[ICML 2022, Oral] The PyTorch Implementation of Adaptive Inertia Methods. The algorithms are based on our paper: "Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum".
License: MIT License
If I define a simple linear model like this:
class TinyModel(torch.nn.Module):
def __init__(self):
super(TinyModel, self).__init__()
self.layer1 = torch.nn.Linear(1000, 100, bias=True)
self.relu = torch.nn.ReLU()
def forward(self, x):
x = self.layer1(x)
x = self.relu(x)
return x
Linear layer has two parameters, y=xA' +b.
In your adai.py code, state['step'] will be 1 for A, and 2 for b. If we unroll the for loop:
param_size = param_size +sizeA
grad = p.grad.data# A's grad
bias_correction2 = 1 - beta2
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
exp_avg_sq_hat_sum += exp_avg_sq.sum() / bias_correction2
param_size = param_size +sizeb
grad = p.grad.data# b's grad
bias_correction2 = 1 - beta2**2
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
exp_avg_sq_hat_sum += exp_avg_sq.sum() / bias_correction2
Is it a bug for a layer with multiple parameters?
I tested some simple models on pytorch, Adai does have better performance over Adam, therefore, I tried to use Adai to fit bortfeld function. I implemented two matlab functions to compare the performance of Adai and Adam. And I found Adai cannot converge while Adam converged. Is my implementation wrong?
Bortfeld function() is a function used to fit proton bragg peak, An analytical approximation of the Bragg curve for therapeutic proton beams
function [theta_best,loss] = adai(depth,para,idd_i,lb,ub,lr)
% adam inertia
T = 2000;
beta0 = 0.1;
beta1_cum_prod = 1;
beta2 = 0.99;
epsilon = 1e-3;
loss = zeros(T,1);
m_tm1 = 0;
v_tm1 = 0;
theta_tm1 = para;
v_t_mean = 0;
theta_best = para;
loss_best = 1e9;
loss(1) = norm((bf_mex(depth,theta_tm1,'idd') - idd_i),'fro');
for t = 2:T
% get gradient = jacobian*error
g_t = 2*bf_mex(depth,theta_tm1,'jacobian')'*(bf_mex(depth,theta_tm1,'idd') - idd_i);
% Update biased second raw moment estimate
v_t = beta2*v_tm1 + (1-beta2)*g_t.^2;
% Compute bias-corrected second raw moment estimate
v_t_hat = v_t / (1-beta2^(t-1));
v_t_mean = mean(v_t_hat);
beta1t = max(min(1-(v_t_hat./v_t_mean).*beta0, 1-epsilon),0);
% Update biased first moment estimate
m_t = beta1t.*m_tm1 + (1-beta1t).*g_t;
beta1_cum_prod = beta1_cum_prod.*beta1t;
% Compute bias-corrected first moment estimate
m_t_hat = m_t ./ (1-beta1_cum_prod);
% Update parameters
theta_t = theta_tm1 - lr*m_t_hat;
% constrain
theta_t(theta_t < lb) = lb(theta_t < lb);
theta_t(theta_t > ub) = ub(theta_t > ub);
theta_tm1 = theta_t;
m_tm1 = m_t;
v_tm1 = v_t;
idd_pred = bf_mex(depth,theta_t,'idd');
loss(t) = norm((idd_pred - idd_i),'fro');
if loss(t) < loss_best
loss_best = loss(t);
theta_best = theta_t;
end
if (abs(loss(t) - loss(t-1)) < 1e-6)
break;
end
end
end
function [theta_best,loss] = adam(depth,para,idd_i,lb,ub,lr)
T = 2000;
beta1 = 0.9;
beta2 = 0.999;
epsilon = 1e-8;
loss = zeros(T,1);
m_tm1 = 0;
v_tm1 = 0;
theta_tm1 = para;
theta_best = para;
loss_best = 1e9;
loss(1) = norm((bf_mex(depth,theta_tm1,'idd') - idd_i),'fro');
for t = 2:T
% get gradient = jacobian*error
g_t = 2*bf_mex(depth,theta_tm1,'jacobian')'*(bf_mex(depth,theta_tm1,'idd') - idd_i);
% Update biased first moment estimate
m_t = beta1*m_tm1 + (1-beta1)*g_t;
% Update biased second raw moment estimate
v_t = beta2*v_tm1 + (1-beta2)*g_t.^2;
% Compute bias-corrected first moment estimate
m_t_hat = m_t / (1-beta1^(t-1));
% Compute bias-corrected second raw moment estimate
v_t_hat = v_t / (1-beta2^(t-1));
% Update parameters
theta_t = theta_tm1 - lr*m_t_hat./(sqrt(v_t_hat)+epsilon);
% constrain
theta_t(theta_t < lb) = lb(theta_t < lb);
theta_t(theta_t > ub) = ub(theta_t > ub);
theta_tm1 = theta_t;
m_tm1 = m_t;
v_tm1 = v_t;
idd_pred = bf_mex(depth,theta_t,'idd');
loss(t) = norm((idd_pred - idd_i),'fro');
if loss(t) < loss_best
loss_best = loss(t);
theta_best = theta_t;
end
if (abs(loss(t) - loss(t-1)) < 1e-6)
break;
end
end
end
Can you post your code on pypi?
Hi,
Firstly, thanks for the great work.
I just wonder if adai is suitable for combining together with positive-negative momentum which is another work of you. From my understanding of these two, it is ok to replace the original momentum with pnm in adai. Do you have any suggestions or experiences?
Thanks for the reply.
Test performance of adai on NLP tasks?
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