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1707037 | 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 | import numpy as np
import matplotlib.pyplot as plt
import gradio as gr
def plot_secant(h):
x = np.linspace(-1, 2, 400)
y = x**2
m = (h**2 - 0) / h
fig, axs = plt.subplots(1, 2, figsize=(8, 4))
for ax in axs:
ax.set_xlim(-1, 2); ax.set_ylim(-1, 4)
ax.set_xticks(np.arange(-1, 3, 1)); ax.set_yticks(np.arange(-1, 5, 1))
ax.grid(True, linestyle='--', linewidth=0.5, color='lightgray')
ax.spines['top'].set_visible(False); ax.spines['right'].set_visible(False)
axs[0].plot(x, y, color='black'); axs[0].plot([0, h], [0, h**2], color='red', linewidth=2)
axs[0].scatter([0, h], [0, h**2], color='red', zorder=5)
axs[1].plot(x, m * x, color='red', linewidth=2)
plt.tight_layout(); return fig
def plot_tangent(x0):
x = np.linspace(-1, 2, 400); y = x**2; m = 2 * x0; y0 = x0**2
fig, axs = plt.subplots(1, 2, figsize=(8, 4))
for ax in axs:
ax.set_xlim(-1, 2); ax.set_ylim(-1, 4)
ax.set_xticks(np.arange(-1, 3, 1)); ax.set_yticks(np.arange(-1, 5, 1))
ax.grid(True, linestyle='--', linewidth=0.5, color='lightgray')
ax.spines['top'].set_visible(False); ax.spines['right'].set_visible(False)
axs[0].plot(x, y, color='black'); axs[0].plot(x, m*(x-x0)+y0, color='red', linewidth=2)
axs[0].scatter([x0], [y0], color='red', zorder=5); axs[1].plot(x, 2*x, color='black')
axs[1].scatter([x0], [m], color='red', zorder=5)
plt.tight_layout(); return fig
def plot_gradient_descent(lr, init_x, steps):
n = int(steps); path=[init_x]
for _ in range(n): path.append(path[-1] - lr*2*path[-1])
xv = np.array(path)
fig, axs = plt.subplots(1, 2, figsize=(8, 4))
x_plot = np.linspace(-2, 2, 400); axs[0].plot(x_plot, x_plot**2, color='black')
axs[0].plot(xv, xv**2, marker='o', color='red', linewidth=2)
for i in range(n): axs[0].annotate('', xy=(xv[i+1], xv[i+1]**2), xytext=(xv[i], xv[i]**2), arrowprops=dict(arrowstyle='->', color='red'))
axs[0].set_xlim(-2, 2); axs[0].set_ylim(-0.5, 5); axs[0].set_title('Gradient Descent Path')
axs[0].grid(True, linestyle='--', linewidth=0.5, color='lightgray')
axs[1].plot(range(n+1), xv, marker='o', color='red', linewidth=2)
for i in range(n): axs[1].annotate('', xy=(i+1, xv[i+1]), xytext=(i, xv[i]), arrowprops=dict(arrowstyle='->', color='red'))
axs[1].set_xlim(0, n); axs[1].set_ylim(xv.min()-0.5, xv.max()+0.5)
axs[1].set_xticks(range(0, n+1, 5)); axs[1].set_xlabel('Iteration'); axs[1].set_title('x over Iterations')
axs[1].grid(True, linestyle='--', linewidth=0.5, color='lightgray')
plt.tight_layout(); return fig
def plot_chain_network(x):
y = 2 * x
z = 3 * y
L = 4 * z
fig, ax = plt.subplots(figsize=(6, 2)); ax.axis('off')
pos = {'x':0.1, 'y':0.3, 'z':0.5, 'L':0.7}
for name in pos:
ax.add_patch(plt.Circle((pos[name], 0.5), 0.05, fill=False))
ax.text(pos[name], 0.5, name, ha='center', va='center')
chain = [
('x','y',r'$\partial y/\partial x=2$'),
('y','z',r'$\partial z/\partial y=3$'),
('z','L',r'$\partial L/\partial z=4$')
]
for src, dst, lbl in chain:
sx, sy = pos[src], 0.5
dx, dy = pos[dst], 0.5
ax.annotate('', xy=(dx, dy), xytext=(sx, sy), arrowprops=dict(arrowstyle='->'))
ax.text((sx+dx)/2, 0.6, lbl, ha='center', va='center')
ax.text(0.02, 0.15,
r'$\frac{\partial L}{\partial x}=\frac{\partial L}{\partial z}\cdot\frac{\partial z}{\partial y}\cdot\frac{\partial y}{\partial x}$',
transform=ax.transAxes, ha='left')
ax.text(0.02, 0.02, r'$=4\times3\times2=24$', transform=ax.transAxes, ha='left')
ax.text(pos['x'], 0.3, f"x={x:.2f}", ha='center')
