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In picture captioning, an algorithm is given a picture and tasked with producing a wise caption. It’s a difficult process for a number of causes, not the least being that it entails a notion of saliency or relevance. That is why latest deep studying approaches principally embrace some “consideration” mechanism (generally even multiple) to assist specializing in related picture options.
On this submit, we show a formulation of picture captioning as an encoder-decoder drawback, enhanced by spatial consideration over picture grid cells. The thought comes from a latest paper on Neural Picture Caption Technology with Visible Consideration (Xu et al. 2015), and employs the identical sort of consideration algorithm as detailed in our submit on machine translation.
We’re porting Python code from a latest Google Colaboratory pocket book, utilizing Keras with TensorFlow keen execution to simplify our lives.
Stipulations
The code proven right here will work with the present CRAN variations of tensorflow
, keras
, and tfdatasets
.
Examine that you simply’re utilizing no less than model 1.9 of TensorFlow. If that isn’t the case, as of this writing, this
will get you model 1.10.
When loading libraries, please ensure you’re executing the primary 4 strains on this actual order.
We’d like to verify we’re utilizing the TensorFlow implementation of Keras (tf.keras
in Python land), and we have now to allow keen execution earlier than utilizing TensorFlow in any means.
No must copy-paste any code snippets – you’ll discover the entire code (so as mandatory for execution) right here: eager-image-captioning.R.
The dataset
MS-COCO (“Frequent Objects in Context”) is one among, maybe the, reference dataset in picture captioning (object detection and segmentation, too).
We’ll be utilizing the coaching photos and annotations from 2014 – be warned, relying in your location, the obtain can take a lengthy time.
After unpacking, let’s outline the place the pictures and captions are.
annotation_file <- "train2014/annotations/captions_train2014.json"
image_path <- "train2014/train2014"
The annotations are in JSON format, and there are 414113 of them! Fortunately for us we didn’t should obtain that many photos – each picture comes with 5 completely different captions, for higher generalizability.
annotations <- fromJSON(file = annotation_file)
annot_captions <- annotations[[4]]
num_captions <- size(annot_captions)
We retailer each annotations and picture paths in lists, for later loading.
all_captions <- vector(mode = "checklist", size = num_captions)
all_img_names <- vector(mode = "checklist", size = num_captions)
for (i in seq_len(num_captions)) {
caption <- paste0("<begin> ",
annot_captions[[i]][["caption"]],
" <finish>"
)
image_id <- annot_captions[[i]][["image_id"]]
full_coco_image_path <- sprintf(
"%s/COCO_train2014_percent012d.jpg",
image_path,
image_id
)
all_img_names[[i]] <- full_coco_image_path
all_captions[[i]] <- caption
}
Relying in your computing atmosphere, you’ll for certain wish to prohibit the variety of examples used.
This submit will use 30000 captioned photos, chosen randomly, and put aside 20% for validation.
Beneath, we take random samples, cut up into coaching and validation elements. The companion code can even retailer the indices on disk, so you’ll be able to choose up on verification and evaluation later.
num_examples <- 30000
random_sample <- pattern(1:num_captions, measurement = num_examples)
train_indices <- pattern(random_sample, measurement = size(random_sample) * 0.8)
validation_indices <- setdiff(random_sample, train_indices)
sample_captions <- all_captions[random_sample]
sample_images <- all_img_names[random_sample]
train_captions <- all_captions[train_indices]
train_images <- all_img_names[train_indices]
validation_captions <- all_captions[validation_indices]
validation_images <- all_img_names[validation_indices]
Interlude
Earlier than actually diving into the technical stuff, let’s take a second to mirror on this process.
In typical image-related deep studying walk-throughs, we’re used to seeing well-defined issues – even when in some circumstances, the answer could also be onerous. Take, for instance, the stereotypical canine vs. cat drawback. Some canine could appear to be cats and a few cats could appear to be canine, however that’s about it: All in all, within the standard world we stay in, it must be a kind of binary query.
If, then again, we ask individuals to explain what they see in a scene, it’s to be anticipated from the outset that we’ll get completely different solutions. Nonetheless, how a lot consensus there’s will very a lot depend upon the concrete dataset we’re utilizing.
Let’s check out some picks from the very first 20 coaching objects sampled randomly above.
