Deep Learning

Regularisation for Deep models

Regularisation for Deep models #

Regularisation means adding constraints or techniques that prevent a model from becoming too complex and memorising the training data.

The goal is not only low training error.

The goal is good performance on unseen data.

Key takeaway:
Regularisation helps the model generalise by controlling complexity, stabilising training, and reducing overfitting.

  • Generalization for regression
  • Training Error and Generalization Error
  • Underfitting or Overfitting
  • Model Selection
  • Weight Decay and Norms
  • Generalization in Classification
  • Environment and Distribution Shift
  • Generalization in Deep Learning
  • Dropout
  • Batch Normalization
  • Layer Normalization

Underfitting, Good Fit, and Overfitting ☆ #

CaseModel behaviourTraining errorTest error
Underfittingtoo simplehighhigh
Good fitcaptures useful patternlowlow
Overfittingmemorises training noisevery lowhigh
flowchart LR
    A["Model Complexity"] --> B["Too Simple: Underfitting"]
    A --> C["Just Right: Good Fit"]
    A --> D["Too Complex: Overfitting"]

    style A fill:#E1F5FE,stroke:#4A90E2
    style B fill:#FFF9C4,stroke:#FBC02D
    style C fill:#C8E6C9,stroke:#43A047
    style D fill:#EDE7F6,stroke:#7E57C2

Training Error and Generalisation Error ☆ #

Training error measures performance on data used for learning.

DNN Formula and Numerical Sheet

DNN Formula and Numerical Sheet #

This page consolidates the most useful Deep Neural Networks formulas and numerical patterns for revision.

It is designed for preparation and should be used together with the topic pages.

Revision strategy:
Do not only memorise formulas.

For each formula, know:

  1. what each symbol means
  2. when to apply it
  3. how to substitute values carefully
  4. what the output shape or answer represents

1. Artificial Neuron #

Weighted Sum ☆ #

\[ z = \sum_{i=1}^{n} w_i x_i + b \]

Vector form: