Unigcn_Layer

Implementation of UniGCN layer from Huang et. al.: UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks.

class topomodelx.nn.hypergraph.unigcn_layer.UniGCNLayer(in_channels, hidden_channels, aggr_norm: bool = False, use_bn: bool = False, **kwargs)

Layer of UniGCN.

Implementation of UniGCN layer proposed in [1].

Parameters:

in_channelsint

Dimension of the input features.

hidden_channelsint

Dimension of the hidden features.

aggr_normbool, default=False

Whether to normalize the aggregated message by the neighborhood size.

use_bnbool, default=False

Whether to use bathnorm after the linear transformation.

**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, incidence_1)	[1]_ initially proposed the 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()	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]

Huang and Yang. UniGNN: a unified framework for graph and hypergraph neural networks. IJCAI 2021. https://arxiv.org/pdf/2105.00956.pdf

[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, incidence_1)

[1]_ initially proposed the forward pass.

Its equations are given in [2]_ and graphically illustrated in [3]_.

The forward pass of this layer is composed of three steps.

First, every hyper-edge sums up the features of its constituent edges:

\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow z}^{(0 \rightarrow 1)} = B_1^T \cdot h_y^{t, (0)}\\ &🟧 \quad m_z^{(0 \rightarrow 1)} = \sum_{y \in \mathcal{B}(z)} m_{y \rightarrow z}^{(0 \rightarrow 1)}\\ \end{align*}\end{split}\]

Second, the message to the nodes is the sum of the messages from the incident hyper-edges:

\[\begin{split}\begin{align*} &🟥 \quad m_{z \rightarrow x}^{(1 \rightarrow 0)} = B_1^{t,(1)} \cdot w^{(1)} \cdot m_z^{(0 \rightarrow 1)} \cdot \Theta^t\\ &🟧 \quad m_x^{(1 \rightarrow 0)} = \sum_{y \in \mathcal{C}(x)} m_{z \rightarrow x}^{(1 \rightarrow 0)}\\ \end{align*}\end{split}\]

Third, the node features are updated:

\[\begin{split}\begin{align*} &🟩 \quad m_x^{(0)} = m_x^{(1\rightarrow0)}\\ &🟦 \quad h_x^{t+1,(0)} = m_x^{(0)} \end{align*}\end{split}\]

Parameters:

x_0torch.Tensor, shape = (n_nodes, in_channels)

Input features on the nodes of the hypergraph.

incidence_1torch.sparse, shape = (n_nodes, n_edges)

Incidence matrix mapping edges to nodes (B_1).

Returns:

x_0torch.Tensor

Output node features.

x_1torch.Tensor

Output hyperedge features.

reset_parameters() → None

Reset learnable parameters.