Now this picture doesn’t depart a lot room for choice what to give attention to, and obtained a really factual caption certainly: “There’s a plate with one slice of bacon a half of orange and bread.” If the dataset have been all like this, we’d suppose a machine studying algorithm ought to do fairly effectively right here.
Choosing one other one from the primary 20:
What can be salient data to you right here? The caption supplied goes “A smiling little boy has a checkered shirt.”
Is the look of the shirt as vital as that? You would possibly as effectively give attention to the surroundings, – and even one thing on a totally completely different degree: The age of the picture, or it being an analog one.
Let’s take a remaining instance.
What would you say about this scene? The official label we sampled right here is “A gaggle of individuals posing in a humorous means for the digital camera.” Nicely …
Please don’t neglect that for every picture, the dataset contains 5 completely different captions (though our n = 30000 samples most likely gained’t).
So this isn’t saying the dataset is biased – by no means. As an alternative, we wish to level out the ambiguities and difficulties inherent within the process. Really, given these difficulties, it’s all of the extra superb that the duty we’re tackling right here – having a community routinely generate picture captions – must be potential in any respect!
Now let’s see how we are able to do that.
For the encoding a part of our encoder-decoder community, we are going to make use of InceptionV3 to extract picture options. In precept, which options to extract is as much as experimentation, – right here we simply use the final layer earlier than the absolutely related prime:
image_model <- application_inception_v3(
include_top = FALSE,
weights = "imagenet"
)
For a picture measurement of 299×299, the output can be of measurement (batch_size, 8, 8, 2048)
, that’s, we’re making use of 2048 characteristic maps.
InceptionV3 being a “huge mannequin,” the place each go by means of the mannequin takes time, we wish to precompute options prematurely and retailer them on disk.
We’ll use tfdatasets to stream photos to the mannequin. This implies all our preprocessing has to make use of tensorflow features: That’s why we’re not utilizing the extra acquainted image_load
from keras beneath.
Our customized load_image
will learn in, resize and preprocess the pictures as required to be used with InceptionV3:
Now we’re prepared to avoid wasting the extracted options to disk. The (batch_size, 8, 8, 2048)
-sized options can be flattened to (batch_size, 64, 2048)
. The latter form is what our encoder, quickly to be mentioned, will obtain as enter.
preencode <- distinctive(sample_images) %>% unlist() %>% kind()
num_unique <- size(preencode)
# adapt this in response to your system's capacities
batch_size_4save <- 1
image_dataset <-
tensor_slices_dataset(preencode) %>%
dataset_map(load_image) %>%
dataset_batch(batch_size_4save)
save_iter <- make_iterator_one_shot(image_dataset)
until_out_of_range({
save_count <- save_count + batch_size_4save
batch_4save <- save_iter$get_next()
img <- batch_4save[[1]]
path <- batch_4save[[2]]
batch_features <- image_model(img)
batch_features <- tf$reshape(
batch_features,
checklist(dim(batch_features)[1], -1L, dim(batch_features)[4]
)
)
for (i in 1:dim(batch_features)[1]) {
np$save(path[i]$numpy()$decode("utf-8"),
batch_features[i, , ]$numpy())
}
})
Earlier than we get to the encoder and decoder fashions although, we have to handle the captions.
Processing the captions
We’re utilizing keras text_tokenizer
and the textual content processing features texts_to_sequences
and pad_sequences
to remodel ascii textual content right into a matrix.
