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Related Concept Videos

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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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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Convolution Properties II01:17

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The important convolution properties include width, area, differentiation, and integration properties.
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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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Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
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Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique
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ECBC: Efficient Convolution via Blocked Columnizing.

Tianli Zhao, Qinghao Hu, Xiangyu He

    IEEE Transactions on Neural Networks and Learning Systems
    |July 19, 2021
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    Summary
    This summary is machine-generated.

    Efficient convolution via blocked columnizing (ECBC) offers high performance without significant memory overhead. This indirect convolution method optimizes data layout for better computational efficiency.

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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Direct convolution methods avoid storage issues but require complex data formatting.
    • This formatting leads to increased time and memory usage.
    • Indirect convolution methods, like im2col, can be memory-intensive if not optimized.

    Purpose of the Study:

    • To present an optimized indirect convolution algorithm that achieves high performance.
    • To demonstrate that indirect convolution can avoid substantial memory overhead when implemented properly.
    • To introduce the efficient convolution via blocked columnizing (ECBC) algorithm.

    Main Methods:

    • ECBC is inspired by the im2col algorithm and block matrix multiplication.
    • Convolution computation is performed blockwise.
    • The tensor-to-matrix transformation (im2col) is also done blockwise, reducing memory requirements.

    Main Results:

    • ECBC achieves high computation performance using optimized matrix multiplication subroutines.
    • The blockwise approach minimizes memory overhead during tensor-to-matrix transformation.
    • Experiments show ECBC's effectiveness across various platforms and networks.

    Conclusions:

    • ECBC offers a superior alternative to existing industrial-level convolution algorithms.
    • Properly implemented indirect convolution, like ECBC, balances performance and memory efficiency.
    • The blockwise strategy is key to ECBC's success in optimizing convolution computations.