NoisyLeaky behaviour: spiking and membrane potential reset independently stochastic

[leoauri]

From what I observe of NoisyLeaky neurons, spiking and membrane potential reset are independently stochastic.

I am not at all experienced with SNNs, but wouldn't the expected behaviour be: iff a spike is emitted, membrane potential reset occurs?

Here is code where I observe this. I'm using reset mechanism "zero" here, but "subtract" produces similar behaviour:

import snntorch as snn
from snntorch import NoisyLeaky
import torch

n = NoisyLeaky(beta=0.5, output=True, reset_mechanism="zero")

steps = 20
outs = []
mem = torch.zeros(1)
for t in range(steps):
    out, mem = n(torch.Tensor([[1.0]]), mem)
    outs.append((out, mem))

outs

Example output:

[(tensor([[1.]]), tensor([[1.]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[1.]]), tensor([[1.]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[0.]]), tensor([[1.]])),
 (tensor([[1.]]), tensor([[1.5000]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[1.]]), tensor([[1.]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[0.]]), tensor([[1.]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[1.]]), tensor([[1.]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[1.]]), tensor([[1.]])),
 (tensor([[0.]]), tensor([[1.5000]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[1.]]), tensor([[1.]])),
 (tensor([[1.]]), tensor([[1.5000]])),
 (tensor([[0.]]), tensor([[0.]])),
 (tensor([[1.]]), tensor([[1.]]))]

You can see here that the spikes and the reset do not generally coincide!

Here's a plot of that:

I also adapted one of the tutorials trying to figure this out:

lif2 = snn.NoisyLeaky(beta=0.6)

# Initialize inputs and outputs
cur_in = torch.cat((torch.zeros(10, 1), torch.ones(190, 1)*0.2), 0)
mem = torch.zeros(1)
spk_out = torch.zeros(1) 
mem_rec = [mem]
spk_rec = [spk_out]

# Simulation run across 100 time steps.
for step in range(num_steps):
  spk_out, mem = lif2(cur_in[step], mem)
  mem_rec.append(mem)
  spk_rec.append(spk_out)

# convert lists to tensors
mem_rec = torch.stack(mem_rec)
spk_rec = torch.stack(spk_rec)

plot_cur_mem_spk(cur_in, mem_rec, spk_rec, thr_line=1, vline=109, ylim_max2=1.3, 
                 title="Lapicque Neuron Model With Step Input")

If I have my head screwed on wrong, someone please correct that. Otherwise, it would be great if the authors of the pull request #230 @genema could shed light on this!

[leoauri]

Does leoauri@7fe3f6f reflect the desired/expected behaviour?

...
        for t in range(steps):
            spk, mem = noisyleaky_reset_zero_output_instance(torch.Tensor([[1.0]]), mem)
            assert bool(spk) == (not bool(mem))

[leoauri]

NoisyLeaky seems to mirror the design of Leaky. self.spike_grad is called twice in these classes, in mem_reset and in fire or fire_inhibition. In Leaky, spike_grad is set to SpikingNeuron.ATan.apply, but in NoisyLeaky it is set to one of the various stochastic functions, so you end up with two noise terms in there...

[leoauri]

Is it the case that the membrane potential returned by the forward pass is pre-spike? So the membrane potential change is actually calculated in the subsequent forward pass through Leaky? @jeshraghian @ahenkes1

[leoauri]

Pull request #368 addresses this. Feedback welcome @genema @jeshraghian