Backpropagation through space, time and the brain
Paul Haider*1, Benjamin Ellenberger1, Jakob Jordan1, Kevin Max1, Ismael Jaras1, Laura Kriener1, Federico Benitez1, Mihai A. Petrovici1
1Department of Physiology, University of Bern, Bern, Switzerland
*Email: paul.haider@unibe.ch
Introduction
Effective learning in the brain relies on the adaptation of individual synapses based on their relative contribution to solving a task. However, the challenge of spatio-temporal credit assignment in physical neuronal networks remains largely unsolved due to the biologically implausible assumptions of traditional backpropagation algorithms. This study aims to bridge this gap by proposing a novel framework that efficiently performs credit assignment in real-time, without violating spatio-temporal locality constraints, driven by the need for biological systems to learn continuously and interact with dynamic environments.
Methods
We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. GLE is based on an energy function of neuron-local mismatch errors, from which neuronal dynamics are derived using stationarity and parameter dynamics using gradient descent principles. This framework leverages the morphology of dendritic trees and the ability of neurons to phase-shift their output rates relative to their input (see, e.g., [1]), enabling complex information processing. Additionally, the adjoint method is employed to demonstrate that our learning rules approximate gradient descent on the total integrated cost over time, effectively approximating backpropagation through time (BPTT).
Results
The resulting neuronal dynamics can be interpreted as a real-time, biologically plausible approximation of backpropagation through space and time, incorporating continuous-time leaky-integrator neuronal dynamics and continuously active, phase-free, local synaptic plasticity. The corresponding equations suggest a direct mapping to cortical microcircuitry, with L2/3 pyramidal error neurons counter-posing L5/6 pyramidal representation neurons in a ladder-like fashion. We demonstrate GLE's effectiveness on both spatial and temporal tasks, such as chaotic time series prediction, MNIST-1D [2], and Google Speech Commands datasets, achieving results competitive with powerful ML architectures like GRUs and TCNs trained with offline BPTT.
Discussion
This framework has significant implications for understanding biological learning processes in neural circuits and designing neuromorphic hardware. GLE is applicable to both spatial and temporal tasks, offering advantages over existing alternatives like BPTT and real-time recurrent learning (RTRL) in terms of efficiency and biological plausibility. The framework's locality and reliance on conventional analog components make it an attractive blueprint for efficient neuromorphic hardware. This study contributes to a deeper understanding of how physical neuronal systems can efficiently learn and process information in real-time, bridging the gap between machine learning and biological neural networks.
Acknowledgements
This work was supported by the European Union, the Volkswagen Foundation, ESKAS, and the Manfred Stärk Foundation. We also acknowledge the Fenix Infrastructure and the Insel Data Science Center for their support.
References
1. Brandt, S., Petrovici, M.A., Senn, W., Wilmes, K.A., & Benitez, F. (2024). Prospective and retrospective coding in cortical neurons. https://arxiv.org/abs/2405.14810
2. Greydanus, S., & Kobak, D. (2020). Scaling Down Deep Learning with MNIST-1D. International Conference on Machine Learning. https://arxiv.org/abs/2011.14439
