Transformers converge to invariant algorithmic cores
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915818171793408 |
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| author | Schiffman, Joshua S. |
| author_facet | Schiffman, Joshua S. |
| contents | Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can implement the same function. Which internal structures reflect the computation, and which are accidents of a particular training run? This work extracts algorithmic cores: compact subspaces necessary and sufficient for task performance. Independently trained transformers learn different weights but converge to the same cores. Markov-chain transformers embed 3D cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers discover compact cyclic operators at grokking that later inflate, yielding a predictive model of the memorization-to-generalization transition. GPT-2 language models govern subject-verb agreement through a single axis that, when flipped, inverts grammatical number throughout generation across scales. These results reveal low-dimensional invariants that persist across training runs and scales, suggesting that transformer computations are organized around compact, shared algorithmic structures. Mechanistic interpretability could benefit from targeting such invariants -- the computational essence -- rather than implementation-specific details. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22600 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transformers converge to invariant algorithmic cores Schiffman, Joshua S. Machine Learning Artificial Intelligence Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can implement the same function. Which internal structures reflect the computation, and which are accidents of a particular training run? This work extracts algorithmic cores: compact subspaces necessary and sufficient for task performance. Independently trained transformers learn different weights but converge to the same cores. Markov-chain transformers embed 3D cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers discover compact cyclic operators at grokking that later inflate, yielding a predictive model of the memorization-to-generalization transition. GPT-2 language models govern subject-verb agreement through a single axis that, when flipped, inverts grammatical number throughout generation across scales. These results reveal low-dimensional invariants that persist across training runs and scales, suggesting that transformer computations are organized around compact, shared algorithmic structures. Mechanistic interpretability could benefit from targeting such invariants -- the computational essence -- rather than implementation-specific details. |
| title | Transformers converge to invariant algorithmic cores |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.22600 |