Pith Number

pith:LSD2X252

pith:2026:LSD2X252L6WV7DRWNYTHOEX7MI

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A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures

Fredy Ruiz, Lasse Lensu, Sergio Vanegas

Projecting the quasi-triangular factor from the real Schur decomposition of the state matrix onto its nearest stable peer keeps discrete-time state-space neural-network layers asymptotically stable during training.

arxiv:2605.14489 v1 · 2026-05-14 · cs.LG · cs.SY · eess.SY

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\pithnumber{LSD2X252L6WV7DRWNYTHOEX7MI}

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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 proposed methods dynamically project the quasi-triangular factor of the state matrix's real Schur decomposition onto its nearest stable peer, ensuring stable dynamics with minimal overparameterization.

C2weakest assumption

That repeatedly projecting the state matrix during training does not materially distort the optimization landscape or introduce bias that prevents reaching accurate models on real-world data.

C3one line summary

A real Schur decomposition projection maps the state matrix of discrete-time state-space layers onto its nearest stable counterpart, delivering accuracy comparable to prior stable identification methods with fewer weights.

References

80 extracted · 80 resolved · 4 Pith anchors

[1] Model reduction via balanced realizations: an extension and frequency weighting techniques.IEEE Transactions on Automatic Control, 33(7):687–692, 2002 2002

[2] Efficiently Modeling Long Sequences with Structured State Spaces 2021 · arXiv:2111.00396

[3] Simplified State Space Layers for Sequence Modeling 2022 · arXiv:2208.04933

[4] Mamba: Linear-Time Sequence Modeling with Selective State Spaces 2023 · arXiv:2312.00752

[5] Hippo: Recurrent memory with optimal polynomial projections.Advances in neural information processing systems, 33:1474–1487, 2020 2020

Receipt and verification

First computed	2026-05-17T23:39:06.452878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c87abebba5fad5f8e366e267712ff6231d6cb267eae2e193d6b4792dd0a0e82

Aliases

arxiv: 2605.14489 · arxiv_version: 2605.14489v1 · doi: 10.48550/arxiv.2605.14489 · pith_short_12: LSD2X252L6WV · pith_short_16: LSD2X252L6WV7DRW · pith_short_8: LSD2X252

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LSD2X252L6WV7DRWNYTHOEX7MI \
  | 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: 5c87abebba5fad5f8e366e267712ff6231d6cb267eae2e193d6b4792dd0a0e82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f10647708b472ee71a1581797cf4cfa9952d32476484265695c471b65feffd2",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T07:28:11Z",
    "title_canon_sha256": "f1933359cc85b0c19940d8c7acd55e832d6db5c697b49aadfc9f7facd260cb3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14489",
    "kind": "arxiv",
    "version": 1
  }
}