Can an Easy-to-Hard Curriculum Make Reasoning Emerge in Small Language Models? Evidence from a Four-Stage Curriculum on GPT-2
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912380829564928 |
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| author | Fu, Xiang |
| author_facet | Fu, Xiang |
| contents | We demonstrate that a developmentally ordered curriculum markedly improves reasoning transparency and sample-efficiency in small language models (SLMs). Concretely, we train Cognivolve, a 124 M-parameter GPT-2 model, on a four-stage syllabus that ascends from lexical matching to multi-step symbolic inference and then evaluate it without any task-specific fine-tuning. Cognivolve reaches target accuracy in half the optimization steps of a single-phase baseline, activates an order-of-magnitude more gradient-salient reasoning heads, and shifts those heads toward deeper layers, yielding higher-entropy attention that balances local and long-range context. The same curriculum applied out of order or with optimizer resets fails to reproduce these gains, confirming that progression--not extra compute--drives the effect. We also identify open challenges: final-answer success still lags a conventional run by about 30%, and our saliency probe under-detects verbal-knowledge heads in the hardest stage, suggesting directions for mixed-stage fine-tuning and probe expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Can an Easy-to-Hard Curriculum Make Reasoning Emerge in Small Language Models? Evidence from a Four-Stage Curriculum on GPT-2 Fu, Xiang Computation and Language We demonstrate that a developmentally ordered curriculum markedly improves reasoning transparency and sample-efficiency in small language models (SLMs). Concretely, we train Cognivolve, a 124 M-parameter GPT-2 model, on a four-stage syllabus that ascends from lexical matching to multi-step symbolic inference and then evaluate it without any task-specific fine-tuning. Cognivolve reaches target accuracy in half the optimization steps of a single-phase baseline, activates an order-of-magnitude more gradient-salient reasoning heads, and shifts those heads toward deeper layers, yielding higher-entropy attention that balances local and long-range context. The same curriculum applied out of order or with optimizer resets fails to reproduce these gains, confirming that progression--not extra compute--drives the effect. We also identify open challenges: final-answer success still lags a conventional run by about 30%, and our saliency probe under-detects verbal-knowledge heads in the hardest stage, suggesting directions for mixed-stage fine-tuning and probe expansion. |
| title | Can an Easy-to-Hard Curriculum Make Reasoning Emerge in Small Language Models? Evidence from a Four-Stage Curriculum on GPT-2 |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2505.11643 |