From Latent Causal Models (LCMs) to Fourier Neural Operators (FNOs)

- Latent Causal Models (LCMs)

- Fourier Neural Operators (FNOs)

- Hypernetwork Weight Matching (HWM)

- Reinforcement Learning (RL)

- Transfer Learning

- Convolutional Neural Networks (CNNs)

Latent Causal Models (LCMs)

Latent Causal Models (LCMs) are a new approach to uncovering and utilising hidden causal relationships in complex datasets. Unlike traditional causal inference methods, which rely on observed variables, LCMs aim to infer the causal structure of latent (unobserved) variables that influence the data.

Imagine a company trying to understand why some marketing campaigns work better than others. They see sales numbers and customer behaviour but can't directly observe hidden factors like customer sentiment or brand perception. Latent Causal Models (LCMs) aim to uncover these hidden factors and show how they influence the outcomes, helping the company make better decisions. A streaming service notices some users binge-watch shows while others quit after one episode. The visible factors are genre and viewing history, but hidden factors like mood or peer recommendations might be influencing behaviour. LCMs can help infer these hidden causes and guide the service to recommend shows more effectively.

LCMs use machine learning and causal inference to analyse patterns in data, even when not all relevant variables are visible. They model the latent space, identifying unobserved variables that impact the outcomes. For example, in user behaviour analysis, LCMs could infer hidden motivators like user preferences or external influences (e.g., social trends). LCMs work well in dynamic environments where the relationships between variables change over time. By integrating techniques like graphical models and Bayesian networks, LCMs can simulate how interventions on hidden variables—like tweaking a marketing strategy—affect outcomes.

In supply chain management, LCMs analyse delays in deliveries. Observable factors include traffic and warehouse efficiency, but latent variables like supplier reliability or regional policies influence outcomes. LCMs uncover these hidden variables, helping optimise logistics decisions. In climate modelling, LCMs can uncover latent variables like oceanic patterns or atmospheric conditions that influence global weather systems. By identifying these hidden causal factors, LCMs improve predictions of phenomena such as hurricanes or droughts, aiding in disaster preparedness and mitigation.

Fourier Neural Operators (FNOs)

Fourier Neural Operators (FNOs) are a novel approach to solving complex partial differential equations (PDEs) using deep learning. They leverage the power of the Fourier transform to learn solutions in the frequency domain, making them particularly efficient for high-dimensional and continuous problems.

Think about modelling how heat spreads through a building in winter. Traditional methods use equations to simulate every step, which takes hours. Fourier Neural Operators (FNOs) simplify this by focusing on the recurring patterns of heat flow, letting the model predict outcomes in seconds instead of hours. A wind farm operator wants to predict how wind flows across turbines to optimise energy output. FNOs learn from existing wind data to predict flow patterns across the farm, even under new weather conditions, ensuring maximum efficiency.

FNOs operate in the frequency domain, breaking down complex processes into simpler components using Fourier transforms. In this domain, they identify recurring patterns and relationships in the data, making predictions faster and more scalable. By bypassing the need for grid-based numerical methods, FNOs handle high-resolution simulations without requiring extensive computing resources. FNOs are particularly useful for tasks where physical processes follow predictable patterns but are computationally expensive to model. Their ability to generalise across different conditions or resolutions makes them ideal for real-time applications in fluid dynamics, material science, or environmental modelling.

In tsunami prediction, FNOs analyse ocean dynamics to simulate wave propagation. By training on historical tsunami data, FNOs can predict how future tsunamis might travel across different coastal regions, providing faster warnings compared to traditional hydrodynamic models. In aerodynamics, FNOs have been used to predict airflow patterns around objects like aircraft wings. Traditional computational fluid dynamics (CFD) simulations are computationally expensive and time-consuming, but FNOs provide fast, accurate approximations of flow dynamics, enabling rapid prototyping and design iterations.

Hypernetwork Weight Matching (HWM)

Hypernetwork Weight Matching (HWM) is a technique for aligning and merging neural network weights from multiple trained models. It allows for efficient model ensemble creation or knowledge transfer by learning to match the parameters of different networks in a consistent manner.

Imagine two cities building separate navigation systems for their public transport networks. One system is great for buses, and the other excels at subways. You want a single system that combines both capabilities without starting from scratch. Hypernetwork Weight Matching (HWM) helps merge these systems, ensuring their unique strengths are preserved. A fitness app has separate AI models—one trained to track steps and another to analyse sleep patterns. HWM aligns and combines these models into one unified system that can track fitness and sleep together, giving users holistic insights without retraining from scratch.

HWM uses a hypernetwork—a secondary neural network—to align and merge the parameters (weights) of multiple pre-trained models. This process involves learning a mapping that reconciles differences between the models’ learned representations while retaining their specialised knowledge. Unlike fine-tuning or ensembling, HWM avoids catastrophic forgetting (losing previously learned skills) and enables the seamless integration of models trained on different datasets or tasks. This approach is particularly valuable in federated learning, where data privacy concerns prevent raw data sharing between organisations. By merging models trained separately, HWM ensures collaborative improvements without compromising data security.

