learning_zero.jl

### A Pluto.jl notebook ###
# v0.19.30

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ aab65a5a-7633-11ee-22b9-0fd54ecd9118
begin
	using Plots
	using Lux, Optimisers
	using Random
	using ProgressLogging
	import Flux: onehotbatch, onecold, crossentropy, throttle, softmax
	using Base.Iterators: repeated, partition
	using Distributions
	using LinearAlgebra
	using JuMP, Ipopt
	using PlutoLinks, PlutoHooks
	using PlutoUI
	using HypertextLiteral
	using Statistics
end

# ╔═╡ 730e3bd1-47af-4588-b5bd-a7c5212d7a07
md"""
# Understanding zero with deep learning

## Background
Experiments have been conducted where an animal is presented with two cards and has to choose the card with the smallest number of blobs. Once the animal understands the task, it is presented with two cards where one of the cards has zero blobs. Since the animal has not been shown a zero blob card, it has to use numerical intuition to choose which card has less blobs.

Experiments have shown that animals do have the numerical intuition to understand that zero is less than one:

* [https://science.sciencemag.org/content/334/6063/1664.abstract](https://science.sciencemag.org/content/334/6063/1664.abstract)
* [https://www.ncbi.nlm.nih.gov/pubmed/27666660](https://www.ncbi.nlm.nih.gov/pubmed/27666660)
* [https://www.researchgate.net/publication/325684091_Numerical_ordering_of_zero_in_honey_bees](https://www.researchgate.net/publication/325684091_Numerical_ordering_of_zero_in_honey_bees)

The simplest animal capable of understanding that zero is less than one is a honeybee.

## Results
In this notebook, I train a neural network to predict which of two images has less blobs. Then I give the network a scenario where one image has zero blobs. If the neural network is well trained, then it will correctly identify that zero is less than one.

## Reflections
Thinking about the training process and results broadened my perspective on what "training a neural network" means. The samples where one image has zero blobs come from a very different distribution than the training distribution. However, the model is able to make the correct prediction. Training the neural network on data gives it numerical intuition. Even though the models task is to label data, it has obtained the ability to understand numbers. 
"""

# ╔═╡ f60e0e23-e304-4fa7-813d-c9be87e33f9e
TableOfContents()

# ╔═╡ c266f191-408a-4c7d-b094-69318eadb8d9
md"""
# Choose the image height and width
"""

# ╔═╡ 027a9c72-0e28-41de-88b8-68b717813383
begin
	img_height = 28
	img_width = 28
end

# ╔═╡ bf6f23c9-6062-4017-ad17-e1f3527881e6
md"""
# Generate examples

You can create samples of the data that the model will be trained on.

The code below uses `generate_example`, `generate_batch`, `generate_locations`, `get_title` and `plot_first_example`. Control click on the links below to see the documentation and definitions of these functions.
"""

# ╔═╡ efc39144-ea2a-4e0a-800f-8b6e72868ccf
md"""
Blobs left: $(@bind blobs_left NumberField(0:10, default=1))

Blobs right: $(@bind blobs_right NumberField(0:10, default=3))

Shape: $(@bind shape Select([:square, :gaussian]))

Scale: $(@bind scale Select([false, true]))
"""

# ╔═╡ 6b560bcb-8dc5-4386-beb8-588a73572cc1
md"""
# Use the `generate_batch` function
The `generate_batch` function randomly samples a number of blobs for the right and left images along with shapes for the blobs. For every example it creates, it will create an example where the images are flipped. Since the number of blobs left and right are generated by the function, each example can have a label attached to it. The `plot_first_example` function understands the labelling system and can create a labelled visualization of the first example in a batch.
"""

# ╔═╡ a7eebcab-29bb-4f09-84b9-cb60f23d936d
@bind go_generate_batch Button("Generate batch")

# ╔═╡ 045ac160-430a-4564-b8ed-aefbcf644b07
md"""
## Batch structure

Each batch is a 2 tuple where the first element is the data and the second is the label.

The data is a `img_height`×`img_width`× 2 ×`batch_size` array. Lux will use the last dimension as the batch dimension and each sample will be a `img_height`×`img_width` with two channels. The first channel is the left image and the second channel is the right image.

The labels are 3 × `batch_size` one hot matrices.

