Report
Next-token prediction capacity: general upper bounds and a lower bound for transformers
| العنوان: | Next-token prediction capacity: general upper bounds and a lower bound for transformers |
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| المؤلفون: | Madden, Liam, Fox, Curtis, Thrampoulidis, Christos |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Optimization and Control, 15A03, 26B35 |
| الوصف: | Given a sequence of tokens, such as words, the task of next-token prediction is to predict the next-token conditional probability distribution. Decoder-only transformers have become effective models for this task, but their properties are still not fully understood. In particular, the largest number of distinct context sequences that a decoder-only transformer can interpolate next-token distributions for has not been established. To fill this gap, we prove upper and lower bounds on this number, which are equal up to a multiplicative constant. We prove these bounds in the general setting where next-token distributions can be arbitrary as well as the empirical setting where they are calculated from a finite number of document sequences. Our lower bounds are for one-layer multi-head decoder-only transformers and our proofs highlight an important injectivity property satisfied by self-attention. Furthermore, we provide numerical evidence that the minimal number of parameters for memorization is sufficient for being able to train the model to the entropy lower bound. Comment: V2: added a section axiomatizing the probabilistic assumptions of next-token prediction |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.13718 |
| رقم الانضمام: | edsarx.2405.13718 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |