mirror of
https://github.com/3b1b/manim.git
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NN Part 1 published
This commit is contained in:
Grant Sanderson
386
nn/part1.py
386
nn/part1.py
@ -632,6 +632,8 @@ class LayOutPlan(TeacherStudentsScene, NetworkScene):
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self.remove(self.network_mob)
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def construct(self):
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self.force_skipping()
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self.show_words()
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self.show_network()
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self.show_math()
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@ -757,6 +759,8 @@ class LayOutPlan(TeacherStudentsScene, NetworkScene):
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def show_videos(self):
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network_mob = self.network_mob
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learning = self.learning_word
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structure = TextMobject("Structure")
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structure.highlight(YELLOW)
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videos = VGroup(*[
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VideoIcon().set_fill(RED)
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for x in range(2)
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@ -770,13 +774,17 @@ class LayOutPlan(TeacherStudentsScene, NetworkScene):
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network_mob.target.move_to(videos[0])
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learning.generate_target()
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learning.target.next_to(videos[1], UP)
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structure.next_to(videos[0], UP)
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structure.shift(0.5*SMALL_BUFF*UP)
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self.revert_to_original_skipping_status()
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self.play(
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MoveToTarget(network_mob),
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MoveToTarget(learning)
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)
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self.play(
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DrawBorderThenFill(videos[0]),
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FadeIn(structure),
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self.get_student_changes(*["pondering"]*3)
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)
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self.dither()
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@ -1192,13 +1200,29 @@ class IntroduceEachLayer(PreviewMNistNetwork):
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network_mob = self.network_mob
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neurons = self.neurons
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layer = network_mob.layers[0]
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layer.save_state()
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layer.rotate(np.pi/2)
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layer.center()
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layer.brace_label.rotate_in_place(-np.pi/2)
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n = network_mob.max_shown_neurons/2
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rows = VGroup(*[
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VGroup(*neurons[28*i:28*(i+1)])
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for i in range(28)
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])
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self.play(
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FadeOut(self.braces),
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FadeOut(self.brace_labels),
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FadeOut(VGroup(*self.num_pixels_equation[:-1]))
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)
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self.play(rows.space_out_submobjects, 1.2)
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self.play(
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rows.arrange_submobjects, RIGHT, buff = SMALL_BUFF,
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path_arc = np.pi/2,
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run_time = 2
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)
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self.play(
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ReplacementTransform(
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VGroup(*neurons[:n]),
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@ -1212,15 +1236,15 @@ class IntroduceEachLayer(PreviewMNistNetwork):
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VGroup(*neurons[-n:]),
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VGroup(*layer.neurons[-n:]),
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),
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FadeIn(self.corner_image)
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)
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self.play(
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ReplacementTransform(
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self.num_pixels_equation[-1],
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layer.brace_label
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),
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FadeIn(layer.brace)
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FadeIn(layer.brace),
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)
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self.play(layer.restore, FadeIn(self.corner_image))
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self.dither()
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for edge_group, layer in zip(network_mob.edge_groups, network_mob.layers[1:]):
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self.play(
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@ -1320,6 +1344,69 @@ class IntroduceEachLayer(PreviewMNistNetwork):
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self.remove_random_edges(0.7)
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self.feed_forward(self.image_vect)
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class DiscussChoiceForHiddenLayers(TeacherStudentsScene):
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def construct(self):
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network_mob = MNistNetworkMobject(
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layer_to_layer_buff = 2.5,
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neuron_stroke_color = WHITE,
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)
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network_mob.scale_to_fit_height(4)
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network_mob.to_edge(UP, buff = LARGE_BUFF)
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layers = VGroup(*network_mob.layers[1:3])
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rects = VGroup(*map(SurroundingRectangle, layers))
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self.add(network_mob)
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two_words = TextMobject("2 hidden layers")
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two_words.highlight(YELLOW)
