from typing import Tuple
import torch
from norse.torch.functional.lif_refrac import (
LIFRefracState,
LIFRefracFeedForwardState,
LIFRefracParameters,
lif_refrac_step,
lif_refrac_step_sparse,
lif_refrac_feed_forward_step,
)
from norse.torch.functional.lif import LIFState, LIFFeedForwardState
from norse.torch.functional.heaviside import heaviside
class LIFAdjointRefracFunction(torch.autograd.Function):
@staticmethod
def forward(
ctx,
input_tensor: torch.Tensor,
z: torch.Tensor,
v: torch.Tensor,
i: torch.Tensor,
rho: torch.Tensor,
input_weights: torch.Tensor,
recurrent_weights: torch.Tensor,
p: LIFRefracParameters = LIFRefracParameters(),
dt: float = 0.001,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
ctx.p = p
ctx.dt = dt
s = LIFRefracState(LIFState(z, v, i), rho)
z_new, s_new = lif_refrac_step(
input_tensor, s, input_weights, recurrent_weights, p, dt
)
# dv before spiking
dv_m = p.lif.tau_mem_inv * ((p.lif.v_leak - s.lif.v) + s.lif.i)
# dv after spiking
dv_p = p.lif.tau_mem_inv * ((p.lif.v_leak - s_new.lif.v) + s.lif.i)
ctx.save_for_backward(
input_tensor, z_new, s_new.rho, dv_m, dv_p, input_weights, recurrent_weights
)
return z_new, s_new.lif.v, s_new.lif.i, s_new.rho
@staticmethod
def backward(ctx, doutput, lambda_v, lambda_i, lambda_rho):
(
input_tensor,
z,
rho,
dv_m,
dv_p,
input_weights,
recurrent_weights,
) = ctx.saved_tensors
p = ctx.p
dt = ctx.dt
dw_input = lambda_i.t().mm(input_tensor)
dw_rec = lambda_i.t().mm(z)
refrac_mask = heaviside(rho)
# lambda_i decay
dlambda_i = p.tau_syn_inv * ((1 - refrac_mask) * lambda_v - lambda_i)
lambda_i = lambda_i + dt * dlambda_i
# lambda_v decay
lambda_v = lambda_v - (1 - refrac_mask) * p.tau_mem_inv * dt * lambda_v
output_term = z * (1 / dv_m) * (doutput)
output_term[output_term != output_term] = 0.0
jump_term = z * (dv_p / dv_m)
jump_term[jump_term != jump_term] = 0.0
lambda_v = (1 - z) * lambda_v + jump_term * lambda_v + output_term
dinput = lambda_i.mm(input_weights)
drecurrent = lambda_i.mm(recurrent_weights)
return (
dinput,
drecurrent,
lambda_v,
lambda_i,
lambda_rho,
dw_input,
dw_rec,
None,
None,
)
def lif_refrac_adjoint_step(
input: torch.Tensor,
s: LIFRefracState,
input_weights: torch.Tensor,
recurrent_weights: torch.Tensor,
p: LIFRefracParameters = LIFRefracParameters(),
dt: float = 0.001,
) -> Tuple[torch.Tensor, LIFRefracState]:
"""Implementes a single euler forward and adjoint backward
step of a leaky integrate and fire neuron with current based
exponential synapses and a refractory period.
"""
z, v, i, rho = LIFAdjointRefracFunction.apply(
input, s.lif.z, s.lif.v, s.lif.i, s.rho, input_weights, recurrent_weights, p, dt
)
return z, LIFRefracState(LIFState(z, v, i), rho)
class LIFSparseAdjointRefracFunction(torch.autograd.Function):
@staticmethod
def forward(
ctx,
input: torch.Tensor,
lif_state: LIFState,
rho: torch.Tensor,
input_weights: torch.Tensor,
recurrent_weights: torch.Tensor,
p: LIFRefracParameters = LIFRefracParameters(),
dt: float = 0.001,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
ctx.tau_sys_inv = p.lif.tau_syn_inv
ctx.tau_mem_inv = p.lif.tau_mem_inv
ctx.v_th = p.lif.v_th
ctx.v_reset = p.lif.v_reset
ctx.rho_reset = p.rho_reset
ctx.dt = dt
s = LIFRefracState(lif_state, rho)
z_new, s_new = lif_refrac_step_sparse(
input, s, input_weights, recurrent_weights, p, dt
)
# dv before spiking
dv_m = p.lif.tau_mem_inv * ((p.lif.v_leak - s_new.lif.v) + s.lif.i)
# dev after spiking
dv_p = p.lif.tau_mem_inv * ((p.lif.v_leak - s_new.lif.v) + s.lif.i)
refrac_period_end = (s.rho == 1).float()
ctx.save_for_backward(
input,
z_new,
s_new.rho,
refrac_period_end,
dv_m.sparse_mask(z_new),
dv_p.sparse_mask(z_new),
input_weights,
recurrent_weights,
)
return z_new, s_new.lif.v, s_new.lif.i, s_new.rho
@staticmethod
def backward(
ctx,
