Efficient interventions in a neural circuit from observations: an information-theoretic study

Motivated by rapid advances in neuroengineering, we recently proposed an interventional way of reverse engineering neural circuits that is oriented towards treating disorders. The emphasis is on finding efficient (i.e. sparse) interventions that change the input-output behavior of the circuit to a desirable one. In a subsequent work, we proposed algorithms for arriving at efficient interventions using just observations, and further, demonstrated the efficacy of our algorithms on artificial neural networks, using them as "model organisms". In this work, we examine this problem of arriving at efficient interventions using just observations from an information-theoretic perspective. We provide a simple 2-layer "worst-case" example showing that estimating minimal interventions using just observations is hard: in the worst case, this can require testing every solution in a list of exponentially many (in the size of the network) solutions. Guided by this example, we relax the problem to merely detecting the diseased layer. We focus our attention on cases where disease is induced by carefully choosing a single node intervention that causes immense disruption to the performance. We first use the cut-set bound to provide insights on the layer of the diseased node. Motivated by this bound, we propose a mutual-information-based algorithm to identify the layer of the diseased node, and quantify its performance. Strikingly, we observe that a surprisingly high fraction of networks preserve mutual information post-disease even until the very last layer. We propose an alternate decision rule for these cases which allows detection of diseased layers when mutual-information-based metrics fail due to this property.