<jupyter_start><jupyter_text>DeconvolutionThe term deconvolution is often a misnomer applied to transposed convolutions in neural networks. In this context, deconvolutional layer is meant to refer to the reverse of the convolution layer process. In actuality, it is a transposed convolution layer that does much the same as a regular convolutional layer. In the below images, the blue squares are from the original input, the white squares are added zeros, and the green squares are the output.  Kernel Size 3, Stride 1, Padding 0 ![SegmentLocal](images/YyCu2.gif "segment")  Kernel Size 3, Stride 2, Padding 1 ![SegmentLocal](images/f2RiP.gif "segment") These animations and others can be found at https://github.com/vdumoulin/conv_arithmetic. ***  Bias Nodes A bias can be added to your network layers. It is simply a node that holds the value 1. Treat the bias like the y-intercept value in your regular linear equation.- $y = mx + b$ Here we have the most basic of neural networks, a perceptron consisting of a single input node and single output node with one weight value applied to the input. A sigmoid activation function is then applied to the result. The output of this network is thus given by the following equation:- $y = sigmoid(w_{0}x) = \frac{1}{1 + e^{-(w_{0}x)}}$It is a little easier to read in this format:- $y = sigmoid(w_{0}x) = \frac{1}{1 + exp(-w_{0}x)}$![SegmentLocal](images/bI2Tm.gif "segment")<jupyter_code># PyTorch code to represent this network
import torch
import torch.nn as nn

Perceptron = nn.Sequential(
    nn.Linear(1, 1),
    nn.Sigmoid()
    )<jupyter_output><empty_output><jupyter_text>This is a graph showing the network's output with different weight values. ![SegmentLocal](images/ddyfr.png "segment") Now, if we add the bias node to the input layer... ![SegmentLocal](images/oapHD.gif "segment") The complete network function is now this:- $y = sigmoid(w_{0}x + w_{1})$Equivalently:- $y = \frac{1}{1 + e^{-(w_{0}x + w_{1})}}$- $y = \frac{1}{1 + exp(-(w_{0}x + w_{1}))}$<jupyter_code># Just to show the value of Euler's number
import math
import matplotlib.pyplot as plt
plt.figure(figsize=(6, 0.5))
plt.text(0, 0.9, f"$e = {math.e}$", fontsize=40)
plt.axis('off')
print("Euler's Number:")
plt.show()<jupyter_output>Euler's Number:
{'fraction_non_alphanumeric': 0.11340659340659341, 'fraction_numerical': 0.016703296703296705, 'mean_word_length': 4.911688311688311, 'pattern_counts': {'":': 0, '<': 8, '<?xml version=': 0, '>': 8, 'https://': 1, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '2', 'dir': 'jupyter-structured-clean-dedup', 'id': '438320', 'license': 'MIT', 'n_tokens_mistral': 743, 'n_tokens_neox': 704, 'n_words': 294, 'path': 'graphics.ipynb', 'repo_name': 'noajam/sound-pineapple', 'size': '2275'}