norse.torch.functional.lsnn module

Long-short term memory module, building on the work by [G. Bellec, D. Salaj, A. Subramoney, R. Legenstein, and W. Maass](https://github.com/IGITUGraz/LSNN-official).

The LSNN dynamics is similar to the lif equations, but it adds an adaptive term \(b\):

\[\begin{split}\begin{align*} \dot{v} &= 1/\tau_{\text{mem}} (v_{\text{leak}} - v + i) \\ \dot{i} &= -1/\tau_{\text{syn}}\; i \\ \dot{b} &= -1/\tau_{b}\; b \end{align*}\end{split}\]

This adaptation is applied in the jump condition when the neuron spikes:

\[z = \Theta(v - v_{\text{th}} + b)\]

Contrast this with the regular LIF jump condition:

\[z = \Theta(v - v_{\text{th}})\]

In practice, this means that the LSNN neurons adapt to fire more or less given the same input. The adaptation is determined by the \(\tau_b\) time constant.

class norse.torch.functional.lsnn.LSNNFeedForwardState(v: torch.Tensor, i: torch.Tensor, b: torch.Tensor)[source]

Bases: tuple

Integration state kept for a lsnn module

Parameters

Create new instance of LSNNFeedForwardState(v, i, b)

b: torch.Tensor

Alias for field number 2

i: torch.Tensor

Alias for field number 1

v: torch.Tensor

Alias for field number 0

class norse.torch.functional.lsnn.LSNNParameters(tau_syn_inv: torch.Tensor = tensor(200.), tau_mem_inv: torch.Tensor = tensor(100.), tau_adapt_inv: torch.Tensor = tensor(0.0012), v_leak: torch.Tensor = tensor(0.), v_th: torch.Tensor = tensor(1.), v_reset: torch.Tensor = tensor(0.), beta: torch.Tensor = tensor(1.8000), method: str = 'super', alpha: float = 100.0)[source]

Bases: tuple

Parameters of an LSNN neuron

Parameters

Create new instance of LSNNParameters(tau_syn_inv, tau_mem_inv, tau_adapt_inv, v_leak, v_th, v_reset, beta, method, alpha)

alpha: float

Alias for field number 8

beta: torch.Tensor

Alias for field number 6

method: str

Alias for field number 7

tau_adapt_inv: torch.Tensor

Alias for field number 2

tau_mem_inv: torch.Tensor

Alias for field number 1

tau_syn_inv: torch.Tensor

Alias for field number 0

v_leak: torch.Tensor

Alias for field number 3

v_reset: torch.Tensor

Alias for field number 5

v_th: torch.Tensor

Alias for field number 4

class norse.torch.functional.lsnn.LSNNState(z: torch.Tensor, v: torch.Tensor, i: torch.Tensor, b: torch.Tensor)[source]

Bases: tuple

State of an LSNN neuron

Parameters

Create new instance of LSNNState(z, v, i, b)

b: torch.Tensor

Alias for field number 3

i: torch.Tensor

Alias for field number 2

v: torch.Tensor

Alias for field number 1

z: torch.Tensor

Alias for field number 0

norse.torch.functional.lsnn.ada_lif_step(input_tensor, state, input_weights, recurrent_weights, p=LSNNParameters(tau_syn_inv=tensor(200.), tau_mem_inv=tensor(100.), tau_adapt_inv=tensor(0.0012), v_leak=tensor(0.), v_th=tensor(1.), v_reset=tensor(0.), beta=tensor(1.8000), method='super', alpha=100.0), dt=0.001)[source]

Euler integration step for LIF Neuron with adaptation. More specifically it implements one integration step of the following ODE

\[\begin{split}\begin{align*} \dot{v} &= 1/\tau_{\text{mem}} (v_{\text{leak}} - v + b + i) \\ \dot{i} &= -1/\tau_{\text{syn}} i \\ \dot{b} &= -1/\tau_{b} b \end{align*}\end{split}\]

together with the jump condition

\[z = \Theta(v - v_{\text{th}})\]

and transition equations

\[\begin{split}\begin{align*} v &= (1-z) v + z v_{\\text{reset}} \\ i &= i + w_{\text{input}} z_{\\text{in}} \\ i &= i + w_{\text{rec}} z_{\\text{rec}} \\ b &= b + \beta z \end{align*}\end{split}\]

where \(z_{\text{rec}}\) and \(z_{\text{in}}\) are the recurrent and input spikes respectively.

