Source-linked AI summary
Towards deep learning with segregated dendrites
Jordan Guergiuev, Timothy P. Lillicrap, Blake A. Richards
TL;DR
The paper asks whether deep learning and credit assignment can occur in biologically realistic neural networks. It uses multi-compartment neurons with segregated dendritic processing, showing coordinated multilayer learning, better MNIST classification than single-layer networks, and hierarchical representations.
Problem
Neuroscience lacks a biologically plausible account of credit assignment, while common AI solutions rely on unrealistic non-local feedback or separate pathways.
Method
The model uses neurons with segregated basal and apical dendritic compartments to integrate feedforward and feedback signals separately and form local hidden-layer targets.
Results
The algorithm coordinates learning across layers, classifies MNIST better than single-layer networks, and produces hierarchical abstract representations.
Takeaways & Limitations
Deep learning can be implemented with electrotonically segregated dendritic compartments, offering a biologically feasible account consistent with neocortical pyramidal neuron morphology.
Takeaways & Limitations
The approach assumes distinct dendritic compartments can separately integrate feedforward and feedback signals and support the required local learning targets.
Abstract
from arXiv · showhide
Deep learning has led to significant advances in artificial intelligence, in part, by adopting strategies motivated by neurophysiology. However, it is unclear whether deep learning could occur in the real brain. Here, we show that a deep learning algorithm that utilizes multi-compartment neurons might help us to understand how the brain optimizes cost functions. Like neocortical pyramidal neurons, neurons in our model receive sensory information and higher-order feedback in electrotonically segregated compartments. Thanks to this segregation, the neurons in different layers of the network can coordinate synaptic weight updates. As a result, the network can learn to categorize images better than a single layer network. Furthermore, we show that our algorithm takes advantage of multilayer architectures to identify useful representations---the hallmark of deep learning. This work demonstrates that deep learning can be achieved using segregated dendritic compartments, which may help to explain the dendritic morphology of neocortical pyramidal neurons.
Introduction
The paper addresses how biological neural networks might perform credit assignment and deep learning without biologically unrealistic feedback pathways. It proposes using segregated dendritic compartments to separate feedforward and feedback signals and coordinate learning across layers.
- Credit assignment requires identifying how neurons in early sensory areas contribute to final behavioral or cognitive outputs.
- Hebbian learning and global neuromodulatory signals do not solve the credit assignment problem that deep learning systems address.
- Backpropagation assigns credit through downstream synaptic information, but its non-local weight transport is biologically unrealistic.
- Existing biologically motivated models require separate pathways to keep sensory information distinct from feedback signals that drive hidden-layer updates.
- Pyramidal neurons receive higher-order feedback in distal apical dendrites, electrotonically separated from basal dendrites receiving feedforward sensory information.
- The proposed model uses segregated basal and apical compartments to integrate feedforward and feedback signals separately and construct local targets for hidden layers.
- With random feedback weights, the algorithm coordinates multilayer learning, improves MNIST classification over single-layer networks, and builds hierarchical abstract representations.
Results
The model uses segregated dendritic compartments and local targets to coordinate learning across layers, enabling classification and progressively more abstract representations. Two hidden layers improve learning, while feedback-weight conditions and physiological assumptions constrain the approach.
- Limitations and assumptions: The model's biological realism is limited because synchronized plateau potentials do not accurately reflect the physiological factors governing apical calcium spikes.The algorithm requires temporal control of plateau potentials relative to the teaching signal, although complete synchrony is not critical.
- Credit assignment: During the first epoch, forward and backward functions became approximate inverses, indicating that the network learned credit assignment early in training.The result links the model to feedback-alignment and difference-target-propagation mechanisms.
- Multilayer learning: Two hidden layers achieved a 3.2% average test error by epoch 60 and learned faster than a one-hidden-layer network.Adding more than two hidden layers did not significantly improve the error rate.
- Representations: The two-hidden-layer network formed cleaner category-related activity clusters in its first hidden layer than at the input level.The hidden representation reduced split, merged, and outlier clusters associated with low-level digit features.
- Feedback weights: Sparse feedback achieved 3.7% test error versus 4.1% with fully random feedback by epoch 60, but required appropriately scaled synaptic magnitudes.Unscaled sparse feedback impaired learning, indicating that signal magnitude matters for credit assignment.
- Feedback weights: Symmetric feedback achieved 3.6% test error by epoch 60, whereas adding noise removed its advantage and slightly impaired learning.Noisy symmetry creates a moving feedback target that cannot align appropriately as feedforward weights change.
Discussion
The study argues that electrotonically segregated dendrites can support credit assignment and deep learning without non-local weight transport. Its small network learned multilayer representations, but performance and biological realism remained limited.
- Segregated dendrites separate feedforward and feedback information, enabling local targets that coordinate learning across network layers.The model uses direct feedback pathways and electrotonically distinct dendritic compartments rather than requiring separate anatomical feedback pathways.
- The network achieved better MNIST classification with multiple layers than with a single layer and developed useful hidden-layer digit representations.The authors also report feature detectors resembling those produced by backpropagation.
- The algorithm approximated backpropagation weight updates and continued to work with sparse feedback and partial apical attenuation.Learning remained possible with realistic levels of passive apical-to-somatic conductance, although conductance balance mattered.
- The study is intended to demonstrate that dendritic segregation can subserve credit assignment, not to provide a fully biologically realistic neuron model.The model includes non-biological assumptions such as non-conductance-based synapses, sign-switching weights, and instantaneous plateau potentials.
- The model does not achieve artificial-network or human performance, and error rates stop improving beyond two hidden layers.The authors kept the network small, stopped training before asymptotic performance, and omitted common enhancements such as convolution and pooling.
