Mean-Pooled Cosine Similarity is Not Length-Invariant: Theory and Cross-Domain Evidence for a Length-Invariant Alternative
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917471776145408 |
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| author | Mitra, Sibayan Kumar, Dhruv |
| author_facet | Mitra, Sibayan Kumar, Dhruv |
| contents | Mean-pooled cosine similarity is the default metric for comparing neural representations across languages, modalities, and tasks. We establish that this metric is not length-invariant: under the anisotropy that characterizes modern transformer representations, mean-pooled cosine grows monotonically in sequence length, independent of representational content. Empirically, on HumanEvalPack across four code LLMs, the length ratio alone explains $R^2 = 0.52$--$0.75$ of cross-language "Python proximity," while AST depth and shared-token fraction add less than 3% of explained variance beyond length. Substituting Centered Kernel Alignment (CKA) reduces explained variance by 83% and reverses the sign of the length coefficient ($β_{\mathrm{len}}: +0.86 \to -0.37$). The same pattern holds in Mistral-7B on parallel WMT pairs ($R^2 = 0.23$ EN-FR, $R^2 = 0.33$ EN-DE for cosine; $R^2 < 0.01$ for CKA). In CLIP ViT-B/32, mean-pooling reduces the length effect relative to EOS-pooling ($R^2: 0.21 \to {<}0.01$), as predicted by the theory's dependence on anisotropy. We argue that length-invariant metrics such as CKA should be the default for cross-representation comparisons, and that recent claims of cross-lingual representational convergence built on mean-pooled cosine warrant re-examination. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07345 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean-Pooled Cosine Similarity is Not Length-Invariant: Theory and Cross-Domain Evidence for a Length-Invariant Alternative Mitra, Sibayan Kumar, Dhruv Computation and Language Machine Learning I.2.7; I.2.6 Mean-pooled cosine similarity is the default metric for comparing neural representations across languages, modalities, and tasks. We establish that this metric is not length-invariant: under the anisotropy that characterizes modern transformer representations, mean-pooled cosine grows monotonically in sequence length, independent of representational content. Empirically, on HumanEvalPack across four code LLMs, the length ratio alone explains $R^2 = 0.52$--$0.75$ of cross-language "Python proximity," while AST depth and shared-token fraction add less than 3% of explained variance beyond length. Substituting Centered Kernel Alignment (CKA) reduces explained variance by 83% and reverses the sign of the length coefficient ($β_{\mathrm{len}}: +0.86 \to -0.37$). The same pattern holds in Mistral-7B on parallel WMT pairs ($R^2 = 0.23$ EN-FR, $R^2 = 0.33$ EN-DE for cosine; $R^2 < 0.01$ for CKA). In CLIP ViT-B/32, mean-pooling reduces the length effect relative to EOS-pooling ($R^2: 0.21 \to {<}0.01$), as predicted by the theory's dependence on anisotropy. We argue that length-invariant metrics such as CKA should be the default for cross-representation comparisons, and that recent claims of cross-lingual representational convergence built on mean-pooled cosine warrant re-examination. |
| title | Mean-Pooled Cosine Similarity is Not Length-Invariant: Theory and Cross-Domain Evidence for a Length-Invariant Alternative |
| topic | Computation and Language Machine Learning I.2.7; I.2.6 |
| url | https://arxiv.org/abs/2605.07345 |