Neural model switch with keen execution and Keras


How would your summer season vacation’s pictures look had Edvard Munch painted them? (Maybe it’s higher to not know). Let’s take a extra comforting instance: How would a pleasant, summarly river panorama look if painted by Katsushika Hokusai?

Model switch on pictures will not be new, however acquired a lift when Gatys, Ecker, and Bethge(Gatys, Ecker, and Bethge 2015) confirmed the right way to efficiently do it with deep studying. The principle thought is easy: Create a hybrid that may be a tradeoff between the content material picture we need to manipulate, and a model picture we need to imitate, by optimizing for maximal resemblance to each on the identical time.

For those who’ve learn the chapter on neural model switch from Deep Studying with R, it’s possible you’ll acknowledge a number of the code snippets that observe. Nevertheless, there is a vital distinction: This publish makes use of TensorFlow Keen Execution, permitting for an crucial approach of coding that makes it simple to map ideas to code. Identical to earlier posts on keen execution on this weblog, this can be a port of a Google Colaboratory pocket book that performs the identical process in Python.

As common, please be sure to have the required bundle variations put in. And no want to repeat the snippets – you’ll discover the entire code among the many Keras examples.

Conditions

The code on this publish is dependent upon the newest variations of a number of of the TensorFlow R packages. You possibly can set up these packages as follows:

c(128, 128, 3)

content_path <- "isar.jpg"

content_image <-  image_load(content_path, target_size = img_shape[1:2])
content_image %>% 
  image_to_array() %>%
  `/`(., 255) %>%
  as.raster() %>%
  plot()

And right here’s the model mannequin, Hokusai’s The Nice Wave off Kanagawa, which you’ll be able to obtain from Wikimedia Commons:

style_path <- "The_Great_Wave_off_Kanagawa.jpg"

style_image <-  image_load(content_path, target_size = img_shape[1:2])
style_image %>% 
  image_to_array() %>%
  `/`(., 255) %>%
  as.raster() %>%
  plot()

We create a wrapper that masses and preprocesses the enter pictures for us. As we will likely be working with VGG19, a community that has been skilled on ImageNet, we have to rework our enter pictures in the identical approach that was used coaching it. Later, we’ll apply the inverse transformation to our mixture picture earlier than displaying it.

load_and_preprocess_image <- operate(path) {
  img <- image_load(path, target_size = img_shape[1:2]) %>%
    image_to_array() %>%
    k_expand_dims(axis = 1) %>%
    imagenet_preprocess_input()
}

deprocess_image <- operate(x) {
  x <- x[1, , ,]
  # Take away zero-center by imply pixel
  x[, , 1] <- x[, , 1] + 103.939
  x[, , 2] <- x[, , 2] + 116.779
  x[, , 3] <- x[, , 3] + 123.68
  # 'BGR'->'RGB'
  x <- x[, , c(3, 2, 1)]
  x[x > 255] <- 255
  x[x < 0] <- 0
  x[] <- as.integer(x) / 255
  x
}

Setting the scene

We’re going to use a neural community, however we gained’t be coaching it. Neural model switch is a bit unusual in that we don’t optimize the community’s weights, however again propagate the loss to the enter layer (the picture), so as to transfer it within the desired path.

We will likely be keen on two sorts of outputs from the community, similar to our two objectives. Firstly, we need to hold the mix picture much like the content material picture, on a excessive degree. In a convnet, higher layers map to extra holistic ideas, so we’re selecting a layer excessive up within the graph to check outputs from the supply and the mix.

Secondly, the generated picture ought to “seem like” the model picture. Model corresponds to decrease degree options like texture, shapes, strokes… So to check the mix towards the model instance, we select a set of decrease degree conv blocks for comparability and combination the outcomes.

content_layers <- c("block5_conv2")
style_layers <- c("block1_conv1",
                 "block2_conv1",
                 "block3_conv1",
                 "block4_conv1",
                 "block5_conv1")

num_content_layers <- size(content_layers)
num_style_layers <- size(style_layers)

get_model <- operate() {
  vgg <- application_vgg19(include_top = FALSE, weights = "imagenet")
  vgg$trainable <- FALSE
  style_outputs <- map(style_layers, operate(layer) vgg$get_layer(layer)$output)
  content_outputs <- map(content_layers, operate(layer) vgg$get_layer(layer)$output)
  model_outputs <- c(style_outputs, content_outputs)
  keras_model(vgg$enter, model_outputs)
}

Losses

When optimizing the enter picture, we are going to take into account three sorts of losses. Firstly, the content material loss: How totally different is the mix picture from the supply? Right here, we’re utilizing the sum of the squared errors for comparability.

content_loss <- operate(content_image, goal) {
  k_sum(k_square(goal - content_image))
}

Our second concern is having the kinds match as carefully as potential. Model is often operationalized because the Gram matrix of flattened function maps in a layer. We thus assume that model is said to how maps in a layer correlate with different.

