Pith Number

pith:JGPL3UEP

pith:2026:JGPL3UEPS7ZFCI5QLILN5I54N4

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Impact of Connectivity on Laplacian Representations in Reinforcement Learning

Keyue Jiang, Laura Toni, Matteo Papini, Pierriccardo Olivieri, Tommaso Giorgi

Linear value approximation error using learned Laplacian spectral features is upper-bounded by the algebraic connectivity of the MDP state graph.

arxiv:2603.08558 v3 · 2026-03-09 · cs.LG · stat.ML

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Claims

C1strongest claim

We prove an upper bound on the approximation error of linear value function approximation under the learned spectral features. We show how this error scales with the algebraic connectivity of the state-graph, grounding the approximation quality in the topological structure of the MDP.

C2weakest assumption

The transition graph is treated as undirected or symmetrizable for the Laplacian construction, even though the paper states results hold without symmetry assumptions on the induced kernel; the algebraic connectivity measure may implicitly require a symmetric or reversible structure for the standard Laplacian definition used.

C3one line summary

The approximation error for linear value functions using learned Laplacian spectral features is upper-bounded by the algebraic connectivity of the MDP transition graph, with an additional bound on eigenvector estimation error from trajectories.

Formal links

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Receipt and verification

First computed	2026-06-11T01:10:34.738030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

499ebdd08f97f25123b05a16dea3bc6f287bed26bc18bbfc315c44ef80f6307d

Aliases

arxiv: 2603.08558 · arxiv_version: 2603.08558v3 · doi: 10.48550/arxiv.2603.08558 · pith_short_12: JGPL3UEPS7ZF · pith_short_16: JGPL3UEPS7ZFCI5Q · pith_short_8: JGPL3UEP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JGPL3UEPS7ZFCI5QLILN5I54N4 \
  | 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: 499ebdd08f97f25123b05a16dea3bc6f287bed26bc18bbfc315c44ef80f6307d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "680ff75cdf20e2980cef475fdb034404aab0028d0a88a1b5dd6dcf719ab58bd5",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-09T16:20:31Z",
    "title_canon_sha256": "91b69987c6553d1f8627588aca8f30d2ee7999f9fd8c02b02fd995a8e8927a17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.08558",
    "kind": "arxiv",
    "version": 3
  }
}