Difference between revisions of "Spiking Neural Networks"

Latest revision as of 07:27, 22 October 2022

by Satoko Watanabe

Overview

Spiking Neural Networks (SNN) are a type of artificial neural network inspired by biological neurons. In SNN, when the membrane potential of a neuron exceeds a certain threshold, it generates a discrete signal known as a "spike," which is used to drive the network's computations. Unlike traditional neural networks, which process continuous signals, SNN convert input signals into binary spike trains (spiking or non-spiking events) and perform computations based on these discrete events. SNN offer two significant advantages over conventional artificial neural networks. The first advantage is that SNN model biological neural activity in a more detailed and biologically plausible manner. Traditional neural networks typically handle information as real-valued signals. However, the brain processes information through binary spike trains, which are electrical pulses transmitted between neurons. By utilizing binary signals, SNN more closely resemble the activity of neurons in the human brain, making them valuable for simulating brain function and conducting neuroscience experiments. The second advantage of SNN is their energy efficiency. Because SNNs rely on binary signals for computation, they can describe input-output relationships using only addition operations. In contrast to multiplication-based operations used in conventional networks, addition operations generally require fewer computational resources and lower power consumption, making SNNs more power-efficient.

History and background

The development of SNN has progressed with the aim of creating neural networks that more closely resemble the operating principles of the brain. In 1952, Alan Hodgkin and Andrew Huxley studied the signaling mechanisms of squid neurons, deriving the process that governs membrane potential dynamics. This led to the discovery of what is now known as the action potential and resting potential. Along with Huxley’s experimental data, the Hodgkin-Huxley (H-H) model was proposed, which demonstrated strong performance in numerical simulations of neuronal behavior and a high degree of alignment with experimental data. However, the H-H model is computationally challenging due to the inclusion of higher-order nonlinear differential equations in its calculation process, making numerical computation quite difficult. In 1997, the Spiking Neuron Model was introduced by a group of scientists. This model was compared with other neuron models such as the threshold gate and sigmoid gate models. The Spiking Neuron Model was shown to not only preserve the functional characteristics of neural systems but also offer superior computational power and more efficient numerical modeling capabilities.

Example of a Spiking Neural Network

The Leaky Integrate-and-Fire (LIF) Model

The Leaky Integrate-and-Fire (LIF) model is a commonly used spiking neuron model, which describes the dynamics of the membrane potential V(t) as follows:

<math>\tau_m \frac{dV(t)}{dt} = (-V(t) + E_{\text{rest}}) + I(t)</math> (1)

where \(V(t)\) is the membrane potential, \(I(t)\) is the input current, \(E_{\text{rest}}\) is the resting membrane potential, and \(\tau_m\) is the membrane time constant.

The membrane potential V(t)V(t) changes in response to the input current I(t)I(t), as described by Equation (1). When the membrane potential V(t)V(t) exceeds the threshold VθVθ, depolarization occurs, and the membrane potential rises to the peak potential VpeakVpeak, triggering an action potential (spike). After the spike, the neuron enters a refractory period during which the membrane potential remains unchanged for a fixed duration, denoted as τrefτref. The times and frequencies of the spikes generated by this LIF neuron are then used as outputs to interact with other neurons. The derivation of Equation (1) can be understood by modeling the neuron as an equivalent electrical circuit.

Training and Learning

1. Spike-Timing-Dependent Plasticity (STDP) Spike-Timing-Dependent Plasticity (STDP) is a phenomenon where the synaptic strength between two neurons is updated based on the relative timing of their spikes. It was discovered that both pre- and post-synaptic neurons need to be stimulated simultaneously, and the sequence of spike timings between them plays a crucial role in synaptic strengthening and weakening (Markram et al., 1997; Bi and Poo, 1998). STDP follows a general principle derived from Hebbian learning, which states that if a presynaptic neuron fires just before a postsynaptic neuron, the synaptic weight is enhanced, whereas if the postsynaptic neuron fires before the presynaptic neuron, the synaptic weight is diminished. STDP has the advantage of being well-suited for time-dependent learning and excels at handling temporal data. However, it has the limitation that the convergence of learning is uncertain, and the network can become unstable during the training of complex tasks.

2. Supervised Learning in SNN Supervised learning in SNN is challenging due to the discrete nature of the spikes, which prevents the direct application of traditional backpropagation methods. Consequently, several specialized approaches have been developed for training SNNs. 2.1 SpikeProp SpikeProp is an algorithm designed to adapt the traditional backpropagation method for use with SNNs. This method utilizes the timing of spikes to calculate the error between the output spike and the target spike, which is then used to adjust the synaptic weights in the network. The key idea behind SpikeProp is to compute the timing errors between the target and actual spikes, propagating these errors to update synaptic weights effectively. 2.2 Tempotron Tempotron is a supervised learning algorithm designed for temporal pattern recognition in SNNs. Like SpikeProp, Tempotron also relies on the timing of spikes, but it defines the precise firing time for output neurons. The algorithm then adjusts synaptic weights to ensure that neurons fire at the correct time in response to input signals. Tempotron is particularly useful for tasks that require accurate recognition of temporal patterns.

The supervised learning methods in SNNs offer advantages such as efficient learning for specific tasks like classification and regression, and the ability to achieve precise temporal pattern recognition even for complex tasks. However, applying traditional backpropagation to SNNs remains challenging, and these methods often suffer from slower learning speeds and less stable convergence. Further research is required to overcome these limitations and enhance the efficiency of supervised learning in SNN

Challenges of Spiking Neural Networks (SNN)

SNN are known to pose significant challenges in network training. The back propagation algorithm, commonly used in traditional neural networks, cannot be directly applied to SNN due to the discrete nature of spikes. As a result, there is a need for the development of specialized algorithms tailored specifically for SNN. Additionally, in SNN, the timing of spikes and the occurrence or absence of firing events play a critical role, which makes the network more susceptible to noise and variations in input data. Furthermore, because the timing and sequence of spikes are crucial in SNN, computations that account for temporal dynamics are essential. Therefore, hardware capable of efficiently processing these temporal aspects is required.