neuralogic.nn.module package

Subpackages

Submodules

neuralogic.nn.module.module module

class Module[source]: Bases: ABC

Module contents

class APPNPConv(output_name: str, feature_name: str, edge_name: str, k: int, alpha: float, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Approximate Personalized Propagation of Neural Predictions layer from “Predict then Propagate: Graph Neural Networks meet Personalized PageRank”. Which can be expressed as:

\[\mathbf{x}^{0}_i = \mathbf{x}_i\]

\[\mathbf{x}^{k}_i = \alpha \cdot \mathbf{x}^0_i + (1 - \alpha) \cdot {agg}_{j \in \mathcal{N}(i)}(\mathbf{x}^{k - 1}_j)\]

\[\mathbf{x}^{\prime}_i = act(\mathbf{x}^{K}_i)\]

Where act is an activation function and agg aggregation function.

The first part of the second equation that is “\(\alpha \cdot \mathbf{x}^0_i\)” is expressed in the logic form as:

R.<output_name>__<k>(V.I) <= R.<feature_name>(V.I)[<alpha>].fixed()

The second part of the second equation that is “\((1 - \alpha) \cdot {agg}_{j \in \mathcal{N}(i)}(\mathbf{x}^{k - 1}_j)\)” is expressed as:

R.<output_name>__<k>(V.I) <= (R.<output_name>__<k-1>(V.J)[1 - <alpha>].fixed(), R.<edge_name>(V.J, V.I))

Examples

The whole computation of this module (parametrized as APPNPConv("h1", "h0", "_edge", 3, 0.1, Transformation.SIGMOID)) is as follows:

metadata = Metadata(transformation=Transformation.IDENTITY, aggregation=Aggregation.SUM)

(R.h1__1(V.I) <= R.h0(V.I)[0.1].fixed()) | metadata
(R.h1__1(V.I) <= (R.h0(V.J)[0.9].fixed(), R._edge(V.J, V.I))) | metadata
R.h1__1/1 [Transformation.IDENTITY]

(R.h1__2(V.I) <= <0.1> R.h0(V.I)) | metadata
(R.h1__2(V.I) <= (<0.9> R.h1__1(V.J), R._edge(V.J, V.I))) | metadata
R.h1__2/1 [Transformation.IDENTITY]

(R.h1(V.I) <= <0.1> R.h0(V.I)) | metadata
(R.h1(V.I) <= (<0.9> R.h1__2(V.J), R._edge(V.J, V.I))) | metadata
R.h1 / 1 [Transformation.SIGMOID]

Parameters:

output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
k (int) – Number of iterations
alpha (float) – Teleport probability
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.SUM

class Attention(embed_dim: int, output_name: str, query_name: str, key_name: str, value_name: str, mask_name: str | None = None, arity: int = 1)[source]

Bases: Module

A single-head attention module based on “Attention Is All You Need”.

Parameters:

embed_dim (int) – The number of expected features.
output_name (str) – Output (head) predicate name of the module.
query_name (str) – The name of the queries predicate.
key_name (str) – The name of the keys predicate.
value_name (str) – The name of the values predicate.
mask_name (str, optional) – The name of the input mask predicate. Default: None
arity (int) – Arity of the input and output predicates. Default: 1

class AvgPooling(output_name: str, input_name: str, input_arity: int = 1)[source]

Bases: Pooling

Apply average pooling over the input specified by the input_name and the input arity parameters. Can be expressed as:

\[h = \frac{1}{|N|}\sum_{i_{0}, .., i_{n} \in N} x_{(i_{0}, .., i_{n})}\]

Where \(N\) is a set of tuples of length \(n\) (specified by the input arity parameter) that are valid arguments for the input predicate.

This module extends the generic pooling Pooling.

Examples

The whole computation of this module (parametrized as AvgPooling("h1", "h0")) is as follows:

(R.h1 <= R.h0(V.X0)) | [Aggregation.AVG, Transformation.IDENTITY]
R.h1 / 0 | [Transformation.IDENTITY]

Parameters:

output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input name.
input_arity (int) – Arity of the input predicate input_name. Default: 1

class GATv2Conv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, share_weights: bool = False, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>)[source]

Bases: Module

GATv2 layer from “How Attentive are Graph Attention Networks?”.

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
share_weights (bool) – Share weights in attention. Default: False
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY

class GCNConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>, add_self_loops: bool | None = None, normalize: bool = True)[source]

Bases: Module

Graph Convolutional layer from “Semi-supervised Classification with Graph Convolutional Networks”.

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.SUM
add_self_loops (bool | None) – Add self loops if either set to True or None (if normalize is True). Default: None
normalize (bool) – Add normalization. Default : True

class GENConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, aggregation: AggregationFunction = <neuralogic.core.constructs.function.softmax.SoftmaxAggregation object>, num_layers: int = 2, expansion: int = 2, eps: float = 1e-07, train_eps: bool = False, edge_dim: int | None = None)[source]

Bases: Module

GENConv layer from “DeeperGCN: All You Need to Train Deeper GCNs”.

