Fig 1.
This figure illustrates the basic architecture of message passing in hierarchical predictive coding.
Here, 3 hierarchical levels are shown in schematic form (blue boxes). These levels are populated by pairs of populations—encoding prediction errors (red triangles) and expectations (blue triangles). Sensory input enters at the lowest level of the hierarchy (denoted by the eye). The equations describe the mathematical form of predictive coding, expressed as a Kalman-Bucy filter. Here, μ represents an expectation (i.e., mean) of some state of the world. Conversely, ε represents prediction error, which is just the difference between sensory input s and predictions of that input under some generative model g, given expected states of affairs. This form means that prediction errors are weighted by their precision Π to drive expectations, which, in turn, supply predictions to error units, thereby suppressing them. The architecture on the left is the canonical or standard architecture [6], in which prediction errors ascend from one level to the next and are complemented by a descending counter-stream of predictions. However, exactly the same message passing can be implemented by simply moving the expectation units down a little (depicted by the blue arrow) to produce the architecture on the right. Although nothing changes in terms of inference, now the predictions ascend the hierarchy, while prediction errors are conveyed by extrinsic (between cortical level) connections. The self-connections (in blue) stand in for a precision or gain control that modulates the disinhibition of error units. The precision of prediction errors at different hierarchical levels can have profound effects on message passing and subsequent belief updating or evidence accumulation. Please see main text.
Fig 2.
This schematic illustrates forward and backwards travelling alpha waves as they are envisaged to transverse the cortical hierarchy.
The schematic on the top borrows from Fig 1 and illustrates a succession of reciprocally coupled populations encoding errors (red triangles) and expectation units (blue triangles). Following a sensory perturbation, prediction errors ascend the hierarchy, producing a wave of excitation that is ‘reflected’ at each level to produce wavelike spatiotemporal dynamics. This is illustrated here in terms of waves in water that could stand in for the ‘active matter’ that constitutes coupled neuronal oscillators, when densely packed.