25 citations · 27 across the 2 of their papers we have counts for
7 papers
Finding Critical Scenarios for Automated Driving Systems: A Systematic Literature Review
Xinhai Zhang, Jianbo Tao, Kaige Tan +9
Scenario-based approaches have been receiving a huge amount of attention in research and engineering of automated driving systems. Due to the complexity and uncertainty of the driv…
The Future is Log-Gaussian: ResNets and Their Infinite-Depth-and-Width Limit at Initialization
Mufan Bill Li, Mihai Nica, Daniel M. Roy
Theoretical results show that neural networks can be approximated by Gaussian processes in the infinite-width limit. However, for fully connected networks, it has been previously s…
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks
Jihun Han, Mihai Nica, Adam R Stinchcombe
We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network wh…
Finite Depth and Width Corrections to the Neural Tangent Kernel
Boris Hanin, Mihai Nica
We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation…
Solution of the Kolmogorov equation for TASEP
Mihai Nica, Jeremy Quastel, Daniel Remenik
We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov back…
Products of Many Large Random Matrices and Gradients in Deep Neural Networks
Boris Hanin, Mihai Nica
We study products of random matrices in the regime where the number of terms and the size of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of…