Interactive Visualizations

Here, we present one of the key strengths of this online SNN book - Interactive Visualizations! Such interactive visualizations - accompanied with their code - can help you build a clear and thorough understanding of the core concepts of SNNs. You can engage with these visualizations / demonstrations -right on the spot - to quickly learn the presented concept’s intricacies and the effects of its variable parameters.

Try to move the sliders of the animation of Leaky Integrate & Fire (LIF) neuron below!

1Example of Leaky Integrate & Fire neuron¶

In the example above, we simulate a LIF neuron to demonstrate its interactive visualization. We now describe its dynamics; following is the discrete-time voltage equation of a typical LIF neuron:

where $V[t]$ is LIF’s voltage state, $I[t]$ is its input current, and $v_\text{decay}$ is its voltage decay parameter. When $V[t]$ reaches or crosses a voltage threshold (say $V_\text{thr}$), the LIF neuron:

• produces a spike $S[t]$, which can be modeled as a Heaviside Step Function $\Theta(.)$, i.e.,

• and its voltage $V[t]$ is hard reset to 0, i.e.,

1.1LIF neuron visualization¶

If you move the sliders in the animation above, you will observe the following behaviours:

Keeping Input Current (I) fixed:

• If you decrease Voltage Decay, you will find that the frequency of spikes increases; this is because:

  • the Voltage (V) does not decay rapidly, and

  • it quickly crosses the voltage threshold (i.e., 1.0).

• If you increase Voltage Decay, you will find that either the frequency of spikes decreases or the neuron does not spike at all!; this is because:

  • the Voltage (V) either crosses the threshold late (due to increased decay), or

  • it never crosses the threshold (due to the decay being too much), thus, no spikes!

Similarly, keeping the Voltage Decay fixed:

• If you increase the Input Current (I), you will observe that the frequency of spikes increases; this is because:

  • a higher Current (I) value is fed to the neuron, and

  • its Voltage (V) is updated by a large value,

  • thus, V quickly crosses the threshold

• If you decrease the Input Current (I), you will observe that either the frequency of spikes decreases or the neuron does not spike at all!; this is because:

  • a smaller Current (I) value is fed to the neuron, and

  • its Voltage (V) is updated by a small value,

  • thus, V either takes longer to cross the threshold, or

  • the update in V is too small to overcome the voltage decaying effect, thus no spikes!

1.2Code¶

Our visualization relies on the DynSim library, developed by the editors of the SNN book. It works as a Plugin to the platform that we have used to build this book: Jupyter Book. Users and contributors using DynSim can simply write the Python code in a step() function as below. Following is the example code for the LIF visualization above.

import numpy as np

def step(x, state, p):
  """
  Leaky Integrate & Fire neuron.

  Args:
    x: Input current `I` from the slider.
    state: State variable dict, i.e., `state["V"]`.
    p: Other parameters dict, i.e., `p[v_decay]`.

  Returns:
    Tuple of (new `I` value, new `state` dict).
  """

  V_new = (1 - p["v_decay"])*state["V"] + x # Update Voltage.

  S = 0
  if V_new > 1.0:
    S = 1
    V_new = 0.0

  return (V_new, {"V": V_new, "S": S})

And that is it! We cannot wait to see what you will build with it.