# we are going to use the 5000 most frequent phrases solely
top_k <- 5000
tokenizer <- text_tokenizer(
num_words = top_k,
oov_token = "<unk>",
filters = '!"#$%&()*+.,-/:;=?@[]^_`~ ')
tokenizer$fit_on_texts(sample_captions)
train_captions_tokenized <-
tokenizer %>% texts_to_sequences(train_captions)
validation_captions_tokenized <-
tokenizer %>% texts_to_sequences(validation_captions)
# pad_sequences will use 0 to pad all captions to the identical size
tokenizer$word_index["<pad>"] <- 0
# create a lookup dataframe that enables us to go in each instructions
word_index_df <- information.body(
phrase = tokenizer$word_index %>% names(),
index = tokenizer$word_index %>% unlist(use.names = FALSE),
stringsAsFactors = FALSE
)
word_index_df <- word_index_df %>% organize(index)
decode_caption <- operate(textual content) {
paste(map(textual content, operate(quantity)
word_index_df %>%
filter(index == quantity) %>%
choose(phrase) %>%
pull()),
collapse = " ")
}
# pad all sequences to the identical size (the utmost size, in our case)
# may experiment with shorter padding (truncating the very longest captions)
caption_lengths <- map(
all_captions[1:num_examples],
operate(c) str_split(c," ")[[1]] %>% size()
) %>% unlist()
max_length <- fivenum(caption_lengths)[5]
train_captions_padded <- pad_sequences(
train_captions_tokenized,
maxlen = max_length,
padding = "submit",
truncating = "submit"
)
validation_captions_padded <- pad_sequences(
validation_captions_tokenized,
maxlen = max_length,
padding = "submit",
truncating = "submit"
)
Loading the information for coaching
Now that we’ve taken care of pre-extracting the options and preprocessing the captions, we want a solution to stream them to our captioning mannequin. For that, we’re utilizing tensor_slices_dataset
from tfdatasets, passing within the checklist of paths to the pictures and the preprocessed captions. Loading the pictures is then carried out as a TensorFlow graph operation (utilizing tf$pyfunc).
The unique Colab code additionally shuffles the information on each iteration. Relying in your {hardware}, this may occasionally take a very long time, and given the dimensions of the dataset it isn’t strictly essential to get cheap outcomes. (The outcomes reported beneath have been obtained with out shuffling.)
batch_size <- 10
buffer_size <- num_examples
map_func <- operate(img_name, cap) {
p <- paste0(img_name$decode("utf-8"), ".npy")
img_tensor <- np$load(p)
img_tensor <- tf$solid(img_tensor, tf$float32)
checklist(img_tensor, cap)
}
train_dataset <-
tensor_slices_dataset(checklist(train_images, train_captions_padded)) %>%
dataset_map(
operate(item1, item2) tf$py_func(map_func, checklist(item1, item2), checklist(tf$float32, tf$int32))
) %>%
# optionally shuffle the dataset
# dataset_shuffle(buffer_size) %>%
dataset_batch(batch_size)
Captioning mannequin
The mannequin is principally the identical as that mentioned within the machine translation submit. Please discuss with that article for a proof of the ideas, in addition to an in depth walk-through of the tensor shapes concerned at each step. Right here, we offer the tensor shapes as feedback within the code snippets, for fast overview/comparability.
Nevertheless, if you happen to develop your personal fashions, with keen execution you’ll be able to merely insert debugging/logging statements at arbitrary locations within the code – even in mannequin definitions. So you’ll be able to have a operate
And if you happen to now set
you’ll be able to hint – not solely tensor shapes, however precise tensor values by means of your fashions, as proven beneath for the encoder. (We don’t show any debugging statements after that, however the pattern code has many extra.)
Encoder
Now it’s time to outline some some sizing-related hyperparameters and housekeeping variables:
# for encoder output
embedding_dim <- 256
# decoder (LSTM) capability
gru_units <- 512
# for decoder output
vocab_size <- top_k
# variety of characteristic maps gotten from Inception V3
features_shape <- 2048
# form of consideration options (flattened from 8x8)
attention_features_shape <- 64
The encoder on this case is only a absolutely related layer, taking within the options extracted from Inception V3 (in flattened type, as they have been written to disk), and embedding them in 256-dimensional area.
cnn_encoder <- operate(embedding_dim, title = NULL) {
keras_model_custom(title = title, operate(self) {
self$fc <- layer_dense(models = embedding_dim, activation = "relu")
operate(x, masks = NULL) {
# enter form: (batch_size, 64, features_shape)
maybecat("encoder enter", x)
# form after fc: (batch_size, 64, embedding_dim)
x <- self$fc(x)
maybecat("encoder output", x)
x
}
})
}
Consideration module
Not like within the machine translation submit, right here the eye module is separated out into its personal customized mannequin.
