text: 253,49,1321462223097790468,2180768821,Erik Hoel,"How do artificial neural networks generalize? The answer may be in their causal structure. In this new paper we use information theory to track nodes’ causal relationships becoming more sensitive or degenerate. Training traces a path in this “causal plane” <LINK> <LINK> Some really interesting results of this collaboration with Simon Mattsson and @ericjmichaud_ : the informativeness of a causal relationship between two nodes peaks at a certain characteristic edge weight, no matter what bin size you use (there is a manifold for multiple edges) <LINK> We can even measure a variant of the integrated information using these techniques. Normally the phi of a feedforward network is zero... but there are still integrated joint effects of one layer to another. Here we introduce a measure to capture those: ""phi feedfoward"" <LINK> There's a great github package for those who want to try out these techniques. Ultimately we are hoping to offer a kind of alternative to the information bottleneck approach (although its not contradictory) that focuses more on causation <LINK> @BlaiseLucey00 @ericjmichaud_ I recently learned how to make gifs so get used to it",https://arxiv.org/abs/2010.13871,"Deep Neural Networks (DNNs) are often examined at the level of their response to input, such as analyzing the mutual information between nodes and data sets. Yet DNNs can also be examined at the level of causation, exploring ""what does what"" within the layers of the network itself. Historically, analyzing the causal structure of DNNs has received less attention than understanding their responses to input. Yet definitionally, generalizability must be a function of a DNN's causal structure since it reflects how the DNN responds to unseen or even not-yet-defined future inputs. Here, we introduce a suite of metrics based on information theory to quantify and track changes in the causal structure of DNNs during training. Specifically, we introduce the effective information (EI) of a feedforward DNN, which is the mutual information between layer input and output following a maximum-entropy perturbation. The EI can be used to assess the degree of causal influence nodes and edges have over their downstream targets in each layer. We show that the EI can be further decomposed in order to examine the sensitivity of a layer (measured by how well edges transmit perturbations) and the degeneracy of a layer (measured by how edge overlap interferes with transmission), along with estimates of the amount of integrated information of a layer. Together, these properties define where each layer lies in the ""causal plane"" which can be used to visualize how layer connectivity becomes more sensitive or degenerate over time, and how integration changes during training, revealing how the layer-by-layer causal structure differentiates. These results may help in understanding the generalization capabilities of DNNs and provide foundational tools for making DNNs both more generalizable and more explainable. ","Examining the causal structures of deep neural networks using