Researchers have demonstrated that a single-layer softmax attention network with random, untrained weights can approximate any Hölder function on a compact manifold when guided by an appropriate soft prompt. This finding suggests that pretraining may be optional for certain approximation tasks. The study connects softmax attention to kernel methods, constructing explicit soft prompts that enable the frozen transformer to emulate classical Nadaraya-Watson kernel estimators. The theoretical guarantees of kernel regression are inherited, leading to universal approximation theorems with rates dependent on intrinsic dimension, and revealing a trade-off between prompt norm, length, and hidden dimension. AI
IMPACT Suggests that pretraining may not be essential for certain approximation tasks in transformers, potentially simplifying model development.
RANK_REASON The cluster contains a research paper detailing theoretical findings about transformer models. [lever_c_demoted from research: ic=1 ai=1.0]
- arXiv
- Gaussian initialization
- Hölder function
- Hugging Face
- kernel method
- kernel regression
- Nadaraya-Watson kernel estimator
- softmax attention
- soft prompt
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