athena__duvenaud_msgpass

Module implementing Duvenaud message passing for molecular graphs

This module implements the graph neural network architecture from Duvenaud et al. (2015) for learning on molecular graphs with both vertex (node) and edge features.

Mathematical operation (per time step t): $h_v^{(t+1)} = \sigma\left( h_v^{(t)} + \sum_{u \in \mathcal{N}(v)} M(h_v^{(t)}, h_u^{(t)}, e_{vu}) \right)$

Graph readout (aggregation to fixed-size vector): $h_{\text{graph}} = \sigma_{\text{readout}}\left( \sum_{d=1}^D \sum_{v:\deg(v)=d} W_d h_v^{(T)} \right)$

where $M$ is a learned message function, $\sigma$ is activation function, $\mathcal{N}(v)$ are neighbors of $v$ , $e_{vu}$ are edge features, $W_d$ are degree-specific weight matrices, and $D$ is max vertex degree.

Reference: Duvenaud et al. (2015), NeurIPS

Uses

- diffstruc
- athena__msgpass_layer
- athena__base_layer
- coreutils
- graphstruc
- athena__diffstruc_extd
- athena__misc_types

Variables

Type	Visibility	Attributes		Name		Initial
character(len=*),	private,	parameter	::	default_message_actv_name	=	"sigmoid"
character(len=*),	private,	parameter	::	default_readout_actv_name	=	"softmax"

Interfaces

public interface duvenaud_msgpass_layer_type

Interface for setting up the MPNN layer

private module function layer_setup(num_vertex_features, num_edge_features, num_time_steps, max_vertex_degree, num_outputs, min_vertex_degree, message_activation, readout_activation, kernel_initialiser, verbose) result(layer)

Set up the message passing layer

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		dimension(:)	::	num_vertex_features	Number of vertex features
integer,	intent(in),		dimension(:)	::	num_edge_features	Number of edge features
integer,	intent(in)			::	num_time_steps	Number of time steps
integer,	intent(in)			::	max_vertex_degree	Maximum vertex degree
integer,	intent(in)			::	num_outputs	Number of outputs
integer,	intent(in),	optional		::	min_vertex_degree	Minimum vertex degree
class(*),	intent(in),	optional		::	message_activation	Message and readout activation functions
class(*),	intent(in),	optional		::	readout_activation	Message and readout activation functions
character(len=*),	intent(in),	optional		::	kernel_initialiser
integer,	intent(in),	optional		::	verbose	Kernel initialiser ! Kernel initialiser Verbosity level

Return Value type(duvenaud_msgpass_layer_type)

Instance of the message passing layer

Derived Types

type, public, extends(msgpass_layer_type) :: duvenaud_msgpass_layer_type

Components

Type	Visibility	Attributes		Name		Initial
class(base_actv_type),	public,	allocatable	::	activation			Activation function
class(base_actv_type),	public,	allocatable	::	activation_readout			Activation function
class(base_init_type),	public,	allocatable	::	bias_init			Initialisers for kernel and bias
character(len=14),	public		::	bias_initialiser	=	''	Initialisers for kernel and bias
integer,	public,	allocatable, dimension(:)	::	bias_shape			Shape of biases
type(graph_type),	public,	allocatable, dimension(:)	::	graph			Graph structure of input data
integer,	public		::	id			Unique identifier
logical,	public		::	inference	=	.false.	Inference mode
integer,	public		::	input_rank	=	0	Rank of input data
integer,	public,	allocatable, dimension(:)	::	input_shape			Input shape
class(base_init_type),	public,	allocatable	::	kernel_init			Initialisers for kernel and bias
character(len=14),	public		::	kernel_initialiser	=	''	Initialisers for kernel and bias
integer,	public		::	max_vertex_degree	=	0	Maximum vertex degree
integer,	public		::	min_vertex_degree	=	1
character(len=:),	public,	allocatable	::	name			Layer name
integer,	public,	dimension(:), allocatable	::	num_edge_features			Number of edge features for each time step
integer,	public		::	num_output_edge_features			Number of output edge features
integer,	public		::	num_output_vertex_features			Number of output vertex features
integer,	public		::	num_outputs			Number of outputs (if output is not graph structure)
integer,	public		::	num_params	=	0	Number of learnable parameters
integer,	public,	dimension(:), allocatable	::	num_params_msg			Number of learnable parameters for each message
integer,	public		::	num_params_readout			Number of learnable parameters for the readout
integer,	public		::	num_time_steps			Number of time steps
integer,	public,	dimension(:), allocatable	::	num_vertex_features			Number of vertex features for each time step
class(array_type),	public,	allocatable, dimension(:,:)	::	output			Output
integer,	public		::	output_rank	=	0	Rank of output data
integer,	public,	allocatable, dimension(:)	::	output_shape			Output shape
type(array_type),	public,	allocatable, dimension(:)	::	params			Learnable parameters
character(len=20),	public		::	subtype	=	repeat(" ", 20)
character(len=4),	public		::	type	=	'base'	Layer type
logical,	public		::	use_bias	=	.false.	Layer has bias
logical,	public		::	use_graph_input	=	.false.	Use graph input
logical,	public		::	use_graph_output	=	.false.	Use graph output
integer,	public,	allocatable, dimension(:,:)	::	weight_shape			Shape of weights
type(array_type),	public,	allocatable, dimension(:,:)	::	z
type(array_type),	public,	allocatable, dimension(:,:)	::	z_readout			Input gradients

