PyTorch does not seem to be optimizing correctly
$begingroup$
I am trying to minimize the following function:
$$f(theta_1, dots, theta_n) = frac{1}{s}sum_{j =1}^sleft(sum_{i=1}^n sin(t_j + theta_i)right)^2$$
with respect to $(theta_1, dots, theta_n)$. Here ${t_j}$ are regularly spaced points in the interval $[0, 2pi)$.
So here is the Python (PyTorch) code for that. The optimization does not seem to be computed correctly (the gradients seem to only advance along the line $theta_1 = cdots = theta_n$, which of of course incorrect).
import numpy as np
import torch
def phaseOptimize(n, s = 48000, nsteps = 1000):
learning_rate = 1e-3
theta = torch.zeros([n, 1], requires_grad=True)
l = torch.linspace(0, 2 * np.pi, s)
t = torch.stack([l] * n)
T = t + theta
for jj in range(nsteps):
loss = T.sin().sum(0).pow(2).sum() / s
loss.backward()
theta.data -= learning_rate * theta.grad.data
print('Optimal theta: nn', theta.data)
print('nnMaximum value:', T.sin().sum(0).abs().max().item())
Below is a sample output.
phaseOptimize(5, nsteps=100)
Optimal theta:
tensor([[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07]], requires_grad=True)
Maximum value: 5.0
I am assuming this has something to do with broadcasting in
T = t + theta
and/or the way I am computing the loss function.
One way to verify that optimization is incorrect, is to simply evaluate the loss function at random values for the array $theta_1, dots, theta_n$, say uniformly distributed in $[0, 2pi]$. The maximum value in this case is almost always much lower than the maximum value reported by phaseOptimize(). Much easier in fact is to consider the case with $n = 2$, and simply evaluate at $theta_1 = 0$ and $theta_2 = pi$. In that case we get:
phaseOptimize(2, nsteps=100)
Optimal theta:
tensor([[2.8599e-08],
[2.8599e-08]])
Maximum value: 2.0
On the other hand,
theta = torch.FloatTensor([[0], [np.pi]])
l = torch.linspace(0, 2 * np.pi, 48000)
t = torch.stack([l] * 2)
T = t + theta
T.sin().sum(0).abs().max().item()
produces
3.2782554626464844e-07
pytorch
asked 5 mins ago
wnywny
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
I am trying to minimize the following function:
$$f(theta_1, dots, theta_n) = frac{1}{s}sum_{j =1}^sleft(sum_{i=1}^n sin(t_j + theta_i)right)^2$$
with respect to $(theta_1, dots, theta_n)$. Here ${t_j}$ are regularly spaced points in the interval $[0, 2pi)$.
So here is the Python (PyTorch) code for that. The optimization does not seem to be computed correctly (the gradients seem to only advance along the line $theta_1 = cdots = theta_n$, which of of course incorrect).
import numpy as np
import torch
def phaseOptimize(n, s = 48000, nsteps = 1000):
learning_rate = 1e-3
theta = torch.zeros([n, 1], requires_grad=True)
l = torch.linspace(0, 2 * np.pi, s)
t = torch.stack([l] * n)
T = t + theta
for jj in range(nsteps):
loss = T.sin().sum(0).pow(2).sum() / s
loss.backward()
theta.data -= learning_rate * theta.grad.data
print('Optimal theta: nn', theta.data)
print('nnMaximum value:', T.sin().sum(0).abs().max().item())
Below is a sample output.
phaseOptimize(5, nsteps=100)
Optimal theta:
tensor([[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07]], requires_grad=True)
Maximum value: 5.0
I am assuming this has something to do with broadcasting in
T = t + theta
and/or the way I am computing the loss function.
One way to verify that optimization is incorrect, is to simply evaluate the loss function at random values for the array $theta_1, dots, theta_n$, say uniformly distributed in $[0, 2pi]$. The maximum value in this case is almost always much lower than the maximum value reported by phaseOptimize(). Much easier in fact is to consider the case with $n = 2$, and simply evaluate at $theta_1 = 0$ and $theta_2 = pi$. In that case we get:
phaseOptimize(2, nsteps=100)
Optimal theta:
tensor([[2.8599e-08],
[2.8599e-08]])
Maximum value: 2.0
On the other hand,
theta = torch.FloatTensor([[0], [np.pi]])
l = torch.linspace(0, 2 * np.pi, 48000)
t = torch.stack([l] * 2)
T = t + theta
T.sin().sum(0).abs().max().item()
produces
3.2782554626464844e-07
pytorch
asked 5 mins ago
wnywny
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am trying to minimize the following function:
$$f(theta_1, dots, theta_n) = frac{1}{s}sum_{j =1}^sleft(sum_{i=1}^n sin(t_j + theta_i)right)^2$$
with respect to $(theta_1, dots, theta_n)$. Here ${t_j}$ are regularly spaced points in the interval $[0, 2pi)$.
