The Crystalline Engine
A Teaser for a Self-Crystallizing Geometric AI Stack
Shrink the experiment. Grow the result. The math speaks for itself.
A modular, cost-savvy, geometry-first system for rapid research, disposable training, and careful curation.
Abstract
We introduce the Crystalline Engine, a geometric AI stack that represents concepts and observations as pentachora (5-vertex crystals) in a shared field and trains by composing small, disposable blocks rather than monoliths. The system anchors continuity in a Vocabulary Register (tokens ↔ crystals/volumes), standardizes intake with bucketed, any-size dataloaders, and governs exploration through a bounded Chaos Corridor and gentle Zoning. A configurable guidance layer (Infinity-CFG) enables controlled cross-inference without collapsing geometry; canonical classifiers remain deterministic and explainable. The result is a self-crystallizing model that can be attached, coupled, decoupled, and grown with minimal waste—targeting a step-change in research velocity per GPU-hour.
1. Motivation
Modern training cycles over-spend on monolithic retrains. Researchers want to:
- Try more hypotheses per dollar.
- Keep what works, discard what doesn’t—without losing continuity.
- Scale from small pilots to large benchmarks without re-architecting.
We respond with a system that compartmentalizes training and reuses geometry. Rather than making the model ever larger, we let it self-crystallize: new capability forms as additional crystals, subspaces, and guidance blocks that can be audited, retired, or kept.
2. Overview of the Approach
- Geometric Core — Images and tokens become pentachora (5×D tensors). Decisions are made by MAE crystal energy to dictionary blueprints—simple, explainable, and geometry-safe (no L2 routing or structural normalization).
- Vocabulary Register — A reusable dictionary maintains tokens → crystals, pooled vectors, and volumes; loads only what’s needed; resolves OOV tokens by Top-3 cosine mixing. This prevents throwaway work and gives the system a memory.
- Assistant Fabric — Small, disposable blocks manage exploration: a bounded Chaos Corridor (orthogonal subspace), light Zoning (group-wise geometric separation), and Infinity-CFG, a controllable guidance layer. Blocks can be attached/retired without touching the Core.
- Canonical Dataloaders — Bucketed, any-size intake with multi-stage interpretations (the same image is learned multiple ways per epoch), optional tiling for big frames, and feature-space chaos augmentation.
Together, these pieces convert expensive monoliths into cheap, composable experiments that compound.
3. Architecture (three strata + register)
3.1 Vocabulary Register (continuity & growth)
What it holds
- Pentas (5×D), pooled vectors, and Cayley–Menger volumes for each token.
- An indexed store for fast O(1) queries and batched prefetch.
- An OOV resolver: if a token is missing, compose a crystal from the Top-3 cosine neighbors (mean mix).
Why it matters
- Keeps regularized continuity across runs.
- Logs block expansions (who spawned, why, what stayed), so the model can grow without losing its map.
3.2 Core Structure (geometric, deterministic, safe)
- Geometric Encoder: multi-scale features → role routing (softmin-MAE) → a pentachoron V ∈ ℝ^{5×D}.
- Prototype Classifier: class logits via MAE crystal energy E(V, C_k); no L2 routing, no structural normalization.
- (Optional) Flow Head: discrete flow-matching with geometry-aware conditioning; the classifier remains canonical.
Property: Decisions are direct and auditable; the Core stays stable as new blocks come and go.
3.3 Assistant Fabric (expansion & exploration)
- Register Gate: spawns/retire disposable blocks based on confusion/overlap; every action is logged to the Register.
- Chaos Corridor: a bounded orthogonal subspace that enables safe cross-interpolation between “infinities” without destabilizing the main field.
- Zoning: a gentle group-wise geometric regularization (think super-classes) that encourages separation without hard templates.
- Infinity-CFG: configurable guidance that can “breach barriers” for research while canonical classifiers keep production behavior deterministic.
Property: We can add capability without inflating the model’s base complexity.
3.4 Tertiary Mantle (losses, hooks, governance)
- Loss Factory: canonical classification (MAE), diffusion (ε), contrastives, plus light zoning; simple schedules.