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
aggregation (AggregationFunction) – The aggregation function. Default: Aggregation.SOFTMAX
num_layers (int) – The number of MLP layers. Default: 2
expansion (int) – The expansion factor of hidden channels in MLP. Default: 2
eps (float) – \(\epsilon\)-value. Default: 0.0
train_eps (bool) – Is eps trainable parameter. Default: false
edge_dim (int | None) – Dimension of edge features (None is projection to in_channels is not needed). Default: None

class GINConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Implements the Graph Isomorphism Network (GIN) convolution layer. GIN is a powerful GNN layer that can distinguish between different graph structures.

class GINEConv(in_channels: int, feature_name: str, edge_name: str, nn_name: str, eps: float = 0.0, train_eps: bool = False, edge_dim: int | None = None)[source]

Bases: Module

GINEConv layer from “Strategies for Pre-training Graph Neural Networks”.

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
nn_name (str) – Neural network predicate name.
eps (float) – \(\epsilon\)-value. Default: 0.0
train_eps (bool) – Is eps trainable parameter. Default: false
edge_dim (int | None) – Dimension of edge features (None is projection to in_channels is not needed). Default: None

class GRU(input_size: int, hidden_size: int, output_name: str, input_name: str, hidden_0_name: str, arity: int = 1, next_name: str = '_next__positive')[source]

Bases: Module

One-layer Gated Recurrent Unit (GRU) module which is computed as:

\[\begin{split}r_t = \sigma(\mathbf{W}_{xr} \mathbf{x}_t + \mathbf{W}_{hr} \mathbf{h}_{t-1}) \\\end{split}\]

\[\begin{split}z_t = \sigma(\mathbf{W}_{xz} \mathbf{x}_t + \mathbf{W}_{hz} \mathbf{h}_{t-1}) \\\end{split}\]

\[\begin{split}n_t = \tanh(\mathbf{W}_{xn} \mathbf{x}_t + r_t \odot (\mathbf{W}_{hn} \mathbf{h}_{t-1})) \\\end{split}\]

\[h_t = (1 - z_t) \odot n_t + z_t \odot h_{t-1}\]

where \(t \in (1, sequence\_length + 1)\) is a time step. In the template, the \(t\) is referred to as V.T, and \(t - 1\) is referred to as V.Z. This module expresses the first equation as:

(R.<output_name>__r(<...terms>, V.T) <= (
    R.<input_name>(<...terms>, V.T)[<hidden_size>, <input_size>],
    R.<hidden_input_name>(<...terms>, V.Z)[<hidden_size>, <hidden_size>],
    R.<next_name>(V.Z, V.T),
)) | [Transformation.SIGMOID]

R.<output_name>__r / <arity> + 1 | [Transformation.IDENTITY]

The second equation is expressed in the same way, except for a different head predicate name. The third equation is split into three rules. The first two computes the element-wise product - \(r_t * (\mathbf{W}_{hn} \mathbf{h}_{t-1})\).

(R.<output_name>__n_helper_weighted(<...terms>, V.T) <= (
    R.<hidden_input_name>(<...terms>, V.Z)[<hidden_size>, <hidden_size>], R.<next_name>(V.Z, V.T),
)) | [Transformation.IDENTITY],

R.<output_name>__n_helper_weighted / (<arity> + 1) | [Transformation.IDENTITY],

(R.<output_name>__n_helper(<...terms>, V.T) <= (
    R.<output_name>__r(<..terms>, V.T), R.<>__n_helper_weighted(<...terms>, V.T)
)) | [Transformation.IDENTITY, Combination.ELPRODUCT],

R.<output_name>__n_helper / (<arity> + 1) | [Transformation.IDENTITY],

The third one computes the sum and applies the \(tanh\) activation function.

(R.<output_name>__n(<...terms>, V.T) <= (
    R.<input_name>(<...terms>, V.T)[<hidden_size>, <input_size>],
    R.<output_name>__n_helper(<...terms>, V.T)
)) | [Transformation.TANH]
R.<output_name>__n / (<arity> + 1) | [Transformation.IDENTITY],

The last equation is computed via three rules. The first two rules computes element-wise products. That is:

(R.<output_name>__left(<...terms>, V.T) <= (
    R.<output_name>__z(<...terms>, V.T), R.<output_name>__n(<...terms>, V.T)
)) | [Transformation.IDENTITY, Combination.ELPRODUCT]

(R.<output_name>__right(<...terms>, V.T) <= (
    R.<output_name>__z(<...terms>, V.T), R.<hidden_input_name>(<...terms>, V.Z), R.<next_name>(V.Z, V.T),,
)) | [Transformation.IDENTITY, Combination.ELPRODUCT]

R.<output_name>__left / <arity> + 1 | [Transformation.IDENTITY]
R.<output_name>__right / <arity> + 1 | [Transformation.IDENTITY]

The last output rule sums up the element-wise products.

