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).
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:
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 2 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).
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:
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 2 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).
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:
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 2 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).
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:
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 2 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 2 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 2 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 2 mins ago
wnywny
101
asked 2 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.
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "557"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
wny is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdatascience.stackexchange.com%2fquestions%2f48062%2fpytorch-does-not-seem-to-be-optimizing-correctly%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
wny is a new contributor. Be nice, and check out our Code of Conduct.
wny is a new contributor. Be nice, and check out our Code of Conduct.
wny is a new contributor. Be nice, and check out our Code of Conduct.
wny is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Data Science Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdatascience.stackexchange.com%2fquestions%2f48062%2fpytorch-does-not-seem-to-be-optimizing-correctly%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
