Inferring computational dynamics from neural measurements using deep recurrent neural networks

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In theoretical neuroscience, computational processes in the brain are often thought to be implemented in terms of the underlying stochastic neural system dynamics. Cognitive processes like working memory, decision making, interval timing, or thought sequences, have been described in terms of attractor states, probabilistic transitions between these, slow transients, or chains of saddle nodes, for instance. Consequently, from this point of view, for understanding the neural basis of cognition one should unravel the neural system dynamics that underlies behavioral performance and neural activity. However, neural dynamics are not directly observable but have to be inferred from a limited and noisy set of physiological measurements that usually probe only a few of the system’s degrees of freedom. It would therefore be of great value if one had methodological tools for (automatically) recovering the underlying neural dynamics from such ‘sparse’ physiological measurements. The central goal of the present proposal is to develop and validate such methods based on deep recurrent neural networks (RNN), and probe them on neurophysiological data.We have previously used a combination of delay embeddings and nonlinear basis expansions to extract from multiple single-unit (MSU) recordings essential dynamical properties and aspects of the flow, like convergence to putative semi-attracting states. More recently, we have developed a framework for statistical estimation of RNN models from experimental data. RNNs are computationally and dynamically universal in the sense that they can emulate and approximate any dynamical system, thus, in theory, are powerful enough to represent whatever neural dynamics and computational processes underlie the observed neural activity and behavior.Based on this previous and preliminary work, here we will tackle a number of important open issues: 1) Existing methods for statistical inference of (deep) RNN models do not scale very well with system size, yet this is very important for achieving good approximations to the dynamics and dealing with larger physiological data sets. Here we suggest several lines of methodological improvement. 2) More importantly, a systematic validation and comparison of various model architectures and training/inference algorithms on ground truth systems of differing biophysical complexity is still lacking, especially for experimentally realistic scenarios with comparatively sparse data from high-dimensional systems, which were only partially observed, and with high levels of both system-intrinsic and measurement noise. 3) As a case study for the usefulness of such methods, we will re-analyze MSU recordings from rat prefrontal cortex and hippocampus obtained during two different working memory tasks, to address specific issues about the (coupled) dynamics of these areas that were beyond the realm of previous analysis tools.