Simplicial Complex Net Layer.

class topomodelx.nn.simplicial.scone_layer.SCoNeLayer(in_channels: int, out_channels: int, update_func: Literal['relu', 'sigmoid', 'tanh'] = 'tanh')

Implementation of the SCoNe layer proposed in [1].

Parameters:

in_channelsint

Input dimension of features on each edge.

out_channelsint

Output dimension of features on each edge.

update_funcLiteral[‘relu’, ‘sigmoid’, ‘tanh’]

Update function to use when updating edge features.

Methods

add_module(name, module)	Add a child module to the current module.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
bfloat16()	Casts all floating point parameters and buffers to bfloat16 datatype.
buffers([recurse])	Return an iterator over module buffers.
children()	Return an iterator over immediate children modules.
compile(*args, **kwargs)	Compile this Module's forward using torch.compile().
cpu()	Move all model parameters and buffers to the CPU.
cuda([device])	Move all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Set the module in evaluation mode.
extra_repr()	Return the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
forward(x, incidence_1, incidence_2)	Forward pass.
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_extra_state()	Return any extra state to include in the module's state_dict.
get_parameter(target)	Return the parameter given by target if it exists, otherwise throw an error.
get_submodule(target)	Return the submodule given by target if it exists, otherwise throw an error.
half()	Casts all floating point parameters and buffers to half datatype.
ipu([device])	Move all model parameters and buffers to the IPU.
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
modules([remove_duplicate])	Return an iterator over all modules in the network.
mtia([device])	Move all model parameters and buffers to the MTIA.
named_buffers([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
named_modules([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
named_parameters([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
parameters([recurse])	Return an iterator over module parameters.
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Register a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Register a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Register a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Register a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Register a post-hook to be run after module's load_state_dict() is called.
register_load_state_dict_pre_hook(hook)	Register a pre-hook to be run before module's load_state_dict() is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_state_dict_post_hook(hook)	Register a post-hook for the state_dict() method.
register_state_dict_pre_hook(hook)	Register a pre-hook for the state_dict() method.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
reset_parameters([gain])	Reset learnable parameters.
set_extra_state(state)	Set extra state contained in the loaded state_dict.
set_submodule(target, module[, strict])	Set the submodule given by target if it exists, otherwise throw an error.
share_memory()	See torch.Tensor.share_memory_().
state_dict(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Move and/or cast the parameters and buffers.
to_empty(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
train([mode])	Set the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

__call__

Notes

This is the architecture proposed for trajectory prediction on simplicial complexes.

For the trajectory prediction architecture proposed in [1], these layers are stacked before applying the boundary map from 1-chains to 0-chains. Finally, one can apply the softmax operator on the neighbouring nodes of the last node in the given trajectory to predict the next node. When implemented like this, we get a map from (ordered) 1-chains (trajectories) to the neighbouring nodes of the last node in the 1-chain.

References

[1] (1,2)

Roddenberry, Mitchell, Glaze. Principled simplicial neural networks for trajectory prediction. ICML 2021. https://proceedings.mlr.press/v139/roddenberry21a.html

[2]

Papillon, Sanborn, Hajij, Miolane. Equations of topological neural networks (2023). awesome-tnns/awesome-tnns

[3]

Papillon, Sanborn, Hajij, Miolane. Architectures of topological deep learning: a survey on topological neural networks (2023). https://arxiv.org/abs/2304.10031.

forward(x: Tensor, incidence_1: Tensor, incidence_2: Tensor) → Tensor

Forward pass.

The forward pass was initially proposed in [1]_. Its equations are given in [2]_ and graphically illustrated in [3]_.

\[\begin{split}\begin{align*} &🟥 \quad m^{(1 \rightarrow 0 \rightarrow 1)}_{y \rightarrow \{z\} \rightarrow x} = (L_{\downarrow,1})_{xy} \cdot h_y^{t,(1)} \cdot \Theta^{t,(1 \rightarrow 0 \rightarrow 1)}\\ &🟥 \quad m_{x \rightarrow x}^{(1 \rightarrow 1)} = h_x^{t,(1)} \cdot \Theta^{t,(1 \rightarrow 1)}\\ &🟥 \quad m_{y \rightarrow \{z\} \rightarrow x}^{(1 \rightarrow 2 \rightarrow 1)} = (L_{\uparrow,1})_{xy} \cdot h_y^{t,(1)} \cdot \Theta^{t,(1 \rightarrow 2 \rightarrow 1)}\\ &🟧 \quad m_{x}^{(1 \rightarrow 0 \rightarrow 1)} = \sum_{y \in \mathcal{L}_\downarrow(x)} m_{y \rightarrow \{z\} \rightarrow x}^{(1 \rightarrow 0 \rightarrow 1)}\\ &🟧 \quad m_{x}^{(1 \rightarrow 2 \rightarrow 1)} = \sum_{y \in \mathcal{L}_\uparrow(x)} m_{y \rightarrow \{z\} \rightarrow x}^{(1 \rightarrow 2 \rightarrow 1)}\\ &🟩 \quad m_x^{(1)} = m_{x}^{(1 \rightarrow 0 \rightarrow 1)} + m_{x \rightarrow x}^{(1 \rightarrow 1)} + m_{x}^{(1 \rightarrow 2 \rightarrow 1)}\\ &🟦 \quad h_x^{t,(1)} = \sigma(m_x^{(1)}) \end{align*}\end{split}\]

Parameters:

x: torch.Tensor, shape = (n_edges, in_channels)

Input features on the edges of the simplicial complex.

incidence_1torch.sparse, shape = (n_nodes, n_edges)

Incidence matrix \(B_1\) mapping edges to nodes.

incidence_2torch.sparse, shape = (n_edges, n_triangles)

Incidence matrix \(B_2\) mapping triangles to edges.

Returns:

torch.Tensor, shape = (n_edges, out_channels)

Output features on the edges of the simplicial complex.

reset_parameters(gain: float = 1.0) → None

Reset learnable parameters.