(R.<output_name>(<...terms>, V.T) <= (
    R.<output_name>__left(<...terms>, V.T), R.<output_name>__right(<...terms>, V.T)
)) | [Transformation.IDENTITY]
R.<output_name> / <arity> + 1 | [Transformation.IDENTITY],

Additionally, we define a rule for the “stop condition”, that is:

(R.<output_name>(<...terms>, 0) <= R.<hidden_0_name>(<...terms>)) | [Transformation.IDENTITY]

Parameters:

input_size (int) – Input feature size.
hidden_size (int) – Output and hidden feature size.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input feature predicate name to get features from.
hidden_0_name (str) – Predicate name to get initial hidden state from.
arity (int) – Arity of the input and output predicate. Default: 1

class LSTM(input_size: int, hidden_size: int, output_name: str, input_name: str, hidden_0_name: str, cell_state_0_name: str, arity: int = 1)[source]

Bases: Module

One-layer Long Short-Term Memory (LSTM) RNN module which is computed as:

\[i_t = \sigma(\mathbf{W}_{xi} \mathbf{x}_t + \mathbf{W}_{hi} \mathbf{h}_{t-1})\]

\[f_t = \sigma(\mathbf{W}_{xf} \mathbf{x}_t + \mathbf{W}_{hf} \mathbf{h}_{t-1})\]

\[o_t = \sigma(\mathbf{W}_{xo} \mathbf{x}_t + \mathbf{W}_{ho} \mathbf{h}_{t-1})\]

\[\begin{split}g_t = \tanh(\mathbf{W}_{xg} \mathbf{x}_t + \mathbf{W}_{hg} \mathbf{h}_{t-1}) \\\end{split}\]

\[c_t = f_t \odot c_{t-1} + i_t \odot g_t\]

\[h_t = o_t \odot \tanh(c_t)\]

Parameters:

input_size (int) – Input feature size.
hidden_size (int) – Output and hidden feature size.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input feature predicate name to get features from.
hidden_0_name (str) – Predicate name to get initial hidden state from.
cell_state_0_name (str) – Predicate name to get initial cell state from.
arity (int) – Arity of the input and output predicate. Default: 1

class Linear(in_channels: int, out_channels: int, output_name: str, input_name: str, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, arity: int = 1)[source]

Bases: Module

Apply linear transformation on the input. Can be expressed as:

\[h_{i_0, .., i_{n}} = W \cdot x_{i_0, .., i_{n}}\]

Where \(x\) is the input, \(W \in R^{(out\_channels \times in\_channels)}\) is a learnable parameter, and \(n\) is the arity of the input and output.

It is also possible to attach non-linearity via the activation parameter and compute:

\[h_{i_0, .., i_{n}} = act(W \cdot x_{i_0, .., i_{n}})\]

Example

The whole computation of this module (parametrized as Linear(1, 2, "h1", "h0")) is as follows:

(R.h1(V.X0)[2, 1] <= R.h0(V.X0)) | [Transformation.IDENTITY]
R.h1 / 1 | [Transformation.IDENTITY]

Module parametrized as Linear(1, 2, "h1", "h0", Transformation.SIGMOID, 2) translates into:

(R.h1(V.X0, V.X1)[2, 1] <= R.h0(V.X0, V.X1)) | [Transformation.IDENTITY]
R.h1 / 2 | [Transformation.SIGMOID]

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input name.
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
arity (int) – Arity of the input and output predicate. Default: 1

class MAGNNLinear(in_channels: int, out_channels: int, output_name: str, feature_name: str, relation_name: str, type_name: str | None, meta_paths: ~typing.List[str], activation: ~neuralogic.core.constructs.function.function.TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: ~neuralogic.core.constructs.function.function.AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: MAGNNMean

Intra-metapath Aggregation module with Linear encoder from “MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding”. Which can be expressed as:

\[\mathbf{h}_{P(v,u)} = \mathbf{W}_p \cdot MEAN(\{\mathbf{x}_t | \forall t \in P(v,u) \})\]

\[\mathbf{h}^P_{v} = act(\sum_{u \in N^P_v} \mathbf{h}_{P(v,u)})\]

Where act is an activation function, \(P(v,u)\) is a single metapath instance, \(N^P_{v}\) is set of metapath-based neighbors.

