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Vector Algebra: Method of Components01:08

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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
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Sequence Networks of Rotating Machines01:24

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A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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Convolution Properties I01:20

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Convolution computations can be simplified by utilizing their inherent properties.
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Related Experiment Video

Updated: Jan 17, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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Coupled Tensor Decomposition for Compact Network Representation.

Van Tien Pham, Yassine Zniyed, Thanh Phuong Nguyen

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    |September 22, 2025
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    Summary
    This summary is machine-generated.

    This study introduces coupled filters decomposition to reduce redundancy in convolutional neural networks. The method efficiently compresses models by sharing factors among similar filters, lowering parameters and computation.

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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Convolutional layers in deep learning models contain redundant filters that produce overlapping outputs.
    • This redundancy leads to increased model parameters and computational complexity.

    Purpose of the Study:

    • To introduce a novel filter decomposition method that exploits redundancy in convolutional filters.
    • To reduce model size and computational cost while maintaining performance.

    Main Methods:

    • Proposing coupled filters decomposition using coupled canonical polyadic decomposition (CPD).
    • Implementing filter clustering based on a custom metric before decomposition to enhance efficiency.
    • Applying a less restrictive coupling constraint within identified filter groups.

    Main Results:

    • The coupled filters decomposition method significantly reduces model parameters and computational complexity.
    • Experimental validation across diverse architectures, datasets, and tasks shows competitive performance against state-of-the-art compression techniques.
    • The approach effectively addresses filter redundancy in convolutional neural networks.

    Conclusions:

    • Coupled filters decomposition is an effective technique for compressing deep learning models.
    • The method offers a promising direction for efficient neural network design and deployment.
    • The proposed approach achieves a favorable trade-off between model compression and performance.