diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py | 177 |
1 files changed, 177 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py new file mode 100644 index 0000000..eb6bf45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py @@ -0,0 +1,177 @@ +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)
+
+
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