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calesthioandHanzo Dev
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11 production pipelines, 47 tools, 124 agent skills. Supports cloud APIs (fal.ai, OpenAI, ElevenLabs, Suno, HeyGen, Runway) and free local providers (diffusers, Piper TTS, WAN 2.1, Hunyuan, CogVideo). Co-authored-by: Hanzo Dev <[email protected]>
129 lines
3.9 KiB
Python
129 lines
3.9 KiB
Python
"""
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Negative Log Loss (Cross-Entropy) cost function visualization.
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Demonstrates: Graph plotting, labeled axes, mathematical expressions
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"""
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from manimlib import *
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import numpy as np
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class CostFunction(Scene):
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def construct(self):
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# Create axes
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axes = Axes(
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(0, 1, 0.1),
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(0, 5, 1),
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width=10,
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height=6
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)
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axes.center().to_edge(LEFT)
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axes.x_axis.add_numbers(num_decimal_places=1)
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axes.y_axis.add_numbers(num_decimal_places=0, direction=LEFT)
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# Add axis label
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x_label = Tex("p")
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x_label.next_to(axes.x_axis.get_right(), UR)
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axes.add(x_label)
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y_label = Text("Cost", font_size=36)
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y_label.next_to(axes.y_axis.get_top(), RIGHT)
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axes.add(y_label)
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# Create the -log(p) graph
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graph = axes.get_graph(
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lambda x: -np.log(x) if x > 0.001 else 5,
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x_range=(0.001, 1, 0.01)
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)
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graph.set_color(RED)
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# Expression
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expr = Tex(R"\text{Cost} = -\log(p)", font_size=60)
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expr.to_edge(UP)
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# Animate
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self.play(FadeIn(axes))
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self.wait(0.5)
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self.play(
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ShowCreation(graph, run_time=3),
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Write(expr, run_time=2),
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)
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self.wait()
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# Explanation labels
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low_p_label = Text("Low probability\n= High cost", font_size=30, color=RED)
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low_p_label.next_to(axes.i2gp(0.1, graph), RIGHT, buff=0.5)
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high_p_label = Text("High probability\n= Low cost", font_size=30, color=GREEN)
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high_p_label.next_to(axes.i2gp(0.8, graph), UP, buff=0.5)
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self.play(FadeIn(low_p_label, shift=LEFT))
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self.wait()
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self.play(FadeIn(high_p_label, shift=DOWN))
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self.wait()
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# Show a moving dot on the curve
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p_tracker = ValueTracker(0.5)
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dot = Dot(color=YELLOW)
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dot.f_always.move_to(lambda: axes.i2gp(p_tracker.get_value(), graph))
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# Vertical line from x-axis to point
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v_line = always_redraw(lambda: axes.get_line_from_axis_to_point(
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0, axes.i2gp(p_tracker.get_value(), graph),
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line_func=DashedLine
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).set_stroke(YELLOW, 2))
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# Horizontal line from y-axis to point
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h_line = always_redraw(lambda: axes.get_line_from_axis_to_point(
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1, axes.i2gp(p_tracker.get_value(), graph),
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line_func=DashedLine
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).set_stroke(YELLOW, 2))
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# Value labels
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p_label = VGroup(
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Text("p = ", font_size=36),
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DecimalNumber(p_tracker.get_value(), num_decimal_places=2, font_size=36)
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)
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p_label.arrange(RIGHT)
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p_label.to_corner(UR)
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p_label[1].f_always.set_value(p_tracker.get_value)
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cost_label = VGroup(
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Text("Cost = ", font_size=36),
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DecimalNumber(-np.log(0.5), num_decimal_places=2, font_size=36)
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)
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cost_label.arrange(RIGHT)
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cost_label.next_to(p_label, DOWN, aligned_edge=LEFT)
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cost_label[1].f_always.set_value(lambda: -np.log(max(p_tracker.get_value(), 0.001)))
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self.play(
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FadeOut(low_p_label),
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FadeOut(high_p_label),
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FadeIn(dot),
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FadeIn(v_line),
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FadeIn(h_line),
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FadeIn(p_label),
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FadeIn(cost_label),
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)
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self.wait()
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# Animate the dot moving
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self.play(p_tracker.animate.set_value(0.1), run_time=2)
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self.wait()
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self.play(p_tracker.animate.set_value(0.9), run_time=3)
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self.wait()
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self.play(p_tracker.animate.set_value(0.05), run_time=2)
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self.wait()
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self.play(p_tracker.animate.set_value(0.5), run_time=2)
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self.wait()
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# Final message
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message = Text(
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"Goal: Maximize probability of correct answer",
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font_size=36,
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color=BLUE
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)
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message.to_edge(DOWN)
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self.play(FadeIn(message, shift=UP))
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self.wait(2)
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