Pith Number

pith:63NRELHF

pith:2026:63NRELHFFN5IYRD4CHKJSYLPIL

not attested not anchored not stored refs resolved

Common-agency Games for Multi-Objective Test-Time Alignment

Baiting Chen, Rui Yu, Tong Zhu, Xiaowu Dai

CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time.

arxiv:2605.13875 v1 · 2026-05-08 · cs.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{63NRELHFFN5IYRD4CHKJSYLPIL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

CAGE enables flexible and fine-grained trade-offs across objectives at inference time, consistently outperforming existing test-time alignment methods while requiring no retraining. It further supports weak-to-strong generalization, making multi-objective alignment practical in resource-constrained settings.

C2weakest assumption

That modeling heterogeneous objectives as strategic principals allocating token-level incentives produces an equilibrium policy whose joint effect meaningfully captures real user preferences, and that the EPEC-based algorithm reliably computes this equilibrium with the claimed existence, uniqueness, convergence, and stability guarantees.

C3one line summary

CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment.

References

230 extracted · 230 resolved · 19 Pith anchors

[1] TinyLlama: An Open-Source Small Language Model , author=. 2024 , eprint= 2024

[2] International Conference on Learning Representations , year=

[3] The Twelfth International Conference on Learning Representations , year=

[4] C hat D ev: Communicative agents for software development 2024

[5] Encouraging divergent thinking in large language models through multi-agent debate 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:19.262842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756

Aliases

arxiv: 2605.13875 · arxiv_version: 2605.13875v1 · doi: 10.48550/arxiv.2605.13875 · pith_short_12: 63NRELHFFN5I · pith_short_16: 63NRELHFFN5IYRD4 · pith_short_8: 63NRELHF

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/63NRELHFFN5IYRD4CHKJSYLPIL \
  | 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: f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d7b2fceed870fc9915bb543fe1bc4aad71a2254498f74720408394b6965a165",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-08T06:56:35Z",
    "title_canon_sha256": "ec01d02e8ddaea2090a0c9969382906a7bd8f682e5499ce7de30b309fee65ba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13875",
    "kind": "arxiv",
    "version": 1
  }
}