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sixteen_words = TextMobject("16 neurons each")
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sixteen_words.highlight(MAROON_B)
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for words in two_words, sixteen_words:
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words.next_to(rects, UP)
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neurons_anim = LaggedStart(
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Indicate,
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VGroup(*it.chain(*[layer.neurons for layer in layers])),
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rate_func = there_and_back,
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scale_factor = 2,
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color = MAROON_B,
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)
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self.play(
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ShowCreation(rects),
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Write(two_words, run_time = 1),
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self.teacher.change, "raise_right_hand",
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)
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self.dither()
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self.play(
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FadeOut(rects),
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ReplacementTransform(two_words, sixteen_words),
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neurons_anim
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)
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self.dither()
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self.play(self.teacher.change, "shruggie")
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self.change_student_modes("erm", "confused", "sassy")
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self.dither()
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self.student_says(
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"Why 2 \\\\ layers?",
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student_index = 1,
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bubble_kwargs = {"direction" : RIGHT},
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run_time = 1,
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target_mode = "raise_left_hand",
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)
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self.play(self.teacher.change, "happy")
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self.dither()
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self.student_says(
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"Why 16?",
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student_index = 0,
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run_time = 1,
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)
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self.play(neurons_anim, run_time = 3)
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self.play(
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self.teacher.change, "shruggie",
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RemovePiCreatureBubble(self.students[0]),
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)
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self.dither()
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class MoreHonestMNistNetworkPreview(IntroduceEachLayer):
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CONFIG = {
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"network_mob_config" : {
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@ -1597,7 +1684,7 @@ class BreakUpMacroPatterns(IntroduceEachLayer):
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def show_upper_loop_activation(self):
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neuron = self.network_mob.layers[-2].neurons[0]
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words = TextMobject("Upper loop neuron...mabye...")
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words = TextMobject("Upper loop neuron...maybe...")
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words.scale(0.8)
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words.next_to(neuron, UP)
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words.shift(RIGHT)
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@ -1619,11 +1706,11 @@ class BreakUpMacroPatterns(IntroduceEachLayer):
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]
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self.play(FadeIn(nine))
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self.add_foreground_mobject(self.patterns)
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self.play(
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ShowCreation(rect),
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Write(words)
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)
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self.add_foreground_mobject(self.patterns)
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self.feed_forward(np.random.random(784))
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self.dither(2)
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@ -2204,7 +2291,7 @@ class IntroduceWeights(IntroduceEachLayer):
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pixels.next_to(neuron, RIGHT, LARGE_BUFF)
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rect = SurroundingRectangle(pixels, color = BLUE)
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pixels_to_detect = self.get_pixels_to_detect()
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pixels_to_detect = self.get_pixels_to_detect(pixels)
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self.play(
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FadeIn(rect),
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@ -2249,7 +2336,8 @@ class IntroduceWeights(IntroduceEachLayer):
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p_labels[-1].shift(SMALL_BUFF*RIGHT)
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def get_alpha_func(i, start = 0):
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m = int(5*np.sin(2*np.pi*i/128.))
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# m = int(5*np.sin(2*np.pi*i/128.))
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m = random.randint(1, 10)
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return lambda a : start + (1-2*start)*np.sin(np.pi*a*m)**2
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decimals = VGroup()
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@ -2660,12 +2748,16 @@ class IntroduceSigmoid(GraphScene):
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name = TextMobject("Sigmoid")
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name.next_to(ORIGIN, RIGHT, LARGE_BUFF)
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name.to_edge(UP)
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char = self.x_axis_label.replace("$", "")
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equation = TexMobject(
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"\\sigma(x) = \\frac{1}{1+e^{-x}}"
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"\\sigma(%s) = \\frac{1}{1+e^{-%s}}"%(char, char)
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)
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equation.next_to(name, DOWN)
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self.add(equation, name)
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self.equation = equation
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self.sigmoid_name = name
