Gradient Descent for Spiking Neural Networks (1706.04698v2)

Abstract: Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking networks and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (~millisecond) spike-based interactions for efficient encoding of information, and a delayed memory XOR task over extended duration (~second). The results show that our method indeed optimizes the spiking network dynamics on the time scale of individual spikes as well as behavioral time scales. In conclusion, our result offers a general purpose supervised learning algorithm for spiking neural networks, thus advancing further investigations on spike-based computation.

• The paper introduces a novel gradient descent algorithm that transforms non-differentiable spiking dynamics into a tractable framework via a differentiable synapse model.
• It demonstrates the method's effectiveness on tasks like predictive coding and the delayed-memory XOR, highlighting efficient spike-time representation and dynamic processing.
• The approach paves the way for more biologically plausible learning algorithms by bridging the gap between artificial neural models and actual brain function.

Gradient Descent for Spiking Neural Networks

The paper authored by Dongsung Huh and Terrence J. Sejnowski addresses a critical gap in the domain of neural computation, focusing on the optimization of spiking neural networks (SNNs). The authors introduce a differentiable formulation and exact gradient calculation methodology for SNNs, facilitating the application of supervised learning paradigms to networks of dynamic neurons that process information through discrete spikes, overcoming challenges inherent in previous methods.

Overview of the Methodology

At the core of this paper is a novel gradient descent algorithm specifically designed for SNNs. Traditional neural computation largely depends on models of static neurons with analog outputs, which fails to capture the discrete nature of spikes observed in biological systems. The authors rectify this by formulating a differentiable model for spiking dynamics, effectively making the otherwise non-differentiable aspects of spikes amenable to standard optimization techniques, like gradient-based methods.

The proposed method comprises a few novel elements:

• Differentiable Synapse Model: This approach replaces the non-differentiable threshold dynamics typically associated with spikes, utilizing a gate function that allows synaptic currents to gradually accumulate within an 'active zone.' This formulation respects the essential characteristics of spike-driven communication while enabling gradient descent optimization.
• Network Structure and Gradient Calculation: The paper extends this differentiable framework to interconnected networks, detailing the architecture of recurrent connections and readouts. Through the introduction of adjoint state variables, the method backpropagates error signals efficiently, crucially relying on the sparse activation of spikes to perform these updates in a computationally viable manner.

Results and Evaluation

The authors validate their methodology by applying it to dynamic tasks that require time-dependent processing capabilities:

1. Predictive Coding Task: This task demonstrates the method's capability in optimizing spike-time representation for dynamic systems. The spike-based networks derived using the proposed gradient calculation exhibit efficient encoding properties, achieving a tightly balanced state of excitatory and inhibitory neural activities. The results closely match theoretical predictions from non-leaky integrate-and-fire models, showcasing robust efficient coding without necessitating infinitely fast synapses.
2. Delayed-Memory XOR Task: This complex task demands the network to hold and process information over extended durations, a challenge for spike-based computation stretched across time scales. The optimized networks perform the XOR operation on input pulses with delayed cues, resembling capabilities of human-like decision-making processes. The results underscore that spiking networks, once trained, can effectively bridge the gap between the millisecond phenomena of spiking events and behaviorally relevant time scales.

Implications and Future Directions

The introduction of a gradient descent method for SNNs is a significant contribution that harmonizes the principles of biological spiking with advanced learning algorithms. This method could potentially lead to more biologically plausible learning algorithms capable of capturing the nuanced dynamics of brain function. Additionally, the implications for computational neuroscience are profound; understanding the gradient dynamics in spiking networks can offer insights into plausible models of learning and memory as seen in biological systems.

In future work, exploration into the applicability of this approach across different neuron models, including leaky integrate-and-fire and Hodgkin-Huxley-type neurons, could further validate and expand the utility of this method. Furthermore, avenues for biologically realistic approximations of the gradient descent approach, melding concepts like feedback alignment seen in analog networks, may be promising directions that can bridge the current methodological gap between artificial and biological synaptic plasticity.