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
relation_name (str) – Relation predicate name for connectivity checks between entities.
type_name (Optional[str]) – Metapath type predicate name. If none, meta_paths will be used instead.
meta_paths (List[str]) – Name of types forming a single metapath.
activation (TransformationFunction) – Activation function of the output. Default: Transformation.SIGMOID
aggregation (AggregationFunction) – Aggregation function of the output. Default: Aggreagtion.SUM

class MAGNNMean(output_name: str, feature_name: str, relation_name: str, type_name: str | None, meta_paths: ~typing.List[str], activation: ~neuralogic.core.constructs.function.function.TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: ~neuralogic.core.constructs.function.function.AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Intra-metapath Aggregation module with Mean encoder from “MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding”. Which can be expressed as:

\[\mathbf{h}_{P(v,u)} = MEAN(\{\mathbf{x}_t | \forall t \in P(v,u) \})\]

\[\mathbf{h}^P_{v} = act(\sum_{u \in N^P_v} \mathbf{h}_{P(v,u)})\]

Where act is an activation function, \(P(v,u)\) is a single metapath instance, \(N^P_{v}\) is set of metapath-based neighbors.

Parameters:

output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
relation_name (str) – Relation predicate name for connectivity checks between entities.
type_name (Optional[str]) – Metapath type predicate name. If none, meta_paths will be used instead.
meta_paths (List[str]) – Name of types forming a single metapath.
activation (TransformationFunction) – Activation function of the output. Default: Transformation.SIGMOID
aggregation (AggregationFunction) – Aggregation function of the output. Default: Aggreagtion.SUM

class MLP(units: ~typing.List[int], output_name: str, input_name: str, activation: ~neuralogic.core.constructs.function.function.TransformationFunction | ~typing.List[~neuralogic.core.constructs.function.function.TransformationFunction] = <neuralogic.core.constructs.function.function.TransformationFunction object>, arity: int = 1)[source]

Bases: Module

Parameters:

units (List[int]) – List of layer sizes.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input name.
activation (Union[TransformationFunction, List[TransformationFunction]]) – Activation function of all layers or list of activations for each layer. Default: Transformation.RELU
arity (int) – Default: -1

class MaxPooling(output_name: str, input_name: str, input_arity: int = 1)[source]

Bases: Pooling

Apply max pooling over the input specified by the input_name and the input arity parameters. Can be expressed as:

\[h = max_{i_{0}, .., i_{n} \in N}(x_{(i_{0}, .., i_{n})})\]

Where \(N\) is a set of tuples of length \(n\) (specified by the input arity parameter) that are valid arguments for the input predicate.

This module extends the generic pooling Pooling.

Examples

The whole computation of this module (parametrized as MaxPooling("h1", "h0")) is as follows:

(R.h1 <= R.h0(V.X0)) | [Aggregation.MAX, Transformation.IDENTITY]
R.h1 / 0 | [Transformation.IDENTITY]

Parameters:

output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input name.
input_arity (int) – Arity of the input predicate input_name. Default: 1

class MetaConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, role_name: str | None, roles: ~typing.List[str], activation: ~neuralogic.core.constructs.function.function.TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: ~neuralogic.core.constructs.function.function.AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Metagraph Convolutional Unit layer.

From Meta-GNN: metagraph neural network for semi-supervised learning in attributed heterogeneous information networks. Which can be expressed as:

\[\mathbf{x}^{\prime}_i = act(\mathbf{W_0} \cdot \mathbf{x}_i + {agg}_{j \in \mathcal{N}_r(i)} \sum_{k \in \mathcal{K}} (\mathbf{W_k} \cdot \mathbf{x}_j))\]

Where act is an activation function, agg aggregation function (by default average), \(W_0\) is a learnable root parameter and \(W_k\) is a learnable parameter for each role.

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
role_name (str, optional) – Role predicate name to use for role relations. When None, elements from roles are used instead.
roles (List[str]) – List of relations’ names.
activation (TransformationFunction, optional) – Activation function of the output. Default: Transformation.SIGMOID.
aggregation (AggregationFunction, optional) – Aggregation function of nodes’ neighbors. Default: Aggregation.AVG.

class Module[source]: Bases: ABC

class MultiheadAttention(embed_dim: int, num_heads: int, output_name: str, query_name: str, key_name: str, value_name: str, vdim: int | None = None, kdim: int | None = None, mask_name: str | None = None, arity: int = 1)[source]

Bases: Module

A multi-head attention module based on “Attention Is All You Need”.

Parameters:

embed_dim (int) – The number of expected features.
num_heads (int) – The number of heads.
output_name (str) – Output (head) predicate name of the module.
query_name (str) – The name of the queries predicate.
key_name (str) – The name of the keys predicate.
value_name (str) – The name of the values predicate.
vdim (Optional[int]) – Total number of features for values.
kdim (Optional[int]) – Total number of features for keys.
mask_name (str, optional) – The name of the input mask predicate. Default: None
arity (int) – Arity of the input and output predicates. Default: 1

class Pooling(output_name: str, input_name: str, aggregation: AggregationFunction, input_arity: int = 1)[source]

Bases: Module

Apply generic pooling over the input specified by the input_name and the input arity parameters. Can be expressed as:

\[h = agg_{i_{0}, .., i_{n} \in N}(x_{(i_{0}, .., i_{n})})\]

Where \(N\) is a set of tuples of length \(n\) (specified by the input arity parameter) that are valid arguments for the input predicate.

