Towards a Mathematical Framework for Artificial Consciousness
Investigating self-representation, recurrent processing and information integration in artificial systems.
Central question: can we identify mathematical and computational properties that separate systems with a persistent, integrated self-representation from systems that only respond to inputs?
We are not trying to make an AI say it is conscious. Language models can already produce convincing claims about inner experience, and that tells us very little. We want to find which mechanisms could make artificial consciousness possible, and what evidence would tell that apart from sophisticated imitation.
The work builds on the indicator-properties approach, which assesses AI systems against properties drawn from leading neuroscientific theories of consciousness, and on recent adversarial studies that tested competing theories against each other.
- M1
Information integration
How much the parts of a system act as one whole rather than separate modules.
- M2
Persistent self-representation
An internal model of the system's own states that lasts across time and tasks. More
- M3
Recurrent processing
Feedback loops where later stages reshape earlier ones, instead of a single forward pass.
- M4
Internal state regulation
Signals like uncertainty, reward and aversion, modelled on how brains process emotion.
Build two minds. Break one on purpose.
Memory + language
A capable AI that remembers and talks, with no model of itself.
A + recurrent workspace + self-model
The same AI with a feedback workspace and an internal model of its own states.
ΔP = Pintact − Pdisrupted
Switch off parts of System B one at a time and measure performance on tasks that need self-monitoring, memory integration and adaptation. If disrupting the self-model reliably hurts those abilities, it plays a causal role. That is a finding about mechanism, and a step toward, but not proof of, experience.
Mathematics first. Then the mind.
Map what is known
Pin down what neuroscience has established and which questions are still open.
A falsifiable model
Write mathematics that predicts how specific mechanisms should change behaviour.
Test it in code
Implement the model in Python, compare it against simpler systems, and see if the predictions hold.
Publish and invite critique
Document the maths, results and limitations, and seek feedback from researchers before peer review.
We want to build experiments capable of surprising us, even by disproving our favourite hypothesis.
Grounded in real brains.
Our models start from published neural data rather than intuition. Early candidates include the Allen Institute's open brain datasets and the MICrONS dataset, which pairs recorded activity of tens of thousands of neurons in mouse visual cortex with their physical wiring.
That combination of structure (the graph) and activity (what flows over it) is exactly what a mathematical theory of mind needs to explain.
G = (V,E) is open to investors who want to take part in this research and development from the very beginning. Researchers with feedback on the framework are welcome to write too.