5 papers
How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks
Keyulu Xu, Mozhi Zhang, Jingling Li +3
We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical…
Understanding Generalization in Deep Learning via Tensor Methods
Jingling Li, Yanchao Sun, Jiahao Su +2
Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have pr…
What Can Neural Networks Reason About?
Keyulu Xu, Jingling Li, Mozhi Zhang +3
Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many suc…
Tensorial Neural Networks: Generalization of Neural Networks and Application to Model Compression
Jiahao Su, Jingling Li, Bobby Bhattacharjee +1
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The prob…
Nonorthogonal decoy-state Quantum Key Distribution
Jing-Bo Li, Xi-Ming Fang
In practical quantum key distribution (QKD), weak coherent states as the photon sources have a limit in secure key rate and transmission distance because of the existence of multip…