Pith Number

pith:44MJ5GBC

pith:2026:44MJ5GBCUQWUO5A4V2HHQUI6WA

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The Cylindrical Representation Hypothesis for Language Model Steering

Akash Ghosh, Chenxi Wang, Fengxian Ji, Jinghui Zhang, Lang Gao, Preslav Nakov, Wei Liu, Xiuying Chen, Youssef Mohamed, Zirui Song

The Cylindrical Representation Hypothesis models concept representations in LLMs as a central axis for concept presence surrounded by a normal plane containing sensitive sectors that control activation ease, explaining steering unpredictability.

arxiv:2605.01844 v2 · 2026-05-03 · cs.CL

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\usepackage{pith}
\pithnumber{44MJ5GBCUQWUO5A4V2HHQUI6WA}

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Record completeness

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4 Citations open

5 Replications open

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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

By relaxing LRH's orthogonality assumption while preserving linear representations, we show that overlapping concept contributions naturally yield a sample-specific axis-orthogonal structure. We formalize this as the Cylindrical Representation Hypothesis (CRH).

C2weakest assumption

That overlapping concept contributions produce a reliably identifiable normal plane from difference vectors while the sensitive sector within that plane remains intrinsically unidentifiable, introducing unavoidable uncertainty at the sector level.

C3one line summary

Cited by

1 paper in Pith

Decodable but Not Corrected by Fixed Residual-Stream Linear Steering: Evidence from Medical LLM Failure Regimes

Receipt and verification

First computed	2026-06-05T01:15:25.056925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7189e9822a42d47741cae8e78511eb01fbf000447c9c9c3f60d28efe902de94

Aliases

arxiv: 2605.01844 · arxiv_version: 2605.01844v2 · doi: 10.48550/arxiv.2605.01844 · pith_short_12: 44MJ5GBCUQWU · pith_short_16: 44MJ5GBCUQWUO5A4 · pith_short_8: 44MJ5GBC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/44MJ5GBCUQWUO5A4V2HHQUI6WA \
  | 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: e7189e9822a42d47741cae8e78511eb01fbf000447c9c9c3f60d28efe902de94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "664ce3267c40e97b537c90a951368df9b7911e8843b899d9522243a9079d5399",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2026-05-03T12:26:13Z",
    "title_canon_sha256": "b89bd423b4f4bea0de39702db40cf8ee7eac111366eaf5e41628ece2dd9495c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01844",
    "kind": "arxiv",
    "version": 2
  }
}