A more realistic predictive coding model of the cortical hierarchy

Predictive coding (PC) has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain unresolved or controversial. In particular, current implementations often involve biologically unrealistic features such as separate value and error neurons and symmetric forward and backward weights across different brain regions.

In this work, we show that the PC framework in the linear regime can be modified to map faithfully onto the cortical hierarchy in a manner compatible with empirical observations. By employing a disentangling-inspired constraint on hidden-layer neural activities, we derive an upper bound for the PC objective. Optimization of this upper bound leads to an algorithm that shows the same performance as the original objective and maps onto a biologically plausible network. The units of this network can be interpreted as multi-compartmental neurons with non-Hebbian learning rules, with a remarkable resemblance to recent experimental findings. In particular, one of the plasticity mechanisms derived from our objective is akin to recently observed plasticity mediated by the calcium plateau potential in pyramidal neurons. Our circuit does not explicitly compare the output with the desired target, but we demonstrate that in our model, the calcium plateau signal implicitly encodes the relevant error information. We verify our algorithm empirically on a number of datasets and show that it performs comparably to the unconstrained PC framework.