4 papers · 1 filter
Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism
Peiyu Zang, Jiayi Hao, Yongqiang Cai
Predicting observed dynamics does not establish recovery of the underlying physical mechanism. Can machine learning retrace the hidden-state reasoning behind the Hodgkin-Huxley (HH…
FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers
Peiyu Zang, Bosen Xie, Ruoxiang Xu +1
Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differenti…
Vocabulary In-Context Learning in Transformers: Benefits of Positional Encoding
Qian Ma, Ruoxiang Xu, Yongqiang Cai
Numerous studies have demonstrated that the Transformer architecture possesses the capability for in-context learning (ICL). In scenarios involving function approximation, context…
Neural Networks Trained by Weight Permutation are Universal Approximators
Yongqiang Cai, Gaohang Chen, Zhonghua Qiao
The universal approximation property is fundamental to the success of neural networks, and has traditionally been achieved by training networks without any constraints on their par…