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