* first row == 1 => more blobs in the left image
* second row == 1 => same number of blobs in both images
* third row == 1 => more blobs in the right image
"""

# ╔═╡ 0898c0b2-4b2b-4b7d-bb61-27c5fba67708
md"""
Example batch size: $(@bind example_batch_size NumberField(2:2:20, default=6))
"""

# ╔═╡ 20bea86c-3c47-40d3-891d-1164aad54285
md"""
# Deep learning model (using Lux.jl)
"""

# ╔═╡ af10bdf8-1193-4fb3-8154-859025ed79e5
model = Chain(
	# First convolution, operating upon a 28x28 image
	Conv((3, 3), 2 => 16, pad=(1, 1), relu),
	MaxPool((2, 2)),

	# Second convolution, operating upon a 14x14 image
	Conv((3, 3), 16 => 32, pad=(1, 1), relu),
	MaxPool((2, 2)),

	# Third convolution, operating upon a 7x7 image
	Conv((3, 3), 32 => 32, pad=(1, 1), relu),
	MaxPool((2, 2)),

	# Reshape 3d tensor into a 2d one, at this point it should be (3, 3, 32, N)
	# which is where we get the 288 in the `Dense` layer below:
	x -> reshape(x, :, size(x, 4)),
	Dropout(0.2),
	Dense(288, 3, relu),

	# Softmax to get probabilities
	softmax,
)

# ╔═╡ c2c9439d-9adb-40b3-8482-2911a182e898
md"""
## Crossentropy loss
"""

# ╔═╡ 3f8bdd08-dccb-4a79-ba28-27bf0a209385
function loss(model, ps, st, data)
    y_pred, st = Lux.apply(model, data[1], ps, st)
    ce_loss = crossentropy(y_pred, data[2])
    return ce_loss, st, ()
end

# ╔═╡ 6d2d0dde-cb24-41d0-a7e5-3dd3e462d6b0
function accuracy(tstate, data)
	ŷ = onecold(Lux.apply(tstate.model, data[1], tstate.parameters, tstate.states)[1],
		        [-1 0 1])
	mean(ŷ .== onecold(data[2], [-1, 0, 1]))
end

# ╔═╡ 7cef11de-5616-4d4e-b760-2aa1da00be5b
md"""
## Training loop
"""

# ╔═╡ fda7447b-7915-4027-ae28-592476124b42
function train_model(model, opt, train_data, test_data, nepoch)
	rng = MersenneTwister(42)
	tstate = Lux.Training.TrainState(rng, model, opt)
	vjp_rule = Lux.Training.AutoZygote()
	
	test_accuracy_list = Float64[]
	batch_loss_list = Float32[]
	for epoch in 1:nepoch
		for batch in train_data
			grads, loss_value, stats, tstate = Lux.Training.compute_gradients(
				vjp_rule,
				loss,
				batch,
				tstate
			)
		    
		    tstate = Lux.Training.apply_gradients(tstate, grads)
		end
		test_accuracy = accuracy(tstate, test_data)
		train_loss = mean(
			loss(tstate.model, tstate.parameters, tstate.states, batch)[1]
			for batch in train_data
		)
	
		@info "
		Epcoh: $epoch
		Test accuracy: $(test_accuracy)
		Train loss: $train_loss"
			
		push!(test_accuracy_list, test_accuracy)
		push!(batch_loss_list, train_loss)
	end

	tstate, test_accuracy_list, batch_loss_list
end

# ╔═╡ f88e7b88-8730-4d9f-bee6-4594d045135e
md"""
## Generate train/test data
"""

# ╔═╡ 9a959062-2eea-4d3b-a4be-4f99c6668deb
md"""
## Select training parameters
"""

# ╔═╡ a6918b7b-1f91-43dc-8826-59cefa3ad706
opt = Optimisers.Adam(1f-3)

# ╔═╡ cf23ff89-bf31-4b41-ad2e-d82b149df17f
rng = MersenneTwister()

# ╔═╡ 015ad06d-0b40-421d-88f0-0b4204faa7d8
md"""
# Evaluate model

The figure below shows the accuracy of the model given the number of blobs in the left/right images. Since there are three classes and the classes are balanced in the training set, random guessing would give you an accuracy of 1/3, which the model exceeds.

