{
  "abstract": "With the growing number of LLMs available, selecting which one to use for a prompt has become a key question. A large part of the routing literature relies on semantically embedding prompts into a vector space and then applying a lightweight classifier to the embedded representations. These methods perform robustly in-distribution but they struggle to generalize to unseen tasks. By studying the geometry of semantic embeddings, we trace a clear failure mode: features that determine the neighbors of unseen prompts are an unreliable proxy for LLM selection. We therefore replace the semantic embedding with the following map: we run a partial forward pass of Qwen2.5-7B-Instruct on the prompt and use the hidden state of its last token at a deep layer as the representation. When applying kNN and other simple classifiers to this new representation, we obtain a clear result in generalization: on average across cost penalties, their performance improves. Moreover, kNN and another simple classifier that we propose outperform every evaluated semantic-embedding baseline. Our two simple methods also beat a recent SoTA hidden-states based router on RouterBench.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19198",
  "author_total": 5,
  "authors": [
    {
      "name": "Leonardo Torti"
    },
    {
      "name": "Emanuele Rimoldi"
    },
    {
      "name": "Tomer Galanti"
    },
    {
      "name": "Tomaso Poggio"
    },
    {
      "name": "Pierfrancesco Beneventano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgnjk6097wsq5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19198",
  "fulltext_url": null,
  "id": "fgnjk6097wsq5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19198",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7222090589",
  "pdf_url": "https://arxiv.org/pdf/2610.19198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgnjk6097wsq5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Embedding Geometry Shapes LLM Routing: Tracing Failure Modes and Improving Generalization",
  "title_text": "Embedding Geometry Shapes LLM Routing: Tracing Failure Modes and Improving Generalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/fgnjk6097wsq5",
  "venue": "arXiv",
  "versions": []
}