A research team has proposed a new alignment method that works across three or more AI models simultaneously, rather than comparing them two at a time.
The work starts from the Platonic Representation Hypothesis — the idea that independently trained neural networks tend to develop similar internal structures. Current alignment techniques are pairwise, meaning they compare models in pairs, which causes the number of comparisons to grow quadratically as more models are added and produces no consistent shared reference. The researchers adapted Generalized Procrustes Analysis (GPA) to build a single shared coordinate space — an "orthogonal universe" — that preserves the internal geometry of each model. They then found that pure geometric alignment underperforms on retrieval tasks, where methods like Canonical Correlation Analysis tend to win because they maximize agreement between representations rather than geometric fidelity.
The gap between those two goals is where GCPA, or Geometry-Corrected Procrustes Alignment, comes in. It builds the GPA-based shared space first, then applies a targeted correction for directional mismatch — essentially getting the geometry right and then tuning for retrieval. The result, according to the paper, improves any-to-any retrieval while keeping the shared reference space usable for downstream tasks like model stitching.
Pairwise alignment has been the default precisely because it is simple to implement, but it was always an awkward fit for a world where labs routinely train dozens of model variants. GCPA does not claim to solve representation alignment wholesale, but moving from O(n²) comparisons to a single shared universe is the kind of unglamorous infrastructure work that tends to matter more than it sounds.