>CNN runs on a CPU.
No. A neural net can be deployed to run on a CPU or a GPU. So any performance difference between a CNN running on a CPU vs an SNN on *purpose built neuromorphic hardware* is going to be due to the hardware and not a fundamental difference between CNN and SNN. If you run the CNN on a gpu, the magic of parallel processing means the the time taken to process the input will depend more so on the number of layers rather than the size of the inputs.
Here is an example of some benchmarking of performance using GPUs vs CPUs for running a network.
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