Understanding Adam Optimizer in Deep Learning

Optimization is the heart of deep learning. It's what allows neural networks to learn from data and improve over time. Among the many optimization algorithms out there, Adam (Adaptive Moment Estimation) has become one of the most popular — and for good reason. In this blog, we’ll explore what Adam is, how it works, and why it's widely used.

What Is the Adam Optimizer?

The Adam Optimizer is an algorithm for first-order gradient-based optimization. It combines the best parts of two other popular optimizers:

Momentum – which helps accelerate gradients in the right direction.
RMSProp – which adapts the learning rate for each parameter individually.

Adam was introduced by Diederik Kingma and Jimmy Ba in their 2015 paper:

“Adam: A Method for Stochastic Optimization”

How Does Adam Work?

Adam updates the weights of a neural network using the following formulas:

Let:

$g_t$ be the gradient at time step $t$
$m_t$ be the first moment estimate (mean of gradients)
$v_t$ be the second moment estimate (uncentered variance of gradients)

1. Compute the moving averages:

m_{t} = β_{1} \cdot m_{t - 1} + (1 - β_{1}) \cdot g_{t}

v_{t} = β_{2} \cdot v_{t - 1} + (1 - β_{2}) \cdot g_{t}^{2}

2. Bias correction:

\hat{m}_t = \frac{m_t}{1 - \beta_1^t}, \quad \hat{v}_t = \frac{v_t}{1 - \beta_2^t}

3. Update parameters:

\theta_{t+1} = \theta_t - \alpha \cdot \frac{\hat{m}_t}{\sqrt{\hat{v}_t} + \epsilon}

Where:

$\alpha$ is the learning rate
$\beta_1 \approx 0.9$ , $\beta_2 \approx 0.999$ , and $\epsilon \approx 10^{-8}$ (small constant to prevent division by zero)

Why Use Adam?

Adaptive Learning Rates

Adam adjusts the learning rate for each parameter, which helps with faster convergence.

Less Tuning

Often works well with default settings, making it beginner-friendly.

Efficient and Scalable

Well-suited for problems with large datasets or many parameters.

When Not to Use Adam

In some sparse data or generalization-focused tasks, SGD with momentum may outperform Adam.
Adam can converge faster but may generalize worse compared to SGD in some cases.

Adam in Practice

import torch
import torch.nn as nn
import torch.optim as optim

model = nn.Linear(10, 1)
optimizer = optim.Adam(model.parameters(), lr=0.001)

# Training loop
for input, target in data_loader:
    optimizer.zero_grad()
    output = model(input)
    loss = loss_fn(output, target)
    loss.backward()
    optimizer.step()

Final Thoughts

The Adam optimizer is like an all-rounder in your deep learning toolkit. It’s fast, easy to use, and powerful for most scenarios. While not perfect, it's a great starting point when building and training neural networks.

Machine Learning

Thursday, May 1, 2025

Adam Optimizer