Canonical microcircuits for predictive coding

Abstract

This Perspective considers the influential notion of a canonical (cortical) microcircuit in light of recent theories about neuronal processing. Specifically, we conciliate quantitative studies of microcircuitry and the functional logic of neuronal computations. We revisit the established idea that message passing among hierarchical cortical areas implements a form of Bayesian inference-paying careful attention to the implications for intrinsic connections among neuronal populations. By deriving canonical forms for these computations, one can associate specific neuronal populations with specific computational roles. This analysis discloses a remarkable correspondence between the microcircuitry of the cortical column and the connectivity implied by predictive coding. Furthermore, it provides some intuitive insights into the functional asymmetries between feedforward and feedback connections and the characteristic frequencies over which they operate.

Copyright © 2012 Elsevier Inc. All rights reserved.

Figures

Figure 1

This is a schematic of the classical microcircuit adapted from Douglas and Martin (1991). This minimal circuitry comprises superficial (layers 2 and 3) and deep (layers, 5 and 6) pyramidal cells and a population of smooth inhibitory cells. Feedforward inputs – from the thalamus – target all cell populations, but with an emphasis on inhibitory interneurons and superficial and granular layers. Note the symmetrical deployment of inhibitory and excitatory intrinsic connections that maintain a balance of excitation and inhibition.

Figure 2

This is a simplified schematic of the key intrinsic connections among excitatory (E) and inhibitory (I) populations in granular (L4), supragranular (L1/2/3) and infragranular (L5/6) layers. The excitatory interlaminar connections are based largely on Gilbert and Wiesel (1983). Forward connections denote feedforward extrinsic corticocortical or thalamocortical afferents that are reciprocated by backward or feedback connections. Anatomical and functional data suggest that afferent input enters primarily into L4 and is conveyed to superficial layers L2/3 that are rich in pyramidal cells, which project forward to the next cortical area, forming a disynaptic route between thalamus and secondary cortical areas (Callaway, 1998). Information from L2/3 is then sent to L5 and L6, which sends (intrinsic) feedback projections back to L4 (Usrey and Fitzpatrick, 1996). L5 cells originate feedback connections to earlier cortical areas as well as to the pulvinar, superior colliculus, and brain stem. In summary, forward input is segregated by intrinsic connections into a superficial forward stream and a deep backward stream. In this schematic, we have juxtaposed densely interconnected excitatory and inhibitory populations within each layer.

Figure 3

This schematic shows an example of a generative model. Generative models describe how (sensory) data are caused. In this figure, sensory states (blue circles on the periphery) are generated by hidden variables (in the centre). The left panel shows the model as a probabilistic graphical model, where unknown variables (hidden causes and states) are associated with the nodes of a dependency graph and conditional dependencies are indicated by arrows. Hidden states confer memory on the model by virtue of having dynamics, while hidden causes connect nodes. A graphical model describes the conditional dependencies among hidden variables generating data. These dependencies are typically modelled as (differential) equations with nonlinear mappings and random fluctuations ω~(i) with precision (inverse variance) Π(i) (see the equations in the insert on the left). This allows one to specify the precise form of the probabilistic generative model and leads to a simple and efficient inversion scheme (predictive coding; see next figure). Here v~pa(i) denotes the set of hidden causes that constitute the parents of sensory s̃(i) or hidden x̃(i) states. The ~ indicates states in generalised coordinates of motion: x̃ = (x, x′, x″,...). An intuitive version of the model is shown on the right: here, we imagine that a singing bird is the cause of sensations, which – through a cascade of dynamical hidden states – produces modality-specific consequences (e.g., the auditory object of a bird song and the visual object of a song bird). These intermediate causes are themselves (hierarchically) unpacked to generate sensory signals. The generative model therefore maps from causes (e.g., concepts) to consequences (e.g., sensations), while its inversion corresponds to mapping from sensations to concepts or representations. This inversion corresponds to perceptual synthesis – in which the generative model is used to generate predictions. Note that this inversion implicitly resolves the binding problem - by explaining multisensory cues with a single cause.

Figure 4

This figure describes the predictive coding scheme associated with a simple hierarchical model shown on the left. In this model each node has a single parent. The ensuing inversion or generalised predictive coding scheme is shown on the right. The key quantities in this scheme are (conditional) expectations of the hidden states and causes and their associated prediction errors. The basic architecture – implied by the inversion of the graphical (hierarchical) model – suggests that prediction errors (caused by unpredicted fluctuations in hidden variables) are passed up the hierarchy to update conditional expectations. These conditional expectations now provide predictions that are passed down the hierarchy to form prediction errors. We presume that the forward and backward message passing between hierarchical levels is mediated by extrinsic (feedforward and feedback) connections. Neuronal populations encoding conditional expectations and prediction errors now have to be deployed in a canonical microcircuit to understand the computational logic of intrinsic connections – within each level of the hierarchy – as shown in the next figure.

Figure 5

The left hand panel is the canonical microcircuit based on Haeusler and Maass (2007), where we have removed inhibitory cells from the deep layers – because they have very little interlaminar connectivity. The numbers denote connection strengths (mean amplitude of PSPs measured at soma in mV) and connection probabilities (in parentheses) according to Thomson et al. (2002). The right panel shows the proposed cortical microcircuit for predictive coding, where the quantities of the previous figure have been associated with various cell types. Here, prediction error populations are highlighted in pink. Inhibitory connections are shown in red, while excitatory connections are in black. The dotted lines refer to connections that are not present in the microcircuit on the left (but see Figure 2). In this scheme, expectations (about causes and states) are assigned to (excitatory and inhibitory) interneurons in the supragranular layers, which are passed to infragranular layers. The corresponding prediction errors occupy granular layers, while superficial pyramidal cells encode prediction errors that are sent forward to the next hierarchical level. Conditional expectations and prediction errors on hidden causes are associated with excitatory cell types, while the corresponding quantities for hidden states are assigned to inhibitory cells. Dark circles indicate pyramidal cells. Finally, we have placed the precision of the feedforward prediction errors against the superficial pyramidal cells. This quantity controls the postsynaptic sensitivity or gain to (intrinsic and top-down) pre-synaptic inputs. We have previously discussed this in terms of attentional modulation, which may be intimately linked to the synchronisation of pre-synaptic inputs and ensuing postsynaptic responses (Fries et al 2001; Feldman and Friston, 2010).

Figure 6

This schematic illustrates the functional asymmetry between the spectral activity of superficial and deep cells predicted theoretically. In this illustrative example, we have ignored the effects of influences on the expectations of hidden causes (encoded by deep pyramidal cells), other than the prediction error on causes (encoded by superficial pyramidal cells). The lower panel shows the spectral density of deep pyramidal cell activity, given the spectral density of superficial pyramidal cell activity in the upper panel. The equation expresses the spectral density of the deep cells as a function of the spectral density of the superficial cells; using Equation (2). This schematic is meant to illustrate how the relative amounts of low (beta) and high (gamma) frequency activity in superficial and deep cells can be explained by the evidence accumulation implicit in predictive coding.