sheaf_mpnn.nsd.NSDModel#

class NSDModel[source]#

Bases: Module

End-to-end Neural Sheaf Diffusion (NSD) model.

The wrapper lifts raw node features into stalk features, applies a stack of NSD convolution layers, and decodes the flattened stalk representation back to the requested output dimension.

Parameters:

  • in_channels (int)

  • out_channels (int)

  • stalk_dim (int, default: 4)

  • hidden_dim (int, default: 16)

  • num_layers (int, default: 2)

  • variant (NSDVariant, default: <NSDVariant.GENERAL: 2>)

  • alpha (float, default: 1.0)

  • add_self_loops (bool, default: False)

  • orth_strategy (Literal['cayley', 'fasth', 'fasthpp', 'householder'], default: 'cayley')

  • rank (int, default: 1)

  • add_eps (bool, default: True)

  • input_dropout (float, default: 0.0)

  • dropout (float, default: 0.0)

  • normalize_output (bool, default: False)

  • jknet (bool, default: False)

  • add_lp (bool, default: False)

  • add_hp (bool, default: False)

  • sparse_learner (bool, default: False)

  • second_linear (bool, default: False)

  • use_edge_weights (bool, default: False)

  • learn_alpha (bool, default: True)

__init__(in_channels, out_channels, stalk_dim=4, hidden_dim=16, num_layers=2, variant=NSDVariant.GENERAL, alpha=1.0, add_self_loops=False, orth_strategy='cayley', rank=1, add_eps=True, input_dropout=0.0, dropout=0.0, normalize_output=False, jknet=False, add_lp=False, add_hp=False, sparse_learner=False, second_linear=False, use_edge_weights=False, learn_alpha=True)[source]#

Initializes an NSD model for node-level prediction.

Parameters:

  • in_channels (int) – Number of raw input features per node.

  • out_channels (int) – Number of output channels per node (e.g. num classes).

  • stalk_dim (int, default: 4) – Stalk dimension. Each node is represented internally as a matrix with shape [stalk_dim, hidden_dim].

  • hidden_dim (int, default: 16) – Feature dimension inside each stalk channel. The encoded node state has size d * hidden_dim.

  • num_layers (int, default: 2) – Number of NSD convolution layers. Must be positive.

  • variant (NSDVariant, default: NSDVariant.GENERAL) – Restriction-map family. DIAGONAL is cheapest, GENERAL is most expressive, ORTHOGONAL uses orthogonal maps (via Cayley or Householder parameterisation). GENERAL_ATTENTION and ORTHOGONAL_ATTENTION use an attention-based map initialisation.

  • alpha (float, default: 1.0) – Initial diffusion step size per layer. Defaults to 1.0, matching the reference update at init.

  • learn_alpha (bool, default: True) – If False, alpha stays fixed at its initial value (Bodnar-exact update: no step-size parameter); if True it is learned. Defaults to True.

  • add_self_loops (bool, default: False) – If True, self-loops are added to the graph before computing degree normalization in each layer. Defaults to False: the +1/+I degree augmentation now lives inside the normalization itself, so adding self-loops would augment twice.

  • orth_strategy (Literal['cayley', 'fasth', 'fasthpp', 'householder'], default: "cayley") – Orthogonality strategy for the ORTHOGONAL variant: “cayley”, “fasth”, “fasthpp”, or “householder” (reference orgqr; fasthpp computes the same map natively). Defaults to “cayley”.

  • rank (int, default: 1) – Rank of each restriction map for the LOW_RANK variant. Must be positive. Ignored for other variants. Defaults to 1.

  • add_eps (bool, default: True) – If True, each layer applies a learnable per-stalk rescaling eps in R^d to the skip term (Remark 4). Defaults to True (reference parity: the original NSD always gates the skip with 1 + tanh(eps), eps initialized at zero).

  • input_dropout (float, default: 0.0) – Dropout probability applied to raw input features before encoding. Defaults to 0.0.

  • dropout (float, default: 0.0) – Dropout probability applied to stalk features between layers. Defaults to 0.0.

  • normalize_output (bool, default: False) – If True, L2-normalise the representation before the decoder (Lv et al., 2021). If jknet is True, each layer’s output is also normalised before concatenation. Defaults to False (reference parity: the original NSD decodes the raw representation).

  • jknet (bool, default: False) – If True, collect hidden states from every layer and concatenate them before the decoder (Xu et al., 2018). Normalization is controlled by normalize_output. Intended for link prediction. Defaults to False.

  • add_lp (bool, default: False) – Appends one fixed stalk channel diffusing with the signless Laplacian D+A (reference --add_lp).

  • add_hp (bool, default: False) – Appends one fixed stalk channel diffusing with the standard Laplacian D-A (reference --add_hp).

  • sparse_learner (bool, default: False) – Stalk-summed map-generator input (reference LocalConcatSheafLearnerVariant), shrinking the learner from 2*final_d*hidden to 2*hidden inputs.

