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

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.