Working with Sequences#
+17. Working with Sequences#
Training#
+17.1. Training#
Before we focus our attention on text data, let’s first try this out with some continuous-valued synthetic data.
Here, our 1000 synthetic data will follow the trigonometric sin function, applied to 0.01 times the time step. To make the problem a little more interesting, we corrupt each sample with additive noise. From this sequence we extract training examples, each consisting of features and a label.
WIP#
+17.2. WIP#
WIP#
@@ -547,8 +559,8 @@WIP#
diff --git a/notebooks/chapter_recurrent_neural_networks/text-sequence.html b/notebooks/chapter_recurrent_neural_networks/text-sequence.html index 27045f2..c88dfdc 100644 --- a/notebooks/chapter_recurrent_neural_networks/text-sequence.html +++ b/notebooks/chapter_recurrent_neural_networks/text-sequence.html @@ -8,7 +8,7 @@ -Recurrent Neural Networks
+ @@ -391,7 +395,7 @@
-
-
-
+
Reading the Dataset
Converting Raw Text into Sequence Data
+Concise Implementation of Recurrent Neural Networks
@@ -405,6 +409,10 @@ Tokenization
Vocabulary
Exploratory Language Statistics
+Partitioning Sequences
+Recurrent Neural Networks with Hidden States
+Defining the Model
+Training and Predicting
@@ -416,8 +424,8 @@ Contents
Contents
Converting Raw Text into Sequence Data#
+Concise Implementation of Recurrent Neural Networks#
Reading the Dataset#
Here, we will work with H. G. Wells’ The Time Machine, a book containing just over 30,000 words. While real applications will typically involve significantly larger datasets, this is sufficient to demonstrate the preprocessing pipeline. The following _download method reads the raw text into a string.
@@ -425,12 +433,12 @@Reading the Dataset
using Downloads
-file_path = Downloads.download("https://www.gutenberg.org/cache/epub/35/pg35.txt")
+file_path = Downloads.download("http://d2l-data.s3-accelerate.amazonaws.com/timemachine.txt")
using Downloads
-file_path = Downloads.download("https://www.gutenberg.org/cache/epub/35/pg35.txt")
+file_path = Downloads.download("http://d2l-data.s3-accelerate.amazonaws.com/timemachine.txt")
-
@@ -443,7 +451,7 @@ Reading the Dataset
-
"/tmp/jl_eD65mPmPM9"
+"/tmp/jl_gxiB01gPaV"
Reading the Dataset
-"\ufeffThe Project Gutenberg eBook of The Time Machine\r\n \r\nTh"
+"The Time Machine, by H. G. Wells [1898]\n\n\n\n\nI\n\n\nThe Time Tra"
@@ -457,7 +465,7 @@ Reading the Dataset
-" the project gutenberg ebook of the time machine this ebook "
+"the time machine by h g wells i the time traveller for so it"
@@ -474,7 +482,7 @@ Tokenization
-" ,t,h,e, ,p,r,o,j,e,c,t, ,g,u,t,e,n,b,e,r,g, ,e,b,o,o,k, ,o"
+"t,h,e, ,t,i,m,e, ,m,a,c,h,i,n,e, ,b,y, ,h, ,g, ,w,e,l,l,s, "
@@ -500,7 +508,7 @@ Vocabulary
indices:[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-words:[' ', 't', 'h', 'e', 'p', 'r', 'o', 'j', 'c', 'g']
+words:['t', 'h', 'e', ' ', 'i', 'm', 'a', 'c', 'n', 'b']
@@ -513,34 +521,240 @@ Exploratory Language Statistics
using TextAnalysis
-sd = StringDocument(raw_text)
-remove_case!(sd)
-prepare!(sd, strip_non_letters)
+sd = StringDocument(str)
crps = Corpus([sd])
update_lexicon!(crps)
lex_dict = lexicon(crps)
-
-partialsort([lex_dict...], 1:10; by = x -> x[2], rev=true)
+unigram = sort([lex_dict...]; by = x -> x[2], rev=true)
+unigram[1:10]
-10-element view(::Vector{Pair{String, Int64}}, 1:10) with eltype Pair{String, Int64}:
- "the" => 2468
- "and" => 1296
- "of" => 1281
- "i" => 1242
- "a" => 864
- "to" => 760
- "in" => 605
- "was" => 550
- "that" => 451
- "my" => 439
+WARNING: using TextAnalysis.tokens in module Main conflicts with an existing identifier.
+
+
+10-element Vector{Pair{String, Int64}}:
+ "the" => 2261
+ "i" => 1267
+ "and" => 1245
+ "of" => 1155
+ "a" => 816
+ "to" => 695
+ "was" => 552
+ "in" => 541
+ "that" => 443
+ "my" => 440
Word frequency tends to follow a power law distribution (specifically the Zipfian) as we go down the ranks. To get a better idea, we plot the figure of the word frequency.
+
+
+using CairoMakie
+
+fg,ax = lines(last.(unigram); axis=(;xlabel = "token: x",ylabel = "frequency: n(x)", xscale = log10, yscale = log10))
+
+
+
+
+
+
+This should already give us pause for thought if we want to model words by counting statistics. After all, we will significantly overestimate the frequency of the tail, also known as the infrequent words. But what about the other word combinations, such as two consecutive words (bigrams), three consecutive words (trigrams), and beyond? Let’s see whether the bigram frequency behaves in the same manner as the single word (unigram) frequency.
+
+
+bigram = sort([ngrams(sd, 2)...]; by = x -> x[2], rev=true)
+bigram[1:10]
+
+
+
+
+10-element Vector{Pair{AbstractString, Int64}}:
+ "of the" => 309
+ "in the" => 169
+ "i had" => 130
+ "i was" => 112
+ "and the" => 109
+ "the time" => 102
+ "it was" => 99
+ "to the" => 85
+ "as i" => 78
+ "of a" => 73
+
+
+
+
+One thing is notable here. Out of the ten most frequent word pairs, nine are composed of both stop words and only one is relevant to the actual book—“the time”. Furthermore, let’s see whether the trigram frequency behaves in the same manner.
