Source code for norse.torch.functional.lif_ex

from typing import NamedTuple, Tuple

import torch
import torch.jit

from norse.torch.functional.threshold import threshold


[docs]class LIFExParameters(NamedTuple): """Parametrization of an Exponential Leaky Integrate and Fire neuron Parameters: delta_T (torch.Tensor): sharpness or speed of the exponential growth in mV tau_syn_inv (torch.Tensor): inverse synaptic time constant (:math:`1/\\tau_\\text{syn}`) in 1/ms tau_mem_inv (torch.Tensor): inverse membrane time constant (:math:`1/\\tau_\\text{mem}`) in 1/ms v_leak (torch.Tensor): leak potential in mV v_th (torch.Tensor): threshold potential in mV v_reset (torch.Tensor): reset potential in mV method (str): method to determine the spike threshold (relevant for surrogate gradients) alpha (float): hyper parameter to use in surrogate gradient computation """ delta_T: torch.Tensor = torch.as_tensor(0.5) tau_syn_inv: torch.Tensor = torch.as_tensor(1.0 / 5e-3) tau_mem_inv: torch.Tensor = torch.as_tensor(1.0 / 1e-2) v_leak: torch.Tensor = torch.as_tensor(0.0) v_th: torch.Tensor = torch.as_tensor(1.0) v_reset: torch.Tensor = torch.as_tensor(0.0) method: str = "super" alpha: float = 100.0
class LIFExState(NamedTuple): """State of a LIFEx neuron Parameters: z (torch.Tensor): recurrent spikes v (torch.Tensor): membrane potential i (torch.Tensor): synaptic input current """ z: torch.Tensor v: torch.Tensor i: torch.Tensor
[docs]class LIFExFeedForwardState(NamedTuple): """State of a feed forward LIFEx neuron Parameters: v (torch.Tensor): membrane potential i (torch.Tensor): synaptic input current """ v: torch.Tensor i: torch.Tensor
def lif_ex_step( input_tensor: torch.Tensor, state: LIFExState, input_weights: torch.Tensor, recurrent_weights: torch.Tensor, p: LIFExParameters = LIFExParameters(), dt: float = 0.001, ) -> Tuple[torch.Tensor, LIFExState]: r"""Computes a single euler-integration step of an exponential LIF neuron-model adapted from https://neuronaldynamics.epfl.ch/online/Ch5.S2.html. More specifically it implements one integration step of the following ODE .. math:: \begin{align*} \dot{v} &= 1/\tau_{\text{mem}} \left(v_{\text{leak}} - v + i + \Delta_T exp\left({{v - v_{\text{th}}} \over {\Delta_T}}\right)\right) \\ \dot{i} &= -1/\tau_{\text{syn}} i \end{align*} together with the jump condition .. math:: z = \Theta(v - v_{\text{th}}) and transition equations .. math:: \begin{align*} v &= (1-z) v + z v_{\text{reset}} \\ i &= i + w_{\text{input}} z_{\text{in}} \\ i &= i + w_{\text{rec}} z_{\text{rec}} \end{align*} where :math:`z_{\text{rec}}` and :math:`z_{\text{in}}` are the recurrent and input spikes respectively. Parameters: input_tensor (torch.Tensor): the input spikes at the current time step s (LIFExState): current state of the LIF neuron input_weights (torch.Tensor): synaptic weights for incoming spikes recurrent_weights (torch.Tensor): synaptic weights for recurrent spikes p (LIFExParameters): parameters of a leaky integrate and fire neuron dt (float): Integration timestep to use """ # compute voltage updates dv_leak = p.v_leak - state.v dv_exp = p.delta_T * torch.exp((state.v - p.v_th) / p.delta_T) dv = dt * p.tau_mem_inv * (dv_leak + dv_exp + state.i) v_decayed = state.v + dv # compute current updates di = -dt * p.tau_syn_inv * state.i i_decayed = state.i + di # compute new spikes z_new = threshold(v_decayed - p.v_th, p.method, p.alpha) # compute reset v_new = (1 - z_new) * v_decayed + z_new * p.v_reset # compute current jumps i_new = ( i_decayed + torch.nn.functional.linear(input_tensor, input_weights) + torch.nn.functional.linear(state.z, recurrent_weights) ) return z_new, LIFExState(z_new, v_new, i_new)
