Pith Number

pith:Z7S4EGPJ

pith:2025:Z7S4EGPJS44PWAI7BF3OJV6QAL

not attested not anchored not stored refs resolved

Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetry

Behrooz Tahmasebi, Melanie Weber

Approximate symmetry can be enforced with only logarithmic averaging complexity while exact symmetry requires linear complexity in the group size.

arxiv:2512.11855 v2 · 2025-12-05 · cs.LG · cs.AI

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\pithnumber{Z7S4EGPJS44PWAI7BF3OJV6QAL}

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4 Citations open

5 Replications open

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Claims

C1strongest claim

under standard conditions, exact symmetry requires linear averaging complexity, whereas approximate symmetry can be attained with only logarithmic complexity in the group size.

C2weakest assumption

The unspecified 'standard conditions' under which the exponential separation holds, and that averaging complexity is the appropriate measure of the cost of enforcing symmetry.

C3one line summary

Approximate symmetry can be enforced with logarithmic averaging complexity while exact symmetry requires linear complexity in the group size.

References

5 extracted · 5 resolved · 1 Pith anchors

[1] Approximately symmetric neural networks for quantum spin liquids.Physical Review Letters, 135 (5):056702, 2025 2025

[2] On the Burnside-Brauer-Steinberg theorem 2022 · arXiv:1409.7632

[3] Complete sets of representations of algebras.Proceedings of the American Math- ematical Society, 13(5):746–747, 1962 1962

[4] User-friendly tail bounds for sums of random matrices.Foundations of computational mathematics, 12(4):389–434, 2012 2012

[5] 1, 3 13 Preprint A BACKGROUND FORPROOFS This appendix collects the background used in our proofs. We briefly review finite groups, group actions, group representations, character theory, and Fourier a 1977

Cited by

1 paper in Pith

Approximate Label Symmetries Improve Data Scaling

Receipt and verification

First computed	2026-05-17T23:39:16.886020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfe5c219e99738fb011f0976e4d7d002c968d4ee4b54d2014dbe39bdc8a88c0a

Aliases

arxiv: 2512.11855 · arxiv_version: 2512.11855v2 · doi: 10.48550/arxiv.2512.11855 · pith_short_12: Z7S4EGPJS44P · pith_short_16: Z7S4EGPJS44PWAI7 · pith_short_8: Z7S4EGPJ

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/Z7S4EGPJS44PWAI7BF3OJV6QAL \
  | 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: cfe5c219e99738fb011f0976e4d7d002c968d4ee4b54d2014dbe39bdc8a88c0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9cbbf128fe3283786a526e3b12a463660e220dd63e2ab1b9adc10b578404806",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-12-05T03:18:18Z",
    "title_canon_sha256": "1a3b44eba6d740dca13d946bc3ba1fd512fb76f5ec3b5e4a70e13e53c18cdb8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.11855",
    "kind": "arxiv",
    "version": 2
  }
}