For example, a classic pooling over graph nodes represented by relations of arity 1 (node id) would be calculated as:

\[h = agg_{i \in N}(x_{(i)})\]

Here \(N\) refers to a set of all node ids. Lifting the restriction of the input arity via the input_arity parameter allows for pooling not only nodes but also edges (input_arity=2) and other objects (hyperedges etc.)

Examples

The whole computation of this module (parametrized as Pooling("h1", "h0", Aggregation.AVG)) is as follows:

(R.h1 <= R.h0(V.X0)) | [Aggregation.AVG, Transformation.IDENTITY]
R.h1 / 0 | [Transformation.IDENTITY]

Module parametrized as Pooling("h1", "h0", Aggregation.MAX, 2) translates into:

(R.h1 <= R.h0(V.X0, V.X1)) | [Aggregation.MAX, Transformation.IDENTITY]
R.h1 / 0 | [Transformation.IDENTITY]

Parameters:

output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input name.
aggregation (AggregationFunction) – Aggregation function.
input_arity (int) – Arity of the input predicate input_name. Default: 1

class PositionalEncoding(embed_dim: int, max_len: int, output_name: str, input_name: str, arity: int = 1, learnable: bool = False)[source]

Bases: Module

Implements positional encoding for logic sequences. It generates a set of rules that add fixed or learnable positional embeddings to the input features.

class RGCNConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str | None, relations: ~typing.List[str], activation: ~neuralogic.core.constructs.function.function.TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: ~neuralogic.core.constructs.function.function.AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Relational Graph Convolutional layer from Modeling Relational Data with Graph Convolutional Networks. Which can be expressed as:

\[\mathbf{x}^{\prime}_i = act(\mathbf{W_0} \cdot \mathbf{x}_i + \sum_{r \in \mathcal{R}} {agg}_{j \in \mathcal{N}_r(i)}(\mathbf{W_r} \cdot \mathbf{x}_j))\]

Where act is an activation function, agg aggregation function (by default average), \(W_0\) is a learnable root parameter and \(W_r\) is a learnable parameter for each relation.

The first part of the equation that is “\(\mathbf{W_0} \cdot \mathbf{x}_i\)” can be expressed in the logic form as:

R.<output_name>(V.I) <= R.<feature_name>(V.I)[<W0>]

Another part of the equation that is “\({agg}_{j \in \mathcal{N}_r(i)}(\mathbf{W_r} \cdot \mathbf{x}_j)\)” can be expressed as:

R.<output_name>(V.I) <= (R.<feature_name>(V.J)[<Wr>], R.<edge_name>(V.J, relation, V.I))

where “relation” is a constant name, or as:

R.<output_name>(V.I) <= (R.<feature_name>(V.J)[<Wr>], R.<relation>(V.J, V.I))

The outer summation, together with summing it with the first part, is handled by aggregation of all rules with the same head (and substitution).

Examples

The whole computation of this module (parametrized as RGCNConv(1, 2, "h1", "h0", "_edge", ["sibling", "parent"])) is as follows:

metadata = Metadata(activation=Transformation.IDENTITY, aggregation=Aggregation.AVG)

(R.h1(V.I) <= R.h0(V.I)[2, 1]) | metadata
(R.h1(V.I) <= (R.h0(V.J)[2, 1], R._edge(V.J, sibling, V.I))) | metadata
(R.h1(V.I) <= (R.h0(V.J)[2, 1], R._edge(V.J, parent, V.I))) | metadata
R.h1 / 1 [Transformation.IDENTITY]

Module parametrized as RGCNConv(1, 2, "h1", "h0", None, ["sibling", "parent"]) translates into:

metadata = Metadata(activation=Transformation.IDENTITY, aggregation=Aggregation.AVG)

(R.h1(V.I) <= R.h0(V.I)[2, 1]) | metadata
(R.h1(V.I) <= (R.h0(V.J)[2, 1], R.sibling(V.J, V.I))) | metadata
(R.h1(V.I) <= (R.h0(V.J)[2, 1], R.parent(V.J, V.I))) | metadata
R.h1 / 1 [Transformation.IDENTITY]

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str | None) – Edge predicate name to use for neighborhood relations. When None, elements from relations are used instead.
relations (List[str]) – List of relations’ names
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.SUM

class RNN(input_size: int, hidden_size: int, output_name: str, input_name: str, hidden_0_name: str, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, arity: int = 1)[source]

