[Paper Review] Local Information with Feedback Perturbation Suffices for Dictionary Learning in Neural Circuits

Tsung-Han Lin|arXiv (Cornell University)|May 19, 2017

Advanced Memory and Neural Computing17 references3 citations

TL;DR

This paper proposes a spiking neural network (SNN) with feedback synapses that enables synaptically local, biologically plausible dictionary learning by transforming non-local error signals into local feedback perturbations. The method achieves performance comparable or superior to stochastic gradient descent (SGD) on image datasets, even with random weight initialization, by using spike rate dynamics and feedback-induced state changes to approximate gradient descent.

ABSTRACT

While the sparse coding principle can successfully model information processing in sensory neural systems, it remains unclear how learning can be accomplished under neural architectural constraints. Feasible learning rules must rely solely on synaptically local information in order to be implemented on spatially distributed neurons. We describe a neural network with spiking neurons that can address the aforementioned fundamental challenge and solve the L1-minimizing dictionary learning problem, representing the first model able to do so. Our major innovation is to introduce feedback synapses to create a pathway to turn the seemingly non-local information into local ones. The resulting network encodes the error signal needed for learning as the change of network steady states caused by feedback, and operates akin to the classical stochastic gradient descent method.

Motivation & Objective

• To address the fundamental challenge of how dictionary learning can be implemented in neural circuits under strict synaptic locality constraints.
• To develop a learning rule that relies only on locally available information at each synapse, making it feasible for spatially distributed neural networks.
• To solve the ℓ₁-minimizing dictionary learning problem in a spiking neural network using only local dynamics and feedback perturbations.
• To demonstrate that feedback-induced changes in network steady states can serve as a local proxy for global error signals.
• To show that the proposed method achieves competitive performance with SGD while being fully distributed and parallelizable.

Proposed method

• Introduces feedback synapses that perturb the network's steady state, with the change in state serving as a local approximation of the global error signal.
• Uses the imbalance function Δi(t) = ui(t) − θi ai(t) to characterize network dynamics and derive learning rules based on spike rate and current averages.
• Derives local learning rules that resemble stochastic gradient descent by relating feedback-induced state shifts to gradient updates.
• Employs a weight consistency condition between feedforward and feedback weights to ensure that feedback perturbations reflect true error gradients.
• Applies the learning rule in a spiking network with integrate-and-fire neurons, where synaptic weights are updated based on local pre- and postsynaptic activity and feedback-induced changes.
• Uses dynamic threshold adaptation to prevent neurons from becoming inactive, enhancing learning efficiency and convergence.

Experimental results

Research questions

• RQ1 Can dictionary learning be achieved in a spiking neural network using only locally available synaptic information?
• RQ2 How can non-local error signals in dictionary learning be transformed into local, synaptically accessible signals?
• RQ3 Can feedback connections in a spiking network approximate the gradient of the ℓ₁-regularized objective function?
• RQ4 Does the proposed method outperform or match standard SGD in terms of objective function value and convergence speed?
• RQ5 How robust is the method to random weight initialization and varying training sample sizes?

Key findings

• The proposed SNN with feedback perturbation achieves objective function values comparable to or better than SGD across multiple datasets, including MNIST, natural scenes, and Lena.
• The SNN method converges faster and reaches better solutions than SGD when training data is limited, particularly avoiding poor local minima.
• Random weight initialization causes only slightly slower convergence but leads to final solutions of similar or better objective function values.
• Dynamic threshold adaptation prevents neuron inactivity and improves learning by making rarely activated atoms more likely to fire over time.
• The feedback-induced state change provides an effective local proxy for the global error gradient, enabling biologically plausible learning.
• The method enables fully distributed, fine-grained parallel computation, eliminating bottlenecks from centralized processing units.