{"metadata":{"kernelspec":{"name":"ir","display_name":"R","language":"R"},"language_info":{"name":"R","codemirror_mode":"r","pygments_lexer":"r","mimetype":"text/x-r-source","file_extension":".r","version":"4.4.0"},"kaggle":{"accelerator":"gpu","dataSources":[],"dockerImageVersionId":30751,"isInternetEnabled":true,"language":"r","sourceType":"notebook","isGpuEnabled":true}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"install.packages(\"keras\")\ninstall.packages(\"tensorflow\")\ninstall.packages(\"abind\")\n\nlibrary(keras)\nlibrary(tensorflow)\nlibrary(abind)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:23:11.601213Z","iopub.execute_input":"2026-03-11T09:23:11.602670Z","iopub.status.idle":"2026-03-11T09:24:29.431651Z","shell.execute_reply":"2026-03-11T09:24:29.430121Z"}},"outputs":[{"name":"stderr","text":"Installing package into ‘/usr/local/lib/R/site-library’\n(as ‘lib’ is unspecified)\n\nInstalling package into ‘/usr/local/lib/R/site-library’\n(as ‘lib’ is unspecified)\n\nalso installing the dependency ‘reticulate’\n\n\nInstalling package into ‘/usr/local/lib/R/site-library’\n(as ‘lib’ is unspecified)\n\nThe keras package is deprecated. Please use the keras3 package instead.\nAlternatively, to continue using legacy keras, call `py_require_legacy_keras()`.\n\n","output_type":"stream"}],"execution_count":3},{"cell_type":"code","source":"# Load the MNIST dataset\nmnist <- dataset_mnist()\n\n# Extract training and test data\nx_train <- mnist$train$x\ny_train <- mnist$train$y\nx_test <- mnist$test$x\ny_test <- mnist$test$y","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:35:27.972748Z","iopub.execute_input":"2026-03-11T09:35:27.974395Z","iopub.status.idle":"2026-03-11T09:35:28.813856Z","shell.execute_reply":"2026-03-11T09:35:28.812087Z"}},"outputs":[],"execution_count":28},{"cell_type":"code","source":"# Reshape and normalize the data\nx_train <- array_reshape(x_train, c(nrow(x_train), 28, 28, 1))\nx_test <- array_reshape(x_test, c(nrow(x_test), 28, 28, 1))\n\n# Normalize pixel values to [0, 1]\nx_train <- x_train / 255\nx_test <- x_test / 255","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:35:34.322409Z","iopub.execute_input":"2026-03-11T09:35:34.323853Z","iopub.status.idle":"2026-03-11T09:35:35.193146Z","shell.execute_reply":"2026-03-11T09:35:35.191573Z"}},"outputs":[],"execution_count":29},{"cell_type":"code","source":"# Function to generate a batch of data\ngenerate_batch <- function(x_train, batch_size) {\n  indices <- sample(1:nrow(x_train), batch_size)\n  batch <- x_train[indices, , , ]\n  return(batch)\n}","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:35:44.036621Z","iopub.execute_input":"2026-03-11T09:35:44.038026Z","iopub.status.idle":"2026-03-11T09:35:44.049488Z","shell.execute_reply":"2026-03-11T09:35:44.047846Z"}},"outputs":[],"execution_count":30},{"cell_type":"code","source":"# Define the generator model\nbuild_generator <- function() {\n  model <- keras_model_sequential() %>%\n    layer_dense(units = 128 * 7 * 7, activation = 'relu', input_shape = c(100)) %>%\n    layer_reshape(target_shape = c(7, 7, 128)) %>%\n    layer_conv_2d_transpose(filters = 64, kernel_size = c(5, 5), strides = c(2, 2), \n                            padding = 'same', activation = 'relu') %>%\n    layer_conv_2d_transpose(filters = 1, kernel_size = c(5, 5), strides = c(2, 2), \n                            padding = 'same', activation = 'sigmoid')\n  \n  return(model)\n}\n\ngenerator <- build_generator()\nsummary(generator)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:35:51.129205Z","iopub.execute_input":"2026-03-11T09:35:51.130622Z","iopub.status.idle":"2026-03-11T09:35:51.348926Z","shell.execute_reply":"2026-03-11T09:35:51.347488Z"}},"outputs":[{"name":"stdout","text":"Model: \"sequential_8\"\n________________________________________________________________________________\n Layer (type)                       Output Shape                    Param #     \n================================================================================\n dense_8 (Dense)                    (None, 6272)                    633472      \n reshape_3 (Reshape)                (None, 7, 7, 128)               0           \n conv2d_transpose_7 (Conv2DTranspos  (None, 14, 14, 64)             204864      \n e)                                                                             \n conv2d_transpose_6 (Conv2DTranspos  (None, 28, 28, 1)              1601        \n e)                                                                             \n================================================================================\nTotal params: 839,937\nTrainable params: 839,937\nNon-trainable params: 0\n________________________________________________________________________________\n","output_type":"stream"}],"execution_count":31},{"cell_type":"code","source":"# Define the discriminator model\nbuild_discriminator <- function() {\n  model <- keras_model_sequential() %>%\n    layer_conv_2d(filters = 64, kernel_size = c(5, 5), strides = c(2, 2), padding = 'same', \n                  activation = 'relu', input_shape = c(28, 28, 1)) %>%\n    layer_dropout(rate = 0.3) %>%\n    layer_conv_2d(filters = 128, kernel_size = c(5, 5), strides = c(2, 2), padding = 'same', \n                  activation = 'relu') %>%\n    layer_dropout(rate = 0.3) %>%\n    layer_flatten() %>%\n    layer_dense(units = 1, activation = 'sigmoid')\n  \n  return(model)\n}\n\ndiscriminator <- build_discriminator()\nsummary(discriminator)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:35:59.236250Z","iopub.execute_input":"2026-03-11T09:35:59.237587Z","iopub.status.idle":"2026-03-11T09:35:59.307225Z","shell.execute_reply":"2026-03-11T09:35:59.305738Z"}},"outputs":[{"name":"stdout","text":"Model: \"sequential_9\"\n________________________________________________________________________________\n Layer (type)                       Output Shape                    Param #     \n================================================================================\n conv2d_11 (Conv2D)                 (None, 14, 14, 64)              1664        \n dropout_11 (Dropout)               (None, 14, 14, 64)              0           \n conv2d_10 (Conv2D)                 (None, 7, 7, 128)               204928      \n dropout_10 (Dropout)               (None, 7, 7, 128)               0           \n flatten_5 (Flatten)                (None, 6272)                    0           \n dense_9 (Dense)                    (None, 1)                       6273        \n================================================================================\nTotal params: 212,865\nTrainable params: 212,865\nNon-trainable params: 0\n________________________________________________________________________________\n","output_type":"stream"}],"execution_count":32},{"cell_type":"code","source":"# Define the GAN model\ngan_input <- layer_input(shape = c(100)) # Noise input for the generator\nx <- generator(gan_input)  # Pass the noise through the generator\ngan_output <- discriminator(x)  # Pass the generated image through the discriminator\n\n# Create the combined GAN model\ngan_model <- keras_model(inputs = gan_input, outputs = gan_output)\n\n# Compile the discriminator model\ndiscriminator %>% compile(\n  optimizer = optimizer_adam(),\n  loss = 'binary_crossentropy',\n  metrics = c('accuracy')\n)\n\n# Compile the combined GAN model\ngan_model %>% compile(\n  optimizer = optimizer_adam(),\n  loss = 'binary_crossentropy'\n)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:36:07.516250Z","iopub.execute_input":"2026-03-11T09:36:07.517787Z","iopub.status.idle":"2026-03-11T09:36:07.600500Z","shell.execute_reply":"2026-03-11T09:36:07.598945Z"}},"outputs":[],"execution_count":33},{"cell_type":"code","source":"batch_size <- 64\nepochs <- 200\n\n# Function to train the discriminator\ntrain_discriminator <- function(real_images, batch_size) {\n  # Generate fake images\n  noise <- matrix(rnorm(batch_size * 100), nrow = batch_size, ncol = 100)\n  fake_images <- generator %>% predict(noise)\n  \n  # Ensure real images have the same dimensions as fake images\n  if (length(dim(real_images)) == 3) {\n    real_images <- array_reshape(real_images, c(batch_size, 28, 28, 1))\n  }\n  \n  # Print dimensions for debugging\n  print(dim(real_images))\n  print(dim(fake_images))\n  \n  # Ensure real and fake images have the same dimensions\n  if (!identical(dim(real_images), dim(fake_images))) {\n    stop(\"Dimension mismatch between real and fake images.\")\n  }\n  \n  # Combine real and fake images\n  x_combined <- abind(real_images, fake_images, along = 1)\n  \n  # Labels for real and fake images\n  y_combined <- c(rep(1, batch_size), rep(0, batch_size))\n  \n  # Train the discriminator\n  d_loss <- discriminator %>% fit(\n    x_combined, y_combined,\n    epochs = 1,\n    batch_size = batch_size,\n    verbose = 0\n  )\n  \n  return(d_loss)\n}","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:36:27.126668Z","iopub.execute_input":"2026-03-11T09:36:27.128083Z","iopub.status.idle":"2026-03-11T09:36:27.141711Z","shell.execute_reply":"2026-03-11T09:36:27.140223Z"}},"outputs":[],"execution_count":34},{"cell_type":"code","source":"# Function to train the GAN\ntrain_gan <- function(batch_size) {\n  # Generate random noise\n  noise <- matrix(rnorm(batch_size * 100), nrow = batch_size, ncol = 100)\n  \n  # Labels for generated images (all ones, to fool the discriminator)\n  y_gan <- rep(1, batch_size)\n  \n  # Train the GAN\n  g_loss <- gan_model %>% fit(\n    noise, y_gan,\n    epochs = 1,\n    batch_size = batch_size,\n    verbose = 0\n  )\n  \n  return(g_loss)\n}\n\n# Training loop\nfor (epoch in 1:epochs) {\n  cat(sprintf(\"Epoch %d\\n\", epoch))  # Print current epoch\n  \n  # Generate a batch of real images\n  real_batch <- generate_batch(x_train, batch_size)\n  \n  # Train the discriminator\n  d_loss <- train_discriminator(real_batch, batch_size)\n  cat(sprintf(\"Discriminator Loss: %.4f\\n\", d_loss$loss))\n  \n  # Train the generator\n  g_loss <- train_gan(batch_size)\n  cat(sprintf(\"Generator Loss: %.4f\\n\", g_loss$loss))\n  \n  # Print progress every 10 epochs\n  if (epoch %% 10 == 0) {\n    cat(sprintf(\"Epoch %d: Discriminator Loss: %.4f, Generator Loss: %.4f\\n\", \n                epoch, d_loss$loss, g_loss$loss))\n  }\n}","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:36:41.305364Z","iopub.execute_input":"2026-03-11T09:36:41.306938Z","iopub.status.idle":"2026-03-11T09:37:36.510271Z","shell.execute_reply":"2026-03-11T09:37:36.508641Z"}},"outputs":[{"name":"stdout","text":"Epoch 1\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 2\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 3\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 4\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 5\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 6\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 7\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 8\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 9\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 10\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 11\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 12\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 13\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 14\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 15\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 16\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 17\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 18\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 19\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 20\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 21\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 22\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 23\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 24\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 25\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 26\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 27\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 28\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 29\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 30\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 31\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 32\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 33\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 34\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 35\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 36\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 37\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 38\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 39\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 40\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 41\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 42\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 43\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 44\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 45\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 46\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 47\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 48\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 49\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 50\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 51\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 52\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 