Source-linked AI summary
Dendritic cortical microcircuits approximate the backpropagation algorithm
João Sacramento, Rui Ponte Costa, Yoshua Bengio, Walter Senn
TL;DR
The paper asks how the brain might implement backpropagation despite its biological implausibility and proposes a dendritic cortical microcircuit model using local prediction errors. The model learns continuously without separate phases, approximates backpropagation analytically, and performs regression and classification tasks. The authors relate its predictions to cortical observations while identifying limitations including slow iterative learning and restricted interneuron coverage.
Problem
Backpropagation’s biological implementation remains unresolved, despite its role in solving the synaptic credit assignment problem.
Method
The model uses multicompartment pyramidal neurons and interneurons whose dendritic prediction errors drive local synaptic plasticity continuously in time.
Results
The network approximates backpropagation and provides a framework consistent with observations of cortical learning and microcircuit architecture.
Takeaways & Limitations
Dendritic cortical circuits may solve credit assignment for time-continuous input streams through backpropagation-like local learning.
Takeaways & Limitations
The model requires iterating over many training examples rather than supporting human-like one-shot learning and omits several interneuron types.
Abstract
from arXiv · showhide
Deep learning has seen remarkable developments over the last years, many of them inspired by neuroscience. However, the main learning mechanism behind these advances - error backpropagation - appears to be at odds with neurobiology. Here, we introduce a multilayer neuronal network model with simplified dendritic compartments in which error-driven synaptic plasticity adapts the network towards a global desired output. In contrast to previous work our model does not require separate phases and synaptic learning is driven by local dendritic prediction errors continuously in time. Such errors originate at apical dendrites and occur due to a mismatch between predictive input from lateral interneurons and activity from actual top-down feedback. Through the use of simple dendritic compartments and different cell-types our model can represent both error and normal activity within a pyramidal neuron. We demonstrate the learning capabilities of the model in regression and classification tasks, and show analytically that it approximates the error backpropagation algorithm. Moreover, our framework is consistent with recent observations of learning between brain areas and the architecture of cortical microcircuits. Overall, we introduce a novel view of learning on dendritic cortical circuits and on how the brain may solve the long-standing synaptic credit assignment problem.
1 Introduction
The paper addresses how cortical circuits might implement backpropagation-like learning despite its neurobiological implausibility. It proposes dendritic prediction errors and evaluates the model analytically and empirically.
- Backpropagation remains the dominant deep-learning mechanism, but how the brain could implement a backprop-like algorithm remains unresolved.
- Synaptic credit assignment concerns how synapses should be modified so different brain areas can learn associations that drive behavior.
- The model encodes backpropagation-driving prediction errors at pyramidal neurons’ distal dendrites receiving top-down input from downstream areas.
- Local interneuron input predicts top-down feedback, and mismatches between them drive plasticity of bottom-up connections continuously without separate learning phases.
- The study analyzes when the network approximates backpropagation and evaluates it on nonlinear regression and recognition tasks.
2 Error-encoding dendritic cortical microcircuits
The model uses multicompartment pyramidal neurons and interneurons to encode dendritic prediction errors locally. Plasticity combines these errors with presynaptic activity, while learned interneuron cancellation creates a self-predicting regime.
- Neuron and network model: Pyramidal neurons are modeled with somatic, basal, and apical compartments receiving bottom-up and top-down inputs through separate dendritic pathways.
- Neuron and network model: SST-like interneurons receive lateral and cross-layer inputs and project to same-layer apical dendrites to cancel predicted top-down activity.
- Error propagation: A novel output teaching signal creates an apical mismatch that propagates toward the soma and modulates firing, driving bottom-up synaptic plasticity.
- Synaptic learning rules: Synaptic updates equal a dendritic prediction-error term multiplied by presynaptic firing rate, allowing potentiation or depression according to error sign.
- Synaptic learning rules: For basal synapses, the prediction-error factor compares postsynaptic activity with a local dendritic estimate dependent on branch potential.
- Relation to predictive coding: The framework maps backpropagation onto predictive-coding circuitry, whose error representations require specialized network organization.
3 Results
The model propagates dendritic prediction errors through multilayer networks using local plasticity, approximating backpropagation while learning continuously online. It learns nonlinear regression and MNIST classification, including useful updates to hidden-layer weights.
