What Is Geometric Deep Learning?

Introduction: What Is Geometric Deep Learning?

Deep learning is gaining increased interest in several industries. This field forms part of machine learning. The idea behind deep learning is to take cues in the way the brain functions. The structure also mimics that of the brain. The resulting system is an artificial neural network. 

Deep learning has numerous branches, usually measured by the dimensions of the field. While Euclidean data comprises of representations in 1D and 2D depths, geometric deep learning is based on the principle of 3D. We take a look at what geometric deep learning is and how it will play a role in the future. 

Also Read: AI in Drug Discovery

Surpassing Deep Learning Methods

In the past, a majority of research and development with deep learning was related to the first and second dimensions. The Euclidean methods that have been used place certain limitations on the opportunity for expanding deep learning. This is because the real world has a third dimension not targeted by these models of deep learning. 

Geometric deep learning focuses on surpassing the current methods in deep learning, primarily by focusing on including this third dimension in the artificial neural networks created through the technology. 

By focusing on a 3D model instead of the standard 1D and 2D dimensional approaches, it is possible to reach closer to human-level networks, as this is the dimension that manifests itself in the real world. 

Euclidean data models have been focusing on subjects the following subjects throughout the past years:

  • Computer vision
  • Speech recognition
  • Language transition
  • Image generation

While Euclidean data has already provided successful results in the past, the limitations faced have halted progress in certain areas. 

Complex data is processed in areas like biology and physics, as well as in network science. By using Euclidean data, complex data cannot be processed efficiently – due to the simple dimensions used in the process. 

Source: YouTube | Geometric deep learning.

By turning to geometric deep learning, these limitations can be effectively overcome. Researchers have found that non-Euclidean data is able to process data that is complex faster and more efficiently while also delivering results that are closer to a human level. 

Also Read: AI In Robotics: an Assimilation For The Next Phase In Technology.

Non-Euclidean Data Types

There are several examples of how non-Euclidean data types are utilized in the modern world. Among all data types, researchers and scientists generally turn to graphs most frequently. 

A social media platform can be represented by a graph. The graph consists of nodes. A social platform like Facebook would have millions of nodes – as each node represents a user on the network. Graphs in non-Euclidean models consist of more than just the nodes, however. Edges are used as connectors between different nodes in a network. With a platform like Facebook, the edges would represent actions performed by users. 

In this example, two people would form nodes – and a conversation that occurs between the two users creates an edge that runs between the two nodes. 

Geometric deep learning can also include the use of manifolds as a data type. In this data model, a multi-dimensional system is used – which is where the 3D environment of geometric deep learning comes into play. The multi-dimensional space seen in a manifold data type is represented by a shape with three dimensions. The space would have a vast number of points that help in the creation of the shape. 

As geometric deep learning advances, we are seeing this technology implemented in various industries. A good example would be the pharmaceutical industry, where geometric deep learning has the potential to assist with the process of drug discovery. 

With drug discovery, a three-dimensional model of graph data types is used. Molecules that are in existence and previously discovered are modeled into the graph. Nodes in the graph represent the atoms that can be used in the development of molecules, while the edges in the graph represent the bonds between atoms. 

Through geometric deep learning, technology can compare millions of atoms and molecules in order to find new drug options to treat existing diseases. This may be especially helpful in cases where chronic diseases are difficult to treat. New combinations of molecules and atoms can be identified with the help of geometric deep learning. These discoveries can then be analyzed by scientists, allowing them to determine if the molecules would have the potential to help patients with the disease. 

There are a few other examples of non-Euclidean spaces and data types that can be used in real-world scenarios. Social sciences, for example, would create a 3D model of social networks to gain a more advanced understanding of human behavior. This would take the basic graph model of social networks to the next level. 

Also Read: The Role of Artificial Intelligence in Healthcare Documentation.

Categories of Geometric Deep Learning

Geometric Deep Learning (GDL) is a burgeoning field in machine learning that generalizes deep learning models to non-Euclidean domains such as graphs and manifolds. These models have a broad spectrum of applications, including computer vision, neuroscience, and social network analysis.

The categories of Geometric Deep Learning are generally split into three broad areas based on the structure of the data they handle: Graph Neural Networks, Convolutional Neural Networks, and Recurrent Neural Networks.

Graph Neural Networks (GNNs) are designed to operate over data structured as graphs, allowing a more natural representation of a variety of real-world systems, such as social networks, biological networks, or the World Wide Web. They excel in handling relational or structural data by exploiting the inherent properties of the graphs.

By propagating and aggregating information through the nodes and edges of a graph, GNNs can capture complex patterns and interactions, often hidden from traditional machine learning models.

Convolutional Neural Networks (CNNs) in the context of GDL refer to Geometric CNNs. Unlike traditional CNNs, which are typically applied on grid-like data (e.g., images), Geometric CNNs generalize convolutions to non-Euclidean domains. They handle geometric transformations and analyze manifold or graph-structured data, proving particularly effective in 3D data analysis and computer vision tasks.

