Dynamic Predictive Coding: A Model of Hierarchical Sequence Learning and Prediction in the Neocortex

Abstract

We introduce dynamic predictive coding, a new hierarchical model of spatiotemporal prediction and sequence learning in the cortex. The model assumes that higher cortical levels modulate the temporal dynamics of lower levels, correcting their predictions of dynamics using precision-weighted prediction errors. We tested this model using a two-level neural network, where the top-down modulation is implemented as a low-dimensional mixture of possible temporal dynamics. When trained on natural videos, the first-level neurons developed space-time receptive fields similar to those found in simple cells of the primary visual cortex. The second-level responses spanned longer timescales and showed more stability than those at the first level, mimicking temporal response hierarchies in the cortex. After adapting to a repeated visual sequence, the model displayed full recall of the sequence given only the beginning of the sequence, similar to sequence recall in the visual cortex. Our results suggest that sequence learning and temporal prediction in the cortex can be interpreted as dynamic predictive coding based on a hierarchical generative model of input sequences.

A Sensory-Motor Theory of the Neocortex based on Active Predictive Coding

“…The lower-level state neurons (at level i) maintain an estimate of the lower-level state s i t,τ where τ denotes a time step at the lower level within the higher level time interval given by t. In the two-level network, this lower-level state makes a prediction of the input via a "decoder" network D. In the simplest case where D is a linear matrix U , this lowest level of APC is equivalent to the generative model using in sparse coding (I = U s where s is sparse [49]). More generally, D can be a 1-layer RELU network [48] or a multi-layer decoder [11,12].…”

“…This episodic memory can later be retrieved when given an internal or external cue, e.g., a partial input that is the beginning of the episodic sequence. Figure 10B (from [48]) provides an example of such a recall by a two-level memory-augmented dynamic predictive coding model (APC without actions) which was shown 5 episodes of a sequence depicting the digit "5" moving from left to right (top panel in Figure 10B). By storing the sequence information as a vector m in its associative memory, the model was later able to retrieve the entire sequence given only the starting image as a cue (Figure 10B (lower panels)): this is reflected in the similarity between the activation pattern of the network's lower-level neurons during recall ("Start" condition) and the activation pattern observed during training ("Conditioning").…”

“…In addition to being used for self-supervised learning, prediction errors can also be used for inference to correct the estimates of state at each level using gradient-based updates similar to the original Rao-Ballard predictive coding model [1]: here feedforward pathways convey prediction errors to update state estimates and feedback pathways convey top-down modulation as described above (see [48] for an example based on modulatory hypernetworks).…”

“…Episodic recall from memory is indicated by the similarity in activation patterns between "Conditioning" and "Start." ((B) adapted from [48]).…”

Local minimization of prediction errors drives learning of invariant object representations in a generative network model of visual perception

“…To acquire transformation-tolerance from temporal continuity, input sequences are required. Most predictive coding models so far, however, either operate on static inputs (5,18,41) or use non-local learning rules (42) such as backpropagation (43, 44) and biologically implausible LSTM units (16, 45). Here, we train multilayered predictive coding networks on transformation sequences with purely Hebbian learning (based on (5) and (18)).…”