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def add_graph(self):
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graph = self.get_graph(
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lambda x : 1./(1+np.exp(-x)),
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@ -2675,6 +2767,8 @@ class IntroduceSigmoid(GraphScene):
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self.play(ShowCreation(graph))
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self.dither()
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self.sigmoid_graph = graph
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###
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def show_part(self, x_min, x_max, color):
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@ -3494,9 +3588,9 @@ class IntroduceWeightMatrix(NetworkScene):
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"w_{%s, 0}"%i,
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"w_{%s, 1}"%i,
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"\\cdots",
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"w_{%s, k}"%i,
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"w_{%s, n}"%i,
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]))
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for i in "1", "n"
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for i in "1", "k"
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]
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dots_row = VGroup(*map(TexMobject, [
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"\\vdots", "\\vdots", "\\ddots", "\\vdots"
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@ -3591,12 +3685,65 @@ class IntroduceWeightMatrix(NetworkScene):
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FadeIn, VGroup(*result_terms[1:])
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))
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self.dither(2)
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self.show_meaning_of_lower_rows(
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arrow, brace, top_row_rect, result_terms
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)
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self.play(*map(FadeOut, [
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result_terms, result_brackets, equals,
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arrow, brace,
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top_row_rect, column_rect
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result_terms, result_brackets, equals, column_rect
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]))
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def show_meaning_of_lower_rows(self, arrow, brace, row_rect, result_terms):
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n1, n2, nk = neurons = VGroup(*[
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self.network_mob.layers[1].neurons[i]
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for i in 0, 1, -1
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])
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for n in neurons:
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n.save_state()
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n.edges_in.save_state()
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rect2 = SurroundingRectangle(result_terms[1])
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rectk = SurroundingRectangle(result_terms[-1])
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VGroup(rect2, rectk).highlight(WHITE)
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row2 = self.lower_matrix_rows[0]
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rowk = self.lower_matrix_rows[-1]
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def show_edges(neuron):
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self.play(LaggedStart(
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ShowCreationThenDestruction,
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neuron.edges_in.copy().set_stroke(GREEN, 5),
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lag_ratio = 0.7,
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run_time = 1,
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))
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self.play(
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row_rect.move_to, row2,
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n1.fade,
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n1.set_fill, None, 0,
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n1.edges_in.set_stroke, None, 1,
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n2.set_stroke, WHITE, 3,
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n2.edges_in.set_stroke, None, 3,
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ReplacementTransform(arrow, rect2),
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FadeOut(brace),
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)
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show_edges(n2)
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self.play(
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row_rect.move_to, rowk,
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n2.restore,
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n2.edges_in.restore,
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nk.set_stroke, WHITE, 3,
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nk.edges_in.set_stroke, None, 3,
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ReplacementTransform(rect2, rectk),
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)
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show_edges(nk)
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self.play(
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n1.restore,
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n1.edges_in.restore,
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nk.restore,
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nk.edges_in.restore,
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FadeOut(rectk),
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FadeOut(row_rect),
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)
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def add_bias_vector(self):
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bias = self.bias
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bias_name = self.bias_name
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@ -4054,7 +4201,7 @@ class NextVideo(MoreHonestMNistNetworkPreview, PiCreatureScene):
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content = self.content
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video = VideoIcon()
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video.scale_to_fit_height(2)
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video.scale_to_fit_height(3)
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video.set_fill(RED, 0.8)
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video.next_to(morty, UP+LEFT)
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@ -4098,12 +4245,12 @@ class NextVideo(MoreHonestMNistNetworkPreview, PiCreatureScene):
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)
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bang = subscribe_word[1]
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subscribe_word.to_corner(DOWN+RIGHT)
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subscribe_word.shift(2*UP)
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subscribe_word.shift(3*UP)
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q_mark = TextMobject("?")
