{"paper":{"title":"Polar probe linearly decodes semantic structures from LLMs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Large language models encode the existence and type of semantic relations as distance and direction between embeddings in a linear subspace of their activations.","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Jean-R\\'emi King, Pablo J. Diego-Sim\\'on, Pierre Orhan, Yair Lakretz","submitted_at":"2026-05-13T21:21:10Z","abstract_excerpt":"How do artificial neural networks bind concepts to form complex semantic structures? Here, we propose a simple neural code, whereby the existence and the type of relations between entities are represented by the distance and the direction between their embeddings, respectively. We test this hypothesis in a variety of Large Language Models (LLMs), each input with natural-language descriptions of minimalist tasks from five different domains: arithmetic, visual scenes, family trees, metro maps and social interactions. Results show that the true semantic structures can be linearly recovered with a"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the true semantic structures can be linearly recovered with a Polar Probe targeting a subspace of LLMs' layer activations","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LLMs bind semantic relations via polar geometry in embeddings, linearly decodable from middle layers with generalization to new items.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Large language models encode the existence and type of semantic relations as distance and direction between embeddings in a linear subspace of their activations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"15145f4ee4a4a75d059588396ddf88311f6b94c9f4bd73aba78af283a80d5543"},"source":{"id":"2605.14125","kind":"arxiv","version":1},"verdict":{"id":"3ad1e17e-5e49-4531-8d07-586c370591e3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T04:56:34.852465Z","strongest_claim":"the true semantic structures can be linearly recovered with a Polar Probe targeting a subspace of LLMs' layer activations","one_line_summary":"LLMs bind semantic relations via polar geometry in embeddings, linearly decodable from middle layers with generalization to new items.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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","pith_extraction_headline":"Large language models encode the existence and type of semantic relations as distance and direction between embeddings in a linear subspace of their activations."},"references":{"count":112,"sample":[{"doi":"","year":2017,"title":"Understanding intermediate layers using linear classifier probes, 2017","work_id":"9a6797e3-8303-4253-8a12-d138400e0736","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Pythia: a suite for analyzing large language models across training and scaling","work_id":"ac8fbbb8-291b-4844-84a1-34d3bf2a9a70","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Fast differentiable sorting and ranking","work_id":"cfcdb5d4-d4b2-4230-9131-1637b81f4ec4","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1901,"title":"Language models are few-shot learners","work_id":"33f1f5a3-ad49-41fa-b313-857dabbce8e9","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Diego-Simon, St \\'e phane d'Ascoli, Emmanuel Chemla, Yair Lakretz, and Jean-Remi King","work_id":"dfd927f4-f5fa-4e49-a993-6960160f2f68","ref_index":8,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":112,"snapshot_sha256":"7640a76a3297997726cb3b2cb48d8ed95864a548fdcc4c669214b1e4f834201b","internal_anchors":2},"formal_canon":{"evidence_count":3,"snapshot_sha256":"0c5ee8b3dda2b6c106c0312ba7bfae38b73465ba6b0c496297fcb46c8e3d0939"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}