After the Euclidean Highway: Hyperbolic Expert AI as the Next Innovation
Expert domains are trees; the Euclidean transformer is not, diluting parent-child structure exponentially at depth. The hyperbolic turn left one question unasked: not how much of a network to curve, but where curvature may touch the gradient. Placement is a law, not a knob: the same geometry on a trainable adapter collapses training (seventeen training collapses, ~220 GPU-hours), yet at the loss layer alone it trains without one -- this is HySAT (Hyperbolic Structure-Aware Training), hyperbolic losses at the loss layer only. Across six expert SLMs we constructed and deployed (Llama 3.1 and EXAONE 3.5; four adapter strategies; 18.0M-sample corpus; zero NaN over ~317K optimizer steps), a ma...
| Authors | Kwan Soo Shin, In Seok Kang, Munho Lee |
|---|---|
| Primary category | cs.LG |
| Published | 20 July 2026 |
| Last updated at source | 20 July 2026 |
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