Constructor

Interface for setting up the MPNN layer

private module function layer_setup (num_vertex_features, num_edge_features, num_time_steps, max_vertex_degree, num_outputs, min_vertex_degree, message_activation, readout_activation, kernel_initialiser, verbose)	Set up the message passing layer

Finalizations Procedures

final :: finalise_duvenaud	Finalise the message passing layer

Type-Bound Procedures

procedure, public :: add_t_t => add_learnable	Add two layers
procedure, public, pass(this) :: build_from_onnx => build_from_onnx_base	Build layer from ONNX node and initialiser
procedure, public, pass(this) :: emit_onnx_graph_inputs => emit_onnx_graph_inputs_duvenaud	Emit graph input tensor declarations for Duvenaud GNN layer
procedure, public, pass(this) :: emit_onnx_nodes => emit_onnx_nodes_duvenaud	Emit ONNX JSON nodes for Duvenaud GNN layer
procedure, public, pass(this) :: extract_output => extract_output_base	Extract the output of the layer as a standard real array
procedure, public, pass(this) :: forward => forward_msgpass	Forward pass for message passing layer
procedure, public, pass(this) :: forward_eval => forward_eval_base	Forward pass of layer and return output for evaluation
procedure, public, pass(this) :: get_attributes => get_attributes_duvenaud	Get the attributes of the layer (for ONNX export)
procedure, public, pass(this) :: get_gradients	Get parameter gradients of layer
procedure, public, pass(this) :: get_num_params => get_num_params_duvenaud	Get the number of parameters for the message passing layer
procedure, public, pass(this) :: get_params	Get learnable parameters of layer
procedure, public, pass(this) :: init => init_duvenaud	Initialise the message passing layer
procedure, public, pass(this) :: nullify_graph => nullify_graph_base	Nullify the forward pass data of the layer to free memory Read more…
generic, public :: operator(+) => add_t_t	Operator overloading for addition
procedure, public, pass(this) :: print => print_base	Print the layer to a file with additional information
procedure, public, pass(this) :: print_to_unit => print_to_unit_duvenaud
procedure, public, pass(this) :: read => read_duvenaud	Read the message passing layer
procedure, public, pass(this) :: reduce => reduce_learnable	Merge another learnable layer into this one
procedure, public, pass(this) :: set_gradients	Set learnable parameters of layer
procedure, public, pass(this) :: set_graph => set_graph_duvenaud	Set the graph for the message passing layer
procedure, public, pass(this) :: set_hyperparams => set_hyperparams_duvenaud	Set the hyperparameters for the message passing layer
procedure, public, pass(this) :: set_params	Set learnable parameters of layer
procedure, public, pass(this) :: set_rank => set_rank_base	Set the input and output ranks of the layer
procedure, public, pass(this) :: set_shape => set_shape_base	Set the input shape of the layer
procedure, public, pass(this) :: update_message => update_message_duvenaud	Update the message
procedure, public, pass(this) :: update_readout => update_readout_duvenaud	Update the readout

Functions

public function read_duvenaud_msgpass_layer(unit, verbose) result(layer)

Read duvenaud message passing layer from file and return layer

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	unit	Unit number
integer,	intent(in),	optional		::	verbose	Verbosity level

Return Value class(base_layer_type), allocatable

Instance of the message passing layer

private function get_attributes_duvenaud(this) result(attributes)

Get the attributes of the Duvenaud message passing layer (for ONNX export)

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(in)			::	this	Instance of the layer

Return Value type(onnx_attribute_type), allocatable, dimension(:)

Attributes of the layer

private pure function get_num_params_duvenaud(this) result(num_params)

Get the number of parameters for the message passing layer

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(in)			::	this	Instance of the message passing layer

Return Value integer

Number of parameters

private module function layer_setup(num_vertex_features, num_edge_features, num_time_steps, max_vertex_degree, num_outputs, min_vertex_degree, message_activation, readout_activation, kernel_initialiser, verbose) result(layer)

Set up the message passing layer

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		dimension(:)	::	num_vertex_features	Number of vertex features
integer,	intent(in),		dimension(:)	::	num_edge_features	Number of edge features
integer,	intent(in)			::	num_time_steps	Number of time steps
integer,	intent(in)			::	max_vertex_degree	Maximum vertex degree
integer,	intent(in)			::	num_outputs	Number of outputs
integer,	intent(in),	optional		::	min_vertex_degree	Minimum vertex degree
class(*),	intent(in),	optional		::	message_activation	Message and readout activation functions
class(*),	intent(in),	optional		::	readout_activation	Message and readout activation functions
character(len=*),	intent(in),	optional		::	kernel_initialiser
integer,	intent(in),	optional		::	verbose	Kernel initialiser ! Kernel initialiser Verbosity level

Return Value type(duvenaud_msgpass_layer_type)

Instance of the message passing layer

Subroutines

private subroutine emit_duvenaud_degree_update(tp, degree_in, min_degree, max_degree, feature_dim, nv_out, weight_data, aggr_in, nodes, num_nodes, inits, num_inits, sq_out)

Emit the degree-dependent weight selection and update block.

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	tp
character(len=*),	intent(in)		::	degree_in
integer,	intent(in)		::	min_degree
integer,	intent(in)		::	max_degree
integer,	intent(in)		::	feature_dim
integer,	intent(in)		::	nv_out
real(kind=real32),	intent(in)		::	weight_data(:)
character(len=*),	intent(in)		::	aggr_in
type(onnx_node_type),	intent(inout),	dimension(:)	::	nodes
integer,	intent(inout)		::	num_nodes
type(onnx_initialiser_type),	intent(inout),	dimension(:)	::	inits
integer,	intent(inout)		::	num_inits
character(len=128),	intent(out)		::	sq_out

private subroutine emit_duvenaud_readout_impl(prefix, layer, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, readout_output)

Emit ONNX nodes for Duvenaud readout

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	prefix
class(duvenaud_msgpass_layer_type),	intent(in)		::	layer
type(onnx_node_type),	intent(inout),	dimension(:)	::	nodes
integer,	intent(inout)		::	num_nodes
integer,	intent(in)		::	max_nodes
type(onnx_initialiser_type),	intent(inout),	dimension(:)	::	inits
integer,	intent(inout)		::	num_inits
integer,	intent(in)		::	max_inits
character(len=128),	intent(out)		::	readout_output

private subroutine emit_duvenaud_readout_step(prefix, activation_name, t, nv, no, weight_data, nodes, num_nodes, inits, num_inits, step_sum)

Emit one Duvenaud readout timestep.

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	prefix
character(len=*),	intent(in)		::	activation_name
integer,	intent(in)		::	t
integer,	intent(in)		::	nv
integer,	intent(in)		::	no
real(kind=real32),	intent(in)		::	weight_data(:)
type(onnx_node_type),	intent(inout),	dimension(:)	::	nodes
integer,	intent(inout)		::	num_nodes
type(onnx_initialiser_type),	intent(inout),	dimension(:)	::	inits
integer,	intent(inout)		::	num_inits
character(len=128),	intent(out)		::	step_sum

private subroutine emit_duvenaud_timestep(prefix, t, nv_in, ne_in, nv_out, min_degree, max_degree, weight_data, activation_name, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, vertex_out)

Emit ONNX nodes for one Duvenaud message passing time step.

