How Advanced Mathematics is a Game Changer in AI/ML

There has been a strong trend towards the applications of advanced branches of mathematics, such as Algebraic Topology & Differential Geometry, in AI/ML state-of-the-art research. The resulting techniques have shown the potential to enable the discovery of advanced deep neural network architectures that require less training data and are more generalisable than current approaches.

The recent growth in the number of AI/ML conferences & workshops around the exploitations of advanced branches of pure mathematics is a good testimony. An example is the London Geometry and Machine Learning (LOGML) Summer School, for which our parent company Zaiku Group was a proud sponsor in 2022. Below are some excellent examples of projects featured in LOGML 2022:



• Differential geometry for representation learning: A common hypothesis in machine learning is that the data lie near a low dimensional manifold which is embedded in a high dimensional ambient space. This implies that shortest paths between points should respect the underlying geometric structure. In practice, we can capture the geometry of a data manifold through a Riemannian metric in the latent space of a stochastic generative model, relying on meaningful uncertainty estimation for the generative process. This enables us to compute identifiable distances, since the length of the shortest path remains invariant under re-parametrizations of the latent space. Consequently, we are able to study the learned latent representations beyond the classic Euclidean perspective.
  
  
• Group invariant machine learning for Calabi-Yau polyhedra: There are many group invariant machine learning models, i.e. learnable functions that give the same output if the input is acted on by a group. In this project, we will apply invariant machine learning via fundamental domain projections to the Kreuzer-Skarke dataset and compare this with other group invariant machine learning techniques (e.g. data augmentation and deep sets), as well models that are not group invariant. 
  
  
• Learning graph rewiring using RL: Most GNNs are based on the concept of message passing, which is by itself based on information diffusion. In diffusion dynamics, key information lies in closer objects, and distant nodes’ effect is decimated. However, it is not clear that the topological graph structure must dictate the information transfer on the graph. In fact, in many cases, such as combinatorial optimization problems, nodes and edges that are distant from a node may have a major impact on the node’s value or class. To that end, graph rewiring allows adding edges, nodes, or other structures in order to assist information transfer. In practice, it decouples the information graph from the topological (input) graph. In this project, we will investigate how we can (meta) learn to build better information graphs using RL. Specifically, our agent will learn how to modify (add/remove) edges, i.e., perform graph rewiring, to improve learning.
  
  
• Contrastive learning: Contrastive learning seeks to train a representation function that encodes the similarity structure in a data set based on pairs of positive samples (similar data points) and negative samples (dissimilar data points). This project will investigate ways of incorporating geometric information, such as equivariances or symmetries, into Contrastive Learning approaches. Depending on the interests and expertise of the group, both computational and theoretical avenues of investigation may be pursued. 
  

How our Approach is Different?

Firstly, we deeply understand the enormous pressure enterprise organisations face to evolve and embrace next-generation technology in an ever-growing competitive global digital market. The key outcome of our AI/ML consulting service is to help data-driven enterprise organisations build the mathematical capabilities that redefine their business models to stay relevant, compete, and be leaders in their core markets. Secondly, our talent pipeline comprises the brightest young PhD-level mathematicians who complete our tailored academia-to-industry transition program with an emphasis on AI/ML.   Here are some of the benefits of working with us:

• Frictionless remote collaboration with your in-house engineering leads to help identify the critical mathematical gaps in your AI/ML project(s).
  
• Deployment of PhD-level mathematicians to help in-house AI/ML R&D teams leverage advanced branches of mathematics, such as; Algebraic Topology & Differential Geometry.
  
• Source and manage PhD level talent pipeline tailored to your needs and with long term retention in mind.
  
• Upskill your existing AI/ML team members with a tailored mathematical curriculum based on specifics of each R&D project.
  

Our team is ready to help your organisation transform its operations at the intersection of frontier AI/ML research innovation and customer needs.  Would you like to learn how we can unlock your in-house technical talent superpowers with our collaboration while preserving your independence?

 
Get in touch with our team today!