They iteratively modify and resolve linear programs to conduct a depth-first search from any node in the search tree. Existing divers rely on generic decision rules that fail to exploit structural commonality between similar problem instances that often arise in practice.

Various theoretical results provideupper bounds onthedistance between the target and marginal distribution after a fixed number of iterations.

(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.

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.

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.

Compressing neural networks by pruning weights with small magnitudes can significantly reduce the computation and storage cost. Although pruning makes the model smaller,itisdifficult toget apractical speedup inmodern computing platforms such as CPU and GPU due to the irregularity.

The proposed algorithm, termed ProjDiff, effectively harnesses the prior information and the denoising capability of a pre-trained diffusion model within the optimization framework.

Selecting a suitable pretraining dataset is crucial for both general-domain (e.g., GPT -

Consider a player that in each of T rounds chooses one of K arms. An adversary chooses the cost of each arm in a bounded interval, and a sequence of feedback delays {dt} that are unknown to the player. After picking arm at at round t, the player receives the cost of playing this arm dt rounds later. In cases where t + dt > T, this feedback is simply missing.

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