sheaf_mpnn.nsd.OrthogonalNSDConv

class OrthogonalNSDConv

Bases: BaseNSDConv

Orthogonal NSD convolution layer.

Parameters:

• stalk_dim (int)

• in_channels (int)

• hidden_dim (int)

• alpha (float, default: 1.0)

• context_dim (int | None, default: None)

• add_self_loops (bool, default: True)

• clamp_val (float, default: 10.0)

• use_attention (bool, default: False)

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

__init__(stalk_dim, in_channels, hidden_dim, alpha=1.0, context_dim=None, add_self_loops=True, clamp_val=10.0, use_attention=False, orth_strategy='cayley')

Initializes an orthogonal NSD convolution layer.

The map generator outputs parameters for either: (1) entries of a skew-symmetric matrix (cayley), (2) Householder vectors (fasth), or (3) attention-based mappings. All parameterisations produce orthogonal d x d restriction maps.

Parameters:

• stalk_dim (int) – Stalk dimension and orthogonal restriction-map matrix size.

• in_channels (int) – Feature dimension inside each stalk channel.

• hidden_dim (int) – Hidden width of the restriction-map generator MLP.

• alpha (float, default: 1.0) – Initial learnable diffusion step size. Defaults to 1.0.

• context_dim (int | None, default: None) – Width of x_feat. Defaults to d * in_channels when omitted.

• add_self_loops (bool, default: True) – If True, self-loops augment the degree used for normalization. Defaults to True.

• clamp_val (float, default: 10.0) – Maximum absolute value for clamping Cayley-transform parameters. Defaults to 10.0.

• use_attention (bool, default: False) – If True, uses the attention-based Cayley initialization from main. Defaults to False.

• orth_strategy (Literal['cayley', 'fasth'], default: "cayley") – “cayley” or “fasth”. Defaults to “cayley”.

Methods

__init__(stalk_dim, in_channels, hidden_dim)	Initializes an orthogonal NSD convolution layer.
add_module(name, module)	Add a child module to the current module.
aggregate(inputs, index[, ptr, dim_size])	Aggregates messages from neighbors as \(\bigoplus_{j \in \mathcal{N}(i)}\).
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.
edge_update()	Computes or updates features for each edge in the graph.
edge_updater(edge_index[, size])	The initial call to compute or update features for each edge in the graph.
eval()	Set the module in evaluation mode.
explain_message(inputs, dim_size)
extra_repr()	Return the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
forward(x_feat, x_stalk, edge_index)	Applies one NSD diffusion step to lifted node features.
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_map_products(x_feat, edge_index)	Precompute self_map and cross_map restriction-map products per edge.
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.
jittable([typing])	Analyzes the MessagePassing instance and produces a new jittable module that can be used in combination with torch.jit.script().
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
message(z_dst, z_src, self_map, cross_map)	Builds per-edge sheaf Laplacian messages.
message_and_aggregate(edge_index)	Fuses computations of message() and aggregate() into a single function.
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.
propagate(edge_index[, size])	The initial call to start propagating messages.
register_aggregate_forward_hook(hook)	Registers a forward hook on the module.
register_aggregate_forward_pre_hook(hook)	Registers a forward pre-hook on the module.
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_edge_update_forward_hook(hook)	Registers a forward hook on the module.
register_edge_update_forward_pre_hook(hook)	Registers a forward pre-hook on 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_message_and_aggregate_forward_hook(hook)	Registers a forward hook on the module.
register_message_and_aggregate_forward_pre_hook(hook)	Registers a forward pre-hook on the module.
register_message_forward_hook(hook)	Registers a forward hook on the module.
register_message_forward_pre_hook(hook)	Registers a forward pre-hook on the module.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_propagate_forward_hook(hook)	Registers a forward hook on the module.
register_propagate_forward_pre_hook(hook)	Registers a forward pre-hook on 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()	Resets all learnable parameters of the 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, ...])
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.
update(inputs)	Updates node embeddings in analogy to \(\gamma_{\mathbf{\Theta}}\) for each node \(i \in \mathcal{V}\).
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

Attributes

SUPPORTS_FUSED_EDGE_INDEX
T_destination
call_super_init
decomposed_layers
dump_patches
explain
special_args
training

__init__(stalk_dim, in_channels, hidden_dim, alpha=1.0, context_dim=None, add_self_loops=True, clamp_val=10.0, use_attention=False, orth_strategy='cayley')

Initializes an orthogonal NSD convolution layer.

The map generator outputs parameters for either: (1) entries of a skew-symmetric matrix (cayley), (2) Householder vectors (fasth), or (3) attention-based mappings. All parameterisations produce orthogonal d x d restriction maps.

Parameters:

• stalk_dim (int) – Stalk dimension and orthogonal restriction-map matrix size.

• in_channels (int) – Feature dimension inside each stalk channel.

• hidden_dim (int) – Hidden width of the restriction-map generator MLP.

• alpha (float, default: 1.0) – Initial learnable diffusion step size. Defaults to 1.0.

• context_dim (int | None, default: None) – Width of x_feat. Defaults to d * in_channels when omitted.

• add_self_loops (bool, default: True) – If True, self-loops augment the degree used for normalization. Defaults to True.

• clamp_val (float, default: 10.0) – Maximum absolute value for clamping Cayley-transform parameters. Defaults to 10.0.

• use_attention (bool, default: False) – If True, uses the attention-based Cayley initialization from main. Defaults to False.

• orth_strategy (Literal['cayley', 'fasth'], default: "cayley") – “cayley” or “fasth”. Defaults to “cayley”.

get_map_products(x_feat, edge_index)

Precompute self_map and cross_map restriction-map products per edge.

message(z_dst, z_src, self_map, cross_map)

Builds per-edge sheaf Laplacian messages.

Parameters:

• z_dst (Tensor) – Destination-node transformed stalks [E, d, f].

• z_src (Tensor) – Source-node transformed stalks [E, d, f].

• self_map (Tensor) – Normalized F_dst^T F_dst per edge [E, d, d].

• cross_map (Tensor) – Normalized F_dst^T F_src per edge [E, d, d].

Returns:

Per-edge messages [E, d, f].

Return type:

Tensor