  • second_linear (bool, default: False) – Adds a second encoder linear after the ELU+dropout stage (reference --second_linear).

  • use_edge_weights (bool, default: False) – Learned symmetric per-edge scalars rescaling orthogonal maps (reference edge_weights). Defaults to False.

Methods

__init__(in_channels, out_channels[, ...])

Initializes an NSD model for node-level prediction.

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, edge_index)

Runs the NSD encoder, diffusion layers, and decoder.

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()

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()

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, ...])

to(*args, **kwargs)

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.

Attributes

T_destination

call_super_init

dump_patches

training

__init__(in_channels, out_channels, stalk_dim=4, hidden_dim=16, num_layers=2, variant=NSDVariant.GENERAL, alpha=1.0, add_self_loops=False, orth_strategy='cayley', rank=1, add_eps=True, input_dropout=0.0, dropout=0.0, normalize_output=False, jknet=False, add_lp=False, add_hp=False, sparse_learner=False, second_linear=False, use_edge_weights=False, learn_alpha=True)[source]#

Initializes an NSD model for node-level prediction.

Parameters:

  • in_channels (int) – Number of raw input features per node.

  • out_channels (int) – Number of output channels per node (e.g. num classes).

  • stalk_dim (int, default: 4) – Stalk dimension. Each node is represented internally as a matrix with shape [stalk_dim, hidden_dim].

  • hidden_dim (int, default: 16) – Feature dimension inside each stalk channel. The encoded node state has size d * hidden_dim.

  • num_layers (int, default: 2) – Number of NSD convolution layers. Must be positive.

  • variant (NSDVariant, default: NSDVariant.GENERAL) – Restriction-map family. DIAGONAL is cheapest, GENERAL is most expressive, ORTHOGONAL uses orthogonal maps (via Cayley or Householder parameterisation). GENERAL_ATTENTION and ORTHOGONAL_ATTENTION use an attention-based map initialisation.

  • alpha (float, default: 1.0) – Initial diffusion step size per layer. Defaults to 1.0, matching the reference update at init.

  • learn_alpha (bool, default: True) – If False, alpha stays fixed at its initial value (Bodnar-exact update: no step-size parameter); if True it is learned. Defaults to True.

  • add_self_loops (bool, default: False) – If True, self-loops are added to the graph before computing degree normalization in each layer. Defaults to False: the +1/+I degree augmentation now lives inside the normalization itself, so adding self-loops would augment twice.

  • orth_strategy (Literal['cayley', 'fasth', 'fasthpp', 'householder'], default: "cayley") – Orthogonality strategy for the ORTHOGONAL variant: “cayley”, “fasth”, “fasthpp”, or “householder” (reference orgqr; fasthpp computes the same map natively). Defaults to “cayley”.

  • rank (int, default: 1) – Rank of each restriction map for the LOW_RANK variant. Must be positive. Ignored for other variants. Defaults to 1.

  • add_eps (bool, default: True) – If True, each layer applies a learnable per-stalk rescaling eps in R^d to the skip term (Remark 4). Defaults to True (reference parity: the original NSD always gates the skip with 1 + tanh(eps), eps initialized at zero).

  • input_dropout (float, default: 0.0) – Dropout probability applied to raw input features before encoding. Defaults to 0.0.

  • dropout (float, default: 0.0) – Dropout probability applied to stalk features between layers. Defaults to 0.0.

  • normalize_output (bool, default: False) – If True, L2-normalise the representation before the decoder (Lv et al., 2021). If jknet is True, each layer’s output is also normalised before concatenation. Defaults to False (reference parity: the original NSD decodes the raw representation).

  • jknet (bool, default: False) – If True, collect hidden states from every layer and concatenate them before the decoder (Xu et al., 2018). Normalization is controlled by normalize_output. Intended for link prediction. Defaults to False.

  • add_lp (bool, default: False) – Appends one fixed stalk channel diffusing with the signless Laplacian D+A (reference --add_lp).

  • add_hp (bool, default: False) – Appends one fixed stalk channel diffusing with the standard Laplacian D-A (reference --add_hp).

  • sparse_learner (bool, default: False) – Stalk-summed map-generator input (reference LocalConcatSheafLearnerVariant), shrinking the learner from 2*final_d*hidden to 2*hidden inputs.

  • second_linear (bool, default: False) – Adds a second encoder linear after the ELU+dropout stage (reference --second_linear).

  • use_edge_weights (bool, default: False) – Learned symmetric per-edge scalars rescaling orthogonal maps (reference edge_weights). Defaults to False.

reset_parameters()[source]#
forward(x, edge_index)[source]#

Runs the NSD encoder, diffusion layers, and decoder.

Parameters:

  • x (Tensor) – Raw node features with shape [num_nodes, in_channels].

  • edge_index (Tensor) – Graph connectivity in COO format with shape [2, num_edges].

Returns:

Node outputs with shape [num_nodes, out_channels].

Return type:

Tensor