Models of the World

"If you think of Brick, you say to Brick, 'What do you want, Brick?' And Brick says to you, 'I like an Arch.' And if you say to Brick, 'Look, arches are expensive, and I can use a concrete lintel over you. What do you think of that, Brick?' Brick says, 'I like an Arch.' And it's important, you see, that you honor the material that you use." ~ Louis Kahn, 1971

Left of the Blue Wall

Artificial intelligence refers to computer models which are designed to approximate human intelligence. However, human intelligence is anchored within our own physical world. When we decide to act, or reason about a decision, we exercise tacit knowledge of the world around us. The actions we can take, such as expressing a word, moving an arm, fixing our gaze, are physical choices. The physical grounding of our actions means that our intelligence is embedded. Our thoughts and feelings are imprinted and shaped by our own physical movement throughout the world.

The extent to which our understanding of the world is decoupled from our language is unclear. The data we receive from the world are multi-faceted, covering shapes, sounds, colours, contours, and textures. We process these data in different ways and during different times of our lives. In the 1980s and 90s, Elizabeth Spelke, Linda Hermer-Vazquez, and Ken Cheng set out to understand how we use different sources of data to make decisions¹. In the famous "blue wall" experiment, a rat is placed into a rectangular room with a single blue wall and looks on as a small reward, such as a piece of cheese, is placed in one corner. The rat is then spun around until disorientated and has lost track of which way they were facing. The room contains two sources of data to anchor their position, geometric data (the shape of the room), and feature data (a wall of the room is painted blue).

Rats will look to the side of the room which matches the side where they last saw the reward. If the reward was on the left corner of the short wall before being disorientated, they will move to that left corner again, despite facing a different direction. The two corners will fit the geometric description, a short side and a long side, but they will not know if they are moving to the corner with the reward or its reward-less diagonally opposite twin. Geometric data reduces their chance of finding the reward from one in four (corners) to one in two. This is the plateau for rats.

Spelke, Hermer-Vazquez, and Cheng repeated the same experiment with children. A toddler, under the age of six, is placed into a rectangle and shown where a small reward, such as a sweet, is hidden. The child is then spun around to be disorientated. Just as the rat before, the child will move to whichever corner matches the geometry of where they last saw their reward, ignoring any cues from the colour of the walls. However, after the age of six, a child will search the room using both sources of data. Instead of just the shape of the room, they also use featural data. The children will now use the blue wall to choose between the two matching corners, looking, for example, in the corner that is left of the blue wall. The colour breaks the symmetry and their probability of finding the reward improves. They very rarely fail to find their reward.

Children demonstrate the ability to synthesise distinct spatial data around the same age that their language ability develops to include the combination of different properties of an object. Around the age of six, children start to use expressions such as "left of the blue wall". These expressions combine two data sources, both geometric (left) and featural (blue). Whether language acts as the mechanism by which this data are integrated or is the by-product of the integration of data is unclear. However, it is clear that language and data processing are at least coupled in an important way. For example, when adults perform "verbal shadowing", reading some text aloud to occupy their cognitive language system, they revert to the rat-like reorientation ability, using only the geometric data. When the same subjects perform non-verbal shadowing, such as repeating a rhythm, their reorientation was unaffected.

If language is connected to how we process data, our understanding of the world is likely connected to how we describe it. Our thoughts speak of the world but the world is contained within our thoughts. To disconnect our own intelligence from our own world, a kind of disembodied intelligence, feels alien and unnatural. Would we see the world differently if we integrated cues like rats? Would our feeling of thoughts strengthen if our minds were distributed throughout our body like an octopus, rather than centralised in our head? Does our understanding of the geometry of an object change if we could sense it through ultrasonic waves like a bat?²

Though our bodies differ, both human and animal minds are embodied within the same physical world. Today, many of us interact with a fundamentally different type of intelligence than our biological cousins; silicon-based artificial intelligence. This is an intelligence locked into computational hardware. That the response of language and vision models is intelligent is hard to refute. But similarly so, it is rare to find someone who would see this as biological intelligence. Artificial intelligence is that which is contained within zeros and ones, in computer code and tensors, on CPUs and GPUs. As we type prompts to image models, or speak with language models, it might be natural to wonder "what is it like to be an artificial intelligence". Yet, this makes no presumption of an artificial intelligence having either mind or consciousness. Instead, this is closer to asking, 'what do you want, brick?'.