We due to this fact compute the Gram matrices of the layers we’re keen on (outlined above), for the supply picture in addition to the optimization candidate, and evaluate them, once more utilizing the sum of squared errors.

gram_matrix <- operate(x) {
  options <- k_batch_flatten(k_permute_dimensions(x, c(3, 1, 2)))
  gram <- k_dot(options, k_transpose(options))
  gram
}

style_loss <- operate(gram_target, mixture) {
  gram_comb <- gram_matrix(mixture)
  k_sum(k_square(gram_target - gram_comb)) /
    (4 * (img_shape[3] ^ 2) * (img_shape[1] * img_shape[2]) ^ 2)
}

Thirdly, we don’t need the mix picture to look overly pixelated, thus we’re including in a regularization part, the full variation within the picture:

total_variation_loss <- operate(picture) {
  y_ij  <- picture[1:(img_shape[1] - 1L), 1:(img_shape[2] - 1L),]
  y_i1j <- picture[2:(img_shape[1]), 1:(img_shape[2] - 1L),]
  y_ij1 <- picture[1:(img_shape[1] - 1L), 2:(img_shape[2]),]
  a <- k_square(y_ij - y_i1j)
  b <- k_square(y_ij - y_ij1)
  k_sum(k_pow(a + b, 1.25))
}

The difficult factor is the right way to mix these losses. We’ve reached acceptable outcomes with the next weightings, however be happy to mess around as you see match:

content_weight <- 100
style_weight <- 0.8
total_variation_weight <- 0.01

Get mannequin outputs for the content material and elegance pictures

We’d like the mannequin’s output for the content material and elegance pictures, however right here it suffices to do that simply as soon as. We concatenate each pictures alongside the batch dimension, cross that enter to the mannequin, and get again a listing of outputs, the place each factor of the record is a 4-d tensor. For the model picture, we’re within the model outputs at batch place 1, whereas for the content material picture, we’d like the content material output at batch place 2.

Within the under feedback, please word that the sizes of dimensions 2 and three will differ should you’re loading pictures at a unique measurement.

get_feature_representations <-
  operate(mannequin, content_path, style_path) {
    
    # dim == (1, 128, 128, 3)
    style_image <-
      load_and_process_image(style_path) %>% k_cast("float32")
    # dim == (1, 128, 128, 3)
    content_image <-
      load_and_process_image(content_path) %>% k_cast("float32")
    # dim == (2, 128, 128, 3)
    stack_images <- k_concatenate(record(style_image, content_image), axis = 1)
    
    # size(model_outputs) == 6
    # dim(model_outputs[[1]]) = (2, 128, 128, 64)
    # dim(model_outputs[[6]]) = (2, 8, 8, 512)
    model_outputs <- mannequin(stack_images)
    
    style_features <- 
      model_outputs[1:num_style_layers] %>%
      map(operate(batch) batch[1, , , ])
    content_features <- 
      model_outputs[(num_style_layers + 1):(num_style_layers + num_content_layers)] %>%
      map(operate(batch) batch[2, , , ])
    
    record(style_features, content_features)
  }

Computing the losses

On each iteration, we have to cross the mix picture via the mannequin, receive the model and content material outputs, and compute the losses. Once more, the code is extensively commented with tensor sizes for straightforward verification, however please understand that the precise numbers presuppose you’re working with 128×128 pictures.

compute_loss <-
  operate(mannequin, loss_weights, init_image, gram_style_features, content_features) {
    
    c(style_weight, content_weight) %<-% loss_weights
    model_outputs <- mannequin(init_image)
    style_output_features <- model_outputs[1:num_style_layers]
    content_output_features <-
      model_outputs[(num_style_layers + 1):(num_style_layers + num_content_layers)]
    
    # model loss
    weight_per_style_layer <- 1 / num_style_layers
    style_score <- 0
    # dim(style_zip[[5]][[1]]) == (512, 512)
    style_zip <- transpose(record(gram_style_features, style_output_features))
    for (l in 1:size(style_zip)) {
      # for l == 1:
      # dim(target_style) == (64, 64)
      # dim(comb_style) == (1, 128, 128, 64)
      c(target_style, comb_style) %<-% style_zip[[l]]
      style_score <- style_score + weight_per_style_layer * 
        style_loss(target_style, comb_style[1, , , ])
    }
    
    # content material loss
    weight_per_content_layer <- 1 / num_content_layers
    content_score <- 0
    content_zip <- transpose(record(content_features, content_output_features))
    for (l in 1:size(content_zip)) {
      # dim(comb_content) ==  (1, 8, 8, 512)
      # dim(target_content) == (8, 8, 512)
      c(target_content, comb_content) %<-% content_zip[[l]]
      content_score <- content_score + weight_per_content_layer *
        content_loss(comb_content[1, , , ], target_content)
    }
    
    # complete variation loss
    variation_loss <- total_variation_loss(init_image[1, , ,])
    
    style_score <- style_score * style_weight
    content_score <- content_score * content_weight
    variation_score <- variation_loss * total_variation_weight
    
    loss <- style_score + content_score + variation_score
    record(loss, style_score, content_score, variation_score)
  }

