Technology
How the Engine Works
A geometric model of knowledge that tracks every student's position and determines the optimal next step.
The Core Idea
The Riemannian Knowledge Space
Every learning outcome in a curriculum is a point in a connected space. The distance between two points reflects how hard it is for a student to move from one concept to the next.
The metric tensor encodes this pedagogical cost — different curricula parameterise the same underlying space differently. A student's learning journey becomes a path through this space, and the engine's job is to find the optimal route.
The pedagogical thinking behind this geometry is on our approach page.
C = ρλ²
Cognitive cost equals complexity density times the square of the semantic distance. This equation governs how the engine plans every learning path.
Adaptive Intelligence
How the Tutor Decides What to Teach
Four mathematical quantities, each mapping to a real tutoring decision. Every quantity earns its place by answering a concrete question about the student.
Entropy
“How uncertain are we about this student's understanding?”
Target the highest-uncertainty outcomes first — that's where assessment has the most value.
Divergence
“Is the student drifting from the optimal learning path?”
Redirect the conversation when the student's trajectory diverges from the geodesic.
Jacobian
“If the student masters this concept, what else improves?”
Prioritise outcomes with high propagation — mastering fractions unlocks decimals, percentages, ratios.
Green's function
“What's the influence radius of this learning event?”
Determine how far a single session's progress ripples through the knowledge graph.
Curriculum Mapping
Four Curricula. One Space.
A student learning “adding fractions” in Cambridge Primary occupies the same region of the knowledge space as a student learning the equivalent in the UK National Curriculum. The curriculum defines the coordinate system. The knowledge is the same.
Curricula sit on top of the international standards we calibrate against — CEFR for English, TIMSS for Maths, TIMSS Science and NGSS for Science.
Cambridge Primary
Cambridge Early Years
UK National Curriculum
Common Core
Bayesian Framing
Prior, Likelihood, Posterior
The core of BlueberryML is not a prompt, not a model, and not a content library. It is a learned geometry — a coordinate system for human development that gets sharper every time a learner moves through it. The geometry above is a prior. The operators are an inference engine. The student's path is the result. Together they form a complete Bayesian system.
PRIOR
Manifold
The learned coordinate system of human development. Built on the curricula and international standards described above, distilled into a single geometric object. Curriculum-agnostic, culturally tuneable, pre-computed.
LIKELIHOOD
Sequential Inference
Standard machinery for updating beliefs about a hidden learner state as new observations arrive — Markov inference, well-understood mathematics. Each assessment — written, spoken, multiple-choice — is an observation. The operators (H, D, J, G) act here.
POSTERIOR
Trajectory
The student's path through the manifold. Where they are, where they are going, what the next step should be. This is what the tutor renders. This is what the dashboard shows.
The framing is not cosmetic. It explains why the operators are well-defined: they act on a posterior over a manifold, not on a list of topics. It explains why curriculum mapping works: curricula are coordinate charts on a shared prior. And it explains what we are. We are not a knowledge graph company — knowledge graphs are discrete, symbolic, and brittle; a manifold is continuous and learned. We are not a retrieval-augmented generation company — RAG has no model of the learner. We are not a large-language-model company — LLMs are powerful components, but they are not the asset. We are a manifold company. The likelihood machinery — sequential, Markov-class inference — is textbook. The trajectory is the learner's. The manifold is ours.
Proven at Scale
Running at scale
The framework powers Chrysalis, our flagship ClassGrade deployment, run by our distribution partner EZ Vidya across 300,000+ students and 150+ schools in India. Chrysalis runs on EZ Vidya's infrastructure; BlueberryML licenses the framework and is not in the data path.
Read about the partnerships →