Pith Number

pith:RXMOX2BK

pith:2026:RXMOX2BKGDLE6QNAPS4KDJJSHA

not attested not anchored not stored refs pending

Design Conditions for Intra-Group Learning of Sequence-Level Rewards: Token Gradient Cancellation

Fei Ding, Yongkang Zhang, youwei wang, Zijian Zeng

Intra-group objectives for sequence rewards must preserve gradient exchangeability across tokens to enable cancellation on weak-credit high-frequency tokens and block reward-irrelevant drift.

arxiv:2604.13088 v2 · 2026-04-04 · cs.LG · cs.AI

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\usepackage{pith}
\pithnumber{RXMOX2BKGDLE6QNAPS4KDJJSHA}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

to prevent reward-irrelevant drift, intra-group objectives must maintain gradient exchangeability across token updates, enabling gradient cancellation on weak-credit/high-frequency tokens.

C2weakest assumption

That the observed training failures (learning tax, solution probability drift, entropy collapse) are primarily caused by disruption of token-level gradient exchangeability rather than other factors such as reward sparsity itself or optimizer dynamics.

C3one line summary

Intra-group objectives in sparse-reward RL must maintain token gradient exchangeability to enable cancellation on weak-credit tokens and stabilize training.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-26T01:02:34.140627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8dd8ebe82a30d64f41a07cb8a1a532380dc2694bcd29f380244ef81f424422b5

Aliases

arxiv: 2604.13088 · arxiv_version: 2604.13088v2 · doi: 10.48550/arxiv.2604.13088 · pith_short_12: RXMOX2BKGDLE · pith_short_16: RXMOX2BKGDLE6QNA · pith_short_8: RXMOX2BK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RXMOX2BKGDLE6QNAPS4KDJJSHA \
  | 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: 8dd8ebe82a30d64f41a07cb8a1a532380dc2694bcd29f380244ef81f424422b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a24e707f83e0a91d08fdb7046463ad76317ecd108b7c3bcabac36b363346fff",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-04T02:47:28Z",
    "title_canon_sha256": "46d7e74857a28d4a18ccaf7d2c9667372fb0b4eaa2388ddd2b52c1205e6d697b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13088",
    "kind": "arxiv",
    "version": 2
  }
}