+
+
+trigram = sort([ngrams(sd, 3)...]; by = x -> x[2], rev=true)
+trigram[1:10]
+
+
+
+
+10-element Vector{Pair{AbstractString, Int64}}:
+ "the time traveller" => 59
+ "the time machine" => 30
+ "the medical man" => 24
+ "it seemed to" => 16
+ "it was a" => 15
+ "here and there" => 15
+ "i did not" => 14
+ "seemed to me" => 14
+ "i began to" => 13
+ "i saw the" => 13
+
+
+
+
+Now, let’s visualize the token frequency among these three models: unigrams, bigrams, and trigrams.
+
+
+fg2,ax2 = lines(last.(unigram),label="unigram";
+ axis=(;xlabel = "token: x", ylabel = "frequency: n(x)", xscale = log10, yscale = log10))
+lines!(ax2,last.(bigram),label="bigram",linestyle=:dash)
+lines!(ax2,last.(trigram),label="trigram",linestyle=:dashdot)
+axislegend(position = :rt)
+fg2
+
+
+
+
+
+
+
+
+Partitioning Sequences#
+To train language models, we will randomly sample pairs of input sequences and target sequences in minibatches. The following data loader randomly generates a minibatch from the dataset each time. The argument batch_size specifies the number of subsequence examples in each minibatch and num_steps is the subsequence length in tokens.
+
+
+using IterTools
+using Flux
+
+num_steps=10
+batch_size=2
+function time_machine_dataloader(num_steps::Int,batch_size::Int)::Flux.DataLoader
+ partitions = hcat([to_indices([i...]) for i in [i for i in partition(str,num_steps,1)]]...)
+ x = partitions[:,begin:end-1]
+ y = partitions[:,2:end]
+ return Flux.DataLoader((x,y),batchsize = batch_size)
+end
+
+train_loader = time_machine_dataloader(num_steps,batch_size)
+
+
+
+
+86709-element DataLoader(::Tuple{Matrix{Int64}, Matrix{Int64}}, batchsize=2)
+ with first element:
+ (10×2 Matrix{Int64}, 10×2 Matrix{Int64},)
+
+
+
+
+As we can see in the following, a minibatch of target sequences can be obtained by shifting the input sequences by one token.
+
+
+for (x,y) in train_loader
+ print(x)
+ print(y)
+ break
+end
+
+
+
+
+[1 2; 2 3; 3 4; 4 1; 1 5; 5 6; 6 3; 3 4; 4 6; 6 7][2 3; 3 4; 4 1; 1 5; 5 6; 6 3; 3 4; 4 6; 6 7; 7 8]
+
+
+
+
+
+
+
+Defining the Model#
+We define the model using the RNN implemented by high-level APIs.
+
+
+model = Chain(RNN(32 => 32),Dense(32=>32))
+
+
+
+
+Chain(
+ Recur(
+ RNNCell(32 => 32, tanh), # 2_112 parameters
+ ),
+ Dense(32 => 32), # 1_056 parameters
+) # Total: 6 trainable arrays, 3_168 parameters,
+ # plus 1 non-trainable, 32 parameters, summarysize 12.742 KiB.
+
+
+
+
+
+
+Training and Predicting#
+Before training the model, let’s make a prediction with a model initialized with random weights. Given that we have not trained the network, it will generate nonsensical predictions.
+
+
+# train_loader = time_machine_dataloader(32,1024)
+for (x,y) in train_loader
+ @show size(x)
+ @show model(x)
+ break
+end
+
+
+
+
+size(x) = (32, 1024)
+model(x) = Float32[-0.57374346 -0.26441568 -1.9320982 -2.848492 -2.1397445 -2.4540977 -1.7840853 -1.648342 -2.52589 -1.8467429 -1.2987548 -2.2716665 -2.1326025 -2.3978176 -0.98061323 -1.9477181 -1.280873 -0.99040264 -1.2784705 -1.547663 -1.4533584 -1.1009576 -0.8664077 -0.765324 -0.90174484 -1.0487828 -1.0890119 -1.524941 -1.7626832 -1.5131028 -2.7616706 -2.0652514 -2.5642655 -2.3570645 -1.3331244 -1.4287344 -2.0367844 -3.1046817 -1.5357288 -1.78027 -1.4881468 -2.8125029 -1.6947955 -1.1787102 -1.3989516 -1.8456247 -1.6164786 -0.81756485 -1.5439417 -2.0573435 -2.037667 -1.9368472 -1.2108173 -2.0124266 -0.76695687 -2.3218095 -1.1595086 -1.5701432 -1.3880118 -1.3497151 -1.0555056 -1.6395605 -1.16599 -1.3261876 -1.9716663 -2.3760617 -0.8950427 -1.8247905 -0.73746854 -1.910527 -2.9030178 -1.9486053 -1.1859375 -1.7715193 -2.11734 -1.4402977 -0.8455106 -0.7062114 -1.8113012 -0.6173222 -0.52156556 -2.1779416 -2.7480822 -1.1389867 -1.8730501 -1.7934418 -0.3459037 -2.6761012 -0.92483366 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+
+
+Excessive output truncated after 574663 bytes.
