Training-Free Universal Approximation by Prompting Random Transformers
Score
74首次从逼近论角度严格证明随机未训练 Transformer 在提示驱动下具备通用逼近能力，理论增量显著。
构造性证明与理论保证完整，并附数值实验验证，但依赖核回归框架，范围相对聚焦。
对提示工程和推理期计算有启示意义，但主要贡献在理论层面，直接落地到工程仍需进一步转化。
该研究紧跟当前对提示机制与模型表达能力来源的讨论，具有较强时效性。
论文发布于 arXiv AI/CL/LG 分区，预印本尚未经同行评议，但方法严谨、引用规范。
Base 82.5 × T2 Source weight ×0.9 = 74
Curation line 70Selected
Why selected
It provides a rigorous approximation-theoretic framework for characterizing the expressive power of prompted random Transformers, with constructive proofs.
AI commentary
「What makes this paper worth reading is that it turns prompting from black magic into linear algebra: random weights are not a problem if the prompt is constructed right. For prompt engineers and interpretability researchers, it offers a new lens on how much work inference-time computation can actually do.」
Quick overview
This paper addresses a fundamental question: how expressive can a Transformer become via prompting alone? The authors show, in an approximation-theoretic sense, that pretraining is optional. A single-layer softmax attention network with random, untrained weights can approximate any Hölder continuous function on a compact manifold when steered by an appropriate soft prompt. Leveraging the connection between softmax attention and kernel methods, they construct explicit soft prompts as solutions to linear systems that match attention logits to Gaussian kernel exponents, causing the frozen Transformer to emulate the classical Nadaraya-Watson kernel estimator. The construction only requires a mild rank condition that holds almost surely under Gaussian initialization. The prompted network inherits the theoretical guarantees of kernel regression, yielding universal approximation theorems with minimax-optimal rates depending on the intrinsic dimension. They also quantify the cost of prompting in terms of prompt norm, prompt length, and hidden dimension. Numerical experiments corroborate the constructions and predicted rates.
- Shows that a single-layer softmax attention network with random, untrained weights can universally approximate Hölder functions when steered by soft prompts.
- Constructs prompts as solutions to linear systems via the attention-kernel connection, making the frozen network equivalent to Nadaraya-Watson kernel regression.
- Quantifies the cost of prompting, revealing a tradeoff among prompt token norm, prompt length, and hidden dimension.
Full text
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