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Commit 2a01272a authored by Nando Farchmin's avatar Nando Farchmin
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Add script to draw images

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import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
from scipy.stats import multivariate_normal
import neural_networks_101.src as src
def relu(x, slope=0):
ret = np.zeros(x.size)
idx = np.where(x >= 0)[0]
ret[idx] = x[idx]
idx = np.where(x < 0)[0]
ret[idx] = slope * x[idx]
return ret
def softmax(z):
return np.exp(z) / np.sum(np.exp(z))
def argmax(z):
ret = np.zeros(z.size)
idx = np.argmax(z)
ret[idx] = z[idx]
return ret
def maxpool(z):
ret = np.zeros((2, 2))
ret[0, 0] = np.max(z[:2, :2])
ret[0, 1] = np.max(z[:2, 2:])
ret[1, 0] = np.max(z[2:, :2])
ret[1, 1] = np.max(z[2:, 2:])
return ret
def spline_interp(x, y, res):
tck = interpolate.splrep(x, y, s=0, k=3)
x_new = np.linspace(np.min(x), np.max(x), res)
y_fit = interpolate.BSpline(*tck)(x_new)
return x_new, y_fit
def plot_relu(file_name):
x = np.linspace(-2, 2, 200)
with plt.xkcd():
fig = plt.figure()
plt.axvline(x=0, ls="--", color="k")
plt.plot(x, np.zeros(x.size), ls="--", color="k")
plt.plot(x, relu(x))
plt.savefig(file_name, dpi=200)
def plot_leaky_relu(file_name):
x = np.linspace(-2, 2, 200)
with plt.xkcd():
fig = plt.figure()
plt.axvline(x=0, ls="--", color="k")
plt.plot(x, np.zeros(x.size), ls="--", color="k")
plt.plot(x, relu(x, 0.1))
plt.savefig(file_name, dpi=200)
def plot_tanh(file_name):
x = np.linspace(-3, 3, 200)
with plt.xkcd():
fig = plt.figure()
plt.axvline(x=0, ls="--", color="k")
plt.plot(x, np.zeros(x.size), ls="--", color="k")
plt.plot(x, np.tanh(x))
plt.savefig(file_name, dpi=200)
def plot_softmax(file_name):
z = np.array([0.229, 0.070, 1.163, 1.826, 1.184,
1.311, 0.189, 0.200, 1.881, 0.738])
val = softmax(z)
with plt.xkcd():
fig = plt.figure()
plt.bar(range(1, z.size+1), val)
x, y = spline_interp(np.arange(1, z.size+1), val, 200)
plt.plot(x, y, c="k")
plt.savefig(file_name, dpi=200)
def plot_argmax(file_name):
z = np.array([0.229, 0.070, 1.163, 1.826, 1.184,
1.311, 0.189, 0.200, 1.881, 0.738])
with plt.xkcd():
fig = plt.figure()
plt.bar(range(1, z.size+1), z)
plt.bar(range(1, z.size+1), argmax(z), color="grey")
plt.savefig(file_name, dpi=200)
def plot_maxpool(file_name):
row1 = np.concatenate(
[np.random.uniform(0, 1, (2, 2)), np.random.uniform(1, 2, (2, 2))],
axis=1)
row2 = np.concatenate(
[np.random.uniform(2, 3, (2, 2)), np.random.uniform(3, 4, (2, 2))],
axis=1)
mat = np.concatenate([row1, row2], axis=0)
with plt.xkcd():
fig, ax = plt.subplot_mosaic([["big", "arrow", "small"]])
ax["big"].matshow(mat, cmap="Blues")
ax["arrow"].arrow(0.5, 1, 0.8, 0, head_width=0.2, width=0.05)
ax["arrow"].set_xlim(0, 2)
ax["arrow"].set_ylim(0, 2)
ax["arrow"].axis("off")
ax["small"].matshow(maxpool(mat), cmap="Blues")
plt.savefig(file_name, dpi=200)
def plot_venn(file_name):
with plt.xkcd():
fig, ax = plt.subplots()
ai = plt.Circle((0.5, 0.5), 0.45, color="k", fill=False)
ml = plt.Circle((0.6, 0.42), 0.3, color="k", fill=False)
nn = plt.Circle((0.5, 0.4), 0.15, color="k", fill=False)
