What I Inverted
If this holds, capability moves along an axis that is not parameter count — which matters wherever compute binds and data does not.
Architectures are specified in advance and then scaled. Fix self-attention, hold depth and width, and vary parameters, tokens and steps. The reasons are good: a fixed architecture is analysable, reproducible and schedulable. Nobody reopens it because it has not needed reopening.
I made the architecture an output. A predictor fails in structured ways — differently on clusters, on cycles, and on the boundaries between them — and one fixed head must span all of it with a single inductive bias.
Three systems run in a loop. A ViT backbone with an EMA target publishes the energy surface. An explorer walks the regions where the predictor has no strong opinion, under Langevin dynamics preconditioned by the Fisher information metric, so exploration is isotropic in distribution space rather than in coordinate space.
A crystallizer runs Vietoris–Rips persistent homology over those trajectories and turns stable features into typed modules — H₀ into attractors, H₁ into cycles, H₂ into boundaries.
Persistence is the right selection criterion because of the stability theorem: the bottleneck distance between two persistence diagrams is bounded by the sup-norm distance between the functions generating them. Perturb the trajectories slightly and the diagram moves slightly, with a proven bound rather than an empirical hope. Langevin trajectories are stochastic by construction, so that guarantee is exactly what a selection rule needs. Clustering at a chosen k gives none.
What It Shows
Self-supervised link prediction, AUC, on three real heterogeneous entity graphs against baseline JEPA and three supervised GNNs.
| Graph | Crystara | JEPA | Δ | Supervised |
|---|---|---|---|---|
| CSET semiconductor (519) | 82.7% | 46.1% | +36.6 | GAT 70.3 · GCN 63.9 · SAGE 33.8 |
| GDELT news (380) | 69.1% | 47.0% | +22.1 | GAT 92.1 · GCN 85.2 · SAGE 59.9 |
| SEC EDGAR (9,725) | 66.4% | 46.4% | +20.0 | GAT OOM · GCN ~7% cls |
On the semiconductor graph the crystallizer produced sixteen modules mapping one-to-one onto real supply-chain structures, validated against CSET and industry trade data. No labels, no prompting, no supply-chain prior.
| Module | Type | Structure recovered |
|---|---|---|
| CMP pipeline | H₀ | Chemical-mechanical polishing suppliers |
| ASML ecosystem | H₀ | Netherlands lithography dependency cluster |
| Singapore ATP | H₀ | Assembly–test–packaging corridor |
| China packaging | H₀ | Back-end packaging cluster |
| Specialty chemicals | H₀ | Precursor and etchant suppliers |
| Design-to-fab | H₁ | Cyclic design → foundry → validation loop |
| EUV ↔ etch/clean | H₁ | Litho–etch feedback coupling |
| AI ASICs ↔ Hitachi | H₁ | Non-obvious equipment dependency |
| Lithography ↔ CMP | H₂ | Process-stage handoff boundary |
Nine are shown; the remaining seven, with persistence scores and the full validation mapping, are in the repository. The H₁ and H₂ modules are the point — cyclic dependencies and stage boundaries are precisely what a single head averages away, and they are recovered here as typed objects rather than diffuse geometry.
On the controlled Two Rooms environment the same mechanism shows in the embedding: k-NN improves at every k (+23.0% at k=1, +13.8% at k=5, +42.3% at k=20) while the linear probe is unchanged, and cross-seed variance halves from 15.73% to 7.60%.
What It Doesn't Show
Three graphs, all heterogeneous entity networks. That is one modality, not a survey.
Not demonstrated on images, text, or time series. The Two Rooms result is a diagnostic on a 64×64 gridworld, not a vision benchmark. Any claim of generalisation to those modalities is unsupported by anything here.
Not a general claim about post-transformer training. This is one instance of growing an architecture rather than scaling one, evaluated on one modality at small scale, with no compute-matched scaled baseline for comparison.
It loses on GDELT. GAT beats it by 23 points. Event graphs appear to carry less persistent topological structure than physical supply chains — a real limit on where the method applies, not a tuning gap.
The SEC EDGAR result is about scale, not accuracy. 66.4% is not a strong absolute number; it is the only model that completes at 9,725 entities.
Sources
- github.com/direncode/tcd-jepa — the three-system loop, persistent-homology backends (giotto-tda → ripser → scipy), the
DynamicPredictorand router, all sixteen modules with persistence scores and the CSET validation mapping, the three-graph benchmark configurations, nine data adapters, 186 tests. - github.com/direncode/tests — Riemannian energy-descent experiments behind the explorer.
- github.com/direncode/jumpbenchmark — physics-video benchmark harness.