Simplicial Complex Convolutional Network (SCCN) Layer.

class topomodelx.nn.simplicial.sccn_layer.SCCNLayer(channels, max_rank, aggr_func: Literal['mean', 'sum'] = 'sum', update_func: Literal['relu', 'sigmoid', 'tanh'] | None = 'sigmoid')

Simplicial Complex Convolutional Network (SCCN) layer by [1].

This implementation applies to simplicial complexes of any rank.

This layer corresponds to the leftmost tensor diagram labeled Yang22c in Figure 11 of [3].

Parameters:

channelsint

Dimension of features on each simplicial cell.

max_rankint

Maximum rank of the cells in the simplicial complex.

aggr_func{“mean”, “sum”}, default=”sum”

The function to be used for aggregation.

update_func{“relu”, “sigmoid”, “tanh”, None}, default=”sigmoid”

The activation function.

Methods

add_module(name, module)	Adds a child module to the current module.
apply(fn)	Applies 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])	Returns an iterator over module buffers.
children()	Returns an iterator over immediate children modules.
cpu()	Moves all model parameters and buffers to the CPU.
cuda([device])	Moves all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Sets the module in evaluation mode.
extra_repr()	Set the extra representation of the module
float()	Casts all floating point parameters and buffers to float datatype.
forward(features, incidences, adjacencies)	Forward pass.
get_buffer(target)	Returns the buffer given by target if it exists, otherwise throws an error.
get_extra_state()	Returns any extra state to include in the module's state_dict.
get_parameter(target)	Returns the parameter given by target if it exists, otherwise throws an error.
get_submodule(target)	Returns the submodule given by target if it exists, otherwise throws an error.
half()	Casts all floating point parameters and buffers to half datatype.
ipu([device])	Moves all model parameters and buffers to the IPU.
load_state_dict(state_dict[, strict])	Copies parameters and buffers from state_dict into this module and its descendants.
modules()	Returns an iterator over all modules in the network.
named_buffers([prefix, recurse, ...])	Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Returns 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])	Returns 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, ...])	Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
parameters([recurse])	Returns an iterator over module parameters.
register_backward_hook(hook)	Registers a backward hook on the module.
register_buffer(name, tensor[, persistent])	Adds a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Registers a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Registers a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Registers a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Registers a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Registers a post hook to be run after module's load_state_dict is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Adds a parameter to the module.
register_state_dict_pre_hook(hook)	These hooks will be called with arguments: self, prefix, and keep_vars before calling state_dict on self.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
reset_parameters()	Reset learnable parameters.
set_extra_state(state)	This function is called from load_state_dict() to handle any extra state found within the state_dict.
share_memory()	See torch.Tensor.share_memory_()
state_dict(*args[, destination, prefix, ...])	Returns a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Moves and/or casts the parameters and buffers.
to_empty(*, device)	Moves the parameters and buffers to the specified device without copying storage.
train([mode])	Sets the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Moves all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Sets gradients of all model parameters to zero.

__call__

See also

topomodelx.nn.simplicial.scn2_layer.SCN2Layer

SCN layer proposed in [1] for simplicial complexes of rank 2. The difference between SCCN and SCN is that: - SCN passes messages between cells of the same rank, - SCCN passes messages between cells of the same ranks, one rank above and one rank below.

References

[1] (1,2)

Yang, Sala, Bogdan. Efficient representation learning for higher-order data with simplicial complexes (2022). https://proceedings.mlr.press/v198/yang22a.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(features, incidences, adjacencies)

Forward pass.

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

The incidence and adjacency matrices passed into this layer can be normalized as described in [1]_ or unnormalized.

\[\begin{split}\begin{align*} &🟥 \quad m_{{y \rightarrow x}}^{(r \rightarrow r)} = (H_{r})_{xy} \cdot h^{t,(r)}_y \cdot \Theta^{t,(r\to r)} \\ &🟥 \quad m_{{y \rightarrow x}}^{(r-1 \rightarrow r)} = (B_{r}^T)_{xy} \cdot h^{t,(r-1)}_y \cdot \Theta^{t,(r-1\to r)} \\ &🟥 \quad m_{{y \rightarrow x}}^{(r+1 \rightarrow r)} = (B_{r+1})_{xy} \cdot h^{t,(r+1)}_y \cdot \Theta^{t,(r+1\to r)} \\ &🟧 \quad m_{x}^{(r \rightarrow r)} = \sum_{y \in \mathcal{L}_\downarrow(x)\bigcup \mathcal{L}_\uparrow(x)} m_{y \rightarrow x}^{(r \rightarrow r)} \\ &🟧 \quad m_{x}^{(r-1 \rightarrow r)} = \sum_{y \in \mathcal{B}(x)} m_{y \rightarrow x}^{(r-1 \rightarrow r)} \\ &🟧 \quad m_{x}^{(r+1 \rightarrow r)} = \sum_{y \in \mathcal{C}(x)} m_{y \rightarrow x}^{(r+1 \rightarrow r)} \\ &🟩 \quad m_x^{(r)} = m_x^{(r \rightarrow r)} + m_x^{(r-1 \rightarrow r)} + m_x^{(r+1 \rightarrow r)} \\ &🟦 \quad h_x^{t+1,(r)} = \sigma(m_x^{(r)}) \end{align*}\end{split}\]

Parameters:

featuresdict[int, torch.Tensor], length=max_rank+1, shape = (n_rank_r_cells, channels)

Input features on the cells of the simplicial complex.

incidencesdict[int, torch.sparse], length=max_rank, shape = (n_rank_r_minus_1_cells, n_rank_r_cells)

Incidence matrices \(B_r\) mapping r-cells to (r-1)-cells.

adjacenciesdict[int, torch.sparse], length=max_rank, shape = (n_rank_r_cells, n_rank_r_cells)

Adjacency matrices \(H_r\) mapping cells to cells via lower and upper cells.

Returns:

dict[int, torch.Tensor], length=max_rank+1, shape = (n_rank_r_cells, channels)

Output features on the cells of the simplicial complex.

reset_parameters() → None

Reset learnable parameters.