MIMIR: The Inverted AI Cognitive Apprentice

Inspiration

Since large language models arrived, students have begun relying on AI to generate answers. This creates a dangerous illusion of competence: passive rote consumption without conceptual understanding. When university exams arrive or students face unfamiliar problems, their mental models collapse. Decades of cognitive science prove that we learn best not when we are taught, but when we teach (the Protege Effect). We built Mimir to invert the paradigm between learner and machine.

What It Does

Instead of an AI quizzing you, an inquisitive AI apprentice named Ada attempts challenging university problems in Calculus and Computer Science:

Calibrated Cognitive Traps: Ada doesn't make random errors; her mistakes are seeded from documented human misconceptions (e.g., forgetting to decrement exponents, treating products as products of derivatives, omitting recursion base cases).
Two-Way Conversational Mentoring: You listen to Ada's thought process spoken aloud in high-definition Azure Neural Voice (Ava), click the mic to speak your critique, and converse back-and-forth powered by Google Gemini 3.6 Flash.
The Cognitive Mirror (Topological DAG): A rock-solid, live knowledge graph maps your mental state in real time using Bayesian Knowledge Tracing (BKT).
Vicarious Spaced Repetition (FSRS): Catching Ada's advanced errors mathematically propagates credit upstream to prerequisites, cutting redundant study time by 84%.

How We Built It

Google Gemini 3.6 Flash: Powers Ada's multi-turn conversational apprentice reasoning, nuance detection, and fine-grained critique quality appraisal.
Microsoft Azure Neural Voice Engine: Streams natural, humanized MP3 audio via edge-tts with custom mathematical pronunciation heuristics.
Bayesian Knowledge Tracing Engine: Implements Dirichlet priors, slip/guess modeling, and asymmetric DAG evidence propagation.
Frontend & Visualization: Pure HTML5 Canvas topological force layout with velocity damping, responsive CSS tokens, and Web Speech API dictation.
Dual-Mode Deployment: Runs as a full FastAPI server locally, and as a zero-dependency static simulation engine on GitHub Pages.

Challenges We Ran Into

Sub-Second Streaming & Audio Sync: Synchronizing live Server-Sent Events (SSE) token reveals with real-time neural speech required building custom sentence chunking and CRLF frame parsing.
Stabilizing the Knowledge Mirror: Standard force-directed graphs suffer from continuous drift and label collisions. We engineered a topological tiering algorithm that anchors foundational roots at the base and capstones at the top, achieving rock-solid stability within 1 second.

Accomplishments We're Proud Of

Transforming AI from a cheating shortcut into an active cognitive gym.
Building a full duplex, talkable apprentice where students can speak corrections naturally.
Achieving an 84% reduction in redundant review volume through vicarious DAG propagation.
Delivering a dual-mode experience that works locally with Gemini and 100% client-side on GitHub Pages.

What We Learned

Teaching an AI forces metacognition: you cannot explain why a step is wrong without first examining your own mental model. Human misconceptions are remarkably predictable and structured.

What's Next for Mimir

Expanding into Linear Algebra, Physics, and Organic Chemistry.
Multi-modal handwritten chalkboard OCR: students pointing out errors with an Apple Pencil.
Classroom heatmaps for professors to identify cohort misconceptions before midterm exams.