+
+
+
+
@@ -594,6 +808,10 @@ Exploratory Language StatisticsTokenization
Vocabulary
Exploratory Language Statistics
+Partitioning Sequences
+Recurrent Neural Networks with Hidden States
+Defining the Model
+Training and Predicting
diff --git a/objects.inv b/objects.inv
index 7325577..b04fef7 100644
Binary files a/objects.inv and b/objects.inv differ
diff --git a/search.html b/search.html
index f13969b..96501f5 100644
--- a/search.html
+++ b/search.html
@@ -207,6 +207,10 @@
+Recurrent Neural Networks
+
diff --git a/searchindex.js b/searchindex.js
index cff6c59..9522282 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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10, 12, 14, 15, 16, 17, 19], "whether": [9, 17, 19], "which": [0, 4, 5, 6, 9, 10, 12, 14, 16], "while": [4, 9, 10, 12, 13, 14, 15, 17, 19], "white": 4, "whole": [6, 14], "whop": 4, "whose": [12, 14, 15, 19], "why": [6, 10], "wide": 4, "widespread": 5, "width": 4, "wipe": 12, "wisdom": 9, "wish": [6, 12, 14, 16, 17], "wit": 5, "without": [6, 14], "word": 19, "work": [1, 4, 5, 12, 14, 19], "workload": 6, "worri": 5, "would": [1, 4, 9, 17, 19], "wrangl": 9, "write": [0, 2, 6, 14, 15], "x": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19], "x2": [2, 14], "xiao": 4, "xlabel": [3, 6, 7, 8, 9, 13, 17, 18, 19], "xscale": 19, "xtick": [6, 17, 18], "xticklabelsvis": 4, "xticksvis": 4, "y": [2, 3, 4, 5, 7, 8, 12, 14, 15, 16, 18, 19], "y2": 2, "y_clone": 2, "year": [6, 17], "yield": [6, 12], "ylabel": [6, 9, 13, 17, 18, 19], "yml": 0, "you": [0, 4, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17], "your": [0, 10, 11, 15], "yscale": 19, "ytick": [17, 18], "yticklabelsvis": 4, "yticksvis": 4, "z": [12, 19], "za": 19, "zero": [2, 9, 10, 14], "zip": [4, 6], "zipfian": 19, "zone": 10, "zygot": [9, 12], "\u03bc": 6, "\u03c3": 6}, "titles": ["Dive into Deep Learning - Julia", "15. Parameter Management", "16. File I/O", "10. Concise Implementation of Softmax Regression", "9. The Image Classification Dataset", "8. Concise Implementation of Linear Regression", "7. Linear Regression", "14. Dropout", "12. Implementation of Multilayer Perceptrons", "11. Multilayer Perceptrons", "13. Numerical Stability and Initialization", "Predicting House Prices on Kaggle", "5. Automatic Differentiation", "4. Calculus", "1. Data Manipulation", "2. Data Preprocessing", "3. Linear Algebra", "6. Probability and Statistics", "17. Working with Sequences", "Concise Implementation of Recurrent Neural Networks"], "titleterms": {"A": [12, 17], "The": [4, 6], "access": 1, "activ": 9, "algebra": 16, "algorithm": 5, "all": 1, "arithmet": 16, "arrai": 16, "automat": 12, "backward": 12, "basic": 16, "broadcast": 14, "calculu": 13, "classif": 4, "code": 0, "coin": 17, "comput": 12, "concis": [3, 5, 7, 8, 19], "contribut": 0, "control": 12, "convers": 15, "data": [11, 14, 15], "dataset": [4, 5, 15, 19], "deep": 0, "defin": [3, 5, 19], "deriv": 13, "detach": 12, "differenti": [12, 13], "distribut": 6, "dive": 0, "dot": 16, "download": 11, "dropout": 7, "exampl": 17, "explod": 10, "exploratori": 19, "file": 2, "flow": 12, "function": [5, 9, 12], "gener": 5, "get": 14, "gradient": [10, 12], "hidden": 19, "hous": 11, "i": 2, "imag": 4, "implement": [0, 3, 5, 7, 8, 19], "index": 14, "initi": 10, "instal": 0, "julia": [0, 12], "kaggl": 11, "languag": 19, "learn": 0, "linear": [5, 6, 16], "load": [2, 4], "local": 0, "loss": [5, 6], "manag": 1, "manipul": 14, "matric": 16, "matrix": [15, 16], "memori": 14, "minibatch": 4, "model": [2, 3, 5, 8, 19], "multilay": [8, 9], "multipl": 16, "network": 19, "neural": 19, "non": [12, 16], "norm": 16, "normal": 6, "numer": 10, "o": 2, "onc": 1, "oper": 14, "optim": 5, "paramet": [1, 2], "partit": 19, "perceptron": [8, 9], "pre": 0, "predict": [11, 19], "prepar": 15, "preprocess": 15, "price": 11, "probabl": 17, "product": 16, "properti": 16, "read": [4, 5, 15, 19], "recurr": 19, "reduct": 16, "regress": [3, 5, 6], "relu": 9, "requisit": 0, "revisit": 3, "save": [2, 14], "scalar": [12, 16], "sequenc": [18, 19], "sigmoid": 9, "simpl": [12, 17], "slice": 14, "softmax": 3, "speed": 6, "squar": 6, "stabil": 10, "standard": 0, "start": 14, "state": 19, "statist": [17, 19], "sum": 16, "tanh": 9, "ti": 1, "tip": 0, "token": 19, "toss": 17, "train": [3, 5, 8, 18, 19], "util": 13, "vanish": 10, "variabl": 12, "vector": [2, 6, 16], "visual": [4, 13], "vocabulari": 19, "wip": 18, "work": 18}})
\ No newline at end of file
"\ufeffThe Project Gutenberg eBook of The Time Machine\r\n \r\nTh"
+"The Time Machine, by H. G. Wells [1898]\n\n\n\n\nI\n\n\nThe Time Tra"
Reading the Dataset
-" the project gutenberg ebook of the time machine this ebook "
+"the time machine by h g wells i the time traveller for so it"
@@ -474,7 +482,7 @@ Tokenization
-" ,t,h,e, ,p,r,o,j,e,c,t, ,g,u,t,e,n,b,e,r,g, ,e,b,o,o,k, ,o"
+"t,h,e, ,t,i,m,e, ,m,a,c,h,i,n,e, ,b,y, ,h, ,g, ,w,e,l,l,s, "
@@ -500,7 +508,7 @@ Vocabulary
indices:[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-words:[' ', 't', 'h', 'e', 'p', 'r', 'o', 'j', 'c', 'g']
+words:['t', 'h', 'e', ' ', 'i', 'm', 'a', 'c', 'n', 'b']
@@ -513,34 +521,240 @@ Exploratory Language Statistics
using TextAnalysis
-sd = StringDocument(raw_text)
-remove_case!(sd)
-prepare!(sd, strip_non_letters)
+sd = StringDocument(str)
crps = Corpus([sd])
update_lexicon!(crps)
lex_dict = lexicon(crps)
-
-partialsort([lex_dict...], 1:10; by = x -> x[2], rev=true)
+unigram = sort([lex_dict...]; by = x -> x[2], rev=true)
+unigram[1:10]
-10-element view(::Vector{Pair{String, Int64}}, 1:10) with eltype Pair{String, Int64}:
- "the" => 2468
- "and" => 1296
- "of" => 1281
- "i" => 1242
- "a" => 864
- "to" => 760
- "in" => 605
- "was" => 550
- "that" => 451
- "my" => 439
+WARNING: using TextAnalysis.tokens in module Main conflicts with an existing identifier.
