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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.07120 |
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| _version_ | 1866914542930362368 |
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| author | Guan, Wenjie Bradic, Jelena |
| author_facet | Guan, Wenjie Bradic, Jelena |
| contents | Template tasks have emerged as a clean testbed for asking whether transformers reason with abstract symbols rather than concrete token names. We study the fixed-label classification version of this problem, where train and test examples share latent templates but may use disjoint vocabularies. Unlike next-token prediction, the model need not emit unseen symbols; it must learn a decision rule invariant to symbol renaming. We analyze regularized kernel logistic classification in the transformer-kernel regime. Our main result decomposes the learned predictor into an ideal template-level classifier and a finite-sample perturbation caused by accidental token overlaps in the training data. We encode these overlaps by a colored collision graph and prove high-probability margin-transfer guarantees for fresh-symbol classification. This perspective extends template-based analyses to logistic classification and refines scalar diversity conditions: vocabulary size controls the average rate of collisions, but collision geometry controls whether the ideal classification margin is preserved. More broadly, the same perturbation framework applies to abstraction-augmented inputs, yielding a general margin-versus-collision criterion for identifying when prompting strategies improve fresh-symbol generalization. Synthetic template experiments illustrate the predicted roles of regularization, sample size, and transformer-kernel structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07120 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When Symbol Names Should Not Matter: A Logistic Theory of Fresh-Symbol Classification Guan, Wenjie Bradic, Jelena Machine Learning Template tasks have emerged as a clean testbed for asking whether transformers reason with abstract symbols rather than concrete token names. We study the fixed-label classification version of this problem, where train and test examples share latent templates but may use disjoint vocabularies. Unlike next-token prediction, the model need not emit unseen symbols; it must learn a decision rule invariant to symbol renaming. We analyze regularized kernel logistic classification in the transformer-kernel regime. Our main result decomposes the learned predictor into an ideal template-level classifier and a finite-sample perturbation caused by accidental token overlaps in the training data. We encode these overlaps by a colored collision graph and prove high-probability margin-transfer guarantees for fresh-symbol classification. This perspective extends template-based analyses to logistic classification and refines scalar diversity conditions: vocabulary size controls the average rate of collisions, but collision geometry controls whether the ideal classification margin is preserved. More broadly, the same perturbation framework applies to abstraction-augmented inputs, yielding a general margin-versus-collision criterion for identifying when prompting strategies improve fresh-symbol generalization. Synthetic template experiments illustrate the predicted roles of regularization, sample size, and transformer-kernel structure. |
| title | When Symbol Names Should Not Matter: A Logistic Theory of Fresh-Symbol Classification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.07120 |