Adam Optimisation Algorithm: Updating Neural Network Weights Efficiently

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Training a neural network is largely about one recurring step: adjust the model’s weights so the loss goes down. Classical stochastic gradient descent (SGD) does this by moving weights in the opposite direction of the gradient, scaled by a learning rate. While SGD is simple and often effective, it can struggle when gradients are noisy, sparse, or vary in scale across parameters. That is where Adam (Adaptive Moment Estimation) becomes useful. If you are learning optimisation while doing a Data Science Course, understanding Adam will help you train deep learning models faster and with fewer manual tweaks.

From SGD to Adam: The Problem It Solves

SGD applies one learning rate to all parameters, even though different weights may receive gradients with very different magnitudes. In practice, this leads to two common issues:

  1. Slow progress in some directions: If the learning rate is small to maintain stability, parameters with tiny gradients may change very slowly.
  2. Unstable updates in others: If the learning rate is large enough to speed up learning, parameters with large or noisy gradients may overshoot and cause training to diverge.

Another challenge is that gradients in deep networks can be highly stochastic due to mini-batch sampling. Adam tackles these problems by combining two ideas: momentum (to smooth the direction of updates) and per-parameter adaptive learning rates (to scale updates based on gradient history). Many learners in a data scientist course in Hyderabad encounter Adam early because it often “just works” as a default optimiser for modern neural networks.

How Adam Updates Weights

Adam maintains two running estimates for each parameter:

  • A first-moment estimate (often called m): an exponential moving average of past gradients (similar to momentum).
  • A second-moment estimate (often called v): an exponential moving average of past squared gradients (captures gradient scale).

At each step t, given gradient gₜ:

  1. Update the moving average of gradients:
    mₜ = β₁ mₜ₋₁ + (1 − β₁) gₜ
  2. Update the moving average of squared gradients:
    vₜ = β₂ vₜ₋₁ + (1 − β₂) gₜ²
  3. Apply bias correction (important early in training because moving averages start at zero):
    m̂ₜ = mₜ / (1 − β₁ᵗ)
    v̂ₜ = vₜ / (1 − β₂ᵗ)
  4. Update parameters:
    θₜ = θₜ₋₁ − α · m̂ₜ / (√(v̂ₜ) + ε)

Here, α is the learning rate, β₁ and β₂ control how much history is retained (momentum and variance smoothing), and ε prevents division by zero. The key intuition is simple: Adam moves in a smoothed direction (via m̂ₜ) while automatically shrinking steps for parameters with consistently large gradients (via √(v̂ₜ)). This often leads to faster, more stable convergence than plain SGD, especially on complex architectures.

Key Hyperparameters and Practical Defaults

Adam is popular partly because the default settings usually perform reasonably well:

  • Learning rate (α): commonly 0.001 as a starting point.
  • β₁: commonly 0.9 (momentum-like behaviour).
  • β₂: commonly 0.999 (stable second-moment estimate).
  • ε: often 1e-8.

Even with good defaults, a few practical guidelines help:

  • If training is unstable (loss jumps wildly), try lowering α.
  • If learning feels sluggish, slightly increase α or use a learning-rate schedule (warm-up, cosine decay, etc.).
  • For regularisation, prefer AdamW (decoupled weight decay) rather than mixing L2 penalty directly into the gradient update, because AdamW typically behaves more predictably in deep learning setups.

These tuning habits are worth practising in a Data Science Course, because optimiser choice and learning-rate control often matter as much as the model architecture.

Common Pitfalls and When to Consider Alternatives

Although Adam is strong, it is not always the best final choice:

  • Generalisation differences: In some tasks (especially vision models), SGD with momentum can sometimes produce better generalisation than Adam, even if Adam reaches low training loss faster.
  • Over-reliance on defaults: Adam can hide poor feature scaling, label noise, or data leakage issues by making training “look fine” while validation performance remains weak. Always track validation metrics.
  • Weight decay confusion: If you need regularisation, using AdamW is usually safer than relying on implicit effects of Adam’s adaptive scaling.

A good workflow is: start with Adam for quick iteration, then compare against SGD (or AdamW) once your pipeline is stable. This comparison mindset is often emphasised in a data scientist course in Hyderabad, where reproducibility and measurable improvements matter more than optimiser popularity.

Conclusion

Adam is an optimisation algorithm designed to update network weights efficiently by combining momentum with adaptive, per-parameter learning rates. Its moving averages, bias correction, and stable update rule make it a strong default for many deep learning problems, especially when gradients are noisy or unevenly scaled. Used thoughtfully, with good validation checks, sensible learning-rate choices, and AdamW when regularisation is needed, Adam can significantly simplify and speed up neural network training.

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