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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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Interpretability and Optimisation of Convolutional Neural Networks Based on Sinc-Convolution.

Ahsan Habib, Chandan Karmakar, John Yearwood

    IEEE Journal of Biomedical and Health Informatics
    |June 24, 2022
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    Summary
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    This study introduces a novel method using sinc-convolution in deep learning models to enhance interpretability. By analyzing sinc-kernels, researchers can gain domain-specific insights and optimize models for better performance and transparency in critical applications.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Signal Processing

    Background:

    • Deep learning (DL) and machine learning (ML) models often function as black boxes, hindering transparency and trust in critical applications like healthcare.
    • Interpretability aims to extract human-understandable, domain-specific insights from complex models.
    • Achieving model-level transparency requires interpretable components that can explain decisions linked to domain knowledge.

    Purpose of the Study:

    • To explore the interpretability of deep learning models using a constrained first-layer convolutional neural network (CNN) with sinc-convolution.
    • To investigate if sinc-kernels can provide domain-specific insights by analyzing their optimized frequency bands.
    • To demonstrate a novel approach for optimizing CNNs based on identified prominent sinc frequency bands for task-specific interpretability.

    Main Methods:

    • Utilized a CNN with a sinc-convolution first-layer, where sinc-kernels act as band-pass filters with tunable cutoff frequencies.
    • Optimized sinc-kernels through back-propagation and visualized their effects using an explanation vector for identifying significant frequency bands.
    • Developed a CNN optimization strategy by constraining the first layer to prominent sinc frequency bands identified through analysis.

    Main Results:

    • Optimized sinc-kernel frequency bands offered potential domain-specific insights for given tasks.
    • The explanation vector facilitated the identification of significant frequency bands for interpretability.
    • CNNs optimized with prominent sinc frequency bands achieved performance comparable or superior to standard CNNs and those with all sinc-bands.

    Conclusions:

    • Sinc-convolution offers a pathway to enhance the interpretability of deep learning models by providing task-specific insights through sinc-kernels.
    • Optimizing CNNs by leveraging identified prominent sinc frequency bands can lead to more efficient and interpretable models.
    • The proposed method, including explanation-vector-based analysis, represents a novel approach for interpretable time-series signal analysis, validated on ECG tasks.