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q_mark.move_to(bang, LEFT)
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arrow = Arrow(ORIGIN, DOWN, color = RED, buff = 0)
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arrow.next_to(subscribe_word, DOWN)
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arrow.shift(RIGHT)
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arrow.shift(MED_LARGE_BUFF * RIGHT)
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self.play(
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Write(subscribe_word),
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@ -4120,7 +4267,7 @@ class NextVideo(MoreHonestMNistNetworkPreview, PiCreatureScene):
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morty = self.pi_creature
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network_mob, rect, video, words = self.video
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network_mob.generate_target()
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network_mob.generate_target(use_deepcopy = True)
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network_mob.target.scale_to_fit_height(5)
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network_mob.target.to_corner(UP+LEFT)
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neurons = VGroup(*network_mob.target.layers[-1].neurons[:2])
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@ -4216,6 +4363,209 @@ class NNPatreonThanks(PatreonThanks):
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]
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}
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class PiCreatureGesture(PiCreatureScene):
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def construct(self):
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self.play(self.pi_creature.change, "raise_right_hand")
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self.dither(5)
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self.play(self.pi_creature.change, "happy")
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self.dither(4)
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class IntroduceReLU(IntroduceSigmoid):
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CONFIG = {
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"x_axis_label" : "$a$"
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}
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def construct(self):
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self.setup_axes()
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self.add_title()
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self.add_graph()
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self.old_school()
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self.show_ReLU()
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self.label_input_regions()
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def old_school(self):
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sigmoid_graph = self.sigmoid_graph
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sigmoid_title = VGroup(
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self.sigmoid_name,
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self.equation
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)
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cross = Cross(sigmoid_title)
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old_school = TextMobject("Old school")
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old_school.to_corner(UP+RIGHT)
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old_school.highlight(RED)
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arrow = Arrow(
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old_school.get_bottom(),
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self.equation.get_right(),
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color = RED
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)
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self.play(ShowCreation(cross))
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self.play(
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Write(old_school, run_time = 1),
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GrowArrow(arrow)
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||||
)
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||||
self.dither(2)
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||||
self.play(
|
||||
ApplyMethod(
|
||||
VGroup(cross, sigmoid_title).shift,
|
||||
SPACE_WIDTH*RIGHT,
|
||||
rate_func = running_start
|
||||
),
|
||||
FadeOut(old_school),
|
||||
FadeOut(arrow),
|
||||
)
|
||||
self.play(ShowCreation(
|
||||
self.sigmoid_graph,
|
||||
rate_func = lambda t : smooth(1-t),
|
||||
remover = True
|
||||
))
|
||||
|
||||
def show_ReLU(self):
|
||||
graph = VGroup(
|
||||
Line(
