The quest for interpretable models of neural population activity

Constructing neural networks with pre-specified dynamics

A main goal in neuroscience is to understand the computations carried out by neural populations that give animals their cognitive skills. Neural network models allow to formulate explicit hypotheses regarding the algorithms instantiated in the dynamics of a neural population, its firing statistics, and the underlying connectivity. Neural networks can be defined by a small set of parameters, carefully chosen to procure specific capabilities, or by a large set of free parameters, fitted with optimization algorithms that minimize a given loss function. In this work we alternatively propose a method to make a detailed adjustment of the network dynamics and firing statistic to better answer questions that link dynamics, structure, and function. Our algorithm-termed generalised Firing-to-Parameter (gFTP)-provides a way to construct binary recurrent neural networks whose dynamics strictly follows a user pre-specified transition graph that details the transitions between population firing states triggered by stimulus presentations. Our main contribution is a procedure that detects when a transition graph is not realisable in terms of a neural network, and makes the necessary modifications in order to obtain a new transition graph that is realisable and preserves all the information encoded in the transitions of the original graph. With a realisable transition graph, gFTP assigns values to the network firing states associated with each node in the graph, and finds the synaptic weight matrices by solving a set of linear separation problems. We test gFTP performance by constructing networks with random dynamics, continuous attractor-like dynamics that encode position in 2-dimensional space, and discrete attractor dynamics. We then show how gFTP can be employed as a tool to explore the link between structure, function, and the algorithms instantiated in the network dynamics.

Modeling the diverse effects of divisive normalization on noise correlations

Divisive normalization, a prominent descriptive model of neural activity, is employed by theories of neural coding across many different brain areas. Yet, the relationship between normalization and the statistics of neural responses beyond single neurons remains largely unexplored. Here we focus on noise correlations, a widely studied pairwise statistic, because its stimulus and state dependence plays a central role in neural coding. Existing models of covariability typically ignore normalization despite empirical evidence suggesting it affects correlation structure in neural populations. We therefore propose a pairwise stochastic divisive normalization model that accounts for the effects of normalization and other factors on covariability. We first show that normalization modulates noise correlations in qualitatively different ways depending on whether normalization is shared between neurons, and we discuss how to infer when normalization signals are shared. We then apply our model to calcium imaging data from mouse primary visual cortex (V1), and find that it accurately fits the data, often outperforming a popular alternative model of correlations. Our analysis indicates that normalization signals are often shared between V1 neurons in this dataset. Our model will enable quantifying the relation between normalization and covariability in a broad range of neural systems, which could provide new constraints on circuit mechanisms of normalization and their role in information transmission and representation.

Flexible coding schemes in dorsomedial prefrontal cortex underlie decision-making during delay discounting

Determining how an agent decides between a small, immediate versus a larger, delayed reward has provided insight into the psychological and neural basis of decision-making. The tendency to excessively discount the value of delayed rewards is thought to reflect deficits in brain regions critical for impulse control such as the prefrontal cortex (PFC). This study tested the hypothesis that dorsomedial PFC (dmPFC) is critically involved in flexibly managing neural representations of strategies that limit impulsive choices. Optogenetic silencing of neurons in the rat dmPFC increased impulsive choices at an 8 sec, but not 4 sec, delay. Neural recordings from dmPFC ensembles revealed that, at the 8-sec delay, the encoding landscape transitions to reflect a deliberative-like process rather than the schema-like processes observed at the 4-sec delay. These findings show that changes in the encoding landscape reflect changes in task demands and that dmPFC is uniquely involved in decisions requiring deliberation.

Neuroscience and Network Dynamics Toward Brain-Inspired Intelligence

This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications.

Natural behavior is the language of the brain

The breadth and complexity of natural behaviors inspires awe. Understanding how our perceptions, actions, and internal thoughts arise from evolved circuits in the brain has motivated neuroscientists for generations. Researchers have traditionally approached this question by focusing on stereotyped behaviors, either natural or trained, in a limited number of model species. This approach has allowed for the isolation and systematic study of specific brain operations, which has greatly advanced our understanding of the circuits involved. At the same time, the emphasis on experimental reductionism has left most aspects of the natural behaviors that have shaped the evolution of the brain largely unexplored. However, emerging technologies and analytical tools make it possible to comprehensively link natural behaviors to neural activity across a broad range of ethological contexts and timescales, heralding new modes of neuroscience focused on natural behaviors. Here we describe a three-part roadmap that aims to leverage the wealth of behaviors in their naturally occurring distributions, linking their variance with that of underlying neural processes to understand how the brain is able to successfully navigate the everyday challenges of animals' social and ecological landscapes. To achieve this aim, experimenters must harness one challenge faced by all neurobiological systems, namely variability, in order to gain new insights into the language of the brain.

Modelling the neural code in large populations of correlated neurons

Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper, we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.

Building population models for large-scale neural recordings: Opportunities and pitfalls

Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here, we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide.