53\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 54\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 55\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 56\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 57\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 58\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 59\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 60\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 61\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 62\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 63\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 64\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 65\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 66\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 67\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 68\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 69\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 70\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 71\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 72\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 73\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 74\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 75\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 76\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 77\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 78\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 79\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 80\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 81\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 82\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 83\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 84\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 85\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 86\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 87\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 88\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 89\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 90\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 91\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 92\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 93\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 94\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 95\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 96\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 97\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 98\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 99\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 100\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 101\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 102\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 103\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 104\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 105\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 106\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 107\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 108\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 109\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 110\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 111\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 112\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 113\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 114\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 115\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 116\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 117\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 118\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 119\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 120\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 121\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 122\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 123\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 124\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 125\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 126\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 127\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 128\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 129\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 130\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 131\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 132\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 133\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 134\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 135\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 136\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 137\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 138\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 139\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 140\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 141\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 142\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 143\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 144\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 145\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 146\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 147\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 148\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 149\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 150\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 151\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 152\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 153\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 154\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 155\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 156\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 157\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 158\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 159\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 160\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 161\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 162\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 163\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 164\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 165\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 166\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 167\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 168\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 169\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 170\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 171\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 172\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 173\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 174\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 175\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 176\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 177\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 178\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 179\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 180\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 181\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 182\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 183\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 184\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 185\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 186\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 187\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 188\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 189\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 190\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 191\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 192\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 193\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 194\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 195\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 196\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 197\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 198\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 199\n[1] 64 28 28  1\n[1] 64 28 28  1\nEpoch 200\n[1] 64 28 28  1\n[1] 64 28 28  1\n","output_type":"stream"}],"execution_count":35},{"cell_type":"code","source":"# Generate and visualize images\ngenerate_images <- function(num_images) {\n  noise <- matrix(rnorm(num_images * 100), nrow = num_images, ncol = 100)\n  generated_images <- generator %>% predict(noise)\n  \n  # Plot the generated images\n  par(mfrow = c(1, num_images))\n  for (i in 1:num_images) {\n    image(t(generated_images[i,,,1]), col = gray.colors(256), axes = FALSE, \n          main = sprintf(\"Image %d\", i))\n  }\n}\n\n# Generate and plot 5 