# norse.torch.functional.threshold module¶

class norse.torch.functional.threshold.CircDist(*args, **kwargs)[source]

Bases: torch.autograd.function.Function

static backward(ctx, dy)[source]

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, x, alpha)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store arbitrary data that can be then retrieved during the backward pass.

class norse.torch.functional.threshold.HeaviCirc(*args, **kwargs)[source]

Bases: torch.autograd.function.Function

Approximation of the heaviside step function as

$h(x,\alpha) = \frac{1}{2} + \frac{1}{2} \ \frac{x}{(x^2 + \alpha^2)^{1/2}}$
static backward(ctx, dy)[source]

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, x, alpha)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store arbitrary data that can be then retrieved during the backward pass.

class norse.torch.functional.threshold.HeaviErfc(*args, **kwargs)[source]

Bases: torch.autograd.function.Function

Approximation of the heaviside step function as

$h(x,k) = \frac{1}{2} + \frac{1}{2} \text{erfc}(k x)$

where erfc is the error function.

static backward(ctx, dy)[source]

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, x, k)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store arbitrary data that can be then retrieved during the backward pass.

class norse.torch.functional.threshold.HeaviTanh(*args, **kwargs)[source]

Bases: torch.autograd.function.Function

Approximation of the heaviside step function as

$h(x,k) = \frac{1}{2} + \frac{1}{2} \text{tanh}(k x)$
static backward(ctx, dy)[source]

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, x, k)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store arbitrary data that can be then retrieved during the backward pass.

class norse.torch.functional.threshold.Logistic(*args, **kwargs)[source]

Bases: torch.autograd.function.Function

Probalistic approximation of the heaviside step function as

$z \sim p(\frac{1}{2} + \frac{1}{2} \text{tanh}(k x))$
static backward(ctx, dy)[source]

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, x, k)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store arbitrary data that can be then retrieved during the backward pass.

class norse.torch.functional.threshold.Triangle(*args, **kwargs)[source]

Bases: torch.autograd.function.Function

Triangular/piecewise linear surrogate gradient as in

S.K. Esser et al., “Convolutional networks for fast, energy-efficient neuromorphic computing”, Proceedings of the National Academy of Sciences 113(41), 11441-11446, (2016), doi:10.1073/pnas.1604850113 G. Bellec et al., “A solution to the learning dilemma for recurrent networks of spiking neurons”, Nature Communications 11(1), 3625, (2020), doi:10.1038/s41467-020-17236-y

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, x, alpha)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store arbitrary data that can be then retrieved during the backward pass.

Return type

Tensor

norse.torch.functional.threshold.circ_dist_fn(x, k)[source]
norse.torch.functional.threshold.heavi_circ_fn(x, k)[source]
norse.torch.functional.threshold.heavi_erfc_fn(x, k)[source]
norse.torch.functional.threshold.heavi_tanh_fn(x, k)[source]
norse.torch.functional.threshold.logistic_fn(x, k)[source]
norse.torch.functional.threshold.sign(x, method, alpha)[source]
Return type

Tensor

norse.torch.functional.threshold.threshold(x, method, alpha)[source]
Return type

Tensor

norse.torch.functional.threshold.triangle_fn(x, alpha=0.3)[source]
Return type

Tensor