Decision-related feedback in visual cortex lacks spatial selectivity

Feedback in the brain is thought to convey contextual information that underlies our flexibility to perform different tasks. Empirical and computational work on the visual system suggests this is achieved by targeting task-relevant neuronal subpopulations. We combine two tasks, each resulting in selective modulation by feedback, to test whether the feedback reflected the combination of both selectivities. We used visual feature-discrimination specified at one of two possible locations and uncoupled the decision formation from motor plans to report it, while recording in macaque mid-level visual areas. Here we show that although the behavior is spatially selective, using only task-relevant information, modulation by decision-related feedback is spatially unselective. Population responses reveal similar stimulus-choice alignments irrespective of stimulus relevance. The results suggest a common mechanism across tasks, independent of the spatial selectivity these tasks demand. This may reflect biological constraints and facilitate generalization across tasks. Our findings also support a previously hypothesized link between feature-based attention and decision-related activity.

Feedback modulates visual neurons, thought to help achieve flexible task performance. Here, the authors show decision-related feedback is not only relayed to task-relevant neurons, suggesting a broader mechanism and supporting a previously hypothesized link to feature-based attention.

How Cortical Circuits Implement Cortical Computations: Mouse Visual Cortex as a Model

The mouse, as a model organism to study the brain, gives us unprecedented experimental access to the mammalian cerebral cortex. By determining the cortex's cellular composition, revealing the interaction between its different components, and systematically perturbing these components, we are obtaining mechanistic insight into some of the most basic properties of cortical function. In this review, we describe recent advances in our understanding of how circuits of cortical neurons implement computations, as revealed by the study of mouse primary visual cortex. Further, we discuss how studying the mouse has broadened our understanding of the range of computations performed by visual cortex. Finally, we address how future approaches will fulfill the promise of the mouse in elucidating fundamental operations of cortex.

Rational thoughts in neural codes

Complex behaviors are often driven by an internal model, which integrates sensory information over time and facilitates long-term planning to reach subjective goals. A fundamental challenge in neuroscience is, How can we use behavior and neural activity to understand this internal model and its dynamic latent variables? Here we interpret behavioral data by assuming an agent behaves rationally—that is, it takes actions that optimize its subjective reward according to its understanding of the task and its relevant causal variables. We apply a method, inverse rational control (IRC), to learn an agent’s internal model and reward function by maximizing the likelihood of its measured sensory observations and actions. This thereby extracts rational and interpretable thoughts of the agent from its behavior. We also provide a framework for interpreting encoding, recoding, and decoding of neural data in light of this rational model for behavior. When applied to behavioral and neural data from simulated agents performing suboptimally on a naturalistic foraging task, this method successfully recovers their internal model and reward function, as well as the Markovian computational dynamics within the neural manifold that represent the task. This work lays a foundation for discovering how the brain represents and computes with dynamic latent variables.

Precision multidimensional neural population code recovered from single intracellular recordings

Neurons in sensory cortices are more naturally and deeply integrated than any current neural population recording tools (e.g. electrode arrays, fluorescence imaging). Two concepts facilitate efforts to observe population neural code with single-cell recordings. First, even the highest quality single-cell recording studies find a fraction of the stimulus information in high-dimensional population recordings. Finding any of this missing information provides proof of principle. Second, neurons and neural populations are understood as coupled nonlinear differential equations. Therefore, fitted ordinary differential equations provide a basis for single-trial single-cell stimulus decoding. We obtained intracellular recordings of fluctuating transmembrane current and potential in mouse visual cortex during stimulation with drifting gratings. We use mean deflection from baseline when comparing to prior single-cell studies because action potentials are too sparse and the deflection response to drifting grating stimuli (e.g. tuning curves) are well studied. Equation-based decoders allowed more precise single-trial stimulus discrimination than tuning-curve-base decoders. Performance varied across recorded signal types in a manner consistent with population recording studies and both classification bases evinced distinct stimulus-evoked phases of population dynamics, providing further corroboration. Naturally and deeply integrated observations of population dynamics would be invaluable. We offer proof of principle and a versatile framework.

Engineering recurrent neural networks from task-relevant manifolds and dynamics

Many cognitive processes involve transformations of distributed representations in neural populations, creating a need for population-level models. Recurrent neural network models fulfill this need, but there are many open questions about how their connectivity gives rise to dynamics that solve a task. Here, we present a method for finding the connectivity of networks for which the dynamics are specified to solve a task in an interpretable way. We apply our method to a working memory task by synthesizing a network that implements a drift-diffusion process over a ring-shaped manifold. We also use our method to demonstrate how inputs can be used to control network dynamics for cognitive flexibility and explore the relationship between representation geometry and network capacity. Our work fits within the broader context of understanding neural computations as dynamics over relatively low-dimensional manifolds formed by correlated patterns of neurons.

Data-Driven Approaches to Understanding Visual Neuron Activity

With modern neurophysiological methods able to record neural activity throughout the visual pathway in the context of arbitrarily complex visual stimulation, our understanding of visual system function is becoming limited by the available models of visual neurons that can be directly related to such data. Different forms of statistical models are now being used to probe the cellular and circuit mechanisms shaping neural activity, understand how neural selectivity to complex visual features is computed, and derive the ways in which neurons contribute to systems-level visual processing. However, models that are able to more accurately reproduce observed neural activity often defy simple interpretations. As a result, rather than being used solely to connect with existing theories of visual processing, statistical modeling will increasingly drive the evolution of more sophisticated theories.