images\ngenerate_images(5)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:37:36.512537Z","iopub.execute_input":"2026-03-11T09:37:36.513669Z","iopub.status.idle":"2026-03-11T09:37:37.270845Z","shell.execute_reply":"2026-03-11T09:37:37.269149Z"}},"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg\nAElEQVR4nOzceZxV1Znv/++ZqqgJCijmQSZFRFREUcExBjUJmm41iW1rxr7xxoiddPpm0O6O\nN+r9mdhJjDGTt01ilBg1KkGMOIFgVARBEJB5hoKqoubxDHXO74+H2nf3KUSkpHbVOp/3H77O\ns9c5u1btZ6+1vx7QUCaTEQAAAHq/cNATAAAAwEeDYAcAAOAIgh0AAIAjCHYAAACOINgBAAA4\ngmAHAADgCIIdAACAIwh2AAAAjiDYAQAAOIJgBwAA4AiCHQAAgCMIdgAAAI4g2AEAADiCYAcA\nAOAIgh0AAIAjCHYAAACOINgBAAA4gmAHAADgCIIdAACAIwh2AAAAjiDYAQAAOIJgBwAA4AiC\nHQAAgCMIdgAAAI6IBj0BAACclG5vz0gKRSJ8iYJu4+DNVhgJh0Khc3+2PuiJHEn5K/85Z86c\nt5uSQU/EHT257+nkgXv/+bMThw/Mj/UZMva0L37vF9WpdNCTckRP7nt7284ffP2zE0YOzo8V\nDJtwxtd+8Egrbf+I9OS+e3584choNBqNRm/cVBP0XBzRk/tet/WW0H8XjhQGMhO+sQtAa+Xr\nN3zm3xfXtp33Hz88qzgW9HRw3N398TP/Y+n+UCjUf3D/ql3rHr7nlpfeOrhv0feDnheOp0zq\nlqln/npjbSgUHTqs3/5ta379/c+/UT5wza8/GfTM0B0q3vjev762P+hZoPtUvfFu0FM4xMFv\n7HqyB7//nS997rJRIy9aXNsW9FzQTVqq/vgfS/dL+t8v7aw+UL39+X+TVL74jvv2NQU9NRxH\nDbt/8OuNtZH8EX8rbyjfd3DJPedIWv+7L/OdXS7ItDd8+dM/6zvmC32jPGRzxd6/7JW0sLym\nqUNjQ1UgM3H8nsu019s3orcueuxjEwaGw3lDx531/cfWN+956apzTyzKLxh14hn/9tAb3vtb\nypfcfO0lo8v6xqJ5/YeN/eSN/2t1Q8IbXffMj84/fXzJoPHX3PyLVfedEwqFBk783aEflKr9\nxXc/f+rowX3yS8ZOmv6/fvJEKnOY+fzhvp/9/omXqpPtx/n3znU9qu/Nex+XlN/vgn+/dLSk\nMZf/4JTCmKSFm+uP82XIOT2q7/HqipNPPnnqzG/PGFog6bRrz5KUaW887M6AruhRfTer7p39\nfHXynhd/Fjmev3iO62l9f+udmnC036VD+xf5HOdr8D4yzikIhySdc9+6TCaTTtXZrxkJhULh\nPHsdjhSeVBQLhWLhUEhSKBT+VXmTvfnigQWSIrF+o8eMsvMMOOW7dtrtj//PQ6fK7yOp/6gi\nSQNO+m0mk8lk0ndcPFxSrGjU9HPPLI2GJU2+/qHOc2tvb0+lUs3VL9mp5lY2d9tlcV6P7Xtr\n5ZI//elPf563zMp0e8ugWETSDesPdte1cVmP7btfvH7n/5k9WtJJ/zD3eF+QHNGT+x6vWzo4\nL3LSF57OZDL9o2FJ12+s7q4L47ie3PezS/Lyik//5rUzB/ftM3TclGu/fs+BRHu3XRm/XAl2\nJ/zdj2sT7bWb/hILhySVnf4ve5qSzeXLRuRHJF346JZMJlO37ZvRaDS/YNi79fFMJnNg2U2S\nQqFIWzqTbm8+szhP0klffrCpPb172UMDYxGv8dXrvysp2mfcqrp4JpOp2zTXfsp9exoPO8O2\nukUEu49cz++7WXjHJZJiBSdtb011x3VxXc/v+3sPXGizKhr6qX3xYDZ69/Tkvv/yspGxoilb\nWpMZgt1Hrcf2PdW2OxQKSQpHi8eNGWKxctgFdwRwjXIn2P3TphobnVQYk/Txv+6y8h8HF0ma\n8esN3sdbq3YufXH+f/38R/8wY4h9ti6Vbthzj71+rT5ub/vLp07wGv/m10+R1Kf/Zf/WYWyf\nqKTpP1l72BkS7I6Hnt/3dKrxF3M+JikcG/CjxeXH71LklJ7f9wN/+8U3v/6Fk0vzJQ2e/rW2\n9PG7GDmkx/a9auWdkm54YruVBLuPVo/te1vdq9ddd931N3x1U1Mik8ls+su/2Dl/vq/p+F+V\nbLnyX8X2ix3624QhSVL+gHx/eUgmcc//uPw/frckpT4nnT719FMn640KG0k0vi0pHCk8v++h\n73vHXTpEz+2y1w3vNUhqq33xrrte9J+vfi1/iSpgPafvzfuWfmn2NU+uPlhQdvaDC/96w7Sy\nj+QXxGH1nL5LGjLz5p/MvPnu73++bNisyuW/+tbmux+Y2L/rvyM66wl9X/1v/1fSon+5cNS/\nSFJ9e0bSvIunXP7Pz7/w3dM+ol8U/01P6Ht+v4see+wirzzpqh+fUfzA6qbEvJUHbxne3X/T\nzvH/eOJD2fvyjd976NVw8blrq2o3rnr9wf89zRuK9hkrKd3e8k7zof/z3IFl1d5oyYklkgZO\nejQrNW/87czu/Q1wLLqh73Ub50496eNPrj44+uO3vrPzdVJdT3C8+75t7pxPfOIT137xMSsL\nBn3spIKopE3bG4/zb4YjOe7rPSNJ5XsPSWcykloOlFfU838tDdLx7nvNOy899dRTz76wreNA\nujWdkRQrCuDrM4Ld/3Pg5Y2SwrGyUf3ylG77w7ee9IaKh88pi0UkfeG2JxMZVa198ot/2emN\nTvifl0pq2PmDZQfbJCXqV182/aypU6fevbG2m38FHIPj3vd027Uz/2lLS7Ls9H9ePf+HY6Lp\neDwej8f5ryODdbz7XjS2ZuHChc/MvXnuir3KpFY89o3VTQlJF59S2h2/Ht7H8e77x5/f5X/8\ne38Uu/r/myYE53j3vWb93ddee+01V1/1t10NSre9/MA/bGpJhkKxf54axL/GH+Mf4fZgh/0z\n+G9tr7NR+z9NfGrZAStv8P0ZfMXyQ38o3mfgqBH9+8SKBlq5pimRyWSWfO88K2NFJZIKBuTL\n+69m0slvTBskKVo45JwLZo4oiEo64Yrbku/zl2n4O3bHQ4/te82GWw+79LzJoCt6bN/TqcZr\nx/S1k0Q6/qho6Pnf675L47Qe2/cs/B27j1aP7Xuydcv00kN/BJzX8T8vnH7rX7rv0vjwjd3/\nM/jsHz/1f/5pwogBkXDklFlzVmx+KhIKSfryD9dJuvDupY/c8ZWzTh6ldl104z2LbvP9bYlQ\n9MdvrP7hnM+M7ZtY9da7+WPO+MYP/7BuwV3R0Pv9KPQgx7vvFUve7tbfB0fnePc9FCn+49q3\nbv/y7LGD+oUysUEnnPqF79y/dtFd3fpLohP2+dx0vPse7TPh1Q2Lb/3crJNGD06H8kdPmXnb\nL/667GdXdesv6U05k+EPhD5YOrH/kcdelDTp6n+YXpIn6fHZY657bteojy/c/dLlQc8Oxwt9\nz030PTfR99zkXt8Jdkcn3XrV6MHP7mvqN+GyOTeeX7vl1V/PXZwJF92/fs/XJ/I3ZtxF33MT\nfc9N9D03udf3QP4AuDeK16+7/ctXjRtaGg1HikqHzvjkjXNf539F5j76npvoe26i77nJsb7z\njR0AAIAj+I8nAAAAHEGwAwAAcATBDgAAwBEEOwAAAEcQ7AAAABxBsAMAAHAEwQ4AAMARBDsA\nAABHEOwAAAAcQbADAABwBMEOAADAEQQ7AAAARxDsAAAAHEGwAwAAcATBDgAAwBEEOwAAAEcQ\n7AAAABxBsAMAAHAEwQ4AAMARBDsAAABHEOwAAAAcQbADAABwROSOO+4Ieg5dlUql0ul0c3Oz\n/dOONDY2ZjKZxsZGK+vr69PpdF1dnaRkMllXV5fJZHpa2dDQYC9isVgQF7KXSSaT6XS6sbGx\nvb29vr5evktaW1srKZFI2IueWXp99yafl5fXbVev9/L33Vsyh11Z3dA71nu3OULfg+os670b\ndE/fHdvno8f7BxxvqVRq6dKlkhYuXChpyJAhdnzDhg2S+vbta+W2bdsklZaWWmmXOD8/38rW\n1lZ/mUgkJHm7rZUFBQVWtrW1dR4tKiryn8objcfjHzhaVlZmZTR6qB0PPvhgV65JLkilUgsW\nLJA0d+5cSSUlJXa8pqZGviuZTCYlhUIhKzOZTOdThcOHvrdOp9Od33zk0SOf+chv9pZ3JBKx\nF48//vjR/v65KpVKvfjii5KeeOIJ+Vb03r175VvCTU1N8t0GqVRKnVp55FFvkdpo1h1VWFho\nZdZucDTrvX///lZ653zooYe6ck1ygbfe//jHP0rq16+fHa+qqtIHrfessiudzXoKZH3We7OV\nWXcU6/0YpFKpl19+WdLDDz8s3wO9oqJCH3KfP7IPtZO/315h08jaWIqLi630jv/hD3/4sNP7\nsPijWAAAAEcQ7AAAABxBsAMAAHAEwQ4AAMARBDsAAABHEOwAAAAcQbADAABwBMEOAADAEQQ7\nAAAARxDsAAAAHEGwAwAAcATBDgAAwBEEOwAAAEcQ7AAAABxBsAMAAHAEwQ4AAMARBDsAAABH\nEOwAAAAcQbADAABwBMEOAADAEQQ7AAAARxDsAAAAHEGwAwAAcESvD3bt7e1BTwEBoO+5ib7n\nJv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yMGDByVVVlbKdw2TyaSk2tpa/5vt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\nAABJRU5ErkJggg=="},"metadata":{"image/png":{"width":420,"height":420}}}],"execution_count":36},{"cell_type":"code","source":"library(ggplot2)\n\n# Initialize