Source-linked AI summary
Neuromorphic Deep Learning Machines
Emre Neftci, Charles Augustine, Somnath Paul, Georgios Detorakis
TL;DR
Neuromorphic computing needs efficient learning algorithms that fit the brain’s spatial and temporal constraints, whereas gradient BP depends on network-wide information, high-precision memory, and difficult operations. The paper introduces event-driven random BP, an error-modulated plasticity rule for deep spiking networks. It reports classification accuracy near equivalent GPU-based artificial neural network simulations, with a simple update rule and robustness to state quantization.
Problem
Neuromorphic hardware needs general and efficient learning algorithms compatible with brain-like constraints, but gradient BP requires non-local information, high-precision memory, and operations difficult to implement neurally.
Method
The paper introduces eRBP, a presynaptic spike-driven plasticity rule modulated by top-down errors and gated by postsynaptic neuronal state.
Results
Classification accuracies are on par with equivalent machine-learning algorithms, while eRBP uses one addition and two comparisons per synaptic weight update.
Takeaways & Limitations
eRBP enables local, algorithmically simple learning dynamics for deep feed-forward neural networks in neuromorphic hardware.
Takeaways & Limitations
The work focuses on unstructured feed-forward networks and a single benchmark task, while mixed-signal implementation under fabrication mismatch remains ongoing.
Abstract
from arXiv · showhide
An ongoing challenge in neuromorphic computing is to devise general and computationally efficient models of inference and learning which are compatible with the spatial and temporal constraints of the brain. One increasingly popular and successful approach is to take inspiration from inference and learning algorithms used in deep neural networks. However, the workhorse of deep learning, the gradient descent Back Propagation (BP) rule, often relies on the immediate availability of network-wide information stored with high-precision memory, and precise operations that are difficult to realize in neuromorphic hardware. Remarkably, recent work showed that exact backpropagated weights are not essential for learning deep representations. Random BP replaces feedback weights with random ones and encourages the network to adjust its feed-forward weights to learn pseudo-inverses of the (random) feedback weights. Building on these results, we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware. The rule requires only one addition and two comparisons for each synaptic weight using a two-compartment leaky Integrate & Fire (I&F) neuron, making it very suitable for implementation in digital or mixed-signal neuromorphic hardware. Our results show that using eRBP, deep representations are rapidly learned, achieving nearly identical classification accuracies compared to artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.
1 Introduction
Neuromorphic computing needs general, efficient learning algorithms that respect brain-like spatial and temporal constraints. The paper addresses this challenge with event-driven random BP, designed to overcome key implementation difficulties while retaining deep-learning classification performance.
- Motivation: Neuromorphic hardware remains limited by the lack of general and efficient inference and learning algorithms compatible with brain-like spatial and temporal constraints.Deep learning is attractive because of its general-purpose, modular, and fault-tolerant properties, but its learning phase remains difficult to implement on neuromorphic hardware.
- Limitations of gradient BP: Gradient BP is difficult to implement on neural substrates because it requires non-local information, precise computations, high-precision error signals, and alternating forward and backward passes.Additional challenges include symmetric weight transport, changing synaptic-weight signs, and target availability.
- Proposed approach: eRBP addresses these difficulties as an event-driven learning rule for deep spiking neural networks with classification accuracies similar to artificial neural networks.The rule is intended for implementation on dedicated neuromorphic hardware and builds on approximate forms of gradient BP.
- Proposed approach: Random BP replaces backpropagated weights with fixed random feedback weights, while feed-forward weights learn an approximation of their pseudo-inverse.This approach addresses the non-locality problem and has shown little loss in benchmark classification performance.
2 Results
eRBP combines error-modulated, event-driven plasticity with random feedback to train deep spiking networks using hardware-efficient operations. Results on MNIST indicate high accuracy, rapid learning, low-latency classification, and potential energy efficiency, while highlighting transition-related error bursts and mixed-signal implementation as boundaries.
- Event-driven Random Backpropagation: eRBP uses presynaptic spikes, top-down errors, and postsynaptic state to implement a three-factor plasticity rule for deep spiking networks.For hidden layers, errors are randomly projected; the output layer uses the classification error directly.
- Event-driven Random Backpropagation: Each synaptic update requires two comparisons and one addition, with an auxiliary compartment integrating top-down error signals.This operation profile is intended for digital or mixed-signal neuromorphic hardware.
- Accuracy and learning: The study compares online-trained spiking eRBP networks with artificial networks trained using random BP and standard BP on permutation-invariant MNIST.The experiments include networks with one and two hidden layers.
- Accuracy and learning: eRBP achieves classification accuracy comparable to offline-trained spiking networks using standard BP on GPUs.The reported comparison concerns learned classification accuracy rather than absolute benchmark optimization.
