4 papers
Universal Approximation with Softmax Attention
Jerry Yao-Chieh Hu, Hude Liu, Hong-Yu Chen +2
We prove that with linear transformations, both (i) two-layer self-attention and (ii) one-layer self-attention followed by a softmax function are universal approximators for contin…
In-Context Algorithm Emulation in Fixed-Weight Transformers
Jerry Yao-Chieh Hu, Hude Liu, Jennifer Yuntong Zhang +1
We prove that a minimal Transformer with frozen weights emulates a broad class of algorithms by in-context prompting. We formalize two modes of in-context algorithm emulation. In t…
Are Hallucinations Bad Estimations?
Hude Liu, Jerry Yao-Chieh Hu, Jennifer Yuntong Zhang +2
We formalize hallucinations in generative models as failures to link an estimate to any plausible cause. Under this interpretation, we show that even loss-minimizing optimal estima…
Attention Mechanism, Max-Affine Partition, and Universal Approximation
Hude Liu, Jerry Yao-Chieh Hu, Zhao Song +1
We establish the universal approximation capability of single-layer, single-head self- and cross-attention mechanisms with minimal attached structures. Our key insight is to interp…