{"paper":{"title":"PJ-RoPE: A Fourier-Jet-Affine Position Space for Relative Attention","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Yaobo Zhang","submitted_at":"2026-06-03T18:37:46Z","abstract_excerpt":"We unify RoPE's Fourier phase, Jordan-RoPE's finite jets, and ALiBi's affine recency into a single learnable relative-position space, and study which regions of this space are selected by different tasks. PJ-RoPE is a Fourier-Jet-Affine formulation for relative attention, with an optional Poincare-type reading as the affine completion of a homogeneous Fourier-jet positional representation. Algebraically, the same primitives form a finite constant-coefficient difference module: simple roots of the lag-shift operator give Fourier/RoPE characters, repeated nonzero roots give Jordan/Fourier jets, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05345","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05345/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}