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    This study introduces faster methods for computing differentiable matrix square roots and their inverses using Matrix Taylor Polynomials (MTP) and Matrix Padé Approximants (MPA), improving efficiency in computer vision tasks.

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    Area of Science:

    • Computer Vision
    • Numerical Linear Algebra

    Background:

    • Differentiable matrix square root and inverse are crucial for computer vision.
    • Existing methods like SVD and Newton-Schulz iteration lack computational efficiency.

    Purpose of the Study:

    • To develop computationally efficient methods for differentiable matrix square root and inverse computation.
    • To improve performance in various computer vision applications.

    Main Methods:

    • Proposed two novel variants: Matrix Taylor Polynomial (MTP) and Matrix Padé Approximants (MPA) for forward propagation.
    • Utilized iterative solution of continuous-time Lyapunov equation with matrix sign function for backward gradient computation.

    Main Results:

    • Achieved significant speed-up compared to SVD and Newton-Schulz iteration.
    • Demonstrated competitive and improved performance in applications like de-correlated batch normalization and vision transformers.

    Conclusions:

    • The proposed MTP and MPA methods offer a computationally efficient alternative for differentiable matrix square root and inverse.
    • These methods are effective and can enhance performance in diverse computer vision tasks.