult to control for this.
- It would be interesting to test the clustering procedure on a shuffled version of the readout weights (shuffle across features and V1 cells), so as to keep sparsity but not any other structure. Does the t-SNE map look less clustered? Is the GMM fit qualitatively different?
- Fig1(2): add legend/caption. what are the ellipses?