Hypersage_Layer

HyperSAGE layer.

class topomodelx.nn.hypergraph.hypersage_layer.GeneralizedMean(power: int = 2, **kwargs)

Generalized mean aggregation layer.

Parameters:

powerint, default=2

Power for the generalized mean.

**kwargskeyword arguments, optional

Arguments for the base aggregation layer.

forward(x: Tensor)

Forward pass.

Parameters:

xtorch.Tensor

Input features.

Returns:

torch.Tensor

Output features.

class topomodelx.nn.hypergraph.hypersage_layer.HyperSAGELayer(in_channels: int, out_channels: int, alpha: int = -1, aggr_func_intra: Aggregation | None = None, aggr_func_inter: Aggregation | None = None, update_func: Literal['relu', 'sigmoid'] = 'relu', initialization: Literal['uniform', 'xavier_uniform', 'xavier_normal'] = 'uniform', device: str = 'cpu', **kwargs)

Implementation of the HyperSAGE layer proposed in [1].

Parameters:

in_channelsint

Dimension of the input features.

out_channelsint

Dimension of the output features.

alphaint, default=-1

Max number of nodes in a neighborhood to consider. If -1 it considers all the nodes.

aggr_func_intracallable, default=GeneralizedMean(p=2)

Aggregation function. Default is GeneralizedMean(p=2).

aggr_func_intercallable, default=GeneralizedMean(p=2)

Aggregation function. Default is GeneralizedMean(p=2).

update_funcLiteral[“relu”, “sigmoid”], default=”relu”

Update method to apply to message.

initializationLiteral[“uniform”, “xavier_uniform”, “xavier_normal”], default=”uniform”

Initialization method.

devicestr, default=”cpu”

Device name to train layer on.

**kwargsoptional

Additional arguments for the layer modules.

References

[1]

Arya, Gupta, Rudinac and Worring. HyperSAGE: Generalizing inductive representation learning on hypergraphs (2020). https://arxiv.org/abs/2010.04558

[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

aggregate(x_messages: Tensor, mode: str = 'intra')

Aggregate messages on each target cell.

A target cell receives messages from several source cells. This function aggregates these messages into a single output feature per target cell.

This function corresponds to either intra- or inter-aggregation.

Parameters:

x_messagesTensor, shape = (…, n_messages, out_channels)

Features associated with each message. One message is sent from a source cell to a target cell.

modestr, default = “inter”

The mode on which aggregation to compute. If set to “inter”, will compute inter-aggregation, if set to “intra”, will compute intra-aggregation (see [1]).

Returns:

Tensor, shape = (…, n_target_cells, out_channels)

Output features on target cells. Each target cell aggregates messages from several source cells. Assumes that all target cells have the same rank s.

forward(x: Tensor, incidence: Tensor)

Forward pass ([2]_ and [3]_).

\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow z}^{(0 \rightarrow 1)} = (B_1)^T_{zy} \cdot w_y \cdot (h_y^{(0)})^p\\ &🟥 \quad m_z^{(0 \rightarrow 1)} = \left(\frac{1}{\vert \mathcal{B}(z)\vert}\sum_{y \in \mathcal{B}(z)} m_{y \rightarrow z}^{(0 \rightarrow 1)}\right)^{\frac{1}{p}}\\ &🟥 \quad m_{z \rightarrow x}^{(1 \rightarrow 0)} = (B_1)_{xz} \cdot w_z \cdot (m_z^{(0 \rightarrow 1)})^p\\ &🟧 \quad m_x^{(1,0)} = \left(\frac{1}{\vert \mathcal{C}(x) \vert}\sum_{z \in \mathcal{C}(x)} m_{z \rightarrow x}^{(1 \rightarrow 0)}\right)^{\frac{1}{p}}\\ &🟩 \quad m_x^{(0)} = m_x^{(1 \rightarrow 0)}\\ &🟦 \quad h_x^{t+1, (0)} = \sigma \left(\frac{m_x^{(0)} + h_x^{t,(0)}}{\lvert m_x^{(0)} + h_x^{t,(0)}\rvert} \cdot \Theta^t\right) \end{align*}\end{split}\]

Parameters:

xtorch.Tensor

Input features.

incidencetorch.Tensor

Incidence matrix between node/hyperedges.

Returns:

torch.Tensor

Output features.

update(x_message_on_target: Tensor) → Tensor

Update embeddings on each node (step 4).

Parameters:

x_message_on_targettorch.Tensor, shape = (n_target_nodes, out_channels)

Output features on target nodes.

Returns:

torch.Tensor, shape = (n_target_nodes, out_channels)

Updated output features on target nodes.