Interrogating theoretical models of neural computation with emergent property inference

Abstract

1 Abstract 1 A cornerstone of theoretical neuroscience is the circuit model: a system of equations that captures 2 a hypothesized neural mechanism. Such models are valuable when they give rise to an experimen-3 tally observed phenomenon -whether behavioral or in terms of neural activity -and thus can offer 4 insights into neural computation. The operation of these circuits, like all models, critically depends 5 on the choices of model parameters. Historically, the gold standard has been to analytically derive 6 the relationship between model parameters and computational properties. However, this enterprise 7 quickly becomes infeasible as biologically realistic constraints are included into the model increas-8 ing its complexity, often resulting in ad hoc approaches to understanding the relationship between 9 model and computation. We bring recent machine learning techniques -the use of deep generative 10 models for probabilistic inference -to bear on this problem, learning distributions of parameters 11 that produce the specified properties of computation. Importantly, the techniques we introduce 12 offer a principled means to understand the implications of model parameter choices on compu-13 tational properties of interest. We motivate this methodology with a worked example analyzing 14 sensitivity in the stomatogastric ganglion. We then use it to generate insights into neuron-type 15 input-responsivity in a model of primary visual cortex, a new understanding of rapid task switch- 16 ing in superior colliculus models, and attribution of error in recurrent neural networks solving a 17 simple mathematical task. More generally, this work suggests a departure from realism vs tractabil-18 ity considerations, towards the use of modern machine learning for sophisticated interrogation of 19 biologically relevant models. 20 1 2 INTRODUCTION 2 Introduction 21The fundamental practice of theoretical neuroscience is to use a mathematical model to understand 22 neural computation, whether that computation enables perception, action, or some intermediate 23 processing [1]. A neural computation is systematized with a set of equations -the model -and 24 these equations are motivated by biophysics, neurophysiology, and other conceptual considerations. 25The function of this system is governed by the choice of model parameters, which when configured 26 in a particular way, give rise to a measurable signature of a computation. The work of analyzing a 27 model then requires solving the inverse problem: given a computation of interest, how can we reason 28 about these particular parameter configurations? The inverse problem is crucial for reasoning about 29 likely parameter values, uniquenesses and degeneracies, attractor states and phase transitions, and 30 predictions made by the model. 31 Consider the idealized practice: one carefully designs a model and analytically derives how model 32 parameters govern the computation. Seminal examples of this gold standard (which often adopt 33 approaches from statistical physics) include o...

Training deep neural density estimators to identify mechanistic models of neural dynamics

“…Our approach is already finding its first applications in neuroscience–for example, Oesterle et al, 2020 have used a variant of SNPE to constrain biophysical models of retinal neurons, with the goal of optimizing stimulation approaches for neuroprosthetics. Concurrently with our work, Bittner et al, 2019 developed an alternative approach to parameter identification for mechanistic models and showed how it can be used to characterize neural population models which exhibit specific emergent computational properties. Both studies differ in their methodology and domain of applicability (see descriptions of underlying algorithms in our prior work [ Lueckmann et al, 2017 ; Greenberg et al, 2019 ] and theirs [ Loaiza-Ganem et al, 2017 ]), as well in the focus of their neuroscientific contributions.…”

“…For example, the spike shape is known to constrain sodium and potassium conductances ( Druckmann et al, 2007 ; Pospischil et al, 2008 ; Hay et al, 2011 ). When modeling population dynamics, it is often desirable to achieve realistic firing rates, rate-correlations and response nonlinearities ( Rubin et al, 2015 ; Bittner et al, 2019 ), or specified oscillations ( Prinz et al, 2004 ). In models of decision making, one is often interested in reproducing psychometric functions or reaction-time distributions ( Ratcliff and McKoon, 2008 ).…”

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

“…Recently, there has been a surge of interest in Bayesian simulator-based inference with many recently published algorithms ( Gutmann and Corander, 2016 ; Papamakarios and Murray, 2016 ; Lueckmann et al, 2017 ; Lintusaari et al, 2017 ; Papamakarios et al, 2018 ; Wood, 2010 ; Durkan et al, 2018 ; Sisson et al, 2018 ; Gonçalves et al, 2020 ; Bittner et al, 2019 ). While we initially evaluated different algorithms, we did not perform a systematic comparison or benchmarking effort, which is beyond the scope of this project.…”

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

“…Recently, there has been a surge of interest in Bayesian simulator-based inference with many recently published algorithms 16,17,[82][83][84][85][86][87][88][89] . While we initially evaluated different algorithms, we did not perform a systematic comparison or benchmarking effort, which is beyond the scope of this project.…”