Scientific Understanding of Consciousness
Prefrontal Cortex Context-Dependent Recurrent Dynamics
Nature 503, 78–84 (07 November 2013)
Context-dependent computation by recurrent dynamics in prefrontal cortex
Howard Hughes Medical Institute and Department of Neurobiology, Stanford University, Stanford, California 94305, USA
Valerio Mante & William T. Newsome
Department of Electrical Engineering and Neurosciences Program, Stanford University, Stanford, California 94305, USA
David Sussillo & Krishna V. Shenoy
Departments of Neurobiology and Bioengineering, Stanford University, Stanford, California 94305, USA
Krishna V. Shenoy
Institute of Neuroinformatics, University of Zurich/ETH Zurich, CH-8057 Zurich, Switzerland.
Prefrontal cortex is thought to have a fundamental role in flexible, context-dependent behaviour, but the exact nature of the computations underlying this role remains largely unknown. In particular, individual prefrontal neurons often generate remarkably complex responses that defy deep understanding of their contribution to behaviour. Here we study prefrontal cortex activity in macaque monkeys trained to flexibly select and integrate noisy sensory inputs towards a choice. We find that the observed complexity and functional roles of single neurons are readily understood in the framework of a dynamical process unfolding at the level of the population. The population dynamics can be reproduced by a trained recurrent neural network, which suggests a previously unknown mechanism for selection and integration of task-relevant inputs. This mechanism indicates that selection and integration are two aspects of a single dynamical process unfolding within the same prefrontal circuits, and potentially provides a novel, general framework for understanding context-dependent computations.
Our interactions with the world are inherently flexible. Identical sensory stimuli, for example, can lead to very different behavioural responses depending on ‘context’, which includes goals, previous expectations about upcoming events, and relevant past experiences. Animals can switch rapidly between behavioural contexts, implying the existence of rapid modulation, or ‘gating’, mechanisms within the brain that select relevant sensory information for decision-making and action. A large attention literature suggests that relevant information is selected by top-down modulation of neural activity in early sensory areas, which may take the form of modulation of firing rates, or modulation of response synchrony within or across areas. The top-down signals underlying such ‘early’ modulations of sensory activity arise, in part, from prefrontal cortex (PFC), which is known to contribute to representing and maintaining contextual knowledge, ignoring irrelevant information, and suppressing inappropriate actions.
We trained two macaque monkeys to perform two different perceptual discriminations on the same set of visual stimuli. The monkeys were instructed by a contextual cue to either discriminate the direction of motion or the colour of a random-dot display, and to report their choices with a saccade to one of two visual targets.
An appropriately trained recurrent neural network model reproduces key physiological observations and suggests a new mechanism of input selection and integration. The mechanism reflects just two learned features of a dynamical system: an approximate line attractor and a ‘selection vector’, which are only defined at the level of the population.
As is common in PFC, the recorded responses of single neurons appeared to represent several different task-related signals at once, including the monkey’s upcoming choice, the context, and the strength of motion and colour evidence. Rather than attempting to understand the neural mechanism underlying selective integration by studying the responses of single PFC neurons, we focussed on analysing the responses of the population as a whole.
To study how the PFC population as a whole dynamically encodes the task variables underlying the monkeys’ behaviour, we represent population responses as trajectories in neural state space. Each point in state space corresponds to a unique pattern of neural activations across the population. Because activations are dynamic, changing over time, the resulting population responses form trajectories in state space.
We focussed our analyses on responses in a specific low-dimensional subspace that captures across-trial variance, the strength and direction of the motion, the strength and direction of the colour, and context (motion or colour). We estimated this task-related subspace in two steps. First, we used principal component analysis (PCA) to obtain an unbiased estimate of the most prominent features (that is, patterns of activations) in the population response. To ‘de-noise’ the population responses, we restricted subsequent analyses to the subspace spanned by the first 12 principal components. Second, we used linear regression to define the four orthogonal, task-related axes of choice, motion, colour and context. The projection of the population response onto these axes yields de-mixed estimates of the corresponding task variables, which are mixed both at the level of single neurons and at the level of individual principal components.
A neural network model of input selection and integration
PFC is modelled as a network of recurrently connected, nonlinear, rate neurons that receive independent motion, colour and contextual inputs. The network is fully recurrently connected, and each unit receives both motion and colour inputs as well as two inputs that indicate context. At each time step, the sensory inputs are drawn from two normal distributions, the means of which correspond to the average strengths of the motion and colour evidence on a given trial. The contextual inputs take one of two values, which instruct the network to discriminate either the motion or the colour input. The network is read out by a single linear read-out, corresponding to a weighted sum over the responses of all neurons. We trained the network (with back-propagation) to make a binary choice, that is, to generate an output of +1 at the end of the stimulus presentation if the relevant evidence pointed towards choice 1, or a −1 if it pointed towards choice 2. Before training, all synaptic strengths were randomly initialized.
Recurrent network model of selection and integration
We trained a network simulation of recurrently connected, nonlinear neurons to solve a task analogous to the one solved by the monkeys. Notably, we only defined ‘what’ the network should do, with minimal constraints on ‘how’ it should do it. Thus, the solution achieved by the network is not hand-built into the network architecture.
The direction of the selection vector, like the direction of the line attractor, is a property of the recurrent synaptic weights learned by the model during training. Unlike the line attractor, however, the orientation of the selection vector changes with context—it projects strongly onto the relevant input, but is orthogonal to the irrelevant one. As a consequence, the relaxation dynamics around the line attractor are context dependent. This mechanism explains how the same sensory input can result in movement along the line attractor in one context but not the other.
The line attractor and the selection vector are sufficient to explain the linearized dynamics around each fixed point, and approximate well the responses of the full model. Mathematically, the line attractor and the selection vector correspond to the right and left zero-eigenvector of the underlying linear system. Within a context, these locally defined eigenvectors point in a remarkably consistent direction across different fixed points—the selection vector, in particular, is always aligned with the relevant input and orthogonal to the irrelevant input. As a result, the two line attractors show relaxation dynamics appropriate for selecting the relevant input along their entire length.
Our results indicate that computations in prefrontal cortex emerge from the concerted dynamics of large populations of neurons, and are well studied in the framework of dynamical systems. Notably, the rich dynamics of PFC responses during selection and integration of inputs can be characterized and understood with just two features of a dynamical system—the line attractor and the selection vector, which are defined only at the level of the neural population. This parsimonious account of cortical dynamics contrasts markedly with the complexity of single neuron responses typically observed in PFC and other integrative structures, which reveal multiplexed representation of many task-relevant and choice-related signals. In light of our results, these mixtures of signals can be interpreted as separable representations at the level of the neural population. A fundamental function of PFC may be to generate such separable representations, and to flexibly link them through appropriate recurrent dynamics to generate the desired behavioural outputs.
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