doutput: torch.Tensor,
lambda_v: torch.Tensor,
lambda_i: torch.Tensor,
lambda_rho: torch.Tensor,
):
(
input_tensor,
z,
refrac_count,
refrac_period_end,
dv_m,
dv_p,
input_weights,
recurrent_weights,
) = ctx.saved_tensors
tau_syn_inv = ctx.tau_syn_inv
tau_mem_inv = ctx.taus_mem_inv
dt = ctx.dt
refrac_mask = heaviside(refrac_count)
dv_m = dv_m.to_dense()
dv_p = dv_p.to_dense()
z = z.to_dense()
dw_input = lambda_i.t().mm(input_tensor)
dw_rec = lambda_i.t().mm(z)
# lambda_i decay
dlambda_i = tau_syn_inv * ((1 - refrac_mask) * lambda_v - lambda_i)
lambda_i = lambda_i + dt * dlambda_i
# lambda_v decay
lambda_v = lambda_v - (1 - refrac_mask) * tau_mem_inv * dt * lambda_v
output_term = z * (1 / dv_m) * (doutput)
output_term[output_term != output_term] = 0.0
jump_term = z * (dv_p / dv_m)
jump_term[jump_term != jump_term] = 0.0
lambda_v = (1 - z) * lambda_v + jump_term * lambda_v + output_term
lambda_rho = (
1 - refrac_period_end
) * lambda_rho + refrac_period_end * lambda_v * dv_p
dinput = lambda_i.mm(input_weights)
drecurrent = lambda_i.mm(recurrent_weights)
return (
dinput,
drecurrent,
lambda_v,
lambda_i,
lambda_rho,
dw_input,
dw_rec,
None,
None,
)
def lif_refrac_adjoint_step_sparse(
input: torch.Tensor,
s: LIFRefracState,
input_weights: torch.Tensor,
recurrent_weights: torch.Tensor,
p: LIFRefracParameters,
dt: float = 0.001,
) -> Tuple[torch.Tensor, LIFRefracState]:
z, v, i, rho = LIFSparseAdjointRefracFunction.apply(
input, s.lif, s.rho, input_weights, recurrent_weights, p, dt
)
return z, LIFRefracState(LIFState(z, v, i), rho)
class LIFAdjointRefracFeedForwardFunction(torch.autograd.Function):
@staticmethod
def forward(
ctx,
input: torch.Tensor,
v: torch.Tensor,
i: torch.Tensor,
rho: torch.Tensor,
p: LIFRefracParameters = LIFRefracParameters(),
dt: float = 0.001,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
ctx.tau_syn_inv = p.lif.tau_syn_inv
ctx.tau_mem_inv = p.lif.tau_mem_inv
ctx.dt = dt
s = LIFRefracFeedForwardState(LIFFeedForwardState(v, i), rho)
z_new, s_new = lif_refrac_feed_forward_step(input, s, p, dt)
# dv before spiking
dv_m = p.lif.tau_mem_inv * ((p.lif.v_leak - s.lif.v) + s.lif.i)
# dv after spiking
dv_p = p.lif.tau_mem_inv * ((p.lif.v_leak - s_new.lif.v) + s.lif.i)
refrac_period_end = (s.rho == 1).float()
ctx.save_for_backward(input, z_new, s_new.rho, refrac_period_end, dv_m, dv_p)
return z_new, s_new.lif.v, s_new.lif.i, s_new.rho
@staticmethod
def backward(ctx, doutput, lambda_v, lambda_i, lambda_rho):
input, z, refrac_count, refrac_period_end, dv_m, dv_p = ctx.saved_tensors
tau_syn_inv = ctx.tau_syn_inv
tau_mem_inv = ctx.tau_mem_inv
dt = ctx.dt
refrac_mask = heaviside(refrac_count)
# lambda_i decay
dlambda_i = tau_syn_inv * ((1 - refrac_mask) * lambda_v - lambda_i)
lambda_i = lambda_i + dt * dlambda_i
# lambda_v decay
lambda_v = lambda_v - (1 - refrac_mask) * tau_mem_inv * dt * lambda_v
output_term = z * (1 / dv_m) * doutput
output_term[output_term != output_term] = 0.0
jump_term = z * (lambda_rho / dv_m)
jump_term[jump_term != jump_term] = 0.0
lambda_v = (1 - z) * lambda_v + jump_term + output_term
lambda_rho = (
1 - refrac_period_end
) * lambda_rho + refrac_period_end * lambda_v * dv_p
return (lambda_i, lambda_v, lambda_i, lambda_rho, None, None)
[docs]
def lif_refrac_feed_forward_adjoint_step(
input: torch.Tensor,
s: LIFRefracFeedForwardState,
p: LIFRefracParameters = LIFRefracParameters(),
dt: float = 0.001,
) -> Tuple[torch.Tensor, LIFRefracFeedForwardState]:
"""Implementes a single euler forward and adjoint backward
step of a leaky integrate and fire neuron with current based
exponential synapses and a refractory period.
"""
z, v, i, rho = LIFAdjointRefracFeedForwardFunction.apply(
input, s.lif.v, s.lif.i, s.rho, p, dt
)
return z, LIFRefracFeedForwardState(LIFFeedForwardState(v, i), rho)
