https://hvidberrrg.github.io/ https://hvidberrrg.github.io/robots.txt https://hvidberrrg.github.io/deep_learning_and_neural_networks.html https://hvidberrrg.github.io/deep_learning/resources_and_references.html https://hvidberrrg.github.io/deep_learning/activation_functions_in_artificial_neural_networks.html https://hvidberrrg.github.io/deep_learning/assets/sem_image_of_biological_neuron.png Scanning electron microscope (SEM) image of a biological neuron https://hvidberrrg.github.io/deep_learning/assets/activation_function_diagram.png A generic activation function for an artificial neuron https://hvidberrrg.github.io/deep_learning/activation_functions/sigmoid_function_and_derivative.html https://hvidberrrg.github.io/deep_learning/activation_functions/assets/sigmoid_function.png The elongated 'S'-like curve of the sigmoid function (a.k.a. the logistic function) https://hvidberrrg.github.io/deep_learning/activation_functions/assets/sigmoid_derivative.png The bell-shaped curve of the derivative of the sigmoid function (a.k.a. the logistic function) https://hvidberrrg.github.io/deep_learning/activation_functions/unit_step_function.html https://hvidberrrg.github.io/deep_learning/activation_functions/assets/step_function.png The unit step function https://hvidberrrg.github.io/deep_learning/activation_functions/assets/step_function_non_zero_threshold.png The unit step function with a non-zero threshold https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation.html https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/gradient_descent.html https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/assets/gradient_vector_field_of_a_function.png Example function and its gradient vector field https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/assets/gradient_descent_example.png Example of gradient descent https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/assets/gradient_descent_small_steps.png Gradient descent using a small step size https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/assets/gradient_descent_efficient_step_size.png Gradient descent with an "efficient" step size https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/assets/gradient_descent_large_steps.png Gradient descent using too large a step size https://hvidberrrg.github.io/deep_learning/optimization_and_backpropagation/assets/multiple_minima.png Function with multiple minima https://hvidberrrg.github.io/deep_learning/mathematical_foundations_of_deep_learning.html https://hvidberrrg.github.io/deep_learning/mathematical_foundations/vectors_matrices_and_tensors.html https://hvidberrrg.github.io/deep_learning/mathematical_foundations/assets/vector.png An example of a vector https://hvidberrrg.github.io/deep_learning/mathematical_foundations/assets/vector_components.png Vector representing a displacement in 2-dimensional space https://hvidberrrg.github.io/deep_learning/mathematical_foundations/assets/scalar_projection.png Scalar projection of one vector onto another https://hvidberrrg.github.io/deep_learning/mathematical_foundations/assets/vector_addition.png Illustrating the triangle inequality in 2-dimensional space https://hvidberrrg.github.io/deep_learning/mathematical_foundations/assets/unit_circles_in_various_p-norms.png Unit circles in various p-norms