Architecting Intelligence

In the 1950s, Louis Kahn would tell his students to seek advice from their materials when stuck on how to progress³. He advocated for an understanding of the material's wider role in the construction of a building. When he asks what a brick wants, he is asking what is the structure of the brick that is important. He is also asking, what is the role of the brick in relation to its environment. Both object and world are reflected back on one another.

Today, the modern day computer scientist might feel as much an architect as Louis Kahn. The field of artificial intelligence, until recently referring to techniques as varied as evolutionary algorithms, causal inference, and symbolic methods, has been overtaken by artificial neural networks, such that AI has become synonymous with deep learning models (I use the two terms interchangeably throughout this book). The specifications of AI models, such as the number of layers or specific connections, are typically referred to as architectures.

When we build artificial intelligence, we design the intelligence through ones and zeros encoded in computer code. Our raw materials are data, programs, and compute. We construct intelligence with increasingly generalisable abilities (from writing poetry to solving theorems) by architecting models and scaffolding their output to strengthen their reasoning capabilities. The researcher proposing new models or extensions to existing ones can be understood as an architect of computational primitives, in the pursuit of generalised performance at some pre-defined or open-ended set of tasks.

The idea that AI is built from model architectures is a strangely fitting term as we attempt to design models with ever increasing capabilities. Architecture refers to the design and building of structures. Historically, these structures existed within the physical world, as dwellings, places of work or worship, or even as art in their own right. A model architecture refers to the design and building of an algorithm. The structure of an algorithm might mean the loops and conditional statements that allow the algorithm to run. However, for AI models, there is another deeper meaning. Structure can refer to the representations generated by the algorithm. In architecting a model, we architect these representations.

The idea of a representation can make your head spin. What does it mean when we represent something in our mind? What does the representation of a chair or laptop feel like? Worse still, what is a representation of a representation? In asking these seemingly simple questions, it is easy to fall into the play of a toddler, first learning about the world, and ask why, after why, after why, in an infinite recursive loop.

For AI models, things are quite different. The representation within an AI is bounded and interrogable. An AI model, instantiated by a neural network, holds representations as numerical vectorised quantities. Its representations are computed in a fixed layer of the model, and can be used to construct new features to summarise the data. The retrieval part of "Retrieval-Augmented Generation" (RAG), which has become widespread with the rise of language models, refers to text data that is passed through a model and encoded as a representation so that other similar text can be retrieved by finding the nearest representations. Representations for AI models are numerical vectors.

Representations of an AI model are constrained by the architecture of the model. These constraints impose limits and structure to representations. The models that match constraints to the data, imposing architectural choices to make an image model respect the structure of image data or language models respect the form of words and sentences, are known to perform and scale more effectively than those that do not. It may even be that AI models with representations best matching the world also perform best.

These numerical vectors, shaped by the model architecture, have specific geometries or forms. The geometry of a representation means that the semantic content, such as the relationship between "France" and "Spain", can not only be recovered from the representational space of a model but even 'steered' along a semantic direction. Additionally, these representations may be shared between models, even where the datatypes are entirely different. The power of a neural network depends on the strength of its representations and, as we are learning, the representations appear to carry details of the world both inside and outside of the workings of a model. The extent that a neural network has a model of the world is intricately tied to its representations. We have only ever known embodied intelligence, intelligence formed in and by the physical world. Yet, artificial intelligence appears to model the world without ever having had a body. As children, we learn to synthesis data about the world. Now, we can make AI models that synthesise the world into representations. How is this possible, and where are the limits?

An excerpt from an early draft of "World Models".