In disaster response, different AI models might be trained on separate datasets to predict floods, earthquakes, or wildfires. HWM can combine these models into a single system capable of predicting multiple types of disasters, providing a unified decision-making tool for emergency planners. In federated learning for medical AI, HWM can merge models trained on different hospitals’ data (e.g., patient scans) without requiring centralised data sharing. This allows a global model to be created that performs well across diverse patient populations while preserving privacy and improving robustness.

Reinforcement Learning (RL)

Reinforcement Learning (RL) is a cutting-edge AI approach inspired by how humans and animals learn through trial and error. Instead of being told the correct action, an RL agent learns by interacting with its environment and adjusting based on rewards and penalties. Imagine teaching a dog to fetch a ball. Every time the dog does it correctly, you give it a treat. Over time, the dog learns that fetching the ball leads to rewards. This is the basic idea of Reinforcement Learning (RL): training an AI system to make decisions by rewarding good actions and discouraging bad ones.

Self-driving cars use RL to learn how to navigate roads. They’re trained in simulations where they’re rewarded for following traffic rules, avoiding obstacles, and reaching their destination safely. Over time, the car learns to make smarter driving decisions.

In RL, an agent interacts with an environment to achieve a goal. The agent takes actions, receives feedback in the form of rewards or penalties, and learns to maximise cumulative rewards. The learning process involves trial and error, where the agent explores different strategies to determine which actions yield the best outcomes.

Key components of RL include:

• Policy: The strategy the agent follows to decide its actions.
• Reward Signal: The feedback the agent receives after an action.
• Value Function: Estimates the future rewards of being in a certain state or taking an action.
• Exploration vs. Exploitation: Balancing trying new actions (exploration) with sticking to known successful actions (exploitation).

RL is widely used in robotics, gaming, and industrial automation due to its ability to learn complex sequences of decisions in dynamic environments. In warehouse automation, RL is used to optimise the paths of robots moving goods. Robots learn through simulation to minimise travel time and avoid collisions, eventually creating highly efficient logistics workflows.

Transfer Learning

Transfer Learning is a revolutionary approach in AI that leverages knowledge from one domain to solve problems in another. It saves time and computational effort by building on pre-trained models instead of starting from scratch. Imagine you’ve learned to ride a bicycle. When you try a motorcycle for the first time, you don’t start from scratch—you transfer your balance and steering skills from bicycling to motorcycling. Transfer Learning in AI works the same way: models trained on one task use that knowledge to perform a related task more efficiently.

A language model trained to understand English can be adapted to analyse legal documents with minimal extra training. Instead of training from scratch, the AI transfers its understanding of English grammar and vocabulary to specialise in legal terminology. Transfer Learning involves using a pre-trained model (trained on a large dataset for a general task) as the starting point for a new, more specific task. The pre-trained model provides a strong foundation, such as recognising edges in images or understanding basic language patterns, which reduces the amount of data and computation required for the new task.

In computer vision, for example, a model like ResNet trained on millions of general images (e.g., animals, objects) can be fine-tuned to classify medical images, like X-rays, with minimal additional data. Similarly, in natural language processing (NLP), models like BERT or GPT-3 can be adapted to customer service chatbots or sentiment analysis. In healthcare, transfer learning is used to develop AI models for rare diseases. A model trained on general medical images is fine-tuned on a smaller dataset of rare disease scans, enabling accurate diagnosis with limited data.

Convolutional Neural Networks (CNNs)

Convolutional Neural Networks (CNNs) are a specialised type of deep learning model designed to analyse and understand visual data. They are the driving force behind AI breakthroughs in image and video analysis. Think of how your brain processes images. When you look at a photo, you first notice basic features like edges and shapes, and then combine them to recognise objects, like a face or a car. Convolutional Neural Networks (CNNs) mimic this process to help AI analyse and understand visual data. A smartphone uses a CNN to detect faces when you’re taking a picture. It identifies edges, shapes, and patterns in the image to locate and recognise the faces automatically.

CNNs are a type of deep learning model specifically designed for processing image data. They work by applying convolutional filters to input images, which scan the image for specific features like edges, textures, or colours. These filters extract spatial hierarchies of features, starting from simple patterns in early layers to complex objects in deeper layers.

CNNs consist of:

• Convolutional Layers: Apply filters to the image to detect features.
• Pooling Layers: Reduce the spatial dimensions of the data to make the model more efficient.
• Fully Connected Layers: Combine the extracted features to make predictions, such as classifying an object in the image.

This architecture makes CNNs highly effective for tasks like image classification, object detection, and facial recognition. CNNs are also used in other fields, such as analysing medical scans or satellite imagery. In autonomous vehicles, CNNs process camera inputs to detect lane markings, traffic signs, and pedestrians. By identifying and classifying these visual elements, the car can make decisions like stopping at a red light or avoiding obstacles.