+
+
+10-element Vector{Pair{String, Int64}}:
+ "the" => 2261
+ "i" => 1267
+ "and" => 1245
+ "of" => 1155
+ "a" => 816
+ "to" => 695
+ "was" => 552
+ "in" => 541
+ "that" => 443
+ "my" => 440
Word frequency tends to follow a power law distribution (specifically the Zipfian) as we go down the ranks. To get a better idea, we plot the figure of the word frequency.
+
+
+using CairoMakie
+
+fg,ax = lines(last.(unigram); axis=(;xlabel = "token: x",ylabel = "frequency: n(x)", xscale = log10, yscale = log10))
+
+
+
+
+
+
+This should already give us pause for thought if we want to model words by counting statistics. After all, we will significantly overestimate the frequency of the tail, also known as the infrequent words. But what about the other word combinations, such as two consecutive words (bigrams), three consecutive words (trigrams), and beyond? Let’s see whether the bigram frequency behaves in the same manner as the single word (unigram) frequency.
+
+
+bigram = sort([ngrams(sd, 2)...]; by = x -> x[2], rev=true)
+bigram[1:10]
+
+
+
+
+10-element Vector{Pair{AbstractString, Int64}}:
+ "of the" => 309
+ "in the" => 169
+ "i had" => 130
+ "i was" => 112
+ "and the" => 109
+ "the time" => 102
+ "it was" => 99
+ "to the" => 85
+ "as i" => 78
+ "of a" => 73
+
+
+
+
+One thing is notable here. Out of the ten most frequent word pairs, nine are composed of both stop words and only one is relevant to the actual book—“the time”. Furthermore, let’s see whether the trigram frequency behaves in the same manner.
+
+
+trigram = sort([ngrams(sd, 3)...]; by = x -> x[2], rev=true)
+trigram[1:10]
+
+
+
+
+10-element Vector{Pair{AbstractString, Int64}}:
+ "the time traveller" => 59
+ "the time machine" => 30
+ "the medical man" => 24
+ "it seemed to" => 16
+ "it was a" => 15
+ "here and there" => 15
+ "i did not" => 14
+ "seemed to me" => 14
+ "i began to" => 13
+ "i saw the" => 13
+
+
+
+
+Now, let’s visualize the token frequency among these three models: unigrams, bigrams, and trigrams.
+
+
+fg2,ax2 = lines(last.(unigram),label="unigram";
+ axis=(;xlabel = "token: x", ylabel = "frequency: n(x)", xscale = log10, yscale = log10))
+lines!(ax2,last.(bigram),label="bigram",linestyle=:dash)
+lines!(ax2,last.(trigram),label="trigram",linestyle=:dashdot)
+axislegend(position = :rt)
+fg2
+
+
+
+
+
+
+
+
+Partitioning Sequences#
+To train language models, we will randomly sample pairs of input sequences and target sequences in minibatches. The following data loader randomly generates a minibatch from the dataset each time. The argument batch_size specifies the number of subsequence examples in each minibatch and num_steps is the subsequence length in tokens.
+
+
+using IterTools
+using Flux
+
+num_steps=10
+batch_size=2
+function time_machine_dataloader(num_steps::Int,batch_size::Int)::Flux.DataLoader
+ partitions = hcat([to_indices([i...]) for i in [i for i in partition(str,num_steps,1)]]...)
+ x = partitions[:,begin:end-1]
+ y = partitions[:,2:end]
+ return Flux.DataLoader((x,y),batchsize = batch_size)
+end
+
+train_loader = time_machine_dataloader(num_steps,batch_size)
+
+
+
+
+86709-element DataLoader(::Tuple{Matrix{Int64}, Matrix{Int64}}, batchsize=2)
+ with first element:
+ (10×2 Matrix{Int64}, 10×2 Matrix{Int64},)
+
+
+
+
+As we can see in the following, a minibatch of target sequences can be obtained by shifting the input sequences by one token.
+
+
+for (x,y) in train_loader
+ print(x)
+ print(y)
+ break
+end
+
+
+
+
+[1 2; 2 3; 3 4; 4 1; 1 5; 5 6; 6 3; 3 4; 4 6; 6 7][2 3; 3 4; 4 1; 1 5; 5 6; 6 3; 3 4; 4 6; 6 7; 7 8]
+
+
+
+
+
+
+
+Defining the Model#
+We define the model using the RNN implemented by high-level APIs.
+
+
+model = Chain(RNN(32 => 32),Dense(32=>32))
+
+
+
+
+Chain(
+ Recur(
+ RNNCell(32 => 32, tanh), # 2_112 parameters
+ ),
+ Dense(32 => 32), # 1_056 parameters
+) # Total: 6 trainable arrays, 3_168 parameters,
+ # plus 1 non-trainable, 32 parameters, summarysize 12.742 KiB.
+
+
+
+
+
+
+Training and Predicting#
+Before training the model, let’s make a prediction with a model initialized with random weights. Given that we have not trained the network, it will generate nonsensical predictions.
