HNHN_Layer

Template Layer with two conv passing steps.

class topomodelx.nn.hypergraph.hnhn_layer.HNHNLayer(in_channels, hidden_channels, incidence_1=None, use_bias: bool = True, use_normalized_incidence: bool = True, alpha: float = -1.5, beta: float = -0.5, bias_gain: float = 1.414, bias_init: Literal['xavier_uniform', 'xavier_normal'] = 'xavier_uniform', **kwargs)

Layer of a Hypergraph Networks with Hyperedge Neurons (HNHN).

Implementation of a simplified version of the HNHN layer proposed in [1].

This layer is composed of two convolutional layers: 1. A convolutional layer sending messages from edges to nodes. 2. A convolutional layer sending messages from nodes to edges. The incidence matrices can be normalized usign the node and edge cardinality. Two hyperparameters alpha and beta, control the normalization strenght. The convolutional layers support the training of a bias term.

Parameters:

in_channelsint

Dimension of node features.

hidden_channelsint

Dimension of hidden features.

incidence_1torch.sparse, shape = (n_nodes, n_edges)

Incidence matrix mapping edges to nodes (B_1).

use_biasbool

Flag controlling whether to use a bias term in the convolution.

use_normalized_incidencebool

Flag controlling whether to normalize the incidence matrices.

alphafloat

Scalar controlling the importance of edge cardinality.

betafloat

Scalar controlling the importance of node cardinality.

bias_gainfloat

Gain for the bias initialization.

bias_initLiteral[“xavier_uniform”, “xavier_normal”], default=”xavier_uniform”

Controls the bias initialization method.

**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().
compute_normalization_matrices()	Compute the normalization matrices for the incidence matrices.
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])	Forward computation.
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.
init_biases()	Initialize the bias.
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.
normalize_incidence_matrices()	Normalize the incidence matrices.
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__

Notes

This is the architecture proposed for node classification.

References

[1]

Dong, Sawin, Bengio. HNHN: hypergraph networks with hyperedge neurons. Graph Representation Learning and Beyond Workshop at ICML 2020. https://grlplus.github.io/papers/40.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.

compute_normalization_matrices() → None

Compute the normalization matrices for the incidence matrices.

forward(x_0, incidence_1=None)

Forward computation.

The forward pass was initially proposed in [1]_. Its equations are given in [2]_ and graphically illustrated in [3]_.

The equations of one layer of this neural network are given by:

\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow x}^{(0 \rightarrow 1)} = \sigma((B_1^T \cdot W^{(0)})_{xy} \cdot h_y^{t,(0)} \cdot \Theta^{t,(0)} + b^{t,(0)})\\ &🟥 \quad m_{y \rightarrow x}^{(1 \rightarrow 0)} = \sigma((B_1 \cdot W^{(1)})_{xy} \cdot h_y^{t,(1)} \cdot \Theta^{t,(1)} + b^{t,(1)})\\ &🟧 \quad m_x^{(0 \rightarrow 1)} = \sum_{y \in \mathcal{B}(x)} m_{y \rightarrow x}^{(0 \rightarrow 1)}\\ &🟧 \quad m_x^{(1 \rightarrow 0)} = \sum_{y \in \mathcal{C}(x)} m_{y \rightarrow x}^{(1 \rightarrow 0)}\\ &🟩 \quad m_x^{(0)} = m_x^{(1 \rightarrow 0)}\\ &🟩 \quad m_x^{(1)} = m_x^{(0 \rightarrow 1)}\\ &🟦 \quad h_x^{t+1,(0)} = m_x^{(0)}\\ &🟦 \quad h_x^{t+1,(1)} = m_x^{(1)} \end{align*}\end{split}\]

Parameters:

x_0torch.Tensor, shape = (n_nodes, channels_node)

Input features on the hypernodes.

incidence_1torch.Tensor, shape = (n_nodes, n_edges)

Incidence matrix mapping edges to nodes (B_1).

Returns:

x_0torch.Tensor, shape = (n_nodes, channels_node)

Output features on the hypernodes.

x_1torch.Tensor, shape = (n_edges, channels_edge)

Output features on the hyperedges.

init_biases() → None

Initialize the bias.

normalize_incidence_matrices() → None

Normalize the incidence matrices.

reset_parameters() → None

Reset learnable parameters.