- Training dynamics: Error-neuron bursts occur when data samples change class, so weight updates are disabled for the first 50ms after a new digit begins.The paper proposes biasing error and label neurons as a future way to interleave learning and inference without explicit learning-rate control.
- Single-spike classification: Using the first spike after 2τs = 8ms yields about 5% error, with classification improving as output-layer spikes accumulate.The network response begins after approximately one synaptic time constant.
- Single-spike classification: Single-spike classification incurs about 100 k synaptic operations and can potentially require about 2µJ per classification on dedicated neuromorphic hardware.The estimate is comparable to reported digital neuromorphic hardware and lower than current GPU technology; sparsity may reduce energy further.
- Learning speed: Spiking networks reach peak classification performance in fewer dataset iterations than artificial networks trained with batch gradient descent, consistent with online sample-by-sample updates.The paper attributes much of the faster convergence to updating weights after each sample presentation.
3 Discussion
The discussion positions eRBP as a local, event-driven alternative for deep neuromorphic learning, addressing gradient BP's non-locality and hardware demands while retaining artificial-network-level performance. It also relates eRBP to random feedback, spike-driven plasticity, quantized computation, and emerging neuromorphic implementations.
- Motivation: Gradient BP is difficult to implement on neural hardware because it requires network-wide information, precise computations, high-precision error signals, and alternating forward and backward passes.These requirements create non-locality in both space and time.
- eRBP design: eRBP addresses these constraints with one addition and two comparisons per synaptic weight update.The rule is designed for spike-based computations without general linear and non-linear operations or alternating passes.
- Implementation scope: The work implements eRBP in a fixed-point, discrete-time simulator compatible with digital neuromorphic hardware under development, while mixed-signal implementations require neuron-level external modulation.The authors target digital spiking networks with embedded plasticity and describe compatibility conditions for mixed-signal hardware.
- Relation to random backpropagation: Random feedback supplies teaching signals by aligning feed-forward weights with fixed random feedback weights, avoiding the need for symmetric weights.Unlike prior feedback-alignment work, eRBP is event-based, uses physical I&F dynamics, and has one error-coding layer.
- Relation to spike-driven plasticity: Spike-driven plasticity commonly gates synaptic changes using variables reflecting average neural activity, such as calcium concentration or membrane potential.eRBP similarly uses dynamic potentiation and depression magnitudes determined by external modulation, with comparisons based on total synaptic currents.
4 Conclusions and Future Directions
The conclusions emphasize that a simple local learning rule can train deep feed-forward networks at accuracies comparable to equivalent machine-learning algorithms. Future directions include broader random-BP variants, while the present evidence remains limited to unstructured feed-forward networks and one benchmark task.
- Conclusions: The learning rule achieves classification accuracies on par with equivalent machine-learning algorithms using one addition and two comparisons per synaptic update.The rule also keeps all weight-update information local to each neuron and synapse.
- Future directions: Random BP may extend to unsupervised learning, deeper and convolutional networks, recurrent networks, and memory-augmented neural networks.The authors envision applications including pattern recognition, attention, working memory, and action selection.
- Scope and limitations: The study focuses on unstructured feed-forward networks and a single benchmark task, so its evidence does not cover the full range of deep-learning settings.The authors note that convolutional parameter sharing is inherently non-local despite possible neuromorphic implementations.
5 Methods
The methods derive a spike-based learning rule by translating rate-based gradient descent and random backpropagation into event-driven updates for spiking neurons. The approach uses random error feedback, firing-rate derivatives, and presynaptic spike events to obtain hardware-compatible plasticity.
- Rate-based learning: The single-sample objective is mean-squared error between prediction activity and the associated label.The prediction activity is defined through the network activation function, and learning modifies weights opposite to the cost gradient.
- Gradient backpropagation: In deep networks, hidden-layer weights are updated by backpropagating prediction errors through the chain rule and transposed forward weights.This requires forward and backward passes and access to symmetric network information.
- Random backpropagation: Random backpropagation replaces recursively computed backpropagated errors with fixed random feedback, avoiding bidirectional or symmetric synapses with little reported accuracy loss.The resulting feedback term does not depend recursively on the next layer.
- Spike-based formulation: The spike-based derivation represents neuron scalar outputs as instantaneous firing rates and defines prediction error from prediction and label firing rates.Prediction and label neurons provide the firing rates used in the error signal.
- Event-driven updates: eRBP performs asynchronous updates by replacing presynaptic firing rates with spike trains and evaluating the derivative only when a presynaptic spike occurs.Small learning rates justify averaging these event-driven changes at the synaptic weight.
- Hardware-compatible plasticity: A boxcar approximation gates plasticity when synaptic current lies between bmin and bmax, replacing the unavailable Gaussian derivative with two comparisons and one addition.The approximation is compatible with leaky integrate-and-fire dynamics and avoids an explicit multiplication with the modulation.