Computing the gradients

As quickly as we’ve got the losses, acquiring the gradients of the general loss with respect to the enter picture is only a matter of calling tape$gradient on the GradientTape. Word that the nested name to compute_loss, and thus the decision of the mannequin on our mixture picture, occurs contained in the GradientTape context.

compute_grads <- 
  operate(mannequin, loss_weights, init_image, gram_style_features, content_features) {
    with(tf$GradientTape() %as% tape, {
      scores <-
        compute_loss(mannequin,
                     loss_weights,
                     init_image,
                     gram_style_features,
                     content_features)
    })
    total_loss <- scores[[1]]
    record(tape$gradient(total_loss, init_image), scores)
  }

Coaching part

Now it’s time to coach! Whereas the pure continuation of this sentence would have been “… the mannequin,” the mannequin we’re coaching right here will not be VGG19 (that one we’re simply utilizing as a instrument), however a minimal setup of simply:

  • a Variable that holds our to-be-optimized picture
  • the loss capabilities we outlined above
  • an optimizer that may apply the calculated gradients to the picture variable (tf$prepare$AdamOptimizer)

Under, we get the model options (of the model picture) and the content material function (of the content material picture) simply as soon as, then iterate over the optimization course of, saving the output each 100 iterations.

In distinction to the unique article and the Deep Studying with R e-book, however following the Google pocket book as a substitute, we’re not utilizing L-BFGS for optimization, however Adam, as our purpose right here is to supply a concise introduction to keen execution. Nevertheless, you can plug in one other optimization technique should you wished, changing optimizer$apply_gradients(record(tuple(grads, init_image))) by an algorithm of your selection (and naturally, assigning the results of the optimization to the Variable holding the picture).

run_style_transfer <- operate(content_path, style_path) {
  mannequin <- get_model()
  stroll(mannequin$layers, operate(layer) layer$trainable = FALSE)
  
  c(style_features, content_features) %<-% 
    get_feature_representations(mannequin, content_path, style_path)
  # dim(gram_style_features[[1]]) == (64, 64)
  gram_style_features <- map(style_features, operate(function) gram_matrix(function))
  
  init_image <- load_and_process_image(content_path)
  init_image <- tf$contrib$keen$Variable(init_image, dtype = "float32")
  
  optimizer <- tf$prepare$AdamOptimizer(learning_rate = 1,
                                      beta1 = 0.99,
                                      epsilon = 1e-1)
  
  c(best_loss, best_image) %<-% record(Inf, NULL)
  loss_weights <- record(style_weight, content_weight)
  
  start_time <- Sys.time()
  global_start <- Sys.time()
  
  norm_means <- c(103.939, 116.779, 123.68)
  min_vals <- -norm_means
  max_vals <- 255 - norm_means
  
  for (i in seq_len(num_iterations)) {
    # dim(grads) == (1, 128, 128, 3)
    c(grads, all_losses) %<-% compute_grads(mannequin,
                                            loss_weights,
                                            init_image,
                                            gram_style_features,
                                            content_features)
    c(loss, style_score, content_score, variation_score) %<-% all_losses
    optimizer$apply_gradients(record(tuple(grads, init_image)))
    clipped <- tf$clip_by_value(init_image, min_vals, max_vals)
    init_image$assign(clipped)
    
    end_time <- Sys.time()
    
    if (k_cast_to_floatx(loss) < best_loss) {
      best_loss <- k_cast_to_floatx(loss)
      best_image <- init_image
    }
    
    if (i %% 50 == 0) {
      glue("Iteration: {i}") %>% print()
      glue(
        "Complete loss: {k_cast_to_floatx(loss)},
        model loss: {k_cast_to_floatx(style_score)},
        content material loss: {k_cast_to_floatx(content_score)},
        complete variation loss: {k_cast_to_floatx(variation_score)},
        time for 1 iteration: {(Sys.time() - start_time) %>% spherical(2)}"
      ) %>% print()
      
      if (i %% 100 == 0) {
        png(paste0("style_epoch_", i, ".png"))
        plot_image <- best_image$numpy()
        plot_image <- deprocess_image(plot_image)
        plot(as.raster(plot_image), fundamental = glue("Iteration {i}"))
        dev.off()
      }
    }
  }
  
  glue("Complete time: {Sys.time() - global_start} seconds") %>% print()
  record(best_image, best_loss)
}

Able to run

Now, we’re prepared to start out the method:

c(best_image, best_loss) %<-% run_style_transfer(content_path, style_path)

In our case, outcomes didn’t change a lot after ~ iteration 1000, and that is how our river panorama was trying:

… undoubtedly extra inviting than had it been painted by Edvard Munch!

Conclusion

With neural model switch, some fiddling round could also be wanted till you get the end result you need. However as our instance reveals, this doesn’t imply the code must be sophisticated. Moreover to being simple to know, keen execution additionally permits you to add debugging output, and step via the code line-by-line to test on tensor shapes. Till subsequent time in our keen execution collection!

Gatys, Leon A., Alexander S. Ecker, and Matthias Bethge. 2015. “A Neural Algorithm of Creative Model.” CoRR abs/1508.06576. http://arxiv.org/abs/1508.06576.