Lemma 2. Let Assumption 1 hold.

(Liu and Nocedal, 1989). Similar efforts have been made for Polyak stepsizes (Berrada et al., 2020; Loizou et al., 2021), in addition to new methods which combine distance to optimality with online learning convergence bounds (Cutkosky et al., 2023; Classically-inspired methods, however, have generally struggled to gain traction in deep learning.

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In this work, we showthat this "lazy training" phenomenon isnot specific tooverparameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding amodel equivalenttolearning withpositive-definite kernels.

Video Question Answering (VideoQA) has emerged as a vital tool to evaluate agents' ability to understand human daily behaviors. Despite the recent success of large vision language models in many multi-modal tasks, complex situation reasoning over videos involving multiple human-object interaction events still remains challenging.

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Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rather expensive for optimizing objectives involving the spectral function.

We relate the problem of computing pointwise robustness of these networks to that of computing the maximum norm ball with a fixed center that can be contained in a non-convex polytope. This isachallenging problem ingeneral, howeverweshowthat there exists an efficient algorithm to compute this for polyhedral complices. Further we show that piecewise linear neural networks partition the input space into a polyhedralcomplex.

In this paper, we present a novel robust framework for low-level vision tasks, including denoising, object removal, frame interpolation, and super-resolution, that does not require any external training data corpus.