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Related Concept Videos

Implicit Differentiation: Problem Solving01:29

Implicit Differentiation: Problem Solving

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Curves defined implicitly, where variables cannot be separated algebraically, require specialized techniques for analysis. The conchoid of Nicomedes exemplifies such a case. Its equation links x and y in a way that prevents isolation of one variable, making implicit differentiation essential to determine the slope and behavior at any point on the curve.The implicit form of the conchoid can be expressed as:To differentiate this equation, y is treated as a function of x, and the chain rule is...
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Differential leveling is a precise method in surveying used to determine the elevation difference between two points. Its primary goal is to establish accurate vertical measurements to create level surfaces or grade lines critical for designing and constructing infrastructures such as roads, bridges, and buildings.The procedure for differential leveling begins with setting up and leveling the instrument at a point where the benchmark can be seen. The level rod is held on the benchmark (BM), and...
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In classical mechanics, motion is often described through relationships between spatial coordinates and time. A car moving along a straight highway with constant acceleration serves as a simple case where velocity is an explicit function of time. This scenario results in a linear equation, enabling straightforward analysis using basic differentiation techniques.In contrast, a satellite in circular orbit follows a path defined by an implicit function. The position of the satellite is constrained...
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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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$\beta $-DARTS++: Bi-Level Regularization for Proxy-Robust Differentiable Architecture Search.

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    Summary
    This summary is machine-generated.

    Beta-Decay regularization enhances Neural Architecture Search (NAS) by improving stability and generalization. This method, applied to DARTS (differentiable architecture search), also boosts robustness across various proxy settings, leading to better performance.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Deep Learning

    Background:

    • Neural Architecture Search (NAS) automates neural network design, with differentiable NAS (e.g., DARTS) offering efficiency.
    • Existing differentiable NAS methods face challenges in stability, generalization, and robustness to proxy configurations.

    Purpose of the Study:

    • To introduce Beta-Decay regularization to stabilize DARTS-based NAS and improve the generalization of searched architectures.
    • To address the robustness of differentiable NAS methods across diverse proxy settings.
    • To propose Bi-level regularization by combining Beta-Decay with flooding regularization for enhanced proxy robustness.

    Main Methods:

    • Introduced Beta-Decay regularization to constrain architecture parameter values and variance during DARTS training.
    • Conducted comprehensive experiments to benchmark differentiable NAS methods across various proxy configurations (data, channels, layers, epochs).
    • Integrated flooding regularization into the weight optimization of Beta-Decay DARTS, creating Bi-level regularization.

    Main Results:

    • Beta-Decay regularization significantly stabilizes the NAS search process and improves the transferability of searched networks.
    • Beta-Decay DARTS (β-DARTS) demonstrated superior performance across most proxy settings compared to other NAS methods.
    • Bi-level regularization further enhanced the proxy robustness of differentiable NAS methods, validated both experimentally and theoretically.

    Conclusions:

    • Beta-Decay is an effective regularization technique for improving the stability and generalization of DARTS-based NAS.
    • The proposed β-DARTS method exhibits strong robustness to various proxy configurations.
    • Bi-level regularization offers a promising direction for enhancing the proxy robustness of differentiable NAS.