The logic is identical although:
attention_module <- operate(gru_units, title = NULL) {
keras_model_custom(title = title, operate(self) {
self$W1 = layer_dense(models = gru_units)
self$W2 = layer_dense(models = gru_units)
self$V = layer_dense(models = 1)
operate(inputs, masks = NULL) {
options <- inputs[[1]]
hidden <- inputs[[2]]
# options(CNN_encoder output) form == (batch_size, 64, embedding_dim)
# hidden form == (batch_size, gru_units)
# hidden_with_time_axis form == (batch_size, 1, gru_units)
hidden_with_time_axis <- k_expand_dims(hidden, axis = 2)
# rating form == (batch_size, 64, 1)
rating <- self$V(k_tanh(self$W1(options) + self$W2(hidden_with_time_axis)))
# attention_weights form == (batch_size, 64, 1)
attention_weights <- k_softmax(rating, axis = 2)
# context_vector form after sum == (batch_size, embedding_dim)
context_vector <- k_sum(attention_weights * options, axis = 2)
checklist(context_vector, attention_weights)
}
})
}
Decoder
The decoder at every time step calls the eye module with the options it obtained from the encoder and its final hidden state, and receives again an consideration vector. The eye vector will get concatenated with the present enter and additional processed by a GRU and two absolutely related layers, the final of which supplies us the (unnormalized) possibilities for the following phrase within the caption.
The present enter at every time step right here is the earlier phrase: the right one throughout coaching (trainer forcing), the final generated one throughout inference.
rnn_decoder <- operate(embedding_dim, gru_units, vocab_size, title = NULL) {
keras_model_custom(title = title, operate(self) {
self$gru_units <- gru_units
self$embedding <- layer_embedding(input_dim = vocab_size,
output_dim = embedding_dim)
self$gru <- if (tf$check$is_gpu_available()) {
layer_cudnn_gru(
models = gru_units,
return_sequences = TRUE,
return_state = TRUE,
recurrent_initializer = 'glorot_uniform'
)
} else {
layer_gru(
models = gru_units,
return_sequences = TRUE,
return_state = TRUE,
recurrent_initializer = 'glorot_uniform'
)
}
self$fc1 <- layer_dense(models = self$gru_units)
self$fc2 <- layer_dense(models = vocab_size)
self$consideration <- attention_module(self$gru_units)
operate(inputs, masks = NULL) {
x <- inputs[[1]]
options <- inputs[[2]]
hidden <- inputs[[3]]
c(context_vector, attention_weights) %<-%
self$consideration(checklist(options, hidden))
# x form after passing by means of embedding == (batch_size, 1, embedding_dim)
x <- self$embedding(x)
# x form after concatenation == (batch_size, 1, 2 * embedding_dim)
x <- k_concatenate(checklist(k_expand_dims(context_vector, 2), x))
# passing the concatenated vector to the GRU
c(output, state) %<-% self$gru(x)
# form == (batch_size, 1, gru_units)
x <- self$fc1(output)
# x form == (batch_size, gru_units)
x <- k_reshape(x, c(-1, dim(x)[[3]]))
# output form == (batch_size, vocab_size)
x <- self$fc2(x)
checklist(x, state, attention_weights)
}
})
}
Loss operate, and instantiating all of it
Now that we’ve outlined our mannequin (constructed of three customized fashions), we nonetheless want to truly instantiate it (being exact: the 2 lessons we are going to entry from exterior, that’s, the encoder and the decoder).
We additionally must instantiate an optimizer (Adam will do), and outline our loss operate (categorical crossentropy).
Word that tf$nn$sparse_softmax_cross_entropy_with_logits
expects uncooked logits as a substitute of softmax activations, and that we’re utilizing the sparse variant as a result of our labels are usually not one-hot-encoded.
encoder <- cnn_encoder(embedding_dim)
decoder <- rnn_decoder(embedding_dim, gru_units, vocab_size)
optimizer = tf$practice$AdamOptimizer()
cx_loss <- operate(y_true, y_pred) {
masks <- 1 - k_cast(y_true == 0L, dtype = "float32")
loss <- tf$nn$sparse_softmax_cross_entropy_with_logits(
labels = y_true,
logits = y_pred
) * masks
tf$reduce_mean(loss)
}
Coaching
Coaching the captioning mannequin is a time-consuming course of, and you’ll for certain wish to save the mannequin’s weights!
How does this work with keen execution?
