Pith Number

pith:4SJQMRSF

pith:2026:4SJQMRSFWVSHPM257AYDAQXEGM

not attested not anchored not stored refs resolved

Polar probe linearly decodes semantic structures from LLMs

Jean-R\'emi King, Pablo J. Diego-Sim\'on, Pierre Orhan, Yair Lakretz

Large language models encode the existence and type of semantic relations as distance and direction between embeddings in a linear subspace of their activations.

arxiv:2605.14125 v1 · 2026-05-13 · cs.CL

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations 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

the true semantic structures can be linearly recovered with a Polar Probe targeting a subspace of LLMs' layer activations

C2weakest assumption

that the distance-direction geometry is the actual causal mechanism used by the model rather than a convenient post-hoc linear fit that happens to correlate with task performance

C3one line summary

LLMs bind semantic relations via polar geometry in embeddings, linearly decodable from middle layers with generalization to new items.

References

112 extracted · 112 resolved · 2 Pith anchors

[1] Understanding intermediate layers using linear classifier probes, 2017 2017

[2] Pythia: a suite for analyzing large language models across training and scaling 2023

[3] Fast differentiable sorting and ranking 2020

[4] Language models are few-shot learners 1901

[8] Diego-Simon, St \'e phane d'Ascoli, Emmanuel Chemla, Yair Lakretz, and Jean-Remi King 2024

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.856493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e493064645b56477b35df8303042e4330787816c638d00ace3bd6ef331af8b11

Aliases

arxiv: 2605.14125 · arxiv_version: 2605.14125v1 · doi: 10.48550/arxiv.2605.14125 · pith_short_12: 4SJQMRSFWVSH · pith_short_16: 4SJQMRSFWVSHPM25 · pith_short_8: 4SJQMRSF

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4SJQMRSFWVSHPM257AYDAQXEGM \
  | 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: e493064645b56477b35df8303042e4330787816c638d00ace3bd6ef331af8b11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbd664110450ecd094b98f51b6a32875c3edd13bb542e6309805f7eab8620dba",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2026-05-13T21:21:10Z",
    "title_canon_sha256": "4c58f5d0e3aa47dca3aebdc9c6f93c67e35dd7ebe0f26bbc067bd7c18be014de"
  },
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  "source": {
    "id": "2605.14125",
    "kind": "arxiv",
    "version": 1
  }
}