Pith Number

pith:7H7ZXYMA

pith:2026:7H7ZXYMAS22SQM3SKLMYYUDPM6

not attested not anchored not stored refs pending

Relational Preference Encoding in Looped Transformer Internal States

Jan Kirin

Looped transformers encode human preferences relationally through comparisons in their internal states.

arxiv:2604.09870 v2 · 2026-04-10 · cs.LG · cs.AI

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\usepackage{pith}
\pithnumber{7H7ZXYMAS22SQM3SKLMYYUDPM6}

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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

loop states encode preference predominantly relationally: a linear probe on pairwise differences achieves 84.5%, the best nonlinear independent evaluator reaches only 65% test accuracy, and linear independent classification scores 21.75%, below chance and with inverted polarity.

C2weakest assumption

That the high pairwise accuracy and low independent accuracy reflect genuine relational encoding in the model's learned value system rather than an artifact of the 50% argument-swap protocol, the accidental early stopping, or the specific choice of lightweight heads trained on the same model's representations.

C3one line summary

Looped transformer hidden states encode preferences relationally via pairwise differences rather than independent pointwise classification, with the evaluator acting as an internal consistency probe on the model's own value system.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-17T01:21:48.919085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9ff9be18096b528337252d98c506f678a6eeff4f605b22d5e7f8b902c04dac7

Aliases

arxiv: 2604.09870 · arxiv_version: 2604.09870v2 · doi: 10.48550/arxiv.2604.09870 · pith_short_12: 7H7ZXYMAS22S · pith_short_16: 7H7ZXYMAS22SQM3S · pith_short_8: 7H7ZXYMA

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/7H7ZXYMAS22SQM3SKLMYYUDPM6 \
  | 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: f9ff9be18096b528337252d98c506f678a6eeff4f605b22d5e7f8b902c04dac7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbc00ddc9a50c56343ccc7816f66cf17e6d006713f17c1726c2463b5a7c07d73",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-10T20:00:49Z",
    "title_canon_sha256": "d35755bea99d8c5205a3b7b40e76c221753ce8b234cca850a1ce6048eb9f6b8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.09870",
    "kind": "arxiv",
    "version": 2
  }
}