Simplical Complex Autoencoder Layer.

class topomodelx.nn.simplicial.sca_cmps_layer.SCACMPSLayer(channels_list, complex_dim, att: bool = False)

Layer of a Simplicial Complex Autoencoder (SCA) using the Coadjacency Message Passing Scheme (CMPS).

Implementation of the SCA layer proposed in [1].

Parameters:

channels_listlist[int]

Dimension of features at each dimension.

complex_dimint

Highest dimension of chains on the input simplicial complexes.

attbool, default=False

Whether to use attention.

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(x_list, down_lap_list, incidencet_list)	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.
intra_aggr(x)	Based on the use by [1]_.
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 parameters of each layer.
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.
weight_func(x)	Weight function for intra aggregation layer according to [1]_.
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__

Notes

This is the architecture proposed for complex classification.

References

[1]

Hajij, Zamzmi, Papamarkou, Maroulas, Cai. Simplicial complex autoencoder (2022). https://arxiv.org/pdf/2103.04046.pdf

[2]

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

[3]

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

forward(x_list, down_lap_list, incidencet_list)

Forward pass.

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

Coadjacency message passing scheme:

\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow x}^{(r \rightarrow r'' \rightarrow r)} = M(h_{x}^{t, (r)}, h_{y}^{t, (r)},att(h_{x}^{t, (r)}, h_{y}^{t, (r)}),x,y,{\Theta^t}) \qquad \text{where } r'' < r < r'\\ &🟥 \quad m_{y \rightarrow x}^{(r'' \rightarrow r)} = M(h_{x}^{t, (r)}, h_{y}^{t, (r'')},att(h_{x}^{t, (r)}, h_{y}^{t, (r'')}),x,y,{\Theta^t})\\ &🟧 \quad m_x^{(r \rightarrow r)} = AGG_{y \in \mathcal{L}\_\downarrow(x)} m_{y \rightarrow x}^{(r \rightarrow r)}\\ &🟧 \quad m_x^{(r'' \rightarrow r)} = AGG_{y \in \mathcal{B}(x)} m_{y \rightarrow x}^{(r'' \rightarrow r)}\\ &🟩 \quad m_x^{(r)} = \text{AGG}\_{\mathcal{N}\_k \in \mathcal{N}}(m_x^{(k)})\\ &🟦 \quad h_{x}^{t+1, (r)} = U(h_x^{t, (r)}, m_{x}^{(r)}) \end{align*}\end{split}\]

Parameters:

x_listlist[torch.Tensor]

List of tensors holding the features of each chain at each level.

down_lap_listlist[torch.Tensor]

List of down laplacian matrices for skeletons from 1 dimension to the dimension of the simplicial complex.

incidencet_listlist[torch.Tensor]

List of transpose incidence matrices for skeletons from 1 dimension to the dimension of the simplicial complex.

Returns:

list[torch.Tensor]

Output for skeletons of each dimension (the node features are left untouched: x_list[0]).

intra_aggr(x)

Based on the use by [1]_.

Parameters:

xtorch.Tensor

Returns:

torch.Tensor

reset_parameters() → None

Reset parameters of each layer.

weight_func(x)

Weight function for intra aggregation layer according to [1]_.

Parameters:

xtorch.Tensor

Returns:

torch.Tensor