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CNN

Convolutional Neural Networks developed by Yann LeCun

Why CNN

To address the problem of loss of neighborhood information that occurs when input data in 2 dimentinal matrix and single data point share a relationship with its adjusting data points like that happen in Images.

To many learnable parameters in classical neural network.
- Spare Interaction: There are spare connection between layers unlike feed forward neural network.
- Parameter Sharing: ???
- Equivariant Representation: It eradicate the invariance problem of FDN also.
Translation Invariance: CNN are translational invariance networks means they can classify below images as same.

Mathematics

1D Convolution

$(f*g)(t)=\int^{\infty}_{-\infty}f(\tau).g(t-\tau)d\tau$

Where; Right side represents the Area under the intersection of $f(t)$ and $g(t-\tau)$ curves.

Visual Explanation
- Express Each function $f(t)$ and $g(t)$ in terms of any dummy variable let's say $\tau$ .
- Reflect and translate one of the function let say $g(t-\tau)$
- Beginning from the $-\infty$ upto $+\infty$ slide the function $g(-\tau)$ and whenever they intersect compute integral of their multiplication i.e, weighted sum of the funtion $f(\tau)$ where weighing function is $g(-\tau)$ .

Conv Layer from tf.keras

Comments

1. [CNN](#cnn)
    1. [Why CNN](#why-cnn)
    1. [Mathematics](#mathematics)
        1. [1D Convolution](#1d-convolution)
    2. [Conv Layer from tf.keras](#conv-layer-from-tfkeras)

Comments