What can we learn about the functional organization of cortical microcircuits from large-scale recordings of neural activity?   To obtain an explicit and interpretable model of time-dependent functional connections between neurons and to establish the dynamics of the cortical information flow, we develop 'dynamic neural relational inference' (dNRI). We study  both synthetic and real-world neural spiking data and demonstrate that the developed method is able to uncover the dynamic relations between neurons more reliably than existing baselines. Extraction of latent temporal dynamics in complex networks is important to understand their functional connectivity and to predict their behavior. Recently, various machine learning methods were used to encode/decode the behavior from recorded activity of large neuronal populations [2, 3] . However, in these mostly 'static' brain models the temporal dynamics of the firing activity as well as interactions between different neurons are often neglected. It is expected, however, that the dynamic interactions in neural networks might be the key to understanding the brain computations. Addressing this, several methods have been proposed to uncover low-dimensional latent representations of neural network activity and its dynamics, including dimensionality reduction-based techniques such as principal components analysis [1] and tensor components analysis [14] , pattern extraction techniques based on matrix factorization such as ConvNMF [11] and SeqNMF [7] , and autoencoder models such as LFADS [9] . However, temporal correlations between individual neurons in the network are often only modeled implicitly, hindering reconstruction of functional connectivity of the neural circuits. In contrast to these implicit techniques, here, we develop an extension to Neural Relational Inference [6] , which we call 'dynamic Neural Relational Inference' (dNRI). Specifically, we develop a new model to extract rapid dynamic changes of network activity in the form of a time-dependent adjacency matrix. We aim at extracting rapid (tens of milliseconds) correlations between recorded neurons that capture their functional relations across the network. Moreover, our method enables the tracking of the temporal evolution of this functional connectivity over the span of a trial. This means it can provide an interpretable approach to uncover hidden dynamical structure of brain information flows and to reconstruct the underlying functional brain circuitry. We demonstrate the applicability of our method on both synthetic spiking data and data recorded from the cortex of live and behaving mice. We develop a method to explicitly extract time-dependent functional relations from large-scale neural spiking data recordings of cortical networks. Using simulated data of spiking activity where ground truth is available, and real data, we demonstrate that the proposed approach is able to recover the implanted interactions more accurately than baselines which model relations implicitly.
We develop 'dynamic neural relational inference', a variational autoencoder model that can explicitly and interpretably represent the hidden dynamic relations between neurons.
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