We create a tf$practice$Checkpoint
object, passing it the objects to be saved: In our case, the encoder, the decoder, and the optimizer. Later, on the finish of every epoch, we are going to ask it to write down the respective weights to disk.
restore_checkpoint <- FALSE
checkpoint_dir <- "./checkpoints_captions"
checkpoint_prefix <- file.path(checkpoint_dir, "ckpt")
checkpoint <- tf$practice$Checkpoint(
optimizer = optimizer,
encoder = encoder,
decoder = decoder
)
As we’re simply beginning to practice the mannequin, restore_checkpoint
is about to false. Later, restoring the weights can be as straightforward as
if (restore_checkpoint) {
checkpoint$restore(tf$practice$latest_checkpoint(checkpoint_dir))
}
The coaching loop is structured similar to within the machine translation case: We loop over epochs, batches, and the coaching targets, feeding within the right earlier phrase at each timestep.
Once more, tf$GradientTape
takes care of recording the ahead go and calculating the gradients, and the optimizer applies the gradients to the mannequin’s weights.
As every epoch ends, we additionally save the weights.
num_epochs <- 20
if (!restore_checkpoint) {
for (epoch in seq_len(num_epochs)) {
total_loss <- 0
progress <- 0
train_iter <- make_iterator_one_shot(train_dataset)
until_out_of_range({
batch <- iterator_get_next(train_iter)
loss <- 0
img_tensor <- batch[[1]]
target_caption <- batch[[2]]
dec_hidden <- k_zeros(c(batch_size, gru_units))
dec_input <- k_expand_dims(
rep(checklist(word_index_df[word_index_df$word == "<start>", "index"]),
batch_size)
)
with(tf$GradientTape() %as% tape, {
options <- encoder(img_tensor)
for (t in seq_len(dim(target_caption)[2] - 1)) {
c(preds, dec_hidden, weights) %<-%
decoder(checklist(dec_input, options, dec_hidden))
loss <- loss + cx_loss(target_caption[, t], preds)
dec_input <- k_expand_dims(target_caption[, t])
}
})
total_loss <-
total_loss + loss / k_cast_to_floatx(dim(target_caption)[2])
variables <- c(encoder$variables, decoder$variables)
gradients <- tape$gradient(loss, variables)
optimizer$apply_gradients(purrr::transpose(checklist(gradients, variables)),
global_step = tf$practice$get_or_create_global_step()
)
})
cat(paste0(
"nnTotal loss (epoch): ",
epoch,
": ",
(total_loss / k_cast_to_floatx(buffer_size)) %>% as.double() %>% spherical(4),
"n"
))
checkpoint$save(file_prefix = checkpoint_prefix)
}
}
Peeking at outcomes
Identical to within the translation case, it’s fascinating to have a look at mannequin efficiency throughout coaching. The companion code has that performance built-in, so you’ll be able to watch mannequin progress for your self.
The essential operate right here is get_caption
: It will get handed the trail to a picture, masses it, obtains its options from Inception V3, after which asks the encoder-decoder mannequin to generate a caption. If at any level the mannequin produces the finish
image, we cease early. In any other case, we proceed till we hit the predefined most size.
<-
get_caption operate(picture) {
<-
attention_matrix matrix(0, nrow = max_length, ncol = attention_features_shape)
<- k_expand_dims(load_image(picture)[[1]], 1)
temp_input <- image_model(temp_input)
img_tensor_val <- k_reshape(
img_tensor_val
img_tensor_val,checklist(dim(img_tensor_val)[1], -1, dim(img_tensor_val)[4])
)<- encoder(img_tensor_val)
options
<- k_zeros(c(1, gru_units))
dec_hidden <-
dec_input k_expand_dims(
checklist(word_index_df[word_index_df$word == "<start>", "index"])
)
<- ""
end result
for (t in seq_len(max_length - 1)) {
c(preds, dec_hidden, attention_weights) %<-%
decoder(checklist(dec_input, options, dec_hidden))
<- k_reshape(attention_weights, c(-1))
attention_weights <- attention_weights %>% as.double()
attention_matrix[t,]
<- tf$multinomial(exp(preds), num_samples = 1)[1, 1]
pred_idx %>% as.double()
<-
pred_word $index == pred_idx, "word"]
word_index_df[word_index_df
if (pred_word == "<finish>") {
<-
end result paste(end result, pred_word)
<-
attention_matrix 1:length(str_split(result, " ")[[1]]), ,
attention_matrix[= FALSE]
drop return (checklist(end result, attention_matrix))
else {
} <-
end result paste(end result, pred_word)
<- k_expand_dims(checklist(pred_idx))
dec_input
}
}
checklist(str_trim(end result), attention_matrix)
}
With that performance, now let’s truly try this: peek at outcomes whereas the community is studying!