+
+
+# train_loader = time_machine_dataloader(32,1024)
+for (x,y) in train_loader
+ @show size(x)
+ @show model(x)
+ break
+end
+
+
+
+
+size(x) = (32, 1024)
+model(x) = Float32[-0.57374346 -0.26441568 -1.9320982 -2.848492 -2.1397445 -2.4540977 -1.7840853 -1.648342 -2.52589 -1.8467429 -1.2987548 -2.2716665 -2.1326025 -2.3978176 -0.98061323 -1.9477181 -1.280873 -0.99040264 -1.2784705 -1.547663 -1.4533584 -1.1009576 -0.8664077 -0.765324 -0.90174484 -1.0487828 -1.0890119 -1.524941 -1.7626832 -1.5131028 -2.7616706 -2.0652514 -2.5642655 -2.3570645 -1.3331244 -1.4287344 -2.0367844 -3.1046817 -1.5357288 -1.78027 -1.4881468 -2.8125029 -1.6947955 -1.1787102 -1.3989516 -1.8456247 -1.6164786 -0.81756485 -1.5439417 -2.0573435 -2.037667 -1.9368472 -1.2108173 -2.0124266 -0.76695687 -2.3218095 -1.1595086 -1.5701432 -1.3880118 -1.3497151 -1.0555056 -1.6395605 -1.16599 -1.3261876 -1.9716663 -2.3760617 -0.8950427 -1.8247905 -0.73746854 -1.910527 -2.9030178 -1.9486053 -1.1859375 -1.7715193 -2.11734 -1.4402977 -0.8455106 -0.7062114 -1.8113012 -0.6173222 -0.52156556 -2.1779416 -2.7480822 -1.1389867 -1.8730501 -1.7934418 -0.3459037 -2.6761012 -0.92483366 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-0.3368675; -0.0016385913 0.802061 2.0037007 2.5168417 1.3518257 1.6653738 2.6534266 0.56712085 1.0478364 1.364693 1.587614 1.2488842 1.630729 0.9395336 1.1848586 1.5567119 0.17016387 0.87381476 1.4621171 1.4480369 0.51578474 1.0865226 1.2483814 0.991767 1.2354735 0.42278263 1.0607604 1.1815977 2.2797587 1.6007042 1.4137758 1.8949332 1.2501833 1.7835567 0.9103566 0.3512309 0.7173117 1.1971811 0.95582616 1.3551407 2.0379405 1.9578562 0.7836905 1.6568875 0.92666346 1.5616834 1.4019308 1.1006962 2.055909 1.4737612 0.91933143 0.6858049 1.0211495 1.0739725 1.3975056 1.1826026 1.1871897 -0.11979347 0.78321534 0.9141615 1.1552237 1.4975283 1.1177336 0.98852193 1.4795938 1.1938891 1.9074135 1.0164268 1.35282 0.93654877 0.7646304 0.785039 0.8298764 1.1139731 1.4814405 1.0162486 0.27109036 0.3471302 0.9779274 1.000583 1.7981918 2.236491 1.7729279 2.004027 0.8490983 1.2430567 1.3450365 0.95468414 1.5308986 0.777653 0.84447175 1.5576874 0.55562496 1.919859 2.8607655 1.9067467 1.2106029 0.8847688 1.5047102 0.6750939 1.3957872 1.1736059 0.8044681 1.2621553 0.31633106 1.461857 1.2340038 0.2678734 1.280447 2.3749418 1.3767623 0.13751912 1.0320432 0.75317633 -0.12390759 1.3744643 1.0573527 0.72495705 2.5199323 1.8260518 1.0096481 0.4282822 0.0740912 1.440012 0.86690915 1.667445 1.1728804 1.4082054 1.1264229 1.3490953 1.6106701 0.5701908 1.7978722 1.4162621 1.5442412 1.3825622 1.2093616 1.080311 0.45039526 1.58071 1.3257449 0.30989918 1.6683035 1.4692758 0.55166364 0.50616324 0.7492368 0.578613 1.5169735 2.5420675 1.5106093 0.37979802 1.8468075 0.26630574 1.5059508 2.0389872 1.7320678 1.2369871 1.7021351 2.2934742 1.1299379 1.0799475 1.9641529 1.6199504 0.95526594 0.998269 0.58089006 2.9850733 1.2650515 1.3611156 1.8270975 1.6523409 0.85581213 0.38944533 1.5592198 1.4469761 1.8142453 1.3494716 1.5091003 1.0424471 1.0445867 2.0468335 1.6610281 0.8829281 1.2974062 1.879581 2.4894106 1.9354972 -0.22525175 1.9399335 2.3771214 0.28334063 0.19341865 1.7313645 1.3036156 0.7621553 0.6261153 0.044799745 0.85059416 0.92168874 1.396729 2.077967 0.5518469 -0.064249404 0.74348694 0.4802042 0.23363164 1.0522002 1.2047758 1.6867425 1.5777057 1.1208254 1.8798131 0.27003932 2.6447263 2.0114264 0.15339008 0.69002324 1.6519125 1.8489914 0.69469184 0.6824367 2.4171286 1.178986 1.5208845 2.0983868 1.0550636 -0.41712084 0.8680306 1.4335437 1.4382727 1.1240104 0.4784732 0.9813661 0.67994815 1.9033024 1.0010203 0.82551223 1.2702359 2.427364 0.7219236 0.2873453 0.36809903 1.5658785 2.15749 2.9735694 2.06179 1.2717245 0.1675014 0.7490909 1.3604492 1.5645411 1.4043412 1.0078919 1.334746 1.1560919 2.4532175 0.853165 1.6439948 2.4157383 1.2593763 0.728564 0.9962392 1.0164262 2.6441512 0.7134551 1.9829592 1.5677714 1.2090948 0.9842777 1.5058272 1.6469734 2.205821 0.81209844 0.93862724 -0.007283751 1.1325259 1.4391264 1.3825426 0.1277618 1.9025106 0.9602495 0.08048713 1.0023909 1.1936861 1.9026363 2.1753597 0.8698309 1.168138 1.8253871 0.37013564 1.8953046 1.4206016 1.8906456 0.71994567 1.0723088 1.0422578 2.2511878 2.1265597 0.48181185 1.0743836 1.8350022 1.333641 0.3022629 0.71150255 2.215385 0.79234797 1.5633851 1.3632233 1.0583334 1.8516991 2.0567179 2.1116521 0.5224929 0.79339993 0.58205223 0.39740953 