The first column and the last row of the heatmap below are cases where the model was presented with a image with zero blobs. The fact that the model does better than 1/3 in these cases indicates that it understands zero.
"""

# ╔═╡ 5b1fad09-ae8b-4a10-b985-6fb054c2fc78
md"""
## Make predictions with the model
Pressing the button below will generate a sample from the training distribution and predict which side has more blobs. The prediction is compared to the true label and the status of the model prediction is shown.
"""

# ╔═╡ a03d9cf7-7812-449a-a2ea-f76d15e0ce7b
@bind go Button("Generate a sample from the training distribution and compare to model prediction")

# ╔═╡ 553ce5e1-6d21-4cc5-a624-664c2d365035
md"""
## Choose your own adventure
Use the input fields to choose the characteristics of the input data and see how the model performs.
"""

# ╔═╡ e682454f-54fd-4faf-8268-869914f1ec8f
md"""
Blobs left: $(@bind blobs_left_ NumberField(0:10, default=0))

Blobs right: $(@bind blobs_right_ NumberField(0:10, default=3))

Shape: $(@bind shape_ Select([:square, :gaussian]))

Scale: $(@bind scale_ Select([false, true]))

$(@bind go_ Button("Generate another example"))
"""

# ╔═╡ 250fd052-a5fb-4c17-b6b9-dea0b53f6243
md"""
# Appendix (helper functions)
"""

# ╔═╡ 706be74a-e527-418d-8a2f-532af2fe27d5
"""
	generate_locations(nobjects; min_distance=1.0)

Randomly generate coordinates for `nobjects` lying in the square [-1,1]×[-1,1]. Each 
point has to be atleast `min_distance` from all other points.

# Implementation
`generate_locations` will sample `nobjects` points in the square using a uniform
distribution. Then it will find locations that are as close as possible to the sampled
locations while maintaining the distance constraint. JuMP and Ipopt are used to set up
and solve the optimization problem.
"""
function generate_locations(nobjects; min_distance=1.0)
	object_locations = 2rand(2, nobjects) .- 1
	
	model = Model(Ipopt.Optimizer)
	set_attribute(model, "print_level", 0)
	@variable(model, -1.0 <= x[1:nobjects] <= 1.0)
	@variable(model, -1.0 <= y[1:nobjects] <= 1.0)

	pairs = [(i, j) for i in 1:nobjects, j in 1:nobjects if j != i]
	pi = [p[1] for p in pairs]
	pj = [p[2] for p in pairs]
	@constraint(model,
				(x[pi] .- x[pj]).^2 .+
				(y[pi] .- y[pj]).^2 .>= min_distance^2)
	
	@objective(model, Min,
			   sum((x[i] - object_locations[1, i])^2
			       + (y[i] - object_locations[2, i])^2
			       for i in 1:nobjects))

	optimize!(model)

	permutedims([value.(x) value.(y)])
end

# ╔═╡ 288ce71f-4e53-4fab-ae70-32bd7e325da3
function add_blobs!(img, xx, yy, shape, object_locations, object_size, scale)
	nobjects = size(object_locations, 2)
	for index in 1:nobjects
        l_x, l_y = object_locations[:, index]
        if shape == :square
			scaling = scale ? min(nobjects, 4) : 1.0
            img .+= [ifelse((abs(x - l_x) < object_size/scaling)
                             && (abs(y - l_y) < object_size/scaling), 1.0, 0.0)
                      for x in xx, y in yy]
        elseif shape == :gaussian
			scaling = scale ? object_size*sqrt(nobjects) : object_size
            img .+= [exp(-scaling*((x - l_x)^2 + (y - l_y)^2))
				      for x in xx, y in yy]
        end
    end

	img
end

# ╔═╡ efc93fb2-255e-4ef7-8606-1936c7a5f370
"""
    generate_example(img_height, img_width, nobjects::Tuple;
                     μ=50, σ=0.5,
                     min_distance=0.7,
                     noise_strength=0.02,
                     shape=:gaussian,
	                 scale=false))

Generate an example image of height `img_height` and width `img_width` containing 
`nobjects[1]` objects on the left side and `nobjects[2]` objects on the right side.
The shape of the object is determined by the `shape` keyword argument.
"""
function generate_example(img_height, img_width, nobjects::Tuple;
                          μ=50, σ=0.5,
                          min_distance=0.7,
                          noise_strength=0.02,
                          shape=:gaussian,
	                      scale=false)
    object_locations1 = generate_locations(abs(nobjects[1]); min_distance)
    object_locations2 = generate_locations(abs(nobjects[2]); min_distance)

	object_size = shape == :square ? 0.25 : 50.0
    
    img1 = randn(img_height, img_width)*noise_strength
    img2 = randn(img_height, img_width)*noise_strength
    xx = LinRange(-1, 1, img_width)
    yy = LinRange(-1, 1, img_height)

	add_blobs!(img1, xx, yy, shape, object_locations1, object_size, scale)
	add_blobs!(img2, xx, yy, shape, object_locations2, object_size, scale)

    ret = Array{Float32}(undef, size(img1)..., 2)
    ret[:, :, 1] .= img1
    ret[:, :, 2] .= img2
    
