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pith:P6HWEOIA

pith:2026:P6HWEOIAITREBDGKJM4THPONVZ

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Spectral Energy Centroid: a Metric for Improving Performance and Analyzing Spectral Bias in Implicit Neural Representations

Adam Kania, Maciej Rut, Przemys{\l}aw Spurek, Tomasz D\k{a}dela

Spectral Energy Centroid computed from a target signal selects embedding frequencies that improve implicit neural representation performance regardless of model depth.

arxiv:2605.12709 v1 · 2026-05-12 · cs.LG

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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

We show that SEC is a versatile tool for INR analysis, demonstrating its utility across three tasks: (1) a data-driven strategy (SEC-Conf) for hyperparameter selection that outperforms existing heuristics and is robust to model depth, (2) a reliable proxy for signal complexity, and (3) effective alignment of spectral biases across diverse INR architectures.

C2weakest assumption

That the Spectral Energy Centroid computed from the target signal accurately predicts the optimal embedding frequency for an INR of arbitrary depth and architecture without requiring any training-time feedback.

C3one line summary

Spectral Energy Centroid is a new metric that quantifies signal frequency and INR spectral bias, supporting better hyperparameter selection and cross-architecture analysis.

References

23 extracted · 23 resolved · 2 Pith anchors

[1] Shenoy, and Steven H 2025

[2] A scalable Walsh-Hadamard regularizer to overcome the low-degree spectral bias of neural networks 2023

[3] Fresh: Frequency shifting for accelerated neural representation learning 2025

[4] Adam: A Method for Stochastic Optimization 2014 · arXiv:1412.6980

[5] J. Liu, D. Liu, W. Yang, S. Xia, X. Zhang, and Y . Dai. A comprehensive benchmark for single image compression artifact reduction.IEEE Transactions on Image Processing, 29:7845–7860, 2020 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:49.571962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f8f62390044e2408cca4b3933bdcdae4a61dbd3612e16d1269a3b9ea27e2a83

Aliases

arxiv: 2605.12709 · arxiv_version: 2605.12709v1 · doi: 10.48550/arxiv.2605.12709 · pith_short_12: P6HWEOIAITRE · pith_short_16: P6HWEOIAITREBDGK · pith_short_8: P6HWEOIA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/P6HWEOIAITREBDGKJM4THPONVZ \
  | 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: 7f8f62390044e2408cca4b3933bdcdae4a61dbd3612e16d1269a3b9ea27e2a83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84832a61feb1ae43c1b21db4171f72bf6512e37535219643a767cb11eeb33c96",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T20:16:48Z",
    "title_canon_sha256": "a8967f33e4b96de2001bd2bd95c4e47771ccab470fdcff1079d9769fac1a1c5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12709",
    "kind": "arxiv",
    "version": 1
  }
}