### A Pluto.jl notebook ###
# v0.20.28

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)
    #! format: off
    return 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
    #! format: on
end

# ╔═╡ 389012b6-6d05-11f0-2fb9-5bc0a51d3b9d
begin
	using Flux
	using Plots
	using PlutoUI
	using PlutoTeachingTools
	"import packages"
end

# ╔═╡ b7b7156b-1d7d-46a2-a90e-c517efcdf58e
md"""
# Lecture 3: Universal approximation theorem
"""

# ╔═╡ 9d117ec0-6b61-43d5-bb13-d5ce10eefb2e
begin
	c_palette = theme_palette(:wong2)
	c2 = cgrad(c_palette[[1,2]], categorical=true, 2)
	theme(:boxed)
	"color settings"
end

# ╔═╡ 9b179cb6-3c40-49bd-87e1-afb31e4aa8a9
md"""
## Second attempt -- Hidden layer
"""

# ╔═╡ f3926a90-a046-480e-81cf-63cbc3e73975
md"""

```
    w1,b1  [ ]  w5 
 /  w2,b2  [ ]  w6  \
x                    y
 \  w3,b3  [ ]  w7  /
    w4,b4  [ ]  w8

```
"""

# ╔═╡ 01210d85-de83-4318-90fa-2111ea1c9dd2
# weights

# ╔═╡ 6a0ba0ea-6c59-41ae-b706-cca9ba4d7c32
Columns(
	md"""
### Layer-1 W
w1 = $(@bind w1 Slider(range(-2,2,5), default=0, show_value=true))

w2 = $(@bind w2 Slider(range(-2,2,5), default=0, show_value=true))

w3 = $(@bind w3 Slider(range(-2,2,5), default=0, show_value=true))

w4 = $(@bind w4 Slider(range(-2,2,5), default=0, show_value=true))
	""",
	md"""
### Layer-1 b
b1 = $(@bind b1 Slider(range(-2,2,5), default=0, show_value=true))

b2 = $(@bind b2 Slider(range(-2,2,5), default=0, show_value=true))

b3 = $(@bind b3 Slider(range(-2,2,5), default=0, show_value=true))

b4 = $(@bind b4 Slider(range(-2,2,5), default=0, show_value=true))
	""",
	md"""
### Layer-2
	
w5 = $(@bind w5 Slider(range(-2,2,5), default=0, show_value=true))

w6 = $(@bind w6 Slider(range(-2,2,5), default=0, show_value=true))

w7 = $(@bind w7 Slider(range(-2,2,5), default=0, show_value=true))

w8 = $(@bind w8 Slider(range(-2,2,5), default=0, show_value=true))
	"""
	)

# ╔═╡ 743253bf-f559-499f-962d-bcda204f287b
model = Chain(
	Dense(reshape([w1,w2,w3,w4], 1,4) |> transpose, [b1, b2, b3, b4], relu),
	Dense(reshape([w5,w6,w7,w8], 4,1) |> transpose, [0.0], identity),
	)

# ╔═╡ edaeea1e-fc79-4ed6-b29b-06184decba2b
plot(x->model([x])[1], -3,3, aspect_ratio=1, lw=5, lc=3, ylim=(-2,3))

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoTeachingTools = "661c6b06-c737-4d37-b85c-46df65de6f69"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

[compat]
Flux = "~0.16.4"
Plots = "~1.40.17"
PlutoTeachingTools = "~0.3.1"
PlutoUI = "~0.7.68"
"""

# ╔═╡ 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 = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c3b0e6196d50eab0c5ed34021aaa0bb463489510"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.14+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6a34e0e0960190ac2a4363a1bd003504772d631"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.61.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "4bba74fa59ab0755167ad24f98800fe5d727175b"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.12.1+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "125eedcb0a4a0bba65b657251ce1d27c8714e9d6"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.17.4+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.13.4+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "91d05d7f4a9f67205bd6cf395e488009fe85b499"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.28.1+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "07b6a107d926093898e82b3b1db657ebe33134ec"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.50+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "4.1.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "fbf139bce07a534df0e699dbb5f5cc9346f95cc1"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.9.2+0"
"""

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