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Beyond Linear Concepts: Discovering and Aligning Non-Linear Concept Manifolds in Large Language Models — arXiv:2610.01821

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01821
License (as archived): CC0-1.0
Archived: 2026-10-06T13:57:31.392Z
SHA-256 of the archived text: ca5e4c692e913fde053705dfdfcce8026edf8d21420f6bc9a0be8dd958ae77e6
Stable URL of this page: https://metraipolis.com/documento/dc_b56ccbbca613

How to cite

Beyond Linear Concepts: Discovering and Aligning Non-Linear Concept Manifolds in Large Language Models — arXiv:2610.01821 — arXiv (en), https://arxiv.org/abs/2610.01821 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b56ccbbca613 (Metraipolis archive dc_b56ccbbca613, sha256 ca5e4c692e913fde053705dfdfcce8026edf8d21420f6bc9a0be8dd958ae77e6)

BibTeX

@misc{dcb56ccbbca613,
  title = {Beyond Linear Concepts: Discovering and Aligning Non-Linear Concept Manifolds in Large Language Models — arXiv:2610.01821},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01821},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b56ccbbca613; sha256 ca5e4c692e913fde053705dfdfcce8026edf8d21420f6bc9a0be8dd958ae77e6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01821. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Understanding information processing in large language models (LLMs) requires dissecting the geometric organization of their internal token representations. While existing mechanistic interpretability (MI) methods seek to extract concepts, they are constrained by a strong linearity assumption challenged by evidence of non-linear feature manifolds. We move beyond linear concepts by adapting Non-Linear Multi-Dimensional Concept Discovery (NLMCD) from computer vision to token-level LLM activations, modeling concepts as low-dimensional manifolds. To compare concept manifolds across layers and models, we introduce a concept-based alignment (CBA) score, a generalized Rand index that measures geometric proximity without explicit feature matching. Our analysis yields six key findings: (i) a neighboring-layer sanity check shows CBA is more sensitive than PCA- or CKA-based linear baselines; (ii) layer-by-layer alignment matrices reveal two block structures in intermediate and late layers, consistent across models and obscured by linear metrics; (iii) concept composition remains syntax-dominated through most of the network before giving way to increasingly mixed syntactic-semantic concepts in later layers, with increasing output-orientation toward the final layers; (iv) multilingual concept sharing between English and Mandarin is training-dependent rather than universal, strongest in Qwen, weaker in Llama, and absent in GPT-2; (v) inter-model alignment mirrors this structure, with strong correspondence between same-family Qwen models of different scale but weak alignment across model families; and (vi) across Tulu-3 training stages, alignment is highest between adjacent stages, with the largest shift between the base model and SFT, while subsequent preference-alignment stages (DPO, RLVR) leave early layers largely unchanged and RLVR mostly preserves DPO's concepts in late layers.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-10-02 in cs.CL).
Categorie arXiv: Machine Learning (cs.LG) ; Computation and Language (cs.CL).
Pagina del lavoro: https://arxiv.org/abs/2610.01821 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T12:15:34.844Z dalla pagina https://arxiv.org/catchup/cs.CL/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).