Understanding Predictive Coding as an Adaptive Trust-Region Method
This work provides a theoretical foundation for PC in deep networks, which is incremental but addresses a known bottleneck in understanding its advantages over BP.
The paper tackles the problem of understanding the benefits of predictive coding (PC) as a brain-inspired learning algorithm compared to backpropagation (BP), showing that PC acts as an adaptive trust-region method and can escape saddle points faster than BP, with experimental support in deeper networks.
Predictive coding (PC) is a brain-inspired local learning algorithm that has recently been suggested to provide advantages over backpropagation (BP) in biologically relevant scenarios. While theoretical work has mainly focused on showing how PC can approximate BP in various limits, the putative benefits of "natural" PC are less understood. Here we develop a theory of PC as an adaptive trust-region (TR) algorithm that uses second-order information. We show that the learning dynamics of PC can be interpreted as interpolating between BP's loss gradient direction and a TR direction found by the PC inference dynamics. Our theory suggests that PC should escape saddle points faster than BP, a prediction which we prove in a shallow linear model and support with experiments on deeper networks. This work lays a foundation for understanding PC in deep and wide networks.