|
||||
self.coords_to_point(-7, 0),
|
||||
self.coords_to_point(0, 0),
|
||||
),
|
||||
Line(
|
||||
self.coords_to_point(0, 0),
|
||||
self.coords_to_point(4, 4),
|
||||
),
|
||||
)
|
||||
graph.highlight(YELLOW)
|
||||
char = self.x_axis_label.replace("$", "")
|
||||
equation = TextMobject("ReLU($%s$) = max$(0, %s)$"%(char, char))
|
||||
equation.shift(SPACE_WIDTH*LEFT/2)
|
||||
equation.to_edge(UP)
|
||||
equation.add_background_rectangle()
|
||||
name = TextMobject("Rectified linear unit")
|
||||
name.move_to(equation)
|
||||
name.add_background_rectangle()
|
||||
|
||||
self.play(Write(equation))
|
||||
self.play(ShowCreation(graph), Animation(equation))
|
||||
self.dither(2)
|
||||
self.play(
|
||||
Write(name),
|
||||
equation.shift, DOWN
|
||||
)
|
||||
self.dither(2)
|
||||
|
||||
self.ReLU_graph = graph
|
||||
|
||||
def label_input_regions(self):
|
||||
l1, l2 = self.ReLU_graph
|
||||
neg_words = TextMobject("Inactive")
|
||||
neg_words.highlight(RED)
|
||||
neg_words.next_to(self.coords_to_point(-2, 0), UP)
|
||||
|
||||
pos_words = TextMobject("Same as $f(a) = a$")
|
||||
pos_words.highlight(GREEN)
|
||||
pos_words.next_to(
|
||||
self.coords_to_point(1, 1),
|
||||
DOWN+RIGHT
|
||||
)
|
||||
|
||||
self.revert_to_original_skipping_status()
|
||||
self.play(ShowCreation(l1.copy().highlight(RED)))
|
||||
self.play(Write(neg_words))
|
||||
self.dither()
|
||||
self.play(ShowCreation(l2.copy().highlight(GREEN)))
|
||||
self.play(Write(pos_words))
|
||||
self.dither(2)
|
||||
|
||||
class CompareSigmoidReLUOnDeepNetworks(PiCreatureScene):
|
||||
def construct(self):
|
||||
morty, lisha = self.morty, self.lisha
|
||||
sigmoid_graph = FunctionGraph(
|
||||
sigmoid,
|
||||
x_min = -5,
|
||||
x_max = 5,
|
||||
)
|
||||
sigmoid_graph.stretch_to_fit_width(3)
|
||||
sigmoid_graph.highlight(YELLOW)
|
||||
sigmoid_graph.next_to(lisha, UP+LEFT)
|
||||
sigmoid_graph.shift_onto_screen()
|
||||
sigmoid_name = TextMobject("Sigmoid")
|
||||
sigmoid_name.next_to(sigmoid_graph, UP)
|
||||
sigmoid_graph.add(sigmoid_name)
|
||||
|
||||
slow_learner = TextMobject("Slow learner")
|
||||
slow_learner.highlight(YELLOW)
|
||||
slow_learner.to_corner(UP+LEFT)
|
||||
slow_arrow = Arrow(
|
||||
slow_learner.get_bottom(),
|
||||
sigmoid_graph.get_top(),
|
||||
)
|
||||
|
||||
relu_graph = VGroup(
|
||||
Line(2*LEFT, ORIGIN),
|
||||
Line(ORIGIN, np.sqrt(2)*(RIGHT+UP)),
|
||||
)
|
||||
relu_graph.highlight(BLUE)
|
||||
relu_graph.next_to(lisha, UP+RIGHT)
|
||||
relu_name = TextMobject("ReLU")
|
||||
relu_name.move_to(relu_graph, UP)
|
||||
relu_graph.add(relu_name)
|
||||
|
||||
network_mob = NetworkMobject(Network(
|
||||
sizes = [6, 4, 5, 4, 3, 5, 2]
|
||||
))
|
||||
network_mob.scale(0.8)
|
||||
network_mob.to_edge(UP, buff = MED_SMALL_BUFF)
|
||||
network_mob.shift(RIGHT)
|
||||
edge_update = ContinualEdgeUpdate(
|
||||
network_mob, stroke_width_exp = 1,
|
||||
)
|
||||
|
||||
self.play(
|
||||
FadeIn(sigmoid_name),
|
||||
ShowCreation(sigmoid_graph),
|
||||
lisha.change, "raise_left_hand",
|
||||
morty.change, "pondering"
|
||||
)
|
||||
self.play(
|
||||
Write(slow_learner, run_time = 1),
|
||||
GrowArrow(slow_arrow)
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
FadeIn(relu_name),
|
||||
ShowCreation(relu_graph),
|
||||
lisha.change, "raise_right_hand",
|
||||
morty.change, "thinking"
|
||||
)
|
||||
self.play(FadeIn(network_mob))
|
||||
self.add(edge_update)
|
||||
self.dither(10)
|
||||
|
||||
|
||||
|
||||
###
|
||||
def create_pi_creatures(self):
|
||||
morty = Mortimer()
|
||||
morty.shift(SPACE_WIDTH*RIGHT/2).to_edge(DOWN)
|
||||
lisha = PiCreature(color = BLUE_C)
|
||||
lisha.shift(SPACE_WIDTH*LEFT/2).to_edge(DOWN)
|
||||
self.morty, self.lisha = morty, lisha
|
||||
return morty, lisha
|
||||
|
||||
class ShowAmplify(PiCreatureScene):
|
||||
def construct(self):
|
||||
morty = self.pi_creature
|
||||
rect = ScreenRectangle(height = 5)
|
||||
rect.to_corner(UP+LEFT)
|
||||
rect.shift(DOWN)
|
||||
email = TextMobject("3blue1brown@amplifypartners.com")
|
||||
email.next_to(rect, UP)
|
||||
|
||||
self.play(
|
||||
ShowCreation(rect),
|
||||
morty.change, "raise_right_hand"
|
||||
)
|
||||
self.dither(2)
|
||||
self.play(Write(email))
|
||||
self.play(morty.change, "happy", rect)
|
||||
self.dither(10)
|
||||
|
||||
class Thumbnail(NetworkScene):
|
||||
CONFIG = {
|
||||
"network_mob_config" : {
|
||||
@ -4225,11 +4575,13 @@ class Thumbnail(NetworkScene):
|
||||
def construct(self):
|
||||
network_mob = self.network_mob
|
||||
network_mob.scale_to_fit_height(2*SPACE_HEIGHT - 1)
|
||||
for layer in network_mob.layers:
|
||||
layer.neurons.set_stroke(width = 5)
|
||||
|
||||
edge_update = ContinualEdgeUpdate(
|
||||
network_mob,
|
||||
max_stroke_width = 10,
|
||||
stroke_width_exp = 5,
|
||||
stroke_width_exp = 4,
|
||||
)
|
||||
edge_update.internal_time = 3
|
||||
edge_update.update(0)
|
||||
|
||||
Reference in New Issue
Block a user