Unigcnii_Layer

UniGCNII layer implementation.

class topomodelx.nn.hypergraph.unigcnii_layer.UniGCNIILayer(in_channels, hidden_channels, alpha: float, beta: float, use_norm=False, **kwargs)

Implementation of the UniGCNII layer [1].

Parameters:

in_channelsint

Dimension of the input features.

hidden_channelsint

Dimension of the hidden features.

alphafloat

The alpha parameter determining the importance of the self-loop (theta_2).

betafloat

The beta parameter determining the importance of the learned matrix (theta_1).

use_normbool, default=False

Whether to apply row normalization after the layer.

**kwargsoptional

Additional arguments for the layer modules.

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_0, incidence_1[, x_skip])	Forward pass of the UniGCNII layer.
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 the parameters of the 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.
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__

References

[1]

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

forward(x_0, incidence_1, x_skip=None)

Forward pass of the UniGCNII layer.

The forward pass consists of: - two messages, and - a skip connection with a learned update function.

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

\[\begin{split}\begin{align*} & 🟥 \quad m_{y \rightarrow z}^{(0 \rightarrow 1)} = (B^T_1)\_{zy} \cdot h^{t,(0)}_y \\ & 🟧 \quad m_z^{(0\rightarrow1)} = \sum_{y \in \mathcal{B}(z)} m_{y \rightarrow z}^{(0 \rightarrow 1)} \end{align*}\end{split}\]

Second, the second message is normalized with the node and edge degrees:

\[\begin{split}\begin{align*} & 🟥 \quad m_{z \rightarrow x}^{(1 \rightarrow 0)} = B_1 \cdot m_z^{(0 \rightarrow 1)} \\ & 🟧 \quad m_{x}^{(1\rightarrow0)} = \frac{1}{\sqrt{d_x}}\sum_{z \in \mathcal{C}(x)} \frac{1}{\sqrt{d_z}}m_{z \rightarrow x}^{(1\rightarrow0)} \\ \end{align*}\end{split}\]

Third, the computed message is combined with skip connections and a linear transformation using hyperparameters alpha and beta:

\[\begin{split}\begin{align*} & 🟩 \quad m_x^{(0)} = m_x^{(1 \rightarrow 0)} \\ & 🟦 \quad m_x^{(0)} = ((1-\beta)I + \beta W)((1-\alpha)m_x^{(0)} + \alpha \cdot h_x^{t,(0)}) \\ \end{align*}\end{split}\]

Parameters:

x_0torch.Tensor, shape = (num_nodes, in_channels)

Input features of the nodes of the hypergraph.

incidence_1torch.Tensor, shape = (num_nodes, num_edges)

Incidence matrix of the hypergraph. It is expected that the incidence matrix contains self-loops for all nodes.

x_skiptorch.Tensor, shape = (num_nodes, in_channels)

Original node features of the hypergraph used for the skip connections. If not provided, the input to the layer is used as a skip connection.

Returns:

x_0torch.Tensor

Output node features.

x_1torch.Tensor

Output hyperedge features.

reset_parameters() → None

Reset the parameters of the layer.