So here is the Python (PyTorch) code for that. The optimization does not seem to be computed correctly (the gradients seem to only advance along the line $theta_1 = cdots = theta_n$, which of of course incorrect).
import numpy as np
import torch
def phaseOptimize(n, s = 48000, nsteps = 1000):
learning_rate = 1e-3
theta = torch.zeros([n, 1], requires_grad=True)
l = torch.linspace(0, 2 * np.pi, s)
t = torch.stack([l] * n)
T = t + theta
for jj in range(nsteps):
loss = T.sin().sum(0).pow(2).sum() / s
loss.backward()
theta.data -= learning_rate * theta.grad.data
print('Optimal theta: nn', theta.data)
print('nnMaximum value:', T.sin().sum(0).abs().max().item())
Below is a sample output.
phaseOptimize(5, nsteps=100)
Optimal theta:
tensor([[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07]], requires_grad=True)
Maximum value: 5.0
I am assuming this has something to do with broadcasting in
T = t + theta
and/or the way I am computing the loss function.
One way to verify that optimization is incorrect, is to simply evaluate the loss function at random values for the array $theta_1, dots, theta_n$, say uniformly distributed in $[0, 2pi]$. The maximum value in this case is almost always much lower than the maximum value reported by phaseOptimize(). Much easier in fact is to consider the case with $n = 2$, and simply evaluate at $theta_1 = 0$ and $theta_2 = pi$. In that case we get:
phaseOptimize(2, nsteps=100)
Optimal theta:
tensor([[2.8599e-08],
[2.8599e-08]])
Maximum value: 2.0
On the other hand,
theta = torch.FloatTensor([[0], [np.pi]])
l = torch.linspace(0, 2 * np.pi, 48000)
t = torch.stack([l] * 2)
T = t + theta
T.sin().sum(0).abs().max().item()
produces
3.2782554626464844e-07
pytorch
asked 5 mins ago
wnywny
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am trying to minimize the following function:
$$f(theta_1, dots, theta_n) = frac{1}{s}sum_{j =1}^sleft(sum_{i=1}^n sin(t_j + theta_i)right)^2$$
with respect to $(theta_1, dots, theta_n)$. Here ${t_j}$ are regularly spaced points in the interval $[0, 2pi)$.
So here is the Python (PyTorch) code for that. The optimization does not seem to be computed correctly (the gradients seem to only advance along the line $theta_1 = cdots = theta_n$, which of of course incorrect).
import numpy as np
import torch
def phaseOptimize(n, s = 48000, nsteps = 1000):
learning_rate = 1e-3
theta = torch.zeros([n, 1], requires_grad=True)
l = torch.linspace(0, 2 * np.pi, s)
t = torch.stack([l] * n)
T = t + theta
for jj in range(nsteps):
loss = T.sin().sum(0).pow(2).sum() / s
loss.backward()
theta.data -= learning_rate * theta.grad.data
print('Optimal theta: nn', theta.data)
print('nnMaximum value:', T.sin().sum(0).abs().max().item())
Below is a sample output.
phaseOptimize(5, nsteps=100)
Optimal theta:
tensor([[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07],
[1.2812e-07]], requires_grad=True)
Maximum value: 5.0
I am assuming this has something to do with broadcasting in
T = t + theta
and/or the way I am computing the loss function.
One way to verify that optimization is incorrect, is to simply evaluate the loss function at random values for the array $theta_1, dots, theta_n$, say uniformly distributed in $[0, 2pi]$. The maximum value in this case is almost always much lower than the maximum value reported by phaseOptimize(). Much easier in fact is to consider the case with $n = 2$, and simply evaluate at $theta_1 = 0$ and $theta_2 = pi$. In that case we get:
phaseOptimize(2, nsteps=100)
Optimal theta:
tensor([[2.8599e-08],
[2.8599e-08]])
Maximum value: 2.0
On the other hand,
theta = torch.FloatTensor([[0], [np.pi]])
l = torch.linspace(0, 2 * np.pi, 48000)
t = torch.stack([l] * 2)
T = t + theta
T.sin().sum(0).abs().max().item()
produces
3.2782554626464844e-07
pytorch
pytorch
asked 5 mins ago
wnywny
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 mins ago
wnywny
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 5 secs ago
wny
asked 5 mins ago
wnywny
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 mins ago
wnywny
101
asked 5 mins ago
wnywny
101
101
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
wny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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