Bases: Module

One-layer Recurrent Neural Network (RNN) module which is computed as:

\[h_t = act(\mathbf{W}_{ih} \mathbf{x}_t + \mathbf{W}_{hh} \mathbf{h}_{t-1})\]

where \(t \in (1, sequence\_length + 1)\) is a time step. In the template, the \(t\) is referred to as V.T, and \(t - 1\) is referred to as V.Z. This module expresses the first equation as:

(R.<output_name>(<...terms>, V.T) <= (
    R.<input_name>(<...terms>, V.T)[<hidden_size>, <input_size>],
    R.<hidden_input_name>(<...terms>, V.Z)[<hidden_size>, <hidden_size>],
    R.special.next(V.Z, V.T),
)) | [<activation>]

R.<output_name> / <arity> + 1 | [Transformation.IDENTITY]

Additionally, we define a rule for the “stop condition”, that is:

(R.<output_name>(<...terms>, 0) <= R.<hidden_0_name>(<...terms>)) | [Transformation.IDENTITY]

Parameters:

input_size (int) – Input feature size.
hidden_size (int) – Output and hidden feature size.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input feature predicate name to get features from.
hidden_0_name (str) – Predicate name to get initial hidden state from.
activation (TransformationFunction) – Activation function. Default: Transformation.TANH
arity (int) – Arity of the input and output predicate. Default: 1

class ResGatedGraphConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, gating_activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Residual Gated Graph Convolutional layer from “Residual Gated Graph ConvNets”. Which can be expressed as:

\[\mathbf{x}^{\prime}_i = act(\mathbf{W}_1 \mathbf{x}_i + {agg}_{j \in \mathcal{N}(i)}(\eta_{i,j} \odot \mathbf{W}_2 \mathbf{x}_j))\]

\[\mathbf{\eta}_{i,j} = gating\_act(\mathbf{W}_3 \mathbf{x}_i + \mathbf{W}_4 \mathbf{x}_j)\]

Where act is an activation function, agg aggregation function, gating_act is a gating activation function and \(W_n\) are learnable parameters. This equation is translated into the logic form as:

(R.<output_name>__gate(V.I, V.J) <= (R.<feature_name>(V.I)[<W>], R.<feature_name>(V.J)[<W>])) | [Transformation.IDENTITY]
R.<output_name>__gate / 2 | [<activation>]

(R.<output_name>(V.I) <= R.<feature_name>(V.I)[<W>]) | [Transformation.IDENTITY]
(R.<output_name>(V.I) <= (
    R.<output_name>__gate(V.I, V.J), R.<feature_name>(V.J)[<W>], R.<edge_name>(V.J, V.I))
) | Metadata(activation="elementproduct-identity", aggregation=<aggregation>)

R.<output_name> / 1 | [<activation>]

Examples

The whole computation of this module (parametrized as ResGatedGraphConv(1, 2, "h1", "h0", "_edge")) is as follows:

metadata = Metadata(activation="elementproduct-identity", aggregation=Aggregation.SUM)

(R.h1__gate(V.I, V.J) <= (R.h0(V.I)[2, 1], R.h0(V.J)[2, 1])) | [Transformation.IDENTITY]
R.h1__gate / 2 | [Transformation.SIGMOID]

(R.h1(V.I) <= R.h0(V.I)[2, 1]) | [Transformation.IDENTITY]
(R.h1(V.I) <= (R.h1__gate(V.I, V.J), R.h0(V.J)[2, 1], R._edge(V.J, V.I))) | metadata
R.h1 / 1 | [Transformation.IDENTITY]

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
gating_activation (TransformationFunction) – Gating activation function. Default: Transformation.SIGMOID
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.SUM

class RvNN(input_size: int, output_name: str, input_name: str, parent_map_name: str, max_children: int = 2, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>, arity: int = 1)[source]

Bases: Module

Recursive Neural Network (RvNN) module which is computed as:

\[\mathbf{h}_i = act(agg_{j \in \mathcal{Ch(i)}}(\mathbf{W_{id(j)}} \mathbf{h}_j))\]

Where \(act\) is an activation function, \(agg\) aggregation function and \(\mathbf{W}\)’s are learnable parameters. \(\mathcal{Ch(i)}\) represents the ordered list of children of node \(i\). The \(id(j)\) function maps node \(j\) to its index (position) in its parent’s children list.

