pyagc.clusters.SBMClusterHead

class SBMClusterHead(n_clusters: int, n_features: int, variant: str = 'bernoulli', eta: float = 3.0)

Bases: BaseClusterHead

Stochastic Block Model (SBM) Clustering Head from the paper “Differentiable Community Detection with Graph Neural Networks and Stochastic Block Models” (Arliss & Mueller, LoG 2025).

This head learns cluster assignments by maximizing the likelihood of an SBM-based generative model. It supports both Bernoulli and Poisson variants, with optional degree correction.

The cluster assignment matrix \(\mathbf{P} \in [0,1]^{N \times K}\) is obtained via softmax transformation of the similarity between node embeddings and learnable cluster centers, and the structure matrix \(\mathbf{\Theta} \in \mathbb{R}^{K \times K}\) is estimated via MLE as:

\[\hat{\Theta}_{ij} = \frac{M_{ij}}{n_i n_j}\]

where \(M_{ij}\) is the number of edges between communities \(i\) and \(j\), and \(n_i\) is the number of nodes in community \(i\).

Loss Functions:

(1) Bernoulli SBM:

\[\mathcal{L}_B = -\sum_{(u,v) \in E} \ln(\pi_{uv}) - \eta^{-1} \sum_{(u,v) \notin E} \ln(1 - \pi_{uv})\]

where \(\pi_{uv} = \mathbf{P}_u^T \hat{\Theta} \mathbf{P}_v\).

(2) Poisson SBM:

\[\mathcal{L}_P = -\sum_{(u,v) \in E} [\ln(\pi_{uv}) - \pi_{uv}] + \eta^{-1} \sum_{(u,v) \notin E} \pi_{uv}\]

(3) Degree-Corrected variants:

For degree correction, the expected value becomes \(\phi_u \phi_v \mathbf{P}_u^T \hat{\Theta} \mathbf{P}_v\), where:

\[\hat{\phi}_u = (\mathbf{P}_u^T \mathbf{n}) \frac{d_u}{\mathbf{P}_u^T \boldsymbol{\delta}}\]

with \(\boldsymbol{\delta}\) being the sum of degrees in each community.

Parameters:

• n_clusters (int) – Number of clusters.

• n_features (int) – Feature dimension of input node embeddings.

• variant (str, optional) – SBM variant to use. Options: 'bernoulli', 'poisson', 'bernoulli-dc', 'poisson-dc'. (default: 'bernoulli')

• eta (float, optional) – Negative sampling ratio (number of negative samples per positive edge). (default: 3.0)

__init__(n_clusters: int, n_features: int, variant: str = 'bernoulli', eta: float = 3.0)

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

Methods

__init__(n_clusters, n_features[, variant, eta])	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.
cluster(z[, soft])	Predicts cluster assignments.
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(z, edge_index[, num_neg_samples])	Computes the SBM loss.
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_cluster_centers([cluster_centers])	Manually sets the cluster centers.
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
predict	Alias for cluster().

reset_cluster_centers(cluster_centers: Optional[Tensor] = None) → None

Manually sets the cluster centers.

Parameters:

cluster_centers (torch.Tensor, optional) – Tensor of shape (n_clusters, n_features) to initialize the cluster centers. If None, use Xavier uniform initialization.

Return type:

None

forward(z: Tensor, edge_index: Tensor, num_neg_samples: Optional[int] = None) → Tuple[Tensor, Tensor]

Computes the SBM loss.

Parameters:

• z (torch.Tensor) – Node embeddings of shape (N, F).

• edge_index (torch.Tensor) – Edge indices of shape (2, E).

• num_neg_samples (int, optional) – Number of negative samples. If None, uses eta * num_edges. (default: None)

Returns:

Tuple[Tensor, Tensor] – Tuple of (likelihood_loss, regularization_loss).

cluster(z: Tensor, soft: bool = False) → Tensor

Predicts cluster assignments.

Parameters:

• z (torch.Tensor) – Node embeddings of shape (N, F).

• soft (bool, optional) – If True, returns soft assignments; otherwise hard assignments. (default: False)

Returns:

Tensor – Cluster assignments.