    ret
end

# ╔═╡ 1b56681e-c486-498e-bc34-040698b025b7
begin
	example = generate_example(img_height, img_width, (blobs_left, blobs_right),
		                       shape=shape, scale=scale)
    img = hcat(example[:, :, 1], ones(img_height, 1)*NaN, example[:, :, 2])

	heatmap(img, ratio=1)
end

# ╔═╡ 39c4bfff-5c1e-4d40-bceb-cfcee66805f8
heatmap(img, ratio=1)

# ╔═╡ cc5ad985-945d-4186-9ec8-7ce3f6c3ea1c
function test_i_j(state, model, i, j; img_height=img_height, img_width=img_width)
	img = reshape(
		generate_example(img_height, img_width,
			(i, j);
			scale=rand([true, false]),
			shape=rand([:square, :gaussian, :circle])
		),
		(img_height, img_width, 2, 1)
	)

	model_result = Lux.apply(model, img, state.parameters, state.states)[1]
	label = onecold(model_result, [-1 0 1])[1]

	label == sign(j - i)
end

# ╔═╡ cab297cb-ee7a-4413-a545-4c1293ef72d8
"""
	generate_batch(batch_size, img_height, img_width)

Generate `batch_size` examples with images of size `img_height`×`img_width` along
with their (onehot encoded) labels.
"""
function generate_batch(batch_size, img_height, img_width)
	nobjects_range = 1:5
	labels = Array{Int}(undef, batch_size)
	data = Array{Float32}(undef, img_height, img_width, 2, batch_size)
	for i in 1:2:batch_size
	    nobjects = rand(nobjects_range, 2)
	    # Rebalance the training set so that there is approximately the same number
		# of examples with equal as blobs as unequal blob examples.
	    rand() <= 0.2 && (nobjects[1] = nobjects[2])
	    labels[i] = nobjects[1] > nobjects[2] ? -1 :
		            nobjects[1] == nobjects[2] ? 0 : 1

		data[:, :, :, i] .= generate_example(img_height, img_width,
			(nobjects[1], nobjects[2]);
			scale=rand([true, false]),
			shape=rand([:square, :gaussian])
		)

	    # Generate another example where the images flip sides.
	    labels[i + 1] = nobjects[2] > nobjects[1] ? -1 :
		                nobjects[1] == nobjects[2] ? 0 : 1
	    data[:, :, :, i + 1] .= reverse(data[:, :, :, i], dims=3)
	end

	data, onehotbatch(labels, [-1 0 1])
end

# ╔═╡ f56ea23e-8af6-4777-b717-e1d13cd91c8a
begin
    example_batch = generate_batch(example_batch_size, img_width, img_height)
	nothing
end

# ╔═╡ 8a3125f0-90d8-426f-876f-07e28492d1bf
example_batch[1]

# ╔═╡ 7c165cbd-b21b-4150-ad2e-9aedd5629f48
example_batch[2]

# ╔═╡ 06975abb-a62b-42a3-bf9f-199d52f33453
begin
	batch_size = 64
	nbatch_train = 15
	
	ntest = 200
	train_data = [generate_batch(batch_size, img_height, img_width)
		          for _ in 1:nbatch_train]
	test_data = generate_batch(ntest, img_height, img_width)
end

# ╔═╡ 0622c381-faba-4c60-a556-78d0c90cbc64
begin
	nepoch = 60
	trained_state, test_accuracy, batch_loss_list =
		train_model(model, opt, train_data, test_data, nepoch)
end

# ╔═╡ 0c90e26c-e00d-44b1-b692-cde77c294302
let
	p1 = plot(test_accuracy,
			xlabel="Epoch",
			ylabel="Test accuracy",
			legend=false
	)
	p2 = plot(batch_loss_list,
			xlabel="Epoch",
			ylabel="Training loss",
			legend=false
	)
	plot(p1, p2, layout=(2, 1))
end

# ╔═╡ 2eff527d-897d-4606-874f-7b5e645e4c23
begin
	test_range = 0:5
	niters = 20

	accuracy_matrix = [mean(test_i_j(trained_state, model, i, j) for _ in 1:niters)
		               for i in test_range, j in test_range]
	p1 = heatmap(test_range, test_range, accuracy_matrix, colorbar_title="Accuracy")
	xaxis!("# blobs left")
	yaxis!("# blobs right")
end

# ╔═╡ 12b07d79-f13a-42a9-8dc4-12422d760a7e
function get_title(label)
	if label == 1
		"Right has more blobs"
	elseif label == 0
		"Same number of blobs"
	else
		"Left has more blobs"
	end
end

