Are there any machine learning packages that implement spiking neural networks? or any other stand-alone implementations of them that could get me started to work with?
Spiking Neural Network Classifier Implementation
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You can install the Nengo Loihi library for deployment not only of spiking neural networks but also neuromorphic neural networks. here's the link to their website: https://www.nengo.ai/nengo-loihi/v1.0.0/index.html
You can find on Kaggle an implementation of the ciphar10 dataset, locally loaded, using Nengo Loihi library. Here's the link: https://www.kaggle.com/migueltoms/neuromorphic-ciphar-10-loihi-comparison-of-results

Here are links for brain simulator
https://github.com/brian-team/brian2

There are several other SNN platforms these days that allows you to run classification. I have worked with NeuCube (https://kedri.aut.ac.nz/R-and-D-Systems/neucube) which is a Matlab & Java-based SNN platform.
Also, check out Akida Development Environment (ADE) from Brainchip Inc (https://brainchipinc.com/). One of the best features of ADE is that it's APIs are based on tensorflow/keras structure and also supports CNN2SNN converter to use your deep learning models in SNN domain. SNN models developed using this platform can be deployed on their neuromorphic processor Akida.
I believe there are other platforms such as PyNN and Nengo (compatibility to run models on Loihi) within the SNN domain.
A python library named Brian ought to be useful for you.
There's also what I believe is a programing language named NEURON, but Brian is fairly easy to learn, at least for the basics. It took me a while though to figure out how to do a couple small things, since its a really high level language or whatnot.