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

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.