Bilevel optimization has gained prominence in various applications.

Summary: This paper adapts Optimal Brain Surgeon (OBS) method to a local version, and modified the objective function to be the target activation per each layer. Similar to OBS, it uses an approximation to compute Hessian inverse by running through the dataset once. Compare to prior methods, it finishes compression with much less retraining iterations. A theoretical bound on the total error based on local reconstruction error is provided. Pros: - The paper explores a local version of OBS and shows effectiveness of proposed method in terms of less time cost for retraining the pruned network.

Bilevel optimization has seen an increasing presence in various domains of applications. In this work, we propose a framework for solving bilevel optimization problems where variables of both lower and upper level problems are constrained on Riemannian manifolds. We provide several hypergradient estimation strategies on manifolds and study their estimation error. We provide convergence and complexity analysis for the proposed hypergradient descent algorithm on manifolds. We also extend the developments to stochastic bilevel optimization and to the use of general retraction. We showcase the utility of the proposed framework on various applications.

Quasi-Newton methods still face significant challenges in training large-scale neural networks due to additional compute costs in the Hessian related computations and instability issues in stochastic training. A well-known method, L-BFGS that efficiently approximates the Hessian using history parameter and gradient changes, suffers convergence instability in stochastic training. So far, attempts that adapt L-BFGS to large-scale stochastic training incur considerable extra overhead, which offsets its convergence benefits in wall-clock time. In this paper, we propose mL-BFGS, a lightweight momentum-based L-BFGS algorithm that paves the way for quasi-Newton (QN) methods in large-scale distributed deep neural network (DNN) optimization. mL-BFGS introduces a nearly cost-free momentum scheme into L-BFGS update and greatly reduces stochastic noise in the Hessian, therefore stabilizing convergence during stochastic optimization. For model training at a large scale, mL-BFGS approximates a block-wise Hessian, thus enabling distributing compute and memory costs across all computing nodes. We provide a supporting convergence analysis for mL-BFGS in stochastic settings. To investigate mL-BFGS potential in large-scale DNN training, we train benchmark neural models using mL-BFGS and compare performance with baselines (SGD, Adam, and other quasi-Newton methods). Results show that mL-BFGS achieves both noticeable iteration-wise and wall-clock speedup.