DHGCN_Layer

Dynamic hypergraph convolutional network (DHGCN) Layer implementation.

class topomodelx.nn.hypergraph.dhgcn_layer.DHGCNLayer(in_channels, intermediate_channels, out_channels, k_neighbours: int = 3, k_centroids: int = 4, device: str = 'cpu', **kwargs)

Dynamic Topology Layer of a Dynamic hypergraph convolutional network (DHGCN) [1].

Dynamic topology, followed by two-step message passing layer.

Parameters:

in_channelsint

Dimension of input features.

intermediate_channelsint

Dimension of intermediate features.

out_channelsint

Dimension of output features.

k_neighboursint, default=3

Number of neighbours to consider in the local topology.

k_centroidsint, default=4

Number of centroids to consider in the global topology.

devicestr, default=”cpu”

Device to store the tensors.

**kwargsoptional

Additional arguments for the layer modules.

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_0)	Forward pass (see [2]_ and [3]_).
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_dynamic_topology(x_0_features)	Compute dynamic topology.
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.
kmeans(x_0[, k])	Wrap k-means algorithm.
kmeans_graph(x, k[, flow])	Implement k-means algorithm.
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 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__

References

[1]

Yin, Feng, Luo, Zhang, Wang, Luo, Chen and Hua. Dynamic hypergraph convolutional network (2022). https://ieeexplore.ieee.org/abstract/document/9835240

[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_0)

Forward pass (see [2]_ and [3]_).

Dynamic topology module of the DHST Block is implemented here.

\[\begin{split}\begin{align*} &🟧 \quad m_{\rightarrow z}^{\rightarrow 1} = \text{AGG}\_{y \in \mathcal{B}(z)}(h_y^{0, t})\\ &🟦 \quad h_z^{1, t+1} = \sigma(m_{\rightarrow z}^{\rightarrow 1})\\ &🟥 \quad m_{z \rightarrow x}^{1 \rightarrow 0} = M_\mathcal{B}(att(h_z^{1, t+1}), h_z^{1, t+1})\\ &🟧 \quad m_{\rightarrow x}^{\rightarrow 0} = \sum_{z \in \mathcal{C}(x)} m_{z \rightarrow x}^{0\rightarrow 1}\\ &🟦 \quad {h_x^{0, t+1}} = \text{MLP}(m_{\rightarrow x}^{\rightarrow 0}) \end{align*}\end{split}\]

Parameters:

x_0torch.Tensor, shape = (n_nodes, node_channels)

Input features on the nodes of the simplicial complex.

Returns:

x_0torch.Tensor

Output node features.

x_1torch.Tensor

Output hyperedge features.

get_dynamic_topology(x_0_features)

Compute dynamic topology.

Parameters:

x_0_featurestorch.Tensor, shape = (n_nodes, node_features)

Input features on the nodes of the simplicial complex.

Returns:

torch.Tensor

Incidence matrix mapping edges to nodes, shape = (n_nodes, n_nodes + k_centroids).

kmeans(x_0, k=None)

Wrap k-means algorithm.

Parameters:

x_0torch.Tensor, shape = (n_nodes, node_features)

Input features on the nodes of the simplicial complex.

kint

Number of clusters/centroids.

Returns:

torch.Tensor

Indices of the on-zero values in the feature matrix of hypergraph convolutional network.

static kmeans_graph(x, k, flow: str = 'source_to_target')

Implement k-means algorithm.

Parameters:

xtorch.Tensor, shape = (n_nodes, node_features)

Input features on the nodes of the simplicial complex.

kint

Number of clusters/centroids.

flowstr

If this parameter has value “source_to_target”, the output will have the shape [n_nodes, n_hyperedges = k_centroids]. If this parameter has value “target_to_source”, the output shape will be [n_hyperedges = k_centroids, n_nodes]. It corresponds to the flow parameter of the knn_graph method and is defined accordingly.

Returns:

torch.Tensor

Indices of the on-zero values in the feature matrix of hypergraph convolutional network. The order of dimensions of the matrix is defined by the value of the flow parameter.

reset_parameters() → None

Reset learnable parameters.