Gaspard Oliviers

Gaspard Oliviers, Elene Lominadze, Rafal Bogacz

Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

Gaspard Oliviers, Mufeng Tang, Rafal Bogacz

Predictive coding (PC) is an influential computational model of visual learning and inference in the brain. Classical PC was proposed as a top-down generative model, where the brain actively predicts upcoming visual inputs, and inference minimises the prediction errors. Recent studies have also shown that PC can be formulated as a discriminative model, where sensory inputs predict neural activities in a feedforward manner. However, experimental evidence suggests that the brain employs both generative and discriminative inference, while unidirectional PC models show degraded performance in tasks requiring bidirectional processing. In this work, we propose bidirectional PC (bPC), a PC model that incorporates both generative and discriminative inference while maintaining a biologically plausible circuit implementation. We show that bPC matches or outperforms unidirectional models in their specialised generative or discriminative tasks, by developing an energy landscape that simultaneously suits both tasks. We also demonstrate bPC's superior performance in two biologically relevant tasks including multimodal learning and inference with missing information, suggesting that bPC resembles biological visual inference more closely.