1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
|
from manimlib.imports import *
class SigmoidFunc(GraphScene):
CONFIG = {
"x_min": -4,
"x_max": 4,
"y_min": -1,
"y_max": 1,
"graph_origin": ORIGIN + 0.8*DOWN,
"x_labeled_nums": list(range(-4, 5)),
"y_labeled_nums": list(range(-1, 2)),
"y_axis_height": 4.5,
}
def construct(self):
XTD = self.x_axis_width/(self.x_max- self.x_min)
YTD = self.y_axis_height/(self.y_max- self.y_min)
topic = TextMobject("Sigmoid Function")
topic.move_to(3.2*UP)
topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
self.setup_axes(animate = True)
sigmoid_func = self.get_graph(lambda x : (1/(1 + np.exp(-x))), x_min = -4, x_max = 4)
sigmoid_lab = self.get_graph_label(sigmoid_func, label = r"\frac{1}{1 + e^{-z}}")
self.play(ShowCreation(sigmoid_func),Write(sigmoid_lab))
self.play(Write(topic))
self.wait(2)
self.play(FadeOut(sigmoid_func), FadeOut(sigmoid_lab))
self.wait(1)
class NeuralNet(GraphScene):
def construct(self):
sigmoid_exp = TextMobject(r"g(z) = g($\theta^T$ X) = $\frac{1}{1 + e^{-z}}$")
sigmoid_exp.move_to(3*UP + 4*LEFT)
sigmoid_exp.scale(0.8)
sigmoid_exp.set_color(BLUE)
sigmoid_exp1 = TextMobject(r"Predict: 'y = 1'",r"When g(z) $\geq$ 0.5, z $\geq$ 0, $\theta^T$ X $\geq$ 0")
sigmoid_exp2 = TextMobject(r"Predict: 'y = 0'", r"When g(z) $\leq$ 0.5, z $\leq$ 0, $\theta^T$ X $\leq$ 0")
sigmoid_exp1.scale(0.5)
sigmoid_exp2.scale(0.5)
sigmoid_exp1.set_color(PURPLE)
sigmoid_exp2.set_color(PURPLE)
sigmoid_exp1[0].next_to(sigmoid_exp, 1.5*DOWN)
sigmoid_exp1[1].next_to(sigmoid_exp1[0], DOWN)
sigmoid_exp2[0].next_to(sigmoid_exp1[1], 1.5*DOWN)
sigmoid_exp2[1].next_to(sigmoid_exp2[0], DOWN)
self.play(Write(sigmoid_exp))
self.play(Write(sigmoid_exp1[0]), Write(sigmoid_exp1[1]))
self.play(Write(sigmoid_exp2[0]), Write(sigmoid_exp2[1]))
self.wait(2)
neuron1 = Circle()
neuron1.set_fill(YELLOW_A, opacity = 0.5)
neuron2 = Circle()
neuron2.set_fill(ORANGE, opacity = 0.5)
neuron3 = Circle()
neuron3.set_fill(GREEN_E, opacity = 0.5)
neuron1.move_to(2*UP+RIGHT)
neuron2.move_to(2*DOWN+RIGHT)
neuron3.move_to(4*RIGHT)
arrow1 = Arrow(neuron1.get_right(),neuron3.get_left(),buff=0.1)
arrow1.set_color(RED)
arrow2 = Arrow(neuron2.get_right(),neuron3.get_left(),buff=0.1)
arrow2.set_color(RED)
arrow3 = Arrow(neuron3.get_right(),7*RIGHT,buff=0.1)
arrow3.set_color(RED)
sign1 = TextMobject("+1")
sign1.move_to(2*UP+RIGHT)
sign1.scale(2)
sign2 = TextMobject(r"$x_1$")
sign2.move_to(2*DOWN+RIGHT)
sign2.scale(2)
sign3 = TextMobject(r"$h_{\theta}(x)$")
sign3.move_to(6*RIGHT+0.4*DOWN)
sign3.scale(0.7)
sign4 = TextMobject(r"$= g(10 - 20x_1)$")
sign4.next_to(sign3,DOWN)
sign4.scale(0.5)
sign5 = TextMobject(r"$= g(10 - 20x_1)$")
sign5.next_to(sign3,DOWN)
sign5.scale(0.5)
sign6 = TextMobject(r"$= g(10 - 20x_1)$")
sign6.next_to(sign3,DOWN)
sign6.scale(0.5)
weight1 = TextMobject("10")
weight1.next_to(arrow1,UP)
weight2 = TextMobject("-20")
weight2.next_to(arrow2,DOWN)
gate = TextMobject("NOT GATE")
gate.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
gate.scale(1.5)
gate.move_to(3*RIGHT+3.5*UP)
truth_table = TextMobject(r"\begin{displaymath}\begin{array}{|c|c|} x & y\\ \hline 1 & 0 \\0 & 1 \\\end{array}\end{displaymath}")
truth_table.next_to(sigmoid_exp2[1], 3*DOWN)
values = TextMobject("1", "0")
values.scale(2)
sign4_trans1 = TextMobject(r"$= g(10 - 20(1))$")
sign4_trans2 = TextMobject(r"$= g(10 - 20(0))$")
sign4_trans1.next_to(sign3,DOWN)
sign4_trans2.next_to(sign3,DOWN)
sign4_trans1.scale(0.5)
sign4_trans2.scale(0.5)
output1 = TextMobject("y = 0")
output2 = TextMobject("y = 1")
output1.next_to(sign4,DOWN)
output2.next_to(sign4,DOWN)
output1.scale(1.5)
output2.scale(1.5)
self.play(ShowCreation(neuron1),ShowCreation(neuron2))
self.play(ShowCreation(neuron3))
self.play(ShowCreation(sign1),ShowCreation(sign2))
self.wait(1)
self.play(GrowArrow(arrow1))
self.play(GrowArrow(arrow2))
self.play(ShowCreation(weight1),ShowCreation(weight2))
self.play(GrowArrow(arrow3))
self.play(Write(sign3),Write(sign4))
self.play(Write(gate))
self.play(ShowCreation(truth_table))
self.play(ApplyMethod(values[0].move_to, 2*DOWN+RIGHT))
self.play(FadeOut(values[0]))
self.play(Transform(sign4,sign4_trans1))
self.play(Write(output1))
self.wait(1)
self.play(FadeOut(output1))
self.play(Transform(sign4, sign5))
self.play(ApplyMethod(values[1].move_to, 2*DOWN+RIGHT))
self.play(FadeOut(values[1]))
self.play(Transform(sign4,sign4_trans2))
self.play(Write(output2))
self.wait(1)
self.play(FadeOut(output2))
self.play(Transform(sign4, sign6))
self.wait(2)
|
