Pith Number

pith:GLZH27UF

pith:2026:GLZH27UFXVWNKSAVTTTC5L622S

not attested not anchored not stored refs resolved

Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration

Deyu Meng, Feiyu Tan, Qi Xie, Zongben Xu

Equivariance error of the optimal restoration operator is strictly bounded by data symmetry error and discretization mesh size.

arxiv:2605.13744 v1 · 2026-05-13 · cs.CV

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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

the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size. Furthermore, by analyzing the network's empirical risk, we demonstrate that aligning equivariance with data symmetry optimizes the bias variance trade off, minimizing the total expected risk.

C2weakest assumption

that the proposed quantifiable definition of non-strict symmetry at the dataset level (rather than sample level) can be used as a valid constraint to formulate the restoration inverse problem for real-world data with imperfect symmetry.

C3one line summary

A new dataset-level non-strict symmetry measure allows deriving bounded equivariance for restoration models and motivates an adaptive network that aligns with per-sample symmetry to reduce expected risk.

References

70 extracted · 70 resolved · 2 Pith anchors

[1] Communications of the ACM , volume= 1991

[2] IEEE transactions on pattern analysis and machine intelligence , volume= 2019

[3] IEEE Transactions on Acoustics, Speech, and Signal Processing , volume= 2002

[4] SIAM Journal on Scientific Computing , volume= 2008

[5] IEEE Geoscience and Remote Sensing Magazine , volume= 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:16.429267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32f27d7e85bd6cd548159ce62eafdad487ccf080b41b1f77b536ebf14c014512

Aliases

arxiv: 2605.13744 · arxiv_version: 2605.13744v1 · doi: 10.48550/arxiv.2605.13744 · pith_short_12: GLZH27UFXVWN · pith_short_16: GLZH27UFXVWNKSAV · pith_short_8: GLZH27UF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GLZH27UFXVWNKSAVTTTC5L622S \
  | 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: 32f27d7e85bd6cd548159ce62eafdad487ccf080b41b1f77b536ebf14c014512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a826a560ade736fe1ae220528685ff6317481712f57032c62a2050b22a391971",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-05-13T16:22:19Z",
    "title_canon_sha256": "3650522ede89c795edfcd274426e427f420127988dae6f8f43c407cbaa7c3a55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13744",
    "kind": "arxiv",
    "version": 1
  }
}