Encoding the Euler Characteristic Transform
The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Characteristic Transform (ECT) is the injective shape descriptor obtained by collecting ECCs over many directions. How the ECT is encoded for a neural network is itself an inductive bias, conventionally fixed by discretizing each ECC. We introduce a continuous encoding: for each direction and each vertex it records the net Euler-characteristic change attributed to that vertex, producing a per-direction token sequence that a small transformer maps to a feature vector. We separate the resulting pipeline into two stag...
| Authors | Nello Blaser, Odin Hoff Gardaa, Lars M. Salbu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 9 June 2026 |
| Last updated at source | 31 July 2026 |
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