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.

We thank the reviewers for their comments and suggestions. Hereafter, we list reviewers' (sometimes paraphrased) Each answer will translate into a clarification in the final version. Reviewer #2 and #3 felt that our message was lacking clarity. A.2). We will add more pointers to their statistical analysis, from the existing literature (e.g. L81-90 in the main paper, often α(m) = 1/ m in these works).

As mentioned in Section 4.2 Our model can easily adapt to various video backbones. We use QA accuracy as the metric for evaluation. As illustrated in Section 3.2, with event-level annotations, we First, we analyze the effects of different loss functions on model performance. The results are shown in Figure 1. When the coefficient of any loss function is 0, the performance of the model decreases, which indicates their efficiency in event memory extraction. Without it, there is a significant decrease in model performance.

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.