0.7394454 1.2566655 1.1213071 2.3607464 0.8663963 0.14798303 1.1006055 1.1401178 0.27185252 0.85212 1.5598834 1.1309872 1.6617131 0.9445708 0.94244283 1.4141088 0.84239364 1.026464 1.0141324 2.0880842 1.1415961 -0.0036943024 1.0358695 1.3721684 1.8456769 1.9839206 1.3579917 2.0061455 1.2028308 0.9209334 1.155962 2.1019866 1.32247 1.0657133 0.91776276 1.3385104 1.5115077 2.0156174 1.3680869 2.1210241 1.6142793 0.88179576 1.0554961 0.9186571 2.0652246 2.143145 1.623605 0.72379744 1.605683 1.527177 1.4555986 1.5603331 2.0804763 0.9208935 0.85535467 0.2624498 1.5182574 1.7588032 1.3999486 1.8471736 0.41110072 1.3177714 1.3891135 1.7105961 0.6572138 0.7913232 1.7681144 1.6471196 0.5476172 0.3851865 1.7891198 1.6405344 1.1923687 1.4698058 1.7872496 2.2322605 0.9843152 0.9990193 1.1238288 0.7465508 1.9139652 1.2409617 0.46653202 2.347364 1.1866021 1.215608 1.7544926 2.4178264 1.194491 1.7914456 2.0499263 2.059851 0.5599019 0.45363176 1.0705581 2.6268067 1.1124076 0.9666581 1.4993477 1.3846476 0.39592528 2.001877 1.9768736 1.6175267 2.0395296 1.4380869 -0.75396466 0.8348737 0.92274106 0.7367259 1.7980139 2.4424248 0.9837758 1.7303914 1.9614041 0.11535053 0.22790825 2.0038755 2.29595 -0.07922832 0.33331308 1.1665004 1.6921374 1.5045724 1.8768547 1.1294469 1.0990639 1.5603327 0.6981166 2.6766908 0.41256788 0.9346548 1.0380218 1.6386259 0.6607615 0.5460745 0.3273332 3.2248003 1.7440398 1.1321323 1.1057426 0.7667987 1.1637747 0.5137067 0.44800547 1.4083253 1.8326973 1.1476953 1.7231569 1.105807 0.9278172 1.3395277 1.6980969 1.4747326 0.7384681 1.1758769 1.1173404 2.0485935 0.73726547 -0.24986286 1.847671 1.8366069 2.1028278 1.2117419 1.306273 1.6370093 1.1355385 1.2227646 1.0705519 1.374348 1.6893963 1.2409314 1.8035368 0.84765077 1.4404929 1.7097577 1.4730245 0.97365457 0.9437406 0.8030883 1.4582317 1.8393469 2.1552708 0.49089742 -0.15710628 1.3838426 0.9185601 1.7893593 2.7171962 1.2229661 0.21985798 0.36434728 1.1531112 1.3533336 1.1649705 1.3111593 1.7220825 1.6368096 1.1708735 1.38037 1.3915211 0.9130285 1.2957304 1.0160394 1.6510297 1.3922385 1.2726738 1.4033314 2.5599372 1.6790864 1.9882905 1.319412 0.80615145 1.329169 1.723406 2.5353584 1.9391724 0.48878697 0.9338836 1.8044033 0.37920627 1.435362 1.6929351 2.2412271 1.2020972 0.528319 1.3136746 1.5158089 0.70619124 0.92726535 1.4561982 1.5704293 2.1738682 1.0457946 1.9466336 1.7563399 0.54577214 1.3806734 1.2777267 1.9351076 1.0238942 0.77213055 1.9306985 0.61118335 0.08794141 1.3169973 2.2368507 1.36619 0.32568663 1.1851305 1.9468172 1.1825619 1.506998 1.4860315 1.4186689 0.9193576 1.2013324 0.30865034 0.5044585 1.8782437 2.675976 1.2320896 1.429553 1.9794624 0.99969465 0.24147184 1.1863018 1.75407 1.171133 1.6494845 1.391581 0.73865545 0.12982643 2.0911555 1.5742074 0.9184094 1.3171911 1.6254988 1.3936583 1.4592052 2.0080914 0.9487058 1.6436799 1.5142179 0.26922464 -0.14540012 1.4768263 1.2583883 1.0251414 2.5207255 0.7137898 0.823679 1.2292854 2.2788365 1.2918952 1.502809 1.6416938 1.5800918 0.15151958 0.57932407 1.3104914 0.62657934 1.9252974 1.6771791 0.5280933 1.0145136 0.17595175 1.4784636 1.7526417 1.5175325 1.5855827 1.4975423 0.7587297 0.817348 1.559319 0.35085684 1.5257534 1.3610446 1.4804621 2.4580655 1.4400328 0.63583225 1.8575119 1.3835744 1.8599005 1.5729941 0.19019094 0.62525415 1.8508083 1.1434054 0.88196474 1.5130854 2.1796427 1.4532616 0.6753179 2.188434 0.6692312 0.77700204 1.4377464 1.4847317 1.945169 0.901668 0.6960087 2.0866165 2.728611 1.1618242 0.77093667 2.0198424 2.3892915 1.3456236 0.74415 1.4020417 1.8036265 1.1789587 2.1617236 1.5130638 1.5871792 1.5352736 0.74577945 1.294162 1.5329822 2.3053248 2.090938 1.5509108 3.3512955 1.3147599 1.2880926 0.7568443 1.4645797 1.1022848 0.9292211 2.1774666 1.4768634 0.562744 0.4033285 1.7946551 0.4017819 1.0589511 1.316437 0.688862 1.6774738 1.3048122 1.635029 1.9037704 0.9202959 1.13611 1.529777 0.78247344 1.5094951 0.94922805 0.75415707 0.09071993 0.9414086 1.5876709 2.9394333 1.3168383 1.3406792 0.44574857 1.4220244 1.2037588 0.7234367 1.221252 2.4637003 1.5663648 0.69438726 1.6583068 0.74784666 0.65353715 2.0333962 1.9364152 0.95874304 0.7696997 0.21732616 1.6079774 1.5822314 1.490458 0.8719131 1.3892145 0.6231646 1.337933 1.3223895 1.3045589 1.4074064 0.7380625 1.411808 1.7592549 0.94706047 0.79240155 1.3484421 1.8767203 1.534294 0.70237 1.2335588 2.4564369 2.0554633 1.4051056 1.2097194 1.0354654 1.1463068 0.49370426 