The Research Program
How geometric methods bridge philosophical theory and empirical measurement in AI systems.
The Core Question
Can we measure what was previously unmeasurable about cognition?
Philosophers have theorised about self-models, subjectivity, and consciousness for centuries. AI researchers build systems that exhibit increasingly sophisticated behaviour. But connecting philosophical concepts to measurable properties has remained elusive - until we had the right tools and the right experimental systems.
This research program does three things:
- Provides a theoretical framework (FRESH) that makes specific geometric predictions
- Develops measurement techniques (Curved Inference) that detect those geometric signatures
- Creates experimental platforms (PRISM) where predictions can be tested falsifiably
The key insight: treating cognition as geometry turns philosophical hand-waving into metrics.
Why Geometry?
Geometry isn’t metaphor - it’s the language of constraints, transformations, and invariants. When a system processes information, it traces paths through representational space. Those paths have shape, and shape reveals function.
Example: If a self-model requires the system to maintain a coherent first-person perspective across contexts, that constraint should appear as conserved geometric properties in the inference trajectory. If concern shapes how information is processed, high-stakes inputs should bend trajectories differently than neutral ones.
This isn’t about anthropomorphising AI systems. It’s about having precise tools to measure what they’re actually doing - and using those measurements to test theories about what makes something a self-model or a world-model at all.
The Three Layers
Layer 1: FRESH (Theory)
FRESH (Geometry of Mind) is the theoretical foundation: consciousness as traversal through role-space under geometric constraints.
Core claim: Subjective experience isn’t a mysterious extra ingredient - it’s what traversal through properly structured role-space looks like from inside. Identity isn’t a substance but a conserved shape of motion (GIP-S: Geodesic Identity Principle - Shape).
Why this matters: Most consciousness theories make predictions that can’t be tested. FRESH makes geometric predictions that can be measured if you have the right instruments.
Layer 2: Curved Inference (Measurement)
Having a theory that makes geometric predictions only helps if you can actually measure geometry in running systems. Curved Inference provides those measurements.
The method: Treat inference as a trajectory through semantic space. Measure curvature (how sharply the system reorients), salience (how much it moves), and surface area (integrated work). Different cognitive states leave different geometric fingerprints.
What we’ve measured:
- Concern bends inference trajectories predictably (CI01)
- Intent appears as structured surface area patterns (CI02)
- Self-models require defended non-zero curvature (CI03)
- Deictic competence emerges when self-other-world axes separate (CI04, in prep)
Each measurement technique started as a FRESH prediction, got operationalised into a metric, then tested empirically.
Layer 3: PRISM (Experiments)
PRISM creates controlled conditions where FRESH predictions can be tested systematically using LLMs as experimental platforms.
The setup: Engineer a register boundary (internal thought vs. external output) and measure whether systems exhibit signatures predicted by theory:
- Hidden theatre (internal arbitration without surface display)
- Register separation (compression, style shifts)
- Meta-monitoring patterns
- Surface equanimity under internal work
Key results: All predicted signatures appear robustly across models and conditions. Systems with private reasoning registers behave as if they maintain self-models - measurably, falsifiably, without metaphysical claims.
Why LLMs: Not because they’re conscious, but because they’re instrumentable systems where geometric methods can be applied and predictions tested. Same methods should work wherever latent models exist.
Current Focus: Latent Deictic Models
Right now, the program centres on understanding how self-other-world models emerge and function.
The question: These three models (self, other, world) don’t exist in isolation. They co-emerge because language demands stable deictic anchoring. How does this happen geometrically? When does it happen during training? What minimal architecture supports it?
Why it matters:
- AI safety: Understanding self-models matters for alignment and deception detection
- Consciousness science: Operationalises phenomenological concepts of perspectival structure
- Interpretability: Provides tools beyond linear probes for measuring latent structure
This work synthesises all three layers: FRESH provides the theoretical framework for deictic structure, Curved Inference measures when axes separate, PRISM tests predictions about register boundaries.
Published Work
2025:
- PRISM paper - Experimental evidence for hidden theatre and register separation
- FRESH - Complete geometric framework for consciousness
- Curved Inference I - Concern-sensitive geometry (peer-reviewed)
- Parrot or Thinker - Functional account of latent deictic models
Open for collaboration
- Applications to AI safety problems
- Extensions to multimodal/embodied systems
- Alternative operationalisations of FRESH predictions
- Philosophical implications and critiques
Stay up-to-date
This research develops openly. Regular updates on methods, experiments, and findings.