• Derivatives

    Writing derivatives using the Leibniz notation

    All of these are the different ways to write the derivative of a function.

    The derivative of

    constant function

    The derivative equals 0 since there’s no change from one x value to any other x values. It means that there’s no slope.


    linear function

    The derivative normally equals 1. y changes by the same amount for every change of x.

    The derivative of a linear function equals to the slope m (i.e. m = 2).


    quadratic function

    At any point x, the slope of the tangent line will be 6x.


    quadratic function with addition


    multi-dimensional function


    Remember, the derivative of a constant is always 0.

  • Softmax Activation Function

    Exponential function

  • Activating ReLU function in the hidden layers

    Our neural network, which is not densely connected, has 2 hidden layers with 8 neurons each. There’s only a one-to-one correspondence between each neuron in the input, layer 1, layer 2, and the output. We will use both hidden layers to fit the line to the sine wave function.

    We start by assigning baseline values–giving us this output.

    Setting the hidden layers’ weight values to 1.0 results in this linear line (i.e. weights tend to affect the slope of the line).

    Increasing the weights increases the slope even more.

    Increasing layer 2 ’s bias by a half nudges the entire line up by a half.

    Flipping layer 1 ’s weight results in flipping the line (*explanation after the illustration).

    ReLU note: y = 0 if x <= 0 else x that’s why the line does not descend past 0

    Code

    NumPy:


    Moving on. Let’s flip layer 2 ’s weight to flip the line vertically.

    To move that whole line upward by a half, we set the bias of layer 2 of the bottommost neuron to 0.5.

    At this stage we have completed the first section of the process. The slope of the leftmost line, more or less, follows the contour of that section of the sine wave.

    The aim is to get to this stage where every section follow the form of the sine wave.

  • ReLU activation on a two-neuron network

    Starting with a weight = 0 and bias = 0 on a single neuron:

    Setting weight = 1.0 while keeping bias to 0:

    Setting bias to 0.5:

    To flip the line horizontally, negate the weight from 1.0 to -1.0:

    Bias applied on a neuron, an input, and a ReLU activation function

    Now let’s introduce the second neuron with values weight = 1.0 and bias = 1.0:

    This caused a vertical shift of the activation function. Note that the bias moves the line vertically.

    Let’s negate the second neuron’s weight by 2 (i.e. -2.0):

    And now to compute the output:

  • Forward pass on a dense layer neural network

    A dense layer is a fully-connected neural network layer.

  • Generating a random 2x4 matrix in NumPy

    The 0.01 value is for making the randomly generated values a magnitude smaller (akin to a volume knob that controls the volume of a sound).

  • Neural network with two hidden layers

    Hidden layer 1 (with code)

  • A neural network with one hidden layer

    This neural network has 4 features in the input layer and 3 neurons in the hidden layer. Each of the three neurons is composed of 4 different weights (coming from the 4 inputs) and has shape of (3, 4).

  • Visualizing matrix dot product

    Given a pair of variables inputs (3x4 matrix) and weights (3x4 matrix). The matrix on the right side (i.e. weight) must be transposed first.

    Only can then we perform a matrix dot multiplication.

  • Row and column vectors in NumPy

  • Matrix transposition visualization

    Transposition modifies a matrix in such a way that rows become columns and columns become rows.

    matrix transposition

  • Visualizing matrix multiplication

  • Replacing the front caster from a wheel to a ball made from a roll-on deodorant applicator.

  • Update: Light seeking robot project

    Making the wirings pretty.

  • Installing headless JupyterLab on a remote Linux server

    Prerequisite:

    • python3-pip package
    • python3-dev package

    Installation

    This is only done per new project:

    remote@~  $ mkdir project_foo && cd project_foo
    remote@~/project_foo $ python3 -m venv env_foo
    

    This is done every time you launch the JupyterLab server remotely:

    local $ ssh -L 8080:localhost:8080 remote@my.server
    remote@~/project_foo $ source ˜ /project_foo/bin/activate
    (env_foo) $ jupyter lab --no-browser --port 8080
    ...
    [I 17:13:43.778 LabApp] Serving notebooks from local directory: /home/remote
    [I 17:13:43.778 LabApp] Jupyter Notebook 6.1.3 is running at:
    [I 17:13:43.779 LabApp] http://localhost:8080/?token=35a68d738b9cbd72a0910452f8d4446c6b250c34c37b2fa2
    [I 17:13:43.779 LabApp]  or http://127.0.0.1:8080/?token=35a68d738b9cbd72a0910452f8d4446c6b250c34c37b2fa2
    [I 17:13:43.779 LabApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation).
    

    And then in your local browser:

    http://localhost:8080/?token=35a68d738b9cbd72a0910452f8d4446c6b250c34c37b2fa2
    
  • Using a Python 3 virtual environment for Python projects

    $ mkdir proj_foo && cd proj_foo
    or
    $ take proj_foo
    
    $ python3 -m venv  env_foo
    $ source env_foo/bin/activate
    (env_foo) proj_foo $
    
  • When ssh connection drops out after a few minutes of inactivity

    This is the error message it displays:

    … send disconnect: Broken pipe

    Solution:

    In /etc/ssh/sshd_config, make sure these two lines are uncommented:

    ClientAliveInterval 30
    ClientAliveCountMax 5
    
    
  • Prototyping the battery holder bracket.

  • Light following robot project

    It’s finally done–testing and all. Now, to make it a little less messy.

    #arduino #electronics #sensors

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