0.78313506 1.8613504 1.7370286 0.9330865 1.8989669 1.7694237 1.4983909 1.1648738 1.0718546 1.4074113 0.7258331 1.1299126 1.7702923 1.835502 2.4369564 2.1035419 0.45279616 0.89121336 2.0064137 2.0960605 1.1588733 1.47009 0.8115278 0.9784614 1.1365077 1.3025382 1.1108053 1.1571096 1.774653 1.1620114 2.4182858 2.0868783 0.6862319 0.56051975 2.0347037 1.3240284 1.1443073 0.6695985 1.530575 1.6805766 2.0403 0.5215945 1.2249624 1.6309966 1.855207 2.0320017 1.8209753 0.89949083 2.2349958 1.3119063 0.8211781 1.1701456 1.6126602 0.61333686 0.33517355 1.7484405 1.1271259 1.3623847 0.5639588 1.7761114 0.9001859 0.06646119 1.3902465 1.4880302 1.8306949 -0.08938725 0.7861296 1.485556 0.9159959 0.39588434 1.3020797 0.37178776 1.3105526 1.990368 1.060736 0.88953626 1.0233319 1.8264737 1.1088042 1.0274426 1.3595434 0.5563574 0.6133702 1.843389 1.0262158 1.4318419 2.5846214 1.256445 2.7250068 1
+
+
+Excessive output truncated after 574663 bytes.
+
+
+
+
@@ -594,6 +808,10 @@ Exploratory Language StatisticsTokenization
Vocabulary
Exploratory Language Statistics
+Partitioning Sequences
+Recurrent Neural Networks with Hidden States
+Defining the Model
+Training and Predicting
diff --git a/objects.inv b/objects.inv
index 7325577..b04fef7 100644
Binary files a/objects.inv and b/objects.inv differ
diff --git a/search.html b/search.html
index f13969b..96501f5 100644
--- a/search.html
+++ b/search.html
@@ -207,6 +207,10 @@
+Recurrent Neural Networks
+
" the project gutenberg ebook of the time machine this ebook "
+"the time machine by h g wells i the time traveller for so it"
Tokenization
-" ,t,h,e, ,p,r,o,j,e,c,t, ,g,u,t,e,n,b,e,r,g, ,e,b,o,o,k, ,o"
+"t,h,e, ,t,i,m,e, ,m,a,c,h,i,n,e, ,b,y, ,h, ,g, ,w,e,l,l,s, "
@@ -500,7 +508,7 @@ Vocabulary
indices:[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-words:[' ', 't', 'h', 'e', 'p', 'r', 'o', 'j', 'c', 'g']
+words:['t', 'h', 'e', ' ', 'i', 'm', 'a', 'c', 'n', 'b']
@@ -513,34 +521,240 @@ Exploratory Language Statistics
using TextAnalysis
-sd = StringDocument(raw_text)
-remove_case!(sd)
-prepare!(sd, strip_non_letters)
+sd = StringDocument(str)
crps = Corpus([sd])
update_lexicon!(crps)
lex_dict = lexicon(crps)
-
-partialsort([lex_dict...], 1:10; by = x -> x[2], rev=true)
+unigram = sort([lex_dict...]; by = x -> x[2], rev=true)
+unigram[1:10]
" ,t,h,e, ,p,r,o,j,e,c,t, ,g,u,t,e,n,b,e,r,g, ,e,b,o,o,k, ,o"
+"t,h,e, ,t,i,m,e, ,m,a,c,h,i,n,e, ,b,y, ,h, ,g, ,w,e,l,l,s, "
Vocabulary
indices:[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-words:[' ', 't', 'h', 'e', 'p', 'r', 'o', 'j', 'c', 'g']
+words:['t', 'h', 'e', ' ', 'i', 'm', 'a', 'c', 'n', 'b']
indices:[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-words:[' ', 't', 'h', 'e', 'p', 'r', 'o', 'j', 'c', 'g']
+words:['t', 'h', 'e', ' ', 'i', 'm', 'a', 'c', 'n', 'b']
using TextAnalysis
-sd = StringDocument(raw_text)
-remove_case!(sd)
-prepare!(sd, strip_non_letters)
+sd = StringDocument(str)
crps = Corpus([sd])
update_lexicon!(crps)
lex_dict = lexicon(crps)
-
-partialsort([lex_dict...], 1:10; by = x -> x[2], rev=true)
+unigram = sort([lex_dict...]; by = x -> x[2], rev=true)
+unigram[1:10]
10-element view(::Vector{Pair{String, Int64}}, 1:10) with eltype Pair{String, Int64}:
- "the" => 2468
- "and" => 1296
- "of" => 1281
- "i" => 1242
- "a" => 864
- "to" => 760
- "in" => 605
- "was" => 550
- "that" => 451
- "my" => 439
+WARNING: using TextAnalysis.tokens in module Main conflicts with an existing identifier.
+
+
+10-element Vector{Pair{String, Int64}}:
+ "the" => 2261
+ "i" => 1267
+ "and" => 1245
+ "of" => 1155
+ "a" => 816
+ "to" => 695
+ "was" => 552
+ "in" => 541
+ "that" => 443
+ "my" => 440
Word frequency tends to follow a power law distribution (specifically the Zipfian) as we go down the ranks. To get a better idea, we plot the figure of the word frequency.
+
+
+
+
+
+
+using CairoMakie
+
+fg,ax = lines(last.(unigram); axis=(;xlabel = "token: x",ylabel = "frequency: n(x)", xscale = log10, yscale = log10))
+
+
+This should already give us pause for thought if we want to model words by counting statistics. After all, we will significantly overestimate the frequency of the tail, also known as the infrequent words. But what about the other word combinations, such as two consecutive words (bigrams), three consecutive words (trigrams), and beyond? Let’s see whether the bigram frequency behaves in the same manner as the single word (unigram) frequency.
