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Distributed Loads: Problem Solving01:21

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Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Updated: Sep 9, 2025

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mL-BFGS:分散型大規模ニューラルネットワークの最適化のためのモメンタムベースのL-BFGS

Yue Niu1, Zalan Fabian1, Sunwoo Lee2

  • 1Department of Electrical and Computer Engineering, University of Southern California.

Transactions on machine learning research
|September 2, 2025
PubMed
まとめ

mL-BFGSはモメンタムベースのアルゴリズムで ニューロンのような ディープニューラルネットワークのトレーニングを 改善しています この方法は,収束を安定させ,大規模な分散型モデルのトレーニングを加速します.

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科学分野:

  • 機械学習
  • 最適化アルゴリズム
  • ディープニューラルネットワーク

背景:

  • L-BFGSを含む準ニュートン方法は,計算コストとストキャスティック設定の不安定性により,大規模な深層ニューラルネットワークトレーニングで課題に直面しています.
  • ストキャスティックトレーニングのためのL-BFGSの既存の適応は,しばしば重要なオーバーヘッドを導入し,収束の利点を否定する.

研究 の 目的:

  • 効率的な大規模な分散型深部ニューラルネットワークの最適化のために設計された軽量でモメンタムベースのL-BFGSアルゴリズムを提案する.
  • ディープラーニングにおける準ニュートン方法の安定性を高め,計算の負担を軽減する.

主な方法:

  • mL-BFGSを開発し,L-BFGSの更新にモメンタムスキームを組み込み,ヘッセン近似のストキャスティックノイズを軽減しました.
  • 大規模なトレーニングのためにノード間でコンピューティングとメモリコストを分配するために,mL-BFGSでブロックwise Hessian近似を実装しました.
  • ストキャスティック最適化シナリオにおけるmL-BFGSの理論的収束分析を提供した.

主要な成果:

  • mL-BFGSは,Hessian近似のノイズを減らすことでストキャスティック最適化中に安定した収束を示した.
  • ブロック式ヘッシアン近似は,分散型トレーニングのための効率的な計算とメモリスケーリングを可能にしました.
  • ベンチマークニューラルモデルでの経験的結果は,SGDやAdamのようなベースライン方法と比較して,繰り返し賢明で壁時計のスピードアップを示しました.

結論:

  • mL-BFGSは,大規模な深層ニューラルネットワークのトレーニングで準ニュートン法を活用するための有望なアプローチを提供します.
  • 提案されたアルゴリズムは,計算効率と収束の安定性を効果的にバランスさせ,既存の方法を上回ります.