Pith Number

pith:52PJEORW

pith:2025:52PJEORW64UIJCRZUIHCP2Y2CJ

not attested not anchored not stored refs resolved

Group Representational Position Encoding

Andrew Chi-Chih Yao, Huizhuo Yuan, Kangping Xu, Quanquan Gu, Yang Yuan, Yifan Zhang, Yifeng Liu, Zhen Qin, Zixiang Chen

GRAPE models positions as group actions on features, recovering RoPE and ALiBi exactly while adding low-cost extensions for cross-feature coupling.

arxiv:2512.07805 v6 · 2025-12-08 · cs.LG · cs.AI · cs.CL

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1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

GRAPE provides a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases.

C2weakest assumption

That the proposed extensions (learned commuting subspaces and compact non-commuting mixtures) will capture useful cross-subspace feature coupling in practice without introducing new optimization difficulties or performance regressions.

C3one line summary

GRAPE unifies RoPE and ALiBi as special cases of group actions on positions, providing a principled design space for positional encodings via SO(d) rotations and GL unipotent transformations.

References

41 extracted · 41 resolved · 8 Pith anchors

[1] Round and round we go! what makes rotary positional encodings useful? In International Conference on Learning Representations (ICLR 2025), 2025

[2] Round and round we go! what makes rotary positional encodings useful? 2004

[4] Extending Context Window of Large Language Models via Positional Interpolation 2009 · arXiv:2306.15595

[6] Contextual position encoding: Learning to count what’s important

[7] Transformer language models without positional encodings still learn positional information

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Jordan-RoPE: Non-Semisimple Relative Positional Encoding via Complex Jordan Blocks

Receipt and verification

First computed	2026-05-17T23:39:16.917857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee9e923a36f728848a39a20e27eb1a124d03ba10c81624abf903c7f6df821b4d

Aliases

arxiv: 2512.07805 · arxiv_version: 2512.07805v6 · doi: 10.48550/arxiv.2512.07805 · pith_short_12: 52PJEORW64UI · pith_short_16: 52PJEORW64UIJCRZ · pith_short_8: 52PJEORW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/52PJEORW64UIJCRZUIHCP2Y2CJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ee9e923a36f728848a39a20e27eb1a124d03ba10c81624abf903c7f6df821b4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02316880bb419c7d3ae0adc454e4dc4fbcf5dda91d5ba2caf15ac660ea9091a1",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-12-08T18:39:13Z",
    "title_canon_sha256": "2acc2b0c3893d070c6a889405076313e8c7c970709a99d2d17c1afc6b7f1758d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.07805",
    "kind": "arxiv",
    "version": 6
  }
}