The dimensionality of neural representations for control

Abstract

Cognitive control allows us to think and behave flexibly based on our context and goals. At the heart of theories of cognitive control is a control representation that enables the same input to produce different outputs contingent on contextual factors. In this review, we focus on an important property of the control representation's neural code: its representational dimensionality. Dimensionality of a neural representation balances a basic separability/generalizability trade-off in neural computation. We will discuss the implications of this trade-off for cognitive control. We will then briefly review current neuroscience findings regarding the dimensionality of control representations in the brain, particularly the prefrontal cortex. We conclude by highlighting open questions and crucial directions for future research.

Keywords: cognitive control; executive function; frontal lobes; neural computation; neural representation.

Figure 1.

Schematic illustration of representational dimensionality and its computational properties. Each panel plots the response of a toy population of three neurons to stimuli that vary in shape (square or circle) and color (red or black). Axes represent the firing rates of single neurons and collectively define a multi-dimensional firing rate space for the population. Each point within this space represents the population response (i.e., activity pattern) for a given input (identified by colored shapes). Distance between points reflects how distinct responses are, and the jittered cloud of points reflect the trial-by-trial variability in responses to a given input. (a-c) show a low dimensional representation. Though the population is 3-dimensional (i.e., has three neurons), the representation defined by the population responses to the four stimuli defines a lower 2-dimensional plane (traced by solid black lines). A linear ‘readout’ of this representation is implemented by a ‘decision hyperplane’ (yellow) that divides the space into different classes, such as color and shape. The readout can be visualized by projecting (highlighted for red circles) the responses into a readout subspace. (a) In the shape subspace (peach), square and circle stimuli produce distinct, well-separated responses that generalize over different colors. (b) The color subspace (grey) separates red and black but generalizes over shape. (c) illustrates that it is impossible to linearly read out integrated classes (like red-square or black-circle vs black-square or red-circle) in this low-dimensional representation. A non-linear decision surface is required. This problem can be solved by a high-dimensional representation where the response patterns span 3 dimensions (d-f). As before, shape (d) and color (e) information can be linearly read out, though with poorer generalization along the irrelevant dimensions (reflected in the distance between clouds in the irrelevant dimension). Importantly, classes based on color-shape conjunctions (f) can also be linearly read out. Thus, high-dimensional representations are more expressive, making a wider variety of classes linearly separable. A population with a diversity of non-linear mixed selective neurons will have a higher representational dimensionality.

Figure 2.

(a-c) Illustrations of control representations of different dimensionality across modulatory and transmissive architectures for cognitive flexibility. (a) A modulatory model of cognitive control based on the widely recognized Stroop model from Cohen et al. [1]. Localist units represent patterns of activity of a neural population. Input layers with the word and ink color feedforward to a hidden layer which feeds forward to a response layer at the top. A task cue input feeds forward to a low dimensional context layer. This is the control representation that biases the task-relevant response pathway to enable flexibility. (b) A transmissive architecture that achieves flexibility with a high dimensional hidden layer that mixes all inputs into separate pathways. Thus, the hidden layer is an expressive control representation that makes any combination of cue and stimuli available for direct readout by the response layer. (c) A modulatory model with a high dimensional context layer. This expressive control representation can use any combination of task cue and stimuli as a contextual input to bias the route from stimulus to response. (d)-(e) Illustrations of the tradeoffs of dimensionality for control. (d) A simplified representation of the architecture in 2a without the context layer and with an added output, following [32]. The combination of two input types and two ouput types makes four “tasks”. Arrows show pathways from input to output with active unites highlighted and distinguished by fill pattern. A low dimensional control representation can link an input to both verbal and button press responses. This is useful for fast learning; a new task involving auditory input can leverage this low dimensional representation to link to all available outputs. However, if two tasks are performed at once, there is cross-talk interference (red paths) (e) A higher dimensional control representation in the hidden layer, akin to 1b, separates the inputs across the tasks. This allows multitasking without interference, but a new task involving auditory input must learn entirely new pathways.