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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.04469 |
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| _version_ | 1866917385790816256 |
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| author | Cacioli, Jon-Paul |
| author_facet | Cacioli, Jon-Paul |
| contents | Scalar variability -- the finding that representational noise scales proportionally with magnitude, producing a constant coefficient of variation -- is a hallmark of biological magnitude systems. We tested whether transformer language models exhibit this property by analysing the dispersion of hidden-state representations across carrier sentences for 26 numerical magnitudes in three 7-8B parameter models (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base; data from Cacioli, 2026). We found the opposite: representational variability decreased with magnitude along the magnitude axis (scaling exponent alpha approx -0.19; 0/16 primary layers with alpha > 0, all three models). The negative sign was consistent in full-dimensional space (alpha approx -0.04) and after sentence-identity correction (alpha approx -0.007). The anti-scalar pattern was 3-5x stronger along the magnitude axis than orthogonal dimensions, and corpus frequency strongly predicted per-magnitude variability (rho = .84). These results demonstrate that distributional learning alone is insufficient to produce scalar variability: transformers reproduce log-compressive magnitude geometry but not the constant-CV noise signature observed in biological systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04469 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Same Geometry, Opposite Noise: Transformer Magnitude Representations Lack Scalar Variability Cacioli, Jon-Paul Computation and Language Quantitative Methods Scalar variability -- the finding that representational noise scales proportionally with magnitude, producing a constant coefficient of variation -- is a hallmark of biological magnitude systems. We tested whether transformer language models exhibit this property by analysing the dispersion of hidden-state representations across carrier sentences for 26 numerical magnitudes in three 7-8B parameter models (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base; data from Cacioli, 2026). We found the opposite: representational variability decreased with magnitude along the magnitude axis (scaling exponent alpha approx -0.19; 0/16 primary layers with alpha > 0, all three models). The negative sign was consistent in full-dimensional space (alpha approx -0.04) and after sentence-identity correction (alpha approx -0.007). The anti-scalar pattern was 3-5x stronger along the magnitude axis than orthogonal dimensions, and corpus frequency strongly predicted per-magnitude variability (rho = .84). These results demonstrate that distributional learning alone is insufficient to produce scalar variability: transformers reproduce log-compressive magnitude geometry but not the constant-CV noise signature observed in biological systems. |
| title | Same Geometry, Opposite Noise: Transformer Magnitude Representations Lack Scalar Variability |
| topic | Computation and Language Quantitative Methods |
| url | https://arxiv.org/abs/2604.04469 |