ax.text(pos['y'], 0.3, f"y={y:.2f}", ha='center')
ax.text(pos['z'], 0.3, f"z={z:.2f}", ha='center')
ax.text(pos['L'], 0.3, f"L={L:.2f}", ha='center')
plt.tight_layout(); return fig
def plot_backprop_dnn(x, w1, w2, t):
a = w1 * x
y = w2 * a
L = 0.5 * (y - t)**2
fig, ax = plt.subplots(figsize=(6, 2)); ax.axis('off')
pos = {'x':0.1,'a':0.3,'y':0.5,'L':0.7}
for name in pos:
ax.add_patch(plt.Circle((pos[name], 0.5), 0.05, fill=False))
ax.text(pos[name], 0.5, name, ha='center', va='center')
bp = [
('x','a',r'$\partial a/\partial x=w_1$'),
('a','y',r'$\partial y/\partial a=w_2$'),
('y','L',r'$\partial L/\partial y=(y-t)$')
]
for src, dst, lbl in bp:
sx, sy = pos[src], 0.5
dx, dy = pos[dst], 0.5
ax.annotate('', xy=(dx, dy), xytext=(sx, sy), arrowprops=dict(arrowstyle='->'))
ax.text((sx+dx)/2, 0.6, lbl, ha='center', va='center')
ax.text(0.02, 0.15, r'$\partial L/\partial w_2=(y-t)\cdot a$', transform=ax.transAxes, ha='left')
ax.text(0.02, 0.02, r'$\partial L/\partial w_1=(y-t)\cdot w_2\cdot x$', transform=ax.transAxes, ha='left')
ax.text(pos['x'], 0.3, f"x={x:.2f}", ha='center')
ax.text(pos['a'], 0.3, f"a={a:.2f}", ha='center')
ax.text(pos['y'], 0.3, f"y={y:.2f}", ha='center')
ax.text(pos['L'], 0.3, f"L={L:.2f}", ha='center')
plt.tight_layout(); return fig
with gr.Blocks() as demo:
with gr.Tabs():
with gr.TabItem('Secant Approximation'):
h = gr.Slider(1e-9, 2.0, value=0.01, step=0.001, label='h')
p1 = gr.Plot(); m1 = gr.Markdown()
h.change(lambda v: (plot_secant(v), f'**螖x=h={v:.4f}**, (f(x+h)-f(x))/h={(v**2)/v:.4f}'), h, [p1, m1])
p1.figure, m1.value = plot_secant(0.01), '**螖x=h=0.0100**, (f(x+h)-f(x))/h=0.0100'
with gr.TabItem('Tangent Visualization'):
x0 = gr.Slider(-1.0, 2.0, value=0.0, step=0.1, label='x')
p2 = gr.Plot(); m2 = gr.Markdown()
x0.change(lambda v: (plot_tangent(v), f'**x={v:.2f}**, dy/dx={2*v:.2f}'), x0, [p2, m2])
p2.figure, m2.value = plot_tangent(0.0), '**x=0.00**, dy/dx=0.00'
with gr.TabItem('Gradient Descent'):
lr = gr.Slider(0.01, 1.0, value=0.1, step=0.01, label='Learning Rate')
init = gr.Slider(-2.0, 2.0, value=1.0, step=0.1, label='Initial x')
st = gr.Slider(1, 50, value=10, step=1, label='Iterations')
pg = gr.Plot(); mg = gr.Markdown()
for inp in [lr, init, st]:
inp.change(lambda a, b, c: (plot_gradient_descent(a, b, c), f'lr={a:.2f}, init={b:.2f}, steps={c}'), [lr, init, st], [pg, mg])
pg.figure, mg.value = plot_gradient_descent(0.1, 1.0, 10), 'lr=0.10, init=1.00, steps=10'
with gr.TabItem('Chain Rule'):
x_slider = gr.Slider(0.0, 2.0, value=1.0, step=0.1, label='x')
chain_plot = gr.Plot()
chain_note = gr.Markdown()
def update_chain(x):
y = 2 * x
z = 3 * y
L = 4 * z
fig = plot_chain_network(x)
note = (
f"**Current values:** \n"
f"- y = 2路{x:.2f} = {y:.2f} \n"
f"- z = 3路{y:.2f} = {z:.2f} \n"
f"- L = 4路{z:.2f} = {L:.2f} \n\n"
"**Chain Rule:** dL/dx = 4 脳 3 脳 2 = 24"
)
return fig, note
x_slider.change(update_chain, x_slider, [chain_plot, chain_note])
chain_plot.figure, chain_note.value = update_chain(1.0)
with gr.TabItem('Backpropagation'):
xb = gr.Slider(-2.0, 2.0, value=0.5, step=0.1, label='x')
w1b = gr.Slider(-2.0, 2.0, value=1.0, step=0.1, label='w1')
w2b = gr.Slider(-2.0, 2.0, value=1.0, step=0.1, label='w2')
tb = gr.Slider(-2.0, 2.0, value=0.0, step=0.1, label='t')
pb = gr.Plot(); mb = gr.Markdown()
for inp in [xb, w1b, w2b, tb]:
inp.change(lambda a, b, c, d: (plot_backprop_dnn(a, b, c, d), ''), [xb, w1b, w2b, tb], [pb, mb])
pb.figure, mb.value = plot_backprop_dnn(0.5, 1.0, 1.0, 0.0), ''
demo.launch()
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