Research in Neuroscience, as in many scientific disciplines, is undergoing a renaissance based on deep learning. Unique to Neuroscience, deep learning models can be used not only as a tool but interpreted as models of the brain. The central claims of recent deep learning-based models of brain circuits are that they make novel predictions about neural phenomena or shed light on the fundamental functions being optimized. We show, through the case-study of grid cells in the entorhinal-hippocampal circuit, that one may get neither. We begin by reviewing the principles of grid cell mechanism and function obtained from first-principles modeling efforts, then rigorously examine the claims of deep learning models of grid cells. Using large-scale hyperparameter sweeps and theory-driven experimentation, we demonstrate that the results of such models may be more strongly driven by particular, non-fundamental, and post-hoc implementation choices than fundamental truths about neural circuits or the loss function(s) they might optimize. We discuss why these models cannot be expected to produce accurate models of the brain without the addition of substantial amounts of inductive bias, an informal No Free Lunch result for Neuroscience. Based on first principles work, we provide hypotheses for what additional loss functions will produce grid cells more robustly. In conclusion, caution and consideration, together with biological knowledge, are warranted in building and interpreting deep learning models in Neuroscience.
We study how recurrent neural networks (RNNs) solve a hierarchical inference task involving two latent variables and disparate timescales separated by 1-2 orders of magnitude. The task is of interest to the International Brain Laboratory, a global collaboration of experimental and theoretical neuroscientists studying how the mammalian brain generates behavior. We make four discoveries. First, RNNs learn behavior that is quantitatively similar to ideal Bayesian baselines. Second, RNNs perform inference by learning a two-dimensional subspace defining beliefs about the latent variables. Third, the geometry of RNN dynamics reflects an induced coupling between the two separate inference processes necessary to solve the task. Fourth, we perform model compression through a novel form of knowledge distillation on hidden representations -Representations and Dynamics Distillation (RADD)-to reduce the RNN dynamics to a low-dimensional, highly interpretable model. This technique promises a useful tool for interpretability of high dimensional nonlinear dynamical systems. Altogether, this work yields predictions to guide exploration and analysis of mouse neural data and circuity.
The neural representations of prior information about the state of the world are poorly understood. To investigate this issue, we examined brain-wide Neuropixels recordings and widefield calcium imaging collected by the International Brain Laboratory. Mice were trained to indicate the location of a visual grating stimulus, which appeared on the left or right with prior probability alternating between 0.2 and 0.8 in blocks of variable length. We found that mice estimate this prior probability and thereby improve their decision accuracy. Furthermore, we report that this subjective prior is encoded in at least 20% to 30% of brain regions which, remarkably, span all levels of processing, from early sensory areas (LGd, VISp) to motor regions (MOs, MOp, GRN) and high level cortical regions (ACCd, ORBvl). This widespread representation of the prior is consistent with a neural model of Bayesian inference involving loops between areas, as opposed to a model in which the prior is incorporated only in decision making areas. This study offers the first brain-wide perspective on prior encoding at cellular resolution, underscoring the importance of using large scale recordings on a single standardized task.
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