Pith Number

pith:YL2UTCIQ

pith:2026:YL2UTCIQZH2DETA37TS65VKZVB

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Path-Coupled Bellman Flows for Distributional Reinforcement Learning

Boyang Xu, Hao Yan, Qing Zou, Siqin Yang

Path-Coupled Bellman Flows learn return distributions by matching flows along source-consistent paths that couple current and successor distributions through shared noise.

arxiv:2605.08253 v2 · 2026-05-07 · cs.LG · cs.AI

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Claims

C1strongest claim

PCBF learns return distributions with flow matching using source-consistent Bellman-coupled paths: the current path starts from the required base prior at t=0, reaches the Bellman target at t=1, and maintains a pathwise affine relation to the successor flow at intermediate times, with a lambda-parameterized control-variate target that trades controlled bias for variance reduction.

C2weakest assumption

That the pathwise affine relation and coupling via shared base noise preserve the necessary distributional properties for correct Bellman updates without requiring time-t marginals to satisfy a distributional Bellman fixed point for all t, and that this coupling does not introduce new inconsistencies in the continuous-time flow.

C3one line summary

Path-Coupled Bellman Flows use source-consistent Bellman-coupled paths and a lambda-parameterized control-variate to learn return distributions via flow matching, improving fidelity and stability over prior DRL approaches.

Receipt and verification

First computed	2026-06-05T00:13:46.840649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2f5498910c9f4324c1bfce5eed559a84860f86e6108f7c95dee30386050b7ae

Aliases

arxiv: 2605.08253 · arxiv_version: 2605.08253v2 · doi: 10.48550/arxiv.2605.08253 · pith_short_12: YL2UTCIQZH2D · pith_short_16: YL2UTCIQZH2DETA3 · pith_short_8: YL2UTCIQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YL2UTCIQZH2DETA37TS65VKZVB \
  | 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: c2f5498910c9f4324c1bfce5eed559a84860f86e6108f7c95dee30386050b7ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad05c7ad54970ab15a01c138808279e97e8b709b2b3d00f6d050b285446159b7",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-07T19:05:01Z",
    "title_canon_sha256": "8f1de45d5c5fa5cfca37a95d0668f5d2a280f260bae70ef254b4460868c5aead"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08253",
    "kind": "arxiv",
    "version": 2
  }
}