+
+
+
+
+
+
+bigram = sort([ngrams(sd, 2)...]; by = x -> x[2], rev=true)
+bigram[1:10]
+
+
+
+
+10-element Vector{Pair{AbstractString, Int64}}:
+ "of the" => 309
+ "in the" => 169
+ "i had" => 130
+ "i was" => 112
+ "and the" => 109
+ "the time" => 102
+ "it was" => 99
+ "to the" => 85
+ "as i" => 78
+ "of a" => 73
+One thing is notable here. Out of the ten most frequent word pairs, nine are composed of both stop words and only one is relevant to the actual book—“the time”. Furthermore, let’s see whether the trigram frequency behaves in the same manner.
+
+
+
+
+
+
+trigram = sort([ngrams(sd, 3)...]; by = x -> x[2], rev=true)
+trigram[1:10]
+
+
+
+
+10-element Vector{Pair{AbstractString, Int64}}:
+ "the time traveller" => 59
+ "the time machine" => 30
+ "the medical man" => 24
+ "it seemed to" => 16
+ "it was a" => 15
+ "here and there" => 15
+ "i did not" => 14
+ "seemed to me" => 14
+ "i began to" => 13
+ "i saw the" => 13
+Now, let’s visualize the token frequency among these three models: unigrams, bigrams, and trigrams.
+
+
+
+
+
+
+
+fg2,ax2 = lines(last.(unigram),label="unigram";
+ axis=(;xlabel = "token: x", ylabel = "frequency: n(x)", xscale = log10, yscale = log10))
+lines!(ax2,last.(bigram),label="bigram",linestyle=:dash)
+lines!(ax2,last.(trigram),label="trigram",linestyle=:dashdot)
+axislegend(position = :rt)
+fg2
+
+
+Partitioning Sequences#
+To train language models, we will randomly sample pairs of input sequences and target sequences in minibatches. The following data loader randomly generates a minibatch from the dataset each time. The argument batch_size specifies the number of subsequence examples in each minibatch and num_steps is the subsequence length in tokens.
+
+
+
+
+
+
+using IterTools
+using Flux
+
+num_steps=10
+batch_size=2
+function time_machine_dataloader(num_steps::Int,batch_size::Int)::Flux.DataLoader
+ partitions = hcat([to_indices([i...]) for i in [i for i in partition(str,num_steps,1)]]...)
+ x = partitions[:,begin:end-1]
+ y = partitions[:,2:end]
+ return Flux.DataLoader((x,y),batchsize = batch_size)
+end
+
+train_loader = time_machine_dataloader(num_steps,batch_size)
+
+
+
+
+86709-element DataLoader(::Tuple{Matrix{Int64}, Matrix{Int64}}, batchsize=2)
+ with first element:
+ (10×2 Matrix{Int64}, 10×2 Matrix{Int64},)
+As we can see in the following, a minibatch of target sequences can be obtained by shifting the input sequences by one token.
+
+
+
+
+
+
+for (x,y) in train_loader
+ print(x)
+ print(y)
+ break
+end
+
+
+
+
+[1 2; 2 3; 3 4; 4 1; 1 5; 5 6; 6 3; 3 4; 4 6; 6 7][2 3; 3 4; 4 1; 1 5; 5 6; 6 3; 3 4; 4 6; 6 7; 7 8]
+Defining the Model#
+We define the model using the RNN implemented by high-level APIs.
+
+
+
+
+
+
+model = Chain(RNN(32 => 32),Dense(32=>32))
+
+
+
+
+Chain(
+ Recur(
+ RNNCell(32 => 32, tanh), # 2_112 parameters
+ ),
+ Dense(32 => 32), # 1_056 parameters
+) # Total: 6 trainable arrays, 3_168 parameters,
+ # plus 1 non-trainable, 32 parameters, summarysize 12.742 KiB.
+Training and Predicting#
+Before training the model, let’s make a prediction with a model initialized with random weights. Given that we have not trained the network, it will generate nonsensical predictions.
+
+
+
+
+
+# train_loader = time_machine_dataloader(32,1024)
+for (x,y) in train_loader
+ @show size(x)
+ @show model(x)
+ break
+end
+
+
+
+
+
+
+size(x) = (32, 1024)
+model(x) = Float32[-0.57374346 -0.26441568 -1.9320982 -2.848492 -2.1397445 -2.4540977 -1.7840853 -1.648342 -2.52589 -1.8467429 -1.2987548 -2.2716665 -2.1326025 -2.3978176 -0.98061323 -1.9477181 -1.280873 -0.99040264 -1.2784705 -1.547663 -1.4533584 -1.1009576 -0.8664077 -0.765324 -0.90174484 -1.0487828 -1.0890119 -1.524941 -1.7626832 -1.5131028 -2.7616706 -2.0652514 -2.5642655 -2.3570645 -1.3331244 -1.4287344 -2.0367844 -3.1046817 -1.5357288 -1.78027 -1.4881468 -2.8125029 -1.6947955 -1.1787102 -1.3989516 -1.8456247 -1.6164786 -0.81756485 -1.5439417 -2.0573435 -2.037667 -1.9368472 -1.2108173 -2.0124266 -0.76695687 -2.3218095 -1.1595086 -1.5701432 -1.3880118 -1.3497151 -1.0555056 -1.6395605 -1.16599 -1.3261876 -1.9716663 -2.3760617 -0.8950427 -1.8247905 -0.73746854 -1.910527 -2.9030178 -1.9486053 -1.1859375 -1.7715193 -2.11734 -1.4402977 -0.8455106 -0.7062114 -1.8113012 -0.6173222 -0.52156556 -2.1779416 -2.7480822 -1.1389867 -1.8730501 -1.7934418 -0.3459037 -2.6761012 -0.92483366 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+Excessive output truncated after 574663 bytes.
+