Recurrent Neural Networks (RNNs), another category, have been generalized in geometric contexts to handle structured sequential data that resides on non-Euclidean domains, enhancing their capacity to capture dynamic patterns over time.

Applications of Geometric Deep Learning

Computer Vision

Geometric Deep Learning plays a crucial role in recognizing and interpreting patterns in visual data, including image and video processing, 3D shape analysis, and scene understanding.

Social Network Analysis

Graph Neural Networks, a type of GDL model, are used to predict user behavior, detect anomalies, and identify influential nodes in social network graphs.

Drug Discovery

GDL is used in the prediction of molecular properties and drug efficacy, by representing molecules as graphs where atoms are nodes and bonds are edges.

Traffic Prediction

By treating traffic networks as graphs, GDL models can predict future traffic conditions, facilitating efficient route planning and management.

Protein-Protein Interaction

GDL is used to predict protein-protein interaction networks which are crucial for understanding biological processes and diseases.

Recommendation Systems

GDL models are used in recommendation systems to analyze user-item interaction data, which is often represented as a bipartite graph.


GDL models are used to detect anomalies or malicious activities in network data, where nodes represent computers and edges represent communications.


Brain networks can be analyzed using GDL models to understand brain function and diagnose neurological disorders.

3D Object Recognition

Geometric CNNs, a type of GDL model, are used for 3D object recognition and segmentation in areas like autonomous driving and augmented reality.


GDL models are used to understand complex systems in physics, such as particle systems or cosmological phenomena, by modeling them as graphs or manifolds.

Code Examples of Geometric Deep Learning

Here is a simplified example of how Graph Convolutional Networks (GCNs), a type of GDL, can be used in PyTorch with PyTorch Geometric, a geometric deep learning extension library for PyTorch. This example doesn’t directly apply to cybersecurity, but it gives you an idea of how GDL is used in practice. In cybersecurity, the principles would be the same, but the input graph would represent network data, and the task could be to predict whether a node (e.g., a computer in a network) is likely to be part of a cyber attack.

import torch
import torch.nn.functional as F
from torch_geometric.nn import GCNConv
from torch_geometric.datasets import Planetoid

# Load the CORA dataset (a common citation network benchmark dataset)
dataset = Planetoid(root='/tmp/Cora', name='Cora')

class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = GCNConv(dataset.num_features, 16)
        self.conv2 = GCNConv(16, dataset.num_classes)

    def forward(self, data):
        x, edge_index = data.x, data.edge_index

        x = self.conv1(x, edge_index)
        x = F.relu(x)
        x = F.dropout(x,
        x = self.conv2(x, edge_index)

        return F.log_softmax(x, dim=1)

# Training
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
model = Net().to(device)
data = dataset[0].to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)

for epoch in range(200):
    out = model(data)
    loss = F.nll_loss(out[data.train_mask], data.y[data.train_mask])

This example constructs a GCN model for the task of semi-supervised node classification in the Cora citation network. Nodes represent documents, and edges represent citation links. The goal is to classify each document into one of several classes based on its connections to other documents. In the context of cybersecurity, the documents could be replaced with computers or network entities, and the task could be to detect malicious nodes based on their connections to other nodes.

Remember, this is a very simplified example. In a real-world scenario, you would also need to consider data preprocessing, model validation, result evaluation, and many other steps. You should also make sure that you comply with all relevant data privacy regulations when working with real-world network data.

Conclusion: What Is Geometric Deep Learning?

Geometric Deep Learning (GDL) marks a paradigm shift in artificial intelligence by enabling us to extend the power of deep learning architecture to non-Euclidean data. This presents a myriad of opportunities across diverse fields. From the perspective of neural network architecture, GDL uses inductive biases to efficiently process complex data structures, enhancing the receptivity and adaptability of these models.

In Quantum Chemistry and Chemical Theory and Computation, GDL has shown promise for tasks such as predicting molecular properties and aiding in drug design. By encoding the projective geometry of molecules into neural networks, GDL assists in the exploration of chemical space in a more refined manner. It enhances the performance and accuracy of tasks that require understanding of the intricate, geometric structure of molecules.

GDL’s application isn’t restricted to scientific computations. In the world of artificial intelligence, its potential is seen in areas such as speech recognition where complex temporal dependencies exist. Through handling non-euclidean data, GDL is advancing the field, improving the processing and understanding of input signals and making speech recognition systems more robust and reliable.

In essence, the innovations in GDL open up exciting possibilities for various applications where geometric and topological properties play a significant role. From a small receptive field in an input image to the vast landscape of molecular structures, GDL’s impact will continue to be felt as it keeps advancing, pioneering breakthroughs across artificial intelligence, computational chemistry, and beyond.


Ye, Jong Chul. Geometry of Deep Learning: A Signal Processing Perspective. Springer Nature, 2022.