loss vectors\nd_losses <- c()\ng_losses <- c()\n\n# Training parameters\nbatch_size <- 64\nepochs <- 10  # Adjust as needed\n\n# Dummy functions for training; replace with your actual implementation\ntrain_discriminator <- function(real_batch, batch_size) {\n  # Replace with actual implementation\n  list(loss = runif(1))\n}\n\ntrain_gan <- function(batch_size) {\n  # Replace with actual implementation\n  list(loss = runif(1))\n}\n\n# Training loop\nfor (epoch in 1:epochs) {\n  cat(sprintf(\"Epoch %d\\n\", epoch))\n  \n  # Generate a batch of real images\n  real_batch <- generate_batch(x_train, batch_size)\n  \n  # Train the discriminator\n  d_loss <- train_discriminator(real_batch, batch_size)\n  d_losses <- c(d_losses, d_loss$loss)\n  cat(sprintf(\"Discriminator Loss: %.4f\\n\", d_loss$loss))\n  \n  # Train the generator\n  g_loss <- train_gan(batch_size)\n  g_losses <- c(g_losses, g_loss$loss)\n  cat(sprintf(\"Generator Loss: %.4f\\n\", g_loss$loss))\n  \n  # Print progress every 10 epochs\n  if (epoch %% 10 == 0) {\n    cat(sprintf(\"Epoch %d: Discriminator Loss: %.4f, Generator Loss: %.4f\\n\", \n                epoch, d_loss$loss, g_loss$loss))\n  }\n}\n\n# Debugging: Check the lengths and contents of loss vectors\ncat(\"Length of d_losses:\", length(d_losses), \"\\n\")\ncat(\"Length of g_losses:\", length(g_losses), \"\\n\")\ncat(\"Contents of d_losses:\", d_losses, \"\\n\")\ncat(\"Contents of g_losses:\", g_losses, \"\\n\")\n\n# Function to plot training loss\nplot_loss <- function(d_losses, g_losses) {\n  # Ensure d_losses and g_losses have the same length\n  if (length(d_losses) != length(g_losses)) {\n    stop(\"Length of d_losses and g_losses must be the same\")\n  }\n  \n  df <- data.frame(Epoch = 1:length(d_losses), \n                   Discriminator_Loss = d_losses, \n                   Generator_Loss = g_losses)\n  \n  ggplot(df, aes(x = Epoch)) +\n    geom_line(aes(y = Discriminator_Loss, color = \"Discriminator Loss\")) +\n    geom_line(aes(y = Generator_Loss, color = \"Generator Loss\")) +\n    labs(title = \"Training Losses\", x = \"Epoch\", y = \"Loss\") +\n    theme_minimal()\n}\n\n# Plot training losses\nplot_loss(d_losses, g_losses)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-03-11T09:37:37.273201Z","iopub.execute_input":"2026-03-11T09:37:37.274517Z","iopub.status.idle":"2026-03-11T09:37:38.190268Z","shell.execute_reply":"2026-03-11T09:37:38.188550Z"}},"outputs":[{"name":"stdout","text":"Epoch 1\nDiscriminator Loss: 0.8175\nGenerator Loss: 0.5640\nEpoch 2\nDiscriminator Loss: 0.7434\nGenerator Loss: 0.8770\nEpoch 3\nDiscriminator Loss: 0.3223\nGenerator Loss: 0.8389\nEpoch 4\nDiscriminator Loss: 0.6214\nGenerator Loss: 0.6688\nEpoch 5\nDiscriminator Loss: 0.2971\nGenerator Loss: 0.7695\nEpoch 6\nDiscriminator Loss: 0.8965\nGenerator Loss: 0.2870\nEpoch 7\nDiscriminator Loss: 0.2366\nGenerator Loss: 0.3169\nEpoch 8\nDiscriminator Loss: 0.5652\nGenerator Loss: 0.0609\nEpoch 9\nDiscriminator Loss: 0.4508\nGenerator Loss: 0.9357\nEpoch 10\nDiscriminator Loss: 0.2494\nGenerator Loss: 0.0142\nEpoch 10: Discriminator Loss: 0.2494, Generator Loss: 0.0142\nLength of d_losses: 10 \nLength of g_losses: 10 \nContents of d_losses: 0.8174516 0.7433752 0.3223093 0.6213775 0.2971386 0.8965263 0.2365695 0.5652238 0.4507615 0.2494443 \nContents of g_losses: 0.5639856 0.8769876 0.8389135 0.6687756 0.7694828 0.2869661 0.3168722 0.060862 0.9357302 0.01423537 \n","output_type":"stream"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\n6QS3YolMwsCOiCwghgb1bZshhNULIQvIrdgpD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Fc/UYEdAIUdT4iyw8CuOMjA7uQSKrBLWuhxf6ymBsBtbe1RjhgrOcYwsVQCu+oaANB1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\njd3bswAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"width":420,"height":420}}}],"execution_count":37},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null}]}