It is a commonly held belief that enforcing invariance improves generalisation.

First,theobtained high-probability regret bounds are data-dependent and could be much smaller thantheworst-case bounds, which resolvesanopenproblem askedbyNeu[31].

Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, Zhang et al. [2020a] show that clipped (stochastic) Gradient Descent (GD) converges faster than vanilla GD/SGD via introducing a new assumption called (L0,L1)smoothness, which characterizes the violent fluctuation of gradients typically encountered in deep neural networks.

In this supplemental material, we provide additional details on the theory,the algorithms, and the experiments. In Section 2, we continue analyzing the population level difference between Trojaned and clean models, with a focus on the short-cuts. A boundaryoperatorona p-simplextakesallitsadjacent (p 1)-simplices.Inparticular,theboundary of an edges consists of its adjacent nodes; the boundary of a triangle consists of its three edges. More generally, the boundary of ap-chain is the formal sum1 of the boundary of all its elements, (c)= P σ c (c). Afterthereduction,thepivoting entries of the reduced matrix correspond to pairs of simplices.

Thisresultleadstoageneral standpoint that deep quantum circuits would not be feasible for practical tasks.

To validate the robustness, we design extensive experiments across diverse prompts in terms of length, format, and content.