- Hooks: pre/post encode, pre/post optimizer step, and eval capture for confusion & geometry histograms.
- Run Manifests: config hash, vocab subset, expansions, buckets, and metrics—ready for HF publishing & audits.
Property: Clean hand-offs to collaborators; reproducibility as a default.
4. Training Paradigm (canonical & cost-savvy)
- Any-size intake → standardize into buckets (e.g., 256/384/512)
- Multi-stage interpretations: each image contributes 2–4 views per epoch (downscale/upscale, varied crops/tiles), raising info density.
- Chaos-on-command (feature-space, bounded) for diversity without geometric collapse.
- Disposable blocks to test ideas; the Core stays untouched; the Register tracks growth.
Outcome: More hypotheses per GPU-hour and a model that compounds results, rather than restarting.
5. A Hint of Mathematics (select elements)
We keep the canon minimal and stable:
Crystal Readout (MAE):
E(V, C_k) = (1/(5D)) Σ_{v,i} |V_{v,i} − C_{k,v,i}|, logits ℓ_k = −E/τ, CE on ℓ.Cayley–Menger as a Gauge (not a router):
A 4-simplex volume index (autograd-friendly) used sparingly to encourage group-wise stability (“zoning”).Chaos as a Bounded Corridor:
A projected, orthogonal subspace Q ξ with small variance and a deterministic component; turned off for eval.Infinity-CFG (guidance, abstract):
A controllable blend of unconditional/conditional flows plus small geometric offsets that allow cross-inference only when useful.
Deliberately vague: we keep coefficient schedules and corridor projections under wraps for sponsored studies; everything remains auditable and safe.
6. Early Signals (teaser-level)
- MNIST / Fashion / CIFAR-scale pilots show that bucketed multi-stage learning + dictionary-driven classifiers reach strong accuracy with fewer steps and yield crisper failure modes.
- The Vocab Register lets us reuse crystals across datasets, cutting warm-start costs and avoiding repeated token work.
- The Assistant Fabric makes it cheap to try ideas—attach a block, test, detach; the Core and Register keep the lights on.
We’ll publish full structural articles and controlled benchmarks with institutional partners.
7. Why fund this?
- Do more science with less compute.
Small, disposable trainings; geometric reuse; a register that compounds results. - Transparent governance.
Deterministic classifiers, logged expansions, manifests ready for audit. - Grows with your lab.
Attach/couple/decouple new heads without destabilizing the base model.
We’re not selling a monolith; we’re offering a way to stop wasting monolithic cycles.
8. Collaboration & Next Steps
- Research institutions: co-run ImageNet-class studies with bucketing, zoning, and corridor ablations; share ontologies and extend the Register.
- Corporate labs: integrate domain dictionaries; trial rapid iteration pipelines; publish cost-per-accuracy analyses.
- Sponsors & foundations: fund open reports on modularization as the canonical AI form, compact training economics, and introspection protocols.
Final Notes
Core conceptualizations and innovations are subject to official release papers and weights.
Full structural solutions for partners are subject to NDA and immediate curation.
Non-profit in mind - we build to sustain and progress until we are no longer needed.
Official high complexiy curated solution artifacts (demo runners, manifests, sample checkpoints) are available free of charge at all times - unless an explicit deal is struck with a partner under NDA.
Core innovations are available free of charge - geometric vocabulary, baseline structural curations, and the geometric mathematics will be available in a series of papers within the week. Look forward to the future my friends.
Appendix (select definitions)
- Pentachoron — 5-vertex crystal (4-simplex). We encode both images and tokens as 5×D structures.
- Vocab Register — Fast and reusable dictionary; OOV tokens resolved via Top-3 cosine composites.
- Chaos Corridor — A small, orthogonal exploration subspace; bounded, schedulable, and off at eval.
- Zoning — Gentle geometric banding across super-classes; encourages stability and clarity.
- Infinity-CFG — Controllable guidance that explores cross-inference while the canonical classifier preserves deterministic behavior.
Contact
Partnerships & Research Programs — available on request.
We welcome conversations with labs and sponsors who want rapid iteration, disposable training, and careful curation to become the new standard.