[docs]def lif_ex_feed_forward_step( input_tensor: torch.Tensor, state: LIFExFeedForwardState = LIFExFeedForwardState(0, 0), p: LIFExParameters = LIFExParameters(), dt: float = 0.001, ) -> Tuple[torch.Tensor, LIFExFeedForwardState]: r"""Computes a single euler-integration step of an exponential LIF neuron-model adapted from https://neuronaldynamics.epfl.ch/online/Ch5.S2.html. It takes as input the input current as generated by an arbitrary torch module or function. More specifically it implements one integration step of the following ODE .. math:: \begin{align*} \dot{v} &= 1/\tau_{\text{mem}} \left(v_{\text{leak}} - v + i + \Delta_T exp\left({{v - v_{\text{th}}} \over {\Delta_T}}\right)\right) \\ \dot{i} &= -1/\tau_{\text{syn}} i \end{align*} together with the jump condition .. math:: z = \Theta(v - v_{\text{th}}) and transition equations .. math:: \begin{align*} v &= (1-z) v + z v_{\text{reset}} \\ i &= i + i_{\text{in}} \end{align*} where :math:`i_{\text{in}}` is meant to be the result of applying an arbitrary pytorch module (such as a convolution) to input spikes. Parameters: input_tensor (torch.Tensor): the input spikes at the current time step state (LIFExFeedForwardState): current state of the LIF neuron p (LIFExParameters): parameters of a leaky integrate and fire neuron dt (float): Integration timestep to use """ # compute voltage updates dv_leak = p.v_leak - state.v dv_exp = p.delta_T * torch.exp((state.v - p.v_th) / p.delta_T) dv = dt * p.tau_mem_inv * (dv_leak + dv_exp + state.i) v_decayed = state.v + dv # compute current updates di = -dt * p.tau_syn_inv * state.i i_decayed = state.i + di # compute new spikes z_new = threshold(v_decayed - p.v_th, p.method, p.alpha) # compute reset v_new = (1 - z_new) * v_decayed + z_new * p.v_reset # compute current jumps i_new = i_decayed + input_tensor return z_new, LIFExFeedForwardState(v_new, i_new)
[docs]def lif_ex_current_encoder( input_current: torch.Tensor, voltage: torch.Tensor, p: LIFExParameters = LIFExParameters(), dt: float = 0.001, ) -> Tuple[torch.Tensor, torch.Tensor]: r"""Computes a single euler-integration step of a leaky integrator adapted from https://neuronaldynamics.epfl.ch/online/Ch5.S2.html. More specifically it implements one integration step of the following ODE .. math:: \begin{align*} \dot{v} &= 1/\tau_{\text{mem}} \left(v_{\text{leak}} - v + i + \Delta_T exp\left({{v - v_{\text{th}}} \over {\Delta_T}}\right)\right) \\ \dot{i} &= -1/\tau_{\text{syn}} i \end{align*} Parameters: input (torch.Tensor): the input current at the current time step voltage (torch.Tensor): current state of the LIFEx neuron p (LIFExParameters): parameters of a leaky integrate and fire neuron dt (float): Integration timestep to use """ dv_leak = p.v_leak - voltage dv_exp = p.delta_T * torch.exp((voltage - p.v_th) / p.delta_T) dv = dt * p.tau_mem_inv * (dv_leak + dv_exp + input_current) voltage = voltage + dv z = threshold(voltage - p.v_th, p.method, p.alpha) voltage = voltage - z * (voltage - p.v_reset) return z, voltage