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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.
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The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
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Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models.

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    We introduce the ADAptive Nesterov momentum algorithm (Adan), a novel optimizer that accelerates deep learning model training. Adan achieves state-of-the-art performance across various tasks, reducing training costs significantly.

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    Area of Science:

    • Deep Learning
    • Optimization Algorithms
    • Machine Learning

    Background:

    • Deep learning models often require specific optimizers, necessitating extensive trials and inefficient training.
    • Existing optimizers may not offer consistent speed improvements across diverse deep network architectures.

    Purpose of the Study:

    • To develop a novel optimizer, Adan, that enhances deep network training speed and efficiency.
    • To provide a consistently performing optimizer across various deep learning tasks.

    Main Methods:

    • Adan reformulates Nesterov acceleration to create a new Nesterov momentum estimation (NME) method.
    • NME is integrated into adaptive gradient algorithms to estimate gradient moments for faster convergence.
    • Theoretical analysis shows Adan achieves an ϵ-approximate first-order stationary point with O(ϵ^-3.5) complexity.

    Main Results:

    • Adan consistently outperforms state-of-the-art (SoTA) optimizers on vision, language, and reinforcement learning tasks.
    • Adan achieves new SoTAs on popular networks like ResNet, ViT, GPT-2, and BERT.
    • Adan reduces training costs by up to 50% while maintaining or improving performance and demonstrates robustness to large minibatch sizes.

    Conclusions:

    • Adan offers a significant improvement in deep learning training efficiency and performance.
    • The proposed Nesterov momentum estimation method provides a robust and effective approach for adaptive gradient algorithms.
    • Adan is a versatile optimizer suitable for a wide range of deep learning applications and architectures.