Probability density methods for smooth function approximation and learning in populations of tuned spiking neurons

Area of Science:

• Computational neuroscience
• Machine learning

Background:

• Spiking neurons are fundamental units in neural computation, often modeled as rate-modulated random processes.
• Understanding the computational capabilities of spiking neural networks is crucial for advancing artificial intelligence and neuroscience.

Purpose of the Study:

• To propose a new method for interpreting computations in populations of spiking neurons.
• To demonstrate the feasibility of approximating arbitrary neural tuning functions using basic spiking neuron operations.
• To show that standard learning algorithms can be implemented in spiking neural networks.

Main Methods:

• Modeling neural firing as a rate-modulated random process characterized by tuning functions.
• Utilizing spike coincidence detectors and linear operations to approximate desired tuning functions.
• Developing adaptive algorithms based on spike data for supervised and unsupervised learning.

Main Results:

• Demonstrated that any desired tuning function can be approximated using spike coincidence detectors and linear operations.
• Showcased adaptive algorithms that enable cell-tuning curves to converge via supervised and unsupervised learning.
• Revealed that unsupervised learning via principal components analysis results in independent cell spike trains.
• Identified a duality between the discrete behavior of spiking cells and the continuous behavior of their tuning functions.

Conclusions:

• Classical neural network approximation and learning algorithms can be implemented in spiking neural networks.
• This approach bypasses the need for numerical estimation of intermediate cell firing rates.
• The findings suggest a powerful framework for bridging continuous and discrete models in neural computation.