Summary of Exact Gradients For Stochastic Spiking Neural Networks Driven by Rough Signals, By Christian Holberg et al.
Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals
by Christian Holberg, Cristopher Salvi
First submitted to arxiv on: 22 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Probability (math.PR)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents a novel framework for modeling stochastic spiking neural networks (SSNNs) as stochastic differential equations with event discontinuities (Event SDEs), driven by càdlàg rough paths. The formalism allows for potential jumps in both solution trajectories and driving noise, enabling the modeling of complex network dynamics. The authors identify sufficient conditions for the existence of pathwise gradients of solution trajectories and event times with respect to network parameters, which satisfy a recursive relation. A new class of signature kernels indexed on càdlàg rough paths is introduced as a general-purpose loss function, used to train SSNNs as generative models. An end-to-end autodifferentiable solver for Event SDEs is provided, available in the diffrax library. This framework is the first enabling gradient-based training of SSNNs with noise affecting both spike timing and network dynamics. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper creates a new way to understand how noisy brain networks work. It uses math to describe complex patterns of activity in brain cells that fire off electrical impulses, or “spikes”. The researchers develop a set of rules that allow them to study these networks in a more detailed and accurate way than before. They also create a new type of computer program that can learn from examples and generate new patterns of spikes, mimicking the behavior of real brain cells. This could help us better understand how our brains work and maybe even develop new treatments for brain disorders. |
Keywords
» Artificial intelligence » Loss function
