Let A1,...,An Rd d be a collection of (symmetric) positive semidefinite matrices.

Let A1,...,An Rd d be a collection of (symmetric) positive semidefinite matrices.

S1 firsts gives some of the formal definitions and interpretations omitted from the main paper due to space limitations.

In recent years, deep neural networks (DNNs) have become the de facto machine learning tool and have revolutionized a variety of fields such as natural language processing [DCLT18], image perception [KSH12,RBH+21],geometry processing [QSMG17,ZBL+20]and3Dvision[DBI18, GLW+21]. Despite their widespread use, little is known about their theoretical properties.

In our work, we study the video-language pretraining in a specific yet significant domain - the 1st-person view,which ismotivated bytherelease oftheEgo4D dataset. Thevarying clipfrequencies aremainly dependent on manual narrations that are annotated based on the video scenarios and activities. There have average 13.4 clips per minute of video, maximize to175.8 Fig.6(b)displays the distribution of clip duration. In Figure 1 (c), we present the distribution of narration words length.

As illustrated in Tab. 1, the formerly largest egocentric video dataset EPICKITCHENS-100 [14] focuses on kitchens scenarios and its size is far smaller than those of the 3rd-person pretraining sets WebVid-2M [3] and HowTo100M [10].

Gradient-Guided Dynamic Rewiring of GCNs.Contrary toad-hoc addition of skipconnections toimproveGCNs performance, inthis paper,we leverage Gradient Flowto introduce dynamic rewiring strategyof vanilla-GCNs with skip-connections.

A binary logistic regression classifier was implemented inPyTorch (v1.4.0 ) and trained over the rcv1 dataset to illustrate the speed ups possible using a GPU (Nvidia Tesla V100) versus only multithreading (24 CPU threads using an Intel Xeon Gold 5118). Speedups were tested for both batch gradient descent (with a 0.001 learning rate) andL-BFGS.

The paper is organized as follows. In Section 2, we describe relevant previous work speeding up TRON forboth sparse and dense feature sets onshared memory systems.