Parameters

  • input_tensor (torch.Tensor) – the input spikes at the current time step

  • s (LSNNState) – current state of the lsnn unit

  • input_weights (torch.Tensor) – synaptic weights for input spikes

  • recurrent_weights (torch.Tensor) – synaptic weights for recurrent spikes

  • p (LSNNParameters) – parameters of the lsnn unit

  • dt (float) – Integration timestep to use

Return type

Tuple[Tensor, LSNNState]

norse.torch.functional.lsnn.lsnn_feed_forward_step(input_tensor, state, p=LSNNParameters(tau_syn_inv=tensor(200.), tau_mem_inv=tensor(100.), tau_adapt_inv=tensor(0.0012), v_leak=tensor(0.), v_th=tensor(1.), v_reset=tensor(0.), beta=tensor(1.8000), method='super', alpha=100.0), dt=0.001)[source]

Euler integration step for LIF Neuron with threshold adaptation. More specifically it implements one integration step of the following ODE

\[\begin{split}\\begin{align*} \dot{v} &= 1/\tau_{\text{mem}} (v_{\text{leak}} - v + i) \\ \dot{i} &= -1/\tau_{\text{syn}} i \\ \dot{b} &= -1/\tau_{b} b \end{align*}\end{split}\]

together with the jump condition

\[z = \Theta(v - v_{\text{th}} + b)\]

and transition equations

\[\begin{split}\begin{align*} v &= (1-z) v + z v_{\text{reset}} \\ i &= i + \text{input} \\ b &= b + \beta z \end{align*}\end{split}\]
Parameters
Return type

Tuple[Tensor, LSNNFeedForwardState]

norse.torch.functional.lsnn.lsnn_step(input_tensor, state, input_weights, recurrent_weights, p=LSNNParameters(tau_syn_inv=tensor(200.), tau_mem_inv=tensor(100.), tau_adapt_inv=tensor(0.0012), v_leak=tensor(0.), v_th=tensor(1.), v_reset=tensor(0.), beta=tensor(1.8000), method='super', alpha=100.0), dt=0.001)[source]

Euler integration step for LIF Neuron with threshold adaptation More specifically it implements one integration step of the following ODE

\[\begin{split}\begin{align*} \dot{v} &= 1/\tau_{\text{mem}} (v_{\text{leak}} - v + i) \\ \dot{i} &= -1/\tau_{\text{syn}} i \\ \dot{b} &= -1/\tau_{b} b \end{align*}\end{split}\]

together with the jump condition

\[z = \Theta(v - v_{\text{th}} + b)\]

and transition equations

\[\begin{split}\begin{align*} v &= (1-z) v + z v_{\text{reset}} \\ i &= i + w_{\text{input}} z_{\text{in}} \\ i &= i + w_{\text{rec}} z_{\text{rec}} \\ b &= b + \beta z \end{align*}\end{split}\]

where \(z_{\text{rec}}\) and \(z_{\text{in}}\) are the recurrent and input spikes respectively.

Parameters

  • input_tensor (torch.Tensor) – the input spikes at the current time step

  • s (LSNNState) – current state of the lsnn unit

  • input_weights (torch.Tensor) – synaptic weights for input spikes

  • recurrent_weights (torch.Tensor) – synaptic weights for recurrent spikes

  • p (LSNNParameters) – parameters of the lsnn unit

  • dt (float) – Integration timestep to use

Return type

Tuple[Tensor, LSNNState]