pyagc.encoders.SGFormer

class SGFormer(in_channels: int, hidden_channels: int, out_channels: int, trans_num_layers: int = 2, trans_num_heads: int = 1, trans_dropout: float = 0.5, gnn_num_layers: int = 3, gnn_dropout: float = 0.5, graph_weight: float = 0.5, aggregate: str = 'add')

Bases: Module

The sgformer module from the “SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations” paper.

SGFormer integrates a global attention module and a GNN module to jointly capture: - global all-pair node interactions (Transformer-style attention) - local structural information (GNN message passing)

1. Simplified Global Attention

Given input node features \(Z^{(0)} \in \mathbb{R}^{N \times d}\):

\[Q = f_Q(Z^{(0)}), \quad K = f_K(Z^{(0)}), \quad V = f_V(Z^{(0)})\]

Normalize:

\[\tilde{Q} = \frac{Q}{\|Q\|_F}, \quad \tilde{K} = \frac{K}{\|K\|_F}\]

Define diagonal normalization:

\[D = \operatorname{diag}\left(1 + \frac{1}{N} \tilde{Q}(\tilde{K}^\top \mathbf{1}) \right)\]

The attention output is:

\[Z = \beta D^{-1} \left( V + \frac{1}{N} \tilde{Q}(\tilde{K}^\top V) \right) + (1 - \beta) Z^{(0)}\]

This formulation achieves linear complexity :math:`O(N)` compared to \(O(N^2)\) in standard Transformers :contentReference[oaicite:0]{index=0}.

2. GNN-based Local Propagation

Structural information is incorporated via a GNN:

\[Z_{\text{gnn}} = \mathrm{GN}(Z^{(0)}, A)\]

where \(A\) is the adjacency matrix.

3. Aggregation Strategy

The global and local representations are combined as:

(a) Weighted sum (add):

\[Z_{\text{out}} = (1 - \alpha) Z + \alpha Z_{\text{gnn}}\]

(b) Concatenation (cat):

\[Z_{\text{out}} = [Z \, \| \, Z_{\text{gnn}}]\]

4. Output Layer

\[\hat{Y} = f_O(Z_{\text{out}})\]

where \(f_O\) is a linear projection.

Parameters:

• in_channels (int) – Input channels.

• hidden_channels (int) – Hidden channels.

• out_channels (int) – Output channels.

• trans_num_layers (int) – The number of layers for all-pair attention. (default: 2)

• trans_num_heads (int) – The number of heads for attention. (default: 1)

• trans_dropout (float) – Global dropout rate. (default: 0.5)

• gnn_num_layers (int) – The number of layers for GNN. (default: 3)

• gnn_dropout (float) – GNN dropout rate. (default: 0.5)

• graph_weight (float) – The weight balance global and gnn module. (default: 0.5)

• aggregate (str) – Aggregate type. (default: add)

__init__(in_channels: int, hidden_channels: int, out_channels: int, trans_num_layers: int = 2, trans_num_heads: int = 1, trans_dropout: float = 0.5, gnn_num_layers: int = 3, gnn_dropout: float = 0.5, graph_weight: float = 0.5, aggregate: str = 'add')

Initialize internal Module state, shared by both nn.Module and ScriptModule.

Methods

__init__(in_channels, hidden_channels, ...)	Initialize internal Module state, shared by both nn.Module and ScriptModule.
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[, batch])	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()	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()	rtype: None
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.
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	alias of TypeVar('T_destination', bound=dict[str, Any])
call_super_init
dump_patches

reset_parameters() → None

Return type:

None

forward(x: Tensor, edge_index: Tensor, batch: Optional[Tensor] = None) → Tensor

Forward pass.

Parameters:

• x (torch.Tensor) – The input node features.

• edge_index (torch.Tensor or SparseTensor) – The edge indices.

• batch (torch.Tensor, optional) – The batch vector \(\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N\), which assigns each element to a specific example.

Return type:

Tensor