Residual Algebra for Representation-Preserving Learning
Learning from heterogeneous representations is often reduced to feature concatenation, erasing which representation produced each error. We propose residual algebra, in which each representation retains its coordinate system and owns its unresolved residual until an explicit aggregation boundary. Fold instantiates representations as point-in-time conditional-mean fields on 10x10 rank grids, and FPRC-PQ composes them through relax-aggregate-close: each field first fits a correction to its own residual, corrected fields then meet at a fixed mean, and a shared learner closes only the aggregate's fresh residual. We formalize aggregation as a quotient by the zero-sum redistribution kernel, cha...
| Authors | Yao Wu |
|---|---|
| Primary category | cs.LG |
| Published | 7 August 2026 |
| Last updated at source | 18 August 2026 |
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