Parameters:

input_size (int) – Input feature size.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input feature predicate name to get leaf features from.
parent_map_name (str) – Name of the predicate to get mapping from parent to children
max_children (int) – Maximum number of children (specify which <max_children>-ary tree will be considered). Default: 2
activation (TransformationFunction) – Activation function of all layers. Default: Transformation.TANH
aggregation (AggregationFunction) – Aggregation function of a layer. Default: Aggregation.SUM
arity (int) – Arity of the input and output predicate (doesn’t include the node id term). Default: 1

class SAGEConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

GraphSAGE layer from “Inductive Representation Learning on Large Graphs”. Which can be expressed as:

\[\mathbf{x}^{\prime}_i = act(\mathbf{W}_1 \mathbf{x}_i + \mathbf{W}_2 \cdot {agg}_{j \in \mathcal{N}(i)}(\mathbf{x}_j)))\]

Where act is an activation function, agg aggregation function and W’s are learnable parameters. This equation is translated into the logic form as:

(R.<output_name>(V.I)[<W1>] <= (R.<feature_name>(V.J), R.<edge_name>(V.J, V.I))) | [<aggregation>, Transformation.IDENTITY]
(R.<output_name>(V.I)[<W2>] <= R.<feature_name>(V.I)) | [Transformation.IDENTITY]
R.<output_name> / 1 | [<activation>]

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.AVG

class SGConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, k: int = 1, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Simple Graph Convolutional layer from “Simplifying Graph Convolutional Networks”. Which can be expressed as:

\[\mathbf{x}^{\prime}_i = act(\mathbf{W} \cdot {agg}_{j \in \mathcal{N}^k(i)}(\mathbf{x}_j))\]

Where act is an activation function, agg aggregation function, W is a learnable parameter and \(\mathcal{N}^k(i)\) denotes nodes that are k hops away from the node i. This equation is translated into the logic form as:

(R.<output_name>(V.I)[<W>] <= (
    R.<feature_name>(V.I<k>),
    R.<edge_name>(V.I<1>, V.I<0>), R.<edge_name>(V.I<2>, V.I<1>), ..., R.<edge_name>(V.I<k>, V.I<k-1>),
)) | [<aggregation>, Transformation.IDENTITY]

R.<output_name> / 1 | [<activation>]

Examples

The whole computation of this module (parametrized as SGConv(2, 3, "h1", "h0", "_edge", 2)) is as follows:

(R.h1(V.I0)[3, 2] <= (R.h0(V.I2), R._edge(V.I1, V.I0), R._edge(V.I2, V.I1))) | [Transformation.IDENTITY, Aggregation.SUM]
R.h1 / 1 | [Transformation.IDENTITY]

Module parametrized as SGConv(2, 3, "h1", "h0", "_edge", 1) translates into:

(R.h1(V.I0)[3, 2] <= (R.h0(V.I1), R._edge(V.I1, V.I0))) | [Transformation.IDENTITY, Aggregation.SUM]
R.h1 / 1 | [Transformation.IDENTITY]

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
k (int) – Number of hops. Default: 1
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.SUM

class SumPooling(output_name: str, input_name: str, input_arity: int = 1)[source]

Bases: Pooling

Apply sum pooling over the input specified by the input_name and the input arity parameters. Can be expressed as:

\[h = \sum_{i_{0}, .., i_{n} \in N} x_{(i_{0}, .., i_{n})}\]

Where \(N\) is a set of tuples of length \(n\) (specified by the input arity parameter) that are valid arguments for the input predicate.

This module extends the generic pooling Pooling.

Examples

The whole computation of this module (parametrized as SumPooling("h1", "h0")) is as follows:

(R.h1 <= R.h0(V.X0)) | [Aggregation.SUM, Transformation.IDENTITY]
R.h1 / 0 | [Transformation.IDENTITY]

Parameters:

output_name (str) – Output (head) predicate name of the module.
input_name (str) – Input name.
input_arity (int) – Arity of the input predicate input_name. Default: 1

class TAGConv(in_channels: int, out_channels: int, output_name: str, feature_name: str, edge_name: str, k: int = 2, activation: TransformationFunction = <neuralogic.core.constructs.function.function.TransformationFunction object>, aggregation: AggregationFunction = <neuralogic.core.constructs.function.function.AggregationFunction object>)[source]

Bases: Module

Topology Adaptive Graph Convolutional layer from “Topology Adaptive Graph Convolutional Networks”. Which can be expressed as:

\[\mathbf{x}^{\prime}_i = act(\sum_{k=0}^K \mathbf{W}_k \cdot {agg}_{j \in \mathcal{N}^k(i)}(\mathbf{x}_j))\]

Where act is an activation function, agg aggregation function, Wk are learnable parameters and \(\mathcal{N}^k(i)\) denotes nodes that are k hops away from the node i. This equation is translated into the logic form as:

This equation is translated into the logic form as:

(R.<output_name>(V.I0)[<W0>] <= R.<feature_name>(V.I0)) | [<aggregation>, Transformation.IDENTITY]
(R.<output_name>(V.I0)[<W1>] <= (R.<feature_name>(V.I1), R.<edge_name>(V.I1, V.I0))) | [<aggregation>, Transformation.IDENTITY]
(R.<output_name>(V.I0)[<W2>] <= (R.<feature_name>(V.I2), R.<edge_name>(V.I1, V.I0), R.<edge_name>(V.I2, V.I1)) | [<aggregation>, Transformation.IDENTITY]
...
(R.<output_name>(V.I0)[<Wk>] <= (R.<feature_name>(V.I<k>), R.<edge_name>(V.I1, V.I0), ..., R.<edge_name>(V.I<k>, V.I<k-1>)) | [<aggregation>, Transformation.IDENTITY]
R.<output_name> / 1 | [<activation>]

Examples

The whole computation of this module (parametrized as TAGConv(1, 2, "h1", "h0", "_edge")) is as follows:

(R.h1(V.I0)[2, 2] <= R.h0(V.I0)) | [Aggregation.SUM, Transformation.IDENTITY]
(R.h1(V.I0)[2, 1] <= (R.h0(V.I1), R._edge(V.I1, V.I0)) | [Aggregation.SUM, Transformation.IDENTITY]
(R.h1(V.I0)[2, 1] <= (R.h0(V.I2), R._edge(V.I1, V.I0), R._edge(V.I2, V.I1)) | [Aggregation.SUM, Transformation.IDENTITY]
R.h1 / 1 | [Transformation.IDENTITY]

Module parametrized as TAGConv(1, 2, "h1", "h0", "_edge", 1) translates into:

(R.h1(V.I0)[2, 1] <= R.h0(V.I0)) | [Aggregation.SUM, Transformation.IDENTITY]
(R.h1(V.I0)[2, 1] <= (R.h0(V.I1), R._edge(V.I1, V.I0)) | [Aggregation.SUM, Transformation.IDENTITY]
R.h1 / 1 | [Transformation.IDENTITY]

Parameters:

in_channels (int) – Input feature size.
out_channels (int) – Output feature size.
output_name (str) – Output (head) predicate name of the module.
feature_name (str) – Feature predicate name to get features from.
edge_name (str) – Edge predicate name to use for neighborhood relations.
k (int) – Number of hops. Default: 2
activation (TransformationFunction) – Activation function of the output. Default: Transformation.IDENTITY
aggregation (AggregationFunction) – Aggregation function of nodes’ neighbors. Default: Aggregation.SUM

class Transformer(input_dim: int, num_heads: int, dim_feedforward: int, output_name: str, src_name: str, tgt_name: str, src_mask_name: str | None = None, tgt_mask_name: str | None = None, memory_mask_name: str | None = None, arity: int = 1)[source]

Bases: Module

A transformer module based on “Attention Is All You Need”.

Parameters:

input_dim (int) – The number of expected features.
num_heads (int) – The number of heads in the multi-head attention module.
dim_feedforward (int) – The dimension of the feedforward network.
output_name (str) – Output (head) predicate name of the module.
src_name (str) – The name of the predicate of the input to the encoder.
tgt_name (str) – The name of the predicate of the input to the decoder.
src_mask_name (str, optional) – The name of the predicate of the encoder input mask. Default: None
tgt_mask_name (str, optional) – The name of the predicate of the decoder input mask. Default: None
memory_mask_name (str, optional) – The name of the predicate of the encoder output mask. Default: None
arity (int) – Arity of the input and output predicate. Default: 1

class TransformerDecoder(input_dim: int, num_heads: int, dim_feedforward: int, output_name: str, input_name: str, encoder_name: str, mask_name: str | None = None, memory_mask_name: str | None = None, arity: int = 1)[source]

Bases: Module

A transformer decoder module based on “Attention Is All You Need”.

Parameters:

input_dim (int) – The number of expected features.
num_heads (int) – The number of heads in the multi-head attention module.
dim_feedforward (int) – The dimension of the feedforward network.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – The name of the predicate of the input sequence.
input_name – The name of the input encoder.
mask_name (str, optional) – The name of the predicate of the decoder input sequence mask. Default: None
memory_mask_name (str, optional) – The name of the predicate of the encoder output mask. Default: None
arity (int) – Arity of the input and output predicate. Default: 1

class TransformerEncoder(input_dim: int, num_heads: int, dim_feedforward: int, output_name: str, input_name: str, mask_name: str | None = None, arity: int = 1)[source]

Bases: EncoderBlock

A transformer encoder module based on “Attention Is All You Need”.

Parameters:

input_dim (int) – The number of expected features.
num_heads (int) – The number of heads in the multi-head attention module.
dim_feedforward (int) – The dimension of the feedforward network.
output_name (str) – Output (head) predicate name of the module.
input_name (str) – The name of the predicate of the input sequence.
mask_name (str, optional) – The name of the predicate of the input sequence mask. Default: None
arity (int) – Arity of the input and output predicate. Default: 1