# ╔═╡ a240ddb8-7b7e-4cb9-a58b-837ea7232afb
let
	go_
    sample = generate_example(img_height, img_width,
		                      (blobs_left_, blobs_right_),
		                       shape=shape_, scale=scale_)
	img = hcat(sample[:, :, 1], ones(img_height, 1)*NaN, sample[:, :, 2])

	prediction = Lux.apply(trained_state.model,
		                   reshape(sample, (img_height, img_width, 2, 1)),
		                   trained_state.parameters, trained_state.states)[1]

	model_label = onecold(prediction, [-1 0 1])[1]
	
	p = heatmap(img,  ratio=1)

	data_label = sign(blobs_right_ - blobs_left_)
	is_correct = model_label == data_label
	text_color = is_correct ? "green" : "red"
	@htl("""
	$(p)
	<br>
	<b style="color:$(text_color);font-size:2.1em">
	Model $(is_correct ? "correctly" : "incorrectly") predicts "$(get_title(model_label) |> lowercase)"
	</b>
	""")
end

# ╔═╡ 07ca44b6-d8b8-463b-8374-e28af9a50738
function plot_first_example(batch; show_all=true)
	data = batch[1]
	img1 = hcat(data[:, :, 1, 1], ones(img_height)*NaN, data[:, :, 2, 1])
	img2 = hcat(data[:, :, 1, 2], ones(img_height)*NaN, data[:, :, 2, 2])

	label = onecold(batch[2], [-1 0 1])[1]
	title = get_title(label)
	p1 = heatmap(img1; title)

	label = onecold(batch[2], [-1 0 1])[2]
	title = get_title(label)
	p2 = heatmap(img2; title)

	if show_all
	    plot(p1, p2, layout=(2, 1))
	else
		p1
	end
end

# ╔═╡ 5fbeb830-4265-44fc-a2f0-814dfc6728e0
generate_example, generate_batch, generate_locations, get_title, plot_first_example

# ╔═╡ bcb32bfe-1bd5-4c89-b08f-527f23906bc9
let
	go_generate_batch
	batch = generate_batch(2, img_width, img_height)

	plot_first_example(batch)
end

# ╔═╡ 01e8c15b-ada6-4747-920f-47a11117248a
let
	go
	
	batch = generate_batch(2, img_width, img_height)

	p = plot_first_example(batch; show_all=false)

	prediction = Lux.apply(trained_state.model, batch[1],
		                   trained_state.parameters, trained_state.states)[1]
	model_label = onecold(prediction, [-1 0 1])[1]
	data_label = onecold(batch[2], [-1 0 1])[1]

	is_correct = model_label == data_label
    text_color = is_correct ? "green" : "red"
	
	@htl("""
	$(p)
	<b  style="color:$(text_color);font-size:2.1em">
	Model $(is_correct ? "correctly" : "incorrectly") predicts "$(get_title(model_label) |> lowercase)"
	</b>
	""")
end

# ╔═╡ 6f51041b-74f9-4beb-aab8-670ec38ca425
plot()

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Lux = "b2108857-7c20-44ae-9111-449ecde12c47"
Optimisers = "3bd65402-5787-11e9-1adc-39752487f4e2"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoHooks = "0ff47ea0-7a50-410d-8455-4348d5de0774"
PlutoLinks = "0ff47ea0-7a50-410d-8455-4348d5de0420"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
ProgressLogging = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[compat]
Distributions = "~0.25.102"
Flux = "~0.14.6"
HypertextLiteral = "~0.9.4"
Ipopt = "~1.5.1"
JuMP = "~1.16.0"
Lux = "~0.5.9"
Optimisers = "~0.3.1"
Plots = "~1.39.0"
PlutoHooks = "~0.0.5"
PlutoLinks = "~0.1.6"
PlutoUI = "~0.7.52"
ProgressLogging = "~0.1.4"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

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[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "GPUArrays", "GPUArraysCore", "IRTools", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "PrecompileTools", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "5ded212acd815612df112bb895ef3910c5a03f57"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.67"

    [deps.Zygote.extensions]
    ZygoteColorsExt = "Colors"
    ZygoteDistancesExt = "Distances"
    ZygoteTrackerExt = "Tracker"

    [deps.Zygote.weakdeps]
    Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
    Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.ZygoteRules]]
deps = ["ChainRulesCore", "MacroTools"]
git-tree-sha1 = "9d749cd449fb448aeca4feee9a2f4186dbb5d184"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.4"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "47cf33e62e138b920039e8ff9f9841aafe1b733e"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.35.1+0"

[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

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