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	prefix
integer,	intent(in)		::	t
integer,	intent(in)		::	nv_in
integer,	intent(in)		::	ne_in
integer,	intent(in)		::	nv_out
integer,	intent(in)		::	min_degree
integer,	intent(in)		::	max_degree
real(kind=real32),	intent(in)		::	weight_data(:)
character(len=*),	intent(in)		::	activation_name
type(onnx_node_type),	intent(inout),	dimension(:)	::	nodes
integer,	intent(inout)		::	num_nodes
integer,	intent(in)		::	max_nodes
type(onnx_initialiser_type),	intent(inout),	dimension(:)	::	inits
integer,	intent(inout)		::	num_inits
integer,	intent(in)		::	max_inits
character(len=128),	intent(out)		::	vertex_out

private subroutine emit_onnx_graph_inputs_duvenaud(this, prefix, graph_inputs, num_inputs)

Emit graph input tensor declarations for Duvenaud GNN layer

Arguments

Type	Intent	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(in)		::	this	Instance of the layer
character(len=*),	intent(in)		::	prefix	Input name prefix (e.g. "input_1")
type(onnx_tensor_type),	intent(inout),	dimension(:)	::	graph_inputs	Accumulator for graph input tensor declarations
integer,	intent(inout)		::	num_inputs	Current number of graph input declarations

private subroutine emit_onnx_nodes_duvenaud(this, prefix, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, input_name, is_last_layer, format)

Emit ONNX JSON nodes for Duvenaud GNN layer

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(in)			::	this	Instance of the layer
character(len=*),	intent(in)			::	prefix	Node name prefix (e.g. "node_2")
type(onnx_node_type),	intent(inout),		dimension(:)	::	nodes	Accumulator for ONNX nodes
integer,	intent(inout)			::	num_nodes	Current number of nodes
integer,	intent(in)			::	max_nodes	Maximum capacity
type(onnx_initialiser_type),	intent(inout),		dimension(:)	::	inits	Accumulator for ONNX initialisers
integer,	intent(inout)			::	num_inits	Current number of initialisers
integer,	intent(in)			::	max_inits	Maximum capacity
character(len=*),	intent(in),	optional		::	input_name	Unused sequential input name
logical,	intent(in),	optional		::	is_last_layer	Unused last-layer flag
integer,	intent(in),	optional		::	format	Unused export format selector

private subroutine finalise_duvenaud(this)

Finalise the message passing layer

Arguments

Type	Intent	Optional	Attributes		Name
type(duvenaud_msgpass_layer_type),	intent(inout)			::	this	Instance of the fully connected layer

private subroutine init_duvenaud(this, input_shape, verbose)

Initialise the message passing layer

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(inout)			::	this	Instance of the fully connected layer
integer,	intent(in),		dimension(:)	::	input_shape	Input shape
integer,	intent(in),	optional		::	verbose	Verbosity level

private subroutine print_to_unit_duvenaud(this, unit)

Print kipf message passing layer to unit

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(in)			::	this	Instance of the message passing layer
integer,	intent(in)			::	unit	Filename

private subroutine read_duvenaud(this, unit, verbose)

Read the message passing layer

Arguments

Type	Intent	Optional		Name
class(duvenaud_msgpass_layer_type),	intent(inout)		::	this	Instance of the message passing layer
integer,	intent(in)		::	unit	Unit to read from
integer,	intent(in),	optional	::	verbose	Verbosity level

private subroutine set_graph_duvenaud(this, graph)

Set the graph structure of the input data

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(inout)			::	this	Instance of the layer
type(graph_type),	intent(in),		dimension(:)	::	graph	Graph structure of input data

private subroutine set_hyperparams_duvenaud(this, num_vertex_features, num_edge_features, min_vertex_degree, max_vertex_degree, num_time_steps, num_outputs, message_activation, readout_activation, kernel_initialiser, verbose)

