Pith Number

pith:XSKZ3BIB

pith:2024:XSKZ3BIBKLN4IP5EDDL6KHNWDP

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Special Unitary Parameterized Estimators of Rotation

Akshay Chandrasekhar

Reformulating Wahba's problem with SU(2) matrices produces multiple solutions that give linear constraints on quaternion parameters and support two new continuous rotation representations for neural networks.

arxiv:2411.13109 v6 · 2024-11-20 · cs.RO

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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

From this theoretical foundation, we propose two novel continuous representations for learning rotations in neural networks.

C2weakest assumption

The reformulation of Wahba's problem using SU(2) matrices yields multiple solutions that provide linear constraints on corresponding quaternion parameters.

C3one line summary

Reformulates rotation estimation via SU(2) to derive linear quaternion constraints and introduces two new continuous rotation representations for neural networks.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] Theory and implementation of complex-valued neural networks, 2023 2023

[2] Novel results on quaternion modeling and estimation from vector observations 2009

[3] Paul B. Davenport. A vector approach to the algebra of rota- tions with applications. 1968. 1, 7, 17 1968

[4] Learning with 3d rotations, a hitchhiker’s guide to so(3), 2024 2024

[5] R. I. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Second edition, 2004. 7 2004

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T01:03:29.537915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc959d850152dbc43fa418d7e51db61be05d3ddd29979de03d0db5108d9e07f3

Aliases

arxiv: 2411.13109 · arxiv_version: 2411.13109v6 · doi: 10.48550/arxiv.2411.13109 · pith_short_12: XSKZ3BIBKLN4 · pith_short_16: XSKZ3BIBKLN4IP5E · pith_short_8: XSKZ3BIB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XSKZ3BIBKLN4IP5EDDL6KHNWDP \
  | 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: bc959d850152dbc43fa418d7e51db61be05d3ddd29979de03d0db5108d9e07f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "639ffdadf3023de62222f30fe9d2c28eb7273604e29b5b22ca2a0111eecd4b7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.RO",
    "submitted_at": "2024-11-20T08:07:11Z",
    "title_canon_sha256": "e97656d531a899f7b2f5b595d10ff1a94ac61296b058c00fb73b88dd5865a3f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.13109",
    "kind": "arxiv",
    "version": 6
  }
}