Energy optimization induces predictive-coding properties in a multi-compartment spiking neural network model

Predictive coding is a prominent theoretical framework for understanding hierarchical sensory processing in the brain, yet how it could be implemented in networks of cortical neurons is still unclear. While most existing studies have taken a hand-wiring approach to creating microcircuits that match experimental results, recent work in rate-based artificial neural networks revealed that suitable cortical connectivity might result from self-organisation given some fundamental computational principle, such as energy efficiency. As no corresponding approach has studied this in more plausible networks of spiking neurons, we here investigate whether predictive coding properties in a multi-compartment spiking neural network can emerge from energy optimisation. We find that a model trained with an energy objective in addition to a task-relevant objective is able to reconstruct internal representations given top-down expectation signals alone. Additionally, neurons in the energy-optimised model show differential responses to expected versus unexpected stimuli, qualitatively similar to experimental evidence for predictive coding. These findings indicate that predictive-coding-like behaviour might be an emergent property of energy optimisation, providing a new perspective on how predictive coding could be achieved in the cortex.Author summary: Predictive coding is an elegant and influential theoretical framework for understanding learning and processing in the brain, with several experimental findings seemingly in support. Yet, current predictive coding frameworks require specific connectivity motifs to be implemented whose emergence so far has remained unexplained – instantiated with spiking neurons, such motifs become even more intricate and more difficult to explain. An alternative point of view assumes that the brain is capable of efficient deep learning in some manner, for example energy optimization in rate-based RNNs can result in network behavior reminiscent of predictive coding. However, real biological networks differ from RNNs in important ways: first, they operate in continuous time rather than sequential steps, and second, real biological neurons emit binary spikes, which for instance makes it difficult to communicate an error that could be positive or negative. Defining an internal energy-measure for multi-compartment spiking neurons, we demonstrate how the resulting recurrent networks can exhibit several predictive coding like-properties when optimizing for both task and energy efficiency. The energy optimized network then demonstrates lower overall activity, generative behavior, and differential responses to expected vs unexpected stimuli. Energy-minimization in multi-compartment spiking neurons can thus bring tangible benefits and explain predictive-coding like empirical findings.