- Analytical relationship to backpropagation: Self-predicting networks cancel internally generated top-down feedback when no target is provided, leaving apical dendrites silent and producing feedforward output.This state allows synaptic plasticity to approximate the weight changes prescribed by backpropagation.
- Analytical relationship to backpropagation: In the weak-feedback limit λ →0, hidden-layer plasticity matches backpropagation up to a learning-rate factor when top-down weights transpose feedforward weights.With fixed random feedback weights, the same dynamics implement feedback alignment; learned feedback can instead support target propagation.
- Continuous local learning: Local dendritic errors alter somatic activity and drive bottom-up synaptic plasticity concurrently with interneuron updates, allowing the network to predict novel top-down input.The rule uses presynaptic activity, postsynaptic firing, and dendritic branch voltage rather than globally coordinated phases.
- Continuous local learning: Learning proceeds in continuous time without pauses or alternating plasticity phases as input patterns are sequentially presented.This differs from approaches that compute activity differences across distinct phases or switch plasticity rules globally.
- Nonlinear regression: The 30-50-10 network learned a nonlinear regression task online from random weights, outperforming a shallow learner and changing hidden-layer bottom-up weights.The self-predicting state emerged during learning rather than being required at initialization.
4 Conclusions
The paper connects dendritic error signals to cortical microcircuits and proposes a continuous-time approximation to backpropagation for synaptic credit assignment. It also identifies interneuron coverage and rapid learning as important boundaries.
- Predictions and cortical connections: Distal dendrites are proposed to encode errors that instruct learning of lateral and bottom-up connections, consistent with observations of prediction errors in visual cortex.The model links these errors to feedback from downstream cortical areas and their cancellation by local interneurons.
- Predictions and cortical connections: Prediction errors at higher-order cortical areas would imply co-occurring errors in earlier areas, consistent with observations in the macaque face-processing hierarchy.
- Scope and limitations: The framework focuses on SST interneurons, while PV interneurons and other cell types are not modeled and could represent additional prediction errors.The proposed role for PV cells remains a possible extension rather than part of the present framework.
- Scope and limitations: Unlike human one-shot learning, the model requires iterating over many training examples, leaving the neuronal basis of rapid learning unresolved.The paper suggests that interacting subsystems learning at different rates could be relevant to this open problem.
- Overall conclusion: The model provides a view of how cortical circuits may approximate backpropagation for time-continuous inputs and address synaptic credit assignment.
Supplementary Material: Dendritic cortical microcircuits approximate the backpropagation algorithm
The model uses dendritic compartments and lateral interneuron plasticity to establish a self-predicting state, allowing apical mismatches to encode neuron-specific errors and drive approximate backpropagation. Analytical results connect the resulting local synaptic updates to backpropagation under stated conditions.
- Circuit architecture: Pyramidal neurons separate bottom-up input in basal dendrites, top-down feedback in apical dendrites, and integration in the soma.Hidden-layer microcircuits also include lateral inhibitory interneurons that receive pyramidal input and project to pyramidal apical compartments.
- Error signaling: Novel output teaching signals create apical mismatches that cannot be explained by lateral interneurons, yielding neuron-specific errors that drive forward-weight plasticity.The same circuit thereby distinguishes ordinary pyramidal activity from error-related apical activity.
- Self-predicting state: Interneuron plasticity learns to reproduce higher-layer activity and adjusts interneuron-to-pyramidal weights to cancel expected top-down feedback.Together, these changes establish the self-predicting state across activity patterns.
- Error signaling: At fixed points, apical dendritic potentials recursively encode prediction errors traceable to output-layer mismatches.With matched integration time constants, noisy background currents produce zero average prediction error while momentary fluctuations can still induce plasticity.
- Approximate backpropagation: To leading order in λ, hidden neurons combine bottom-up predictions with output-layer errors propagated backward through the network.The model’s objective is differentiable and lower bounded, making it suitable for gradient-descent analysis.
- Approximate backpropagation: Output-layer updates exactly match backpropagation, while hidden-layer updates match it up to a learning-rate factor as λ →0 when top-down weights transpose feedforward weights.This approximation relies on the stated weight-symmetry and weak-feedback conditions.
- Interneuron plasticity: Interneuron weights converge toward their desired values when the relevant activity correlation matrix is positive definite.Saturating nonlinearities can make this matrix nearly singular and slow learning.