pyagc.clusters.NeuromapClusterHead

class NeuromapClusterHead(n_clusters: int, n_features: int, alpha: float = 0.15, n_iters: int = 100)[source]

Bases: BaseClusterHead

Neuromap Clustering Head from the paper “The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks” paper (Blöcker et al., NeurIPS 2024).

This module implements a differentiable version of the map equation for end-to-end optimization with (graph) neural networks.

It learns soft cluster assignments \(\mathbf{S}\) via a linear projection from node embeddings \(\mathbf{Z}\), and computes the Neuromap loss (expected per-step description length) following the Minimum Description Length principle:

\[\mathcal{L}(A, S) = q \log q - \sum_m q_m \log q_m - \sum_m m_{\text{exit}} \log m_{\text{exit}} - \sum_u p_u \log p_u + \sum_m p_m \log p_m\]

where all quantities are computed from the soft cluster assignment matrix.

Parameters:

  • n_clusters (int) – Maximum number of clusters.

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

  • alpha (float, optional) – Teleportation probability for flow. Default: 0.15.

  • n_iters (int, optional) – Number of power iterations for stationary distribution. Default: 100.

__init__(n_clusters: int, n_features: int, alpha: float = 0.15, n_iters: int = 100)[source]

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

Methods

__init__(n_clusters, n_features[, alpha, ...])

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.

build_flow(edge_index, N)

Construct sparse flow matrix F and stationary distribution p.

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)

Compute the Neuromap (Map Equation) loss given node embeddings and adjacency.

forward0(z, edge_index)

Compute the Neuromap (Map Equation) loss given node embeddings and adjacency.

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[source]

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

build_flow(edge_index: Tensor, N: int)[source]

Construct sparse flow matrix F and stationary distribution p.

forward0(z: Tensor, edge_index: Tensor) → Tensor[source]

Compute the Neuromap (Map Equation) loss given node embeddings and adjacency.

Parameters:
Returns:

Map equation loss (codelength)

Return type:

torch.Tensor

forward(z: Tensor, edge_index: Tensor) → Tuple[Tensor, Tensor][source]

Compute the Neuromap (Map Equation) loss given node embeddings and adjacency.

Parameters:
Returns:

Map equation loss (codelength) and collapse_loss

Return type:

Tuple[torch.Tensor, torch.Tensor]

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

Predicts cluster assignments.

Parameters:

  • z (torch.Tensor) – Input tensor of shape (n_samples, n_features).

  • soft (bool, optional) – If True, returns the soft assignment matrix; if False, returns hard cluster assignments. (default: False)

Returns:

Tensor –:

  • If soft is False, (n_samples,) tensor of cluster indices.

  • If soft is True, (n_samples, n_clusters) tensor of probabilities.