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.

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)	Forward pass.
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.
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.
update(inputs)	Update (Step 4).
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

__call__

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.

Methods

add_module(name, module)	Add a child module to the current module.
aggregate(x_messages[, mode])	Aggregate messages on each target cell.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
attention(x_source[, x_target])	Compute attention weights for messages.
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, incidence)	Forward pass ([2]_ and [3]_).
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.
message(x_source[, x_target])	Construct message from source cells to target cells.
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 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.
update(x_message_on_target)	Update embeddings on each node (step 4).
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]

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.