Backpropagation through space, time, and the brain (2403.16933v2)

Abstract: How physical networks of neurons, bound by spatio-temporal locality constraints, can perform efficient credit assignment, remains, to a large extent, an open question. In machine learning, the answer is almost universally given by the error backpropagation algorithm, through both space and time. However, this algorithm is well-known to rely on biologically implausible assumptions, in particular with respect to spatio-temporal (non-)locality. Alternative forward-propagation models such as real-time recurrent learning only partially solve the locality problem, but only at the cost of scaling, due to prohibitive storage requirements. We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. We start by defining an energy based on neuron-local mismatches, from which we derive both neuronal dynamics via stationarity and parameter dynamics via gradient descent. The resulting dynamics can be interpreted as a real-time, biologically plausible approximation of backpropagation through space and time in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the morphology of dendritic trees to enable more complex information storage and processing in single neurons, as well as the ability of biological neurons to phase-shift their output rate with respect to their membrane potential, which is essential in both directions of information propagation. For the forward computation, it enables the mapping of time-continuous inputs to neuronal space, effectively performing a spatio-temporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint variables necessary for useful parameter updates.

An Expert Analysis of "Backpropagation through space, time, and the brain"

The paper "Backpropagation through space, time, and the brain" introduces a novel computational framework, Generalized Latent Equilibrium (GLE), which addresses the spatio-temporal credit assignment problem in physical neuronal networks. This framework provides an alternative to traditional machine learning methods such as backpropagation through time (BPTT), offering a biologically plausible solution devoid of their non-locality issues and excessive memory demands. Below, I provide a comprehensive exploration of the framework, its merits, theoretical underpinnings, and implications for both neuroscience and neuromorphic computing.

Overview and Key Contributions

The authors start by identifying a fundamental constraint in neuronal networks—both biological and artificial—where synaptic updates must rely on local information. Classical algorithms like error backpropagation (BP) and BPTT do not adhere to this constraint, as they rely on non-local information for performing credit assignment. In response, the paper proposes GLE, which integrates biologically plausible neuronal dynamics into an energy-based model that adheres to local constraints both spatially and temporally.

The core of GLE is realized through four postulates. First, it assumes that biological neurons are capable of temporal integration and differentiation, thus performing retrospective and prospective operations. These capabilities, seldom acknowledged in typical models, are pivotal in allowing the neurons to dynamically adjust their temporal attention windows. The second postulate introduces an energy function based on neuron-local mismatches, serving as the foundation for the model's dynamics. The stationarity principle and gradient descent lead to GLE's local synaptic updates without requiring explicit temporal inversion.

Theoretical Underpinnings

From a theoretical perspective, the GLE framework extends the Latent Equilibrium (LE) model. Unlike LE, GLE does not constrain neurons to operate at identical time constants across the network. This flexibility allows for memory effects and dynamic temporal error transmission, which makes GLE apt for spatio-temporal learning tasks. The network dynamics derived from the GLE postulates implement a real-time approximation of AM/BPTT by leveraging prospective coding to align error backpropagation in time.

The authors demonstrate that GLE's neuronal dynamics encompass backward (error) dynamics that utilize inverse temporal operators. This results in error signals that are well-synchronized with local neuronal states, paving the path for efficient learning. Notably, in the Fourier space analysis, the GLE framework accurately replicates the phase shift characteristics of adjoint equations, which is vital for learning temporal dependencies in real-time.

Practical and Theoretical Implications

By situating GLE within an energy-based paradigm, the framework inherits the robustness associated with these approaches. The reduction of complex operations into local interactions makes it well-suited for neuromorphic implementations. The architectural proposal not only translates into significant improvements in energy efficiency for artificial neuronal systems but also suggests viable mechanisms for error propagation in biological circuits, aligning with evidence from neuroscience.

Moreover, the authors demonstrate the practicality of GLE through extensive simulation results. It holds its ground against state-of-the-art methods in challenging spatio-temporal tasks such as MNIST-1D and the Google Speech Commands dataset, maintaining competitive performance levels even while learning in an intrinsically online manner—a feature valuable for both biological learning and real-time applications.

Future Prospects

This framework opens new avenues for neuroscience research, particularly in understanding how learning occurs on multiple timescales in the brain. The physiological basis for prospective coding and its integration into structured neuronal networks require further exploration. It paves the way for more sophisticated models of cortical microcircuits that could offer insights into the intricacies of neuronal computation.

In the field of artificial intelligence and neuromorphic computing, GLE presents a novel blueprint for designing systems that mimic the efficiency of natural intelligence. Its applicability to low-power, continuous learning tasks signals a potential shift in how AI systems interface with dynamic environments.

To conclude, "Backpropagation through space, time, and the brain" contributes significantly to the synthesis of biological insights and machine learning imperatives, pushing the boundary of what is achievable in both theoretical neurosciences and AI hardware design. This framework could very well guide future developments in adaptive systems that learn from spatio-temporal data in real-time.