ai_fill = plt.Circle((0.5, 0.5), 0.45, alpha=0.15)
ml_fill = plt.Circle((0.6, 0.42), 0.3, alpha=0.15)
nn_fill = plt.Circle((0.5, 0.4), 0.15, alpha=0.15)
ax.add_patch(ai_fill)
ax.add_patch(ml_fill)
ax.add_patch(nn_fill)
ax.add_patch(ai)
ax.add_patch(ml)
ax.add_patch(nn)
ax.text(0.2, 0.6, "AI", fontsize="xx-large")
ax.text(0.7, 0.5, "ML", fontsize="xx-large")
ax.text(0.4, 0.35, "NN", fontsize="xx-large")
ax.axis("off")
plt.savefig(file_name, dpi=200)
def landscape(xs):
mean1, cov1 = np.array([1, -1]), np.eye(2)
f1 = multivariate_normal(mean1, cov1)
ret = f1.pdf(xs)/f1.pdf(mean1)
mean2, cov2 = np.array([1, 1]), 0.2*np.array([[1, -.1], [.1, 1]])
f2 = multivariate_normal(mean2, cov2)
ret += f2.pdf(xs)/f2.pdf(mean2)
mean3, cov3 = np.array([-3.5, -1]), 2.0*np.array([[1, 0], [0, 5]])
f3 = multivariate_normal(mean3, cov3)
ret += f3.pdf(xs)/f3.pdf(mean3)
mean4, cov4 = np.array([0, 2]), 0.1*np.array([[1, 0], [0, 5]])
f4 = multivariate_normal(mean4, cov4)
ret += f4.pdf(xs)/f4.pdf(mean4)
mean5, cov5 = np.array([-1.5, 2]), 0.5*np.array([[3, -1], [1, 1]])
f5 = multivariate_normal(mean5, cov5)
ret += f5.pdf(xs)/f5.pdf(mean5)
return ret
def plot_sgd(file_name):
x = np.linspace(-3, 2, 50)
y = np.linspace(-1.5, 2.5, 50)
xs = src.misc.cart_prod([x, y])
fig, ax = plt.subplot_mosaic([["sgd"]])
ax["sgd"].contourf(x, x, landscape(xs).reshape(x.size, -1).T, cmap="Blues")
ax["sgd"].axis("off")
start_end = np.array([[-0.1, 1.7],
[-0.8, -1.4],
])
points1 = np.array([start_end[0],
[-0.6, 0.5],
start_end[-1],
])
points2 = np.array([start_end[0],
[-0.6, 1.6],
[-0.8, 1.7],
[-1.1, 1.4],
[-1.05, 1.2],
[-1.6, 0.7],
[-1.7, 0.4],
[-1.3, 0.0],
[-1.8, -0.3],
[-1.3, -0.8],
[-1.2, -1.4],
[-0.7, -2.4],
[-0.2, -1.6],
[-0.4, -1.0],
[-1.0, -1.2],
[-0.95, -1.5],
[-0.7, -1.6],
start_end[-1],
])
ax["sgd"].plot(points1[:, 0], points1[:, 1], "-o",
lw=4, color="k", ms=8)
ax["sgd"].plot(points1[:, 0], points1[:, 1], "-o",
lw=2, color="green")
ax["sgd"].plot(points2[:, 0], points2[:, 1], "-o",
lw=4, color="k", ms=8)
ax["sgd"].plot(points2[:, 0], points2[:, 1], "-o",
lw=2, color="orange")
ax["sgd"].plot(start_end[:, 0], start_end[:, 1], "o",
lw=4, color="k", ms=8)
ax["sgd"].plot(start_end[:, 0], start_end[:, 1], "o",
lw=2, color="w")
# color1, edgecolor1 = "orange", "k"
# ax["sgd"].arrow(x=-0.05, y=1.7, dx=-0.3, dy=-0.5, width=0.04,
# facecolor=color1, edgecolor=edgecolor1)
# ax["sgd"].arrow(x=-0.45, y=0.99, dx=-0.2, dy=-1.2, width=0.04,
# facecolor=color1, edgecolor=edgecolor1)
# color2, edgecolor2 = "green", "k"
# ax["sgd"].arrow(x=-0.05, y=1.7, dx=-0.4, dy=-0.08, width=0.04,
# facecolor=color2, edgecolor=edgecolor2)
# ax["sgd"].arrow(x=-0.05, y=1.7, dx=-0.4, dy=-0.08, width=0.04,
# facecolor=color2, edgecolor=edgecolor2)
plt.savefig(file_name, dpi=200)
def main():
"""Main."""
# plot_venn("./venn.png")
# plot_relu("./relu.png")
# plot_leaky_relu("./leaky_relu.png")
# plot_tanh("./tanh.png")
# plot_argmax("./argmax.png")
# plot_softmax("./softmax.png")
# plot_maxpool("./maxpool_tmp.png")
plot_sgd("./sgd.png")
if __name__ == "__main__":
main()
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