Set the hyperparameters for the message passing layer

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(inout)			::	this	Instance of the message passing layer
integer,	intent(in),		dimension(:)	::	num_vertex_features	Number of vertex features
integer,	intent(in),		dimension(:)	::	num_edge_features	Number of edge features
integer,	intent(in)			::	min_vertex_degree	Minimum vertex degree
integer,	intent(in)			::	max_vertex_degree	Maximum vertex degree
integer,	intent(in)			::	num_time_steps	Number of time steps
integer,	intent(in)			::	num_outputs	Number of outputs
class(base_actv_type),	intent(in),		allocatable	::	message_activation	Message and readout activation functions
class(base_actv_type),	intent(in),		allocatable	::	readout_activation	Message and readout activation functions
class(base_init_type),	intent(in),		allocatable	::	kernel_initialiser	Kernel and bias initialisers
integer,	intent(in),	optional		::	verbose	Verbosity level

private subroutine update_message_duvenaud(this, input)

Update the message

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(inout),		target	::	this	Instance of the message passing layer
class(array_type),	intent(in),		dimension(:,:), target	::	input	Input to the message passing layer

private subroutine update_readout_duvenaud(this)

Update the readout

Arguments

Type	Intent	Optional	Attributes		Name
class(duvenaud_msgpass_layer_type),	intent(inout),		target	::	this	Instance of the message passing layer

athena__duvenaud_msgpass_layer Module

Contents

Variables

Interfaces

Derived Types

Functions

Subroutines

Uses

Variables

Interfaces

public interface duvenaud_msgpass_layer_type

private module function layer_setup(num_vertex_features, num_edge_features, num_time_steps, max_vertex_degree, num_outputs, min_vertex_degree, message_activation, readout_activation, kernel_initialiser, verbose) result(layer) Implementation →

Arguments

Return Value type(duvenaud_msgpass_layer_type)

Derived Types

type, public, extends(msgpass_layer_type) :: duvenaud_msgpass_layer_type

Components

Constructor

Finalizations Procedures

Type-Bound Procedures

Functions

public function read_duvenaud_msgpass_layer(unit, verbose) result(layer)

Arguments

Return Value class(base_layer_type), allocatable

private function get_attributes_duvenaud(this) result(attributes)

Arguments

Return Value type(onnx_attribute_type), allocatable, dimension(:)

private pure function get_num_params_duvenaud(this) result(num_params)

Arguments

Return Value integer

private module function layer_setup(num_vertex_features, num_edge_features, num_time_steps, max_vertex_degree, num_outputs, min_vertex_degree, message_activation, readout_activation, kernel_initialiser, verbose) result(layer)

Arguments

Return Value type(duvenaud_msgpass_layer_type)

Subroutines

private subroutine emit_duvenaud_degree_update(tp, degree_in, min_degree, max_degree, feature_dim, nv_out, weight_data, aggr_in, nodes, num_nodes, inits, num_inits, sq_out)

Arguments

private subroutine emit_duvenaud_readout_impl(prefix, layer, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, readout_output)

Arguments

private subroutine emit_duvenaud_readout_step(prefix, activation_name, t, nv, no, weight_data, nodes, num_nodes, inits, num_inits, step_sum)

Arguments

private subroutine emit_duvenaud_timestep(prefix, t, nv_in, ne_in, nv_out, min_degree, max_degree, weight_data, activation_name, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, vertex_out)

Arguments

private subroutine emit_onnx_graph_inputs_duvenaud(this, prefix, graph_inputs, num_inputs)

Arguments

private subroutine emit_onnx_nodes_duvenaud(this, prefix, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, input_name, is_last_layer, format)

Arguments

private subroutine finalise_duvenaud(this)

Arguments

private subroutine init_duvenaud(this, input_shape, verbose)

Arguments

private subroutine print_to_unit_duvenaud(this, unit)

Arguments

private subroutine read_duvenaud(this, unit, verbose)

Arguments

private subroutine set_graph_duvenaud(this, graph)

Arguments

private subroutine set_hyperparams_duvenaud(this, num_vertex_features, num_edge_features, min_vertex_degree, max_vertex_degree, num_time_steps, num_outputs, message_activation, readout_activation, kernel_initialiser, verbose)

Arguments

private subroutine update_message_duvenaud(this, input)

Arguments

private subroutine update_readout_duvenaud(this)

Arguments

private module function layer_setup(num_vertex_features, num_edge_features, num_time_steps, max_vertex_degree, num_outputs, min_vertex_degree, message_activation, readout_activation, kernel_initialiser, verbose) result(layer)