http://ravrlab.ru/en/courses/nnmath/ Recent content in Neural Networks Math on RAVR Lab Hugo en-us Thu, 01 Jan 2026 00:00:00 +0000 http://ravrlab.ru/en/courses/nnmath/nnmap/ Thu, 01 Jan 2026 00:00:00 +0000 http://ravrlab.ru/en/courses/nnmath/nnmap/ This is bird-picture overview of NN domain, without going deep into specific applications. Overview Aspects of building NN Initialization methods Forward/Backpropagation Activation functions (sigmoid, tanh, ReLU, …) Layer kinds Cost functions Training/Optimization algorythms Batching/Epochs approaches To sort: dropout, regularization Levels of usage understand math (derive forw/back-prop by hand) program base math (with nothing more than numpy and similar) build NN in framework (pytorch and similar) finetune existing model prompts lol Main domains http://ravrlab.ru/en/courses/nnmath/nn_datasets/ Tue, 30 Dec 2025 00:00:00 +0000 http://ravrlab.ru/en/courses/nnmath/nn_datasets/ MNIST (Modified National Institute Standards and Technology database) Contains grayscale 28x28 images of handwritten digits (from 0 to 9) Contains 60'000 training images and 10'000 testing images. CIFAR-10 (Canadian Institute For Advanced REsearch) Contains 60'000 32x32 color images in 10 different classes There are 6'000 images of each class (airplane, car, bird, cat, deer, dog, frog, horse, ship, truck) ImageNet Full original dataset (ImageNet-21K or ImageNet-22K): Over 14'000'000 images in over 20'000 categories Images are colored, but size vary (from ~50x50 to ~4000x3000) There are various popular subsets like ImageNet-1K http://ravrlab.ru/en/courses/nnmath/fcn_backprop/ Sat, 20 Dec 2025 00:00:00 +0000 http://ravrlab.ru/en/courses/nnmath/fcn_backprop/ Table of Content Model description Forward propagation Backward propagation Math theory Deriving backward propagation formulas Output layer Hidden-2 Layer Hidden-1 Layer Updating weights and biases Optimizing on batch Model description Let’s say we have simple forward propagation neural network with 4 layers: 1 2 3 4 5 6 7 8 9 10 Cost function: C = (a₀ — y₀)² + (a₁ — y₁)² * * Output Layer | 2 neurons, 2*3 weights + 2 biases, Sigmoid activation /\/\\ | * * * Hidden-2 Layer | 3 neurons, 3*4 weights + 3 biases, Sigmoid activation /\//\\\ | * * * * Hidden-1 Layer | 4 neurons, 4*2 weights + 4 biases, Sigmoid activation \/\\/ | * * Input Layer | 2 neurons, 2 input values (say 0. http://ravrlab.ru/en/courses/nnmath/cnn_base/ Fri, 19 Dec 2025 00:00:00 +0000 http://ravrlab.ru/en/courses/nnmath/cnn_base/ Table of Content Convolution 1D-convolution Definitions (calculation examples) Bias Stride Padding 2D-convolution 3D-convolution Pooling Simple CNN Convolution 1D-convolution Definitions (calculation examples) Non-full convolution (reffered to as “valid” in numpy): Output size = Input size — Kernel size + 1 $$ Conv_{valid}\Big( \begin{pmatrix} a \\ b \\ c \\ d \\ e \end{pmatrix}, \begin{pmatrix} k_1 \\ k_2 \end{pmatrix}\Big) = \begin{vmatrix} k_1 & k_2 & 0 & 0 & 0 \\ 0 & k_1 & k_2 & 0 & 0 \\ 0 & 0 & k_1 & k_2 & 0 \\ 0 & 0 & 0 & k_1 & k_2 \end{vmatrix} * \begin{pmatrix} a \\ b \\ c \\ d \\ e \end{pmatrix} = \begin{pmatrix} a * k_1 + b * k_2 \\ b * k_1 + c * k_2 \\ c * k_1 + d * k_2 \\ d * k_1 + e * k_2 \end{pmatrix} $$ http://ravrlab.ru/en/courses/nnmath/rnn_base/ Thu, 18 Dec 2025 00:00:00 +0000 http://ravrlab.ru/en/courses/nnmath/rnn_base/ Table of Content