We’ve picked 3 examples every from the coaching and validation units. Right here they’re.
First, our picks from the coaching set:
Let’s see the goal captions:
- a herd of giraffe standing on prime of a grass lined discipline
- a view of playing cards driving down a avenue
- the skateboarding flips his board off of the sidewalk
Apparently, right here we even have an illustration of how labeled datasets (like something human) could comprise errors. (The samples weren’t picked for that; as a substitute, they have been chosen – with out an excessive amount of screening – for being relatively unequivocal of their visible content material.)
Now for the validation candidates.
and their official captions:
- a left handed pitcher throwing the bottom ball
- a lady taking a chunk of a slice of pizza in a restaraunt
- a lady hitting swinging a tennis racket at a tennis ball on a tennis courtroom
(Once more, any spelling peculiarities haven’t been launched by us.)
Epoch 1
Now, what does our community produce after the primary epoch? Keep in mind that this implies, having seen every one of many 24000 coaching photos as soon as.
First then, listed here are the captions for the practice photos:
a gaggle of sheep standing within the grass
a gaggle of automobiles driving down a avenue
a person is standing on a avenue
Not solely is the syntax right in each case, the content material isn’t that unhealthy both!
How concerning the validation set?
a baseball participant is enjoying baseball uniform is holding a baseball bat
a person is holding a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk with a desk
a tennis participant is holding a tennis courtroom
This definitely tells that the community has been in a position to generalize over – let’s not name them ideas, however mappings between visible and textual entities, say It’s true that it’s going to have seen a few of these photos earlier than, as a result of photos include a number of captions. You would be extra strict establishing your coaching and validation units – however right here, we don’t actually care about goal efficiency scores and so, it does not likely matter.
Let’ skip on to epoch 20, our final coaching epoch, and test for additional enhancements.
Epoch 20
That is what we get for the coaching photos:
a gaggle of many tall giraffe standing subsequent to a sheep
a view of playing cards and white gloves on a avenue
a skateboarding flips his board
And this, for the validation photos.
a baseball catcher and umpire hit a baseball recreation
a person is consuming a sandwich
a feminine tennis participant is within the courtroom
I believe we would agree that this nonetheless leaves room for enchancment – however then, we solely skilled for 20 epochs and on a really small portion of the dataset.
Within the above code snippets, you will have observed the decoder returning an attention_matrix
– however we weren’t commenting on it.
Now lastly, simply as within the translation instance, take a look what we are able to make of that.
The place does the community look?
We are able to visualize the place the community is “wanting” because it generates every phrase by overlaying the unique picture and the eye matrix. This instance is taken from the 4th epoch.
Right here white-ish squares point out areas receiving stronger focus. In comparison with text-to-text translation although, the mapping is inherently much less easy – the place does one “look” when producing phrases like “and,” “the,” or “in?”
Conclusion
It most likely goes with out saying that a lot better outcomes are to be anticipated when coaching on (a lot!) extra information and for far more time.
Other than that, there are different choices, although. The idea carried out right here makes use of spatial consideration over a uniform grid, that’s, the eye mechanism guides the decoder the place on the grid to look subsequent when producing a caption.
Nevertheless, this isn’t the one means, and this isn’t the way it works with people. A way more believable method is a mixture of top-down and bottom-up consideration. E.g., (Anderson et al. 2017) use object detection strategies to bottom-up isolate fascinating objects, and an LSTM stack whereby the primary LSTM computes top-down consideration guided by the output phrase generated by the second.
One other fascinating method involving consideration is utilizing a multimodal attentive translator (Liu et al. 2017), the place the picture options are encoded and offered in a sequence, such that we find yourself with sequence fashions each on the encoding and the decoding sides.
One other various is so as to add a discovered matter to the knowledge enter (Zhu, Xue, and Yuan 2018), which once more is a top-down characteristic present in human cognition.
If you happen to discover one among these, or yet one more, method extra convincing, an keen execution implementation, within the model of the above, will doubtless be a sound means of implementing it.
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