- A remaining limitation is that feedback synapses were fixed, although feedforward weights learned to approximate the inverse feedback mapping required for credit assignment.The authors suggest developing plasticity rules for feedback synapses in future work.
Materials and Methods
The model uses spiking input and multi-compartment hidden neurons to separate feedforward and feedback signals, then updates weights from phase-dependent local activity measures. Simulations evaluate this learning procedure across network sizes and depths.
- Network architecture: The network contains Poisson input neurons, three-compartment hidden neurons, and two-compartment output neurons.Hidden neurons use basal dendrites, apical dendrites, and somata; output neurons use dendrites and somata.
- Neuronal dynamics: Basal and apical synaptic inputs are converted into postsynaptic potentials using a shared temporal response kernel.The kernel depends on short and long time constants and a Heaviside step function.
- Neuronal dynamics: Hidden-neuron firing rates apply a sigmoid nonlinearity to somatic potentials, with a maximum rate of 200 Hz and Poisson spike generation.The average simulated firing rate was 24 Hz, close to reported neocortical firing rates.
- Target phase: During target phases, excitatory and inhibitory nudging conductances drive output units toward the desired target pattern.The target unit receives excitation while units that should be minimal receive inhibition.
- Weight updates: Forward and target phase plateau potentials in apical dendrites provide the local signals used to update hidden-layer basal weights.Plateaus are integrated after a 30 ms settling period and their difference contributes to the local update rule.
- Weight updates: Output weights are updated by gradient descent, while hidden-layer updates use local target rates derived from apical plateau potentials.The hidden-layer rule is described as fully local and includes plateau differences, postsynaptic potentials, and presynaptic activity terms.
- Multiple hidden layers: Deeper networks give each hidden layer direct output feedback through its own fixed, random backward weights and layer-specific local losses.The same hidden-layer learning rules are used when multiple hidden layers are present.
- Simulation procedure: Learning rates were selected by grid search over [0.1, 0.3] in 0.02 increments using one-epoch training on 60,000 images and testing on 10,000 images.
Proofs
The paper modifies prior target-based proofs for spiking, multi-compartment networks and derives conditions under which hidden-layer learning improves output-layer performance. It also establishes the firing-rate approximation needed for the theoretical analysis.
- Theorem 1 adapts Lee et al.’s proof to the model’s spiking neurons, voltages, and compartment structure.
- The theorem requires a sufficiently small output-target error and a largest eigenvalue below 1 for (I − JβJγ)T(I − JβJγ).
- The convergence condition is not guaranteed initially, although the feedforward weights meet it during the first training epoch despite random fixed feedback weights.
- The hidden-layer target ˆλC∗ combines the hidden-layer rate with feedback terms so approaching it moves the upper layer toward its target.
- The implemented hidden-layer target approximates ˆλC∗ using variables accessible to hidden-layer units and yields a learning rule similar to difference target propagation.
- The firing-rate and postsynaptic-potential equivalence holds when averaging windows are sufficiently long relative to synaptic time constants and firing rates are sufficiently low.Simulations used Δt ≥ 50 ms, approximately 20 Hz firing, and time constants τL = 10 ms and τs = 3 ms.
Figures
The figures introduce credit assignment through segregated dendritic compartments and test whether local learning can coordinate errors, support deeper networks, approximate backpropagation, and tolerate feedback constraints.
- Credit assignment: Credit assignment requires early synapses to receive credit for their contribution to downstream behavioral or cognitive outputs.Backpropagation addresses this by using downstream synaptic weights, whereas the proposed framework uses segregated dendritic feedback.
- Multi-compartment model: Segregated basal and apical compartments separate feedforward and feedback signals so hidden neurons can calculate local error signals.The model uses basal dendrites for feedforward integration and apical dendrites for feedback, with plateau potentials transmitting apical influence to the soma.
- Coordinated errors: Hidden-layer errors correlate with output-layer errors, indicating coordinated error signals across layers during learning.The correlation is significantly higher for real pairings than shuffled pairings and is lower during the first training epoch.
- Deep learning: Networks with hidden layers reduce test error relative to the shallow network, and two hidden layers learn increasingly abstract digit representations.The simulations compare networks with zero, one, and two hidden layers using MNIST test images and activity-pattern visualizations.
- Local learning: Local weight updates become more aligned with backpropagation during training and produce qualitatively similar receptive fields.The local algorithm approximates backpropagation, although spikes introduce some loss of accuracy.
- Feedback and dendritic constraints: Learning depends on feedback-synapse conditions and dendritic segregation, with sparse or symmetric feedback improving learning and noisy symmetry impairing it.The two-hidden-layer network was also tested with strong apical attenuation rather than total segregation, connecting performance to biologically motivated dendritic constraints.
Figure Supplements
The supplementary figures examine training dynamics, stochastic plateau timing, and the magnitude and sparsity of feedback weights. Together, they show conditions associated with learning and weight alignment in one-hidden-layer MNIST networks.
- Weight alignment: Feedforward and feedback Jacobian products become more aligned after one epoch of training.The figure compares JβJγ before training with its state after one epoch.
- Sparse feedback weights: Amplified sparse feedback weights improve MNIST training performance, whereas unamplified sparse weights impair learning.The comparison uses regular feedback weights, amplified sparse feedback weights, and unamplified sparse feedback weights across 20 training epochs.
- Sparse feedback weights: The reported differences between regular, amplified sparse, and unamplified sparse feedback weights are statistically significant after Bonferroni correction.The reported tests use n = 20 repeated weight tests and yield P values from 2.8 × 10−47 to 4.4 × 10−34.