Understanding the Efficacy of Over-Parameterization in Neural Networks

Understanding the Efficacy of Over-Parameterization in Neural Networks Understanding the Efficacy of Over-Parameterization in Neural Networks: Mechanisms, Theories, and Practical Implications Introduction Deep neural networks (DNNs) have become the cornerstone of modern artificial intelligence, driving advancements in computer vision, natural language processing, and myriad other domains. A key, albeit counter-intuitive, property of contemporary DNNs is their immense over-parameterization: these models often contain orders of magnitude more parameters than the number of training examples, yet they generalize remarkably well to unseen data. This phenomenon stands in stark contrast to classical statistical learning theory, which posits that models with excessive complexity relative to the available data are prone to overfitting and poor generalization. Intriguingly, empirical evidence shows that increasing the number of parameters in DNNs can lead ...

πŸ“š Python Classes and Objects: A Beginner's Guide

 

“Everything in Python is an object.”
Let’s discover how classes and objects work together to build powerful applications!


πŸš€ What are Classes and Objects?

Classes are blueprints.
Objects are real-world entities created using these blueprints.

πŸ”΅ Diagram:

In Python, everything is an object — integers, strings, lists, even complex numbers!

Example: Complex Numbers as Objects

z = 3 - 5j

Here, z is an instance of the complex class.
Attributes like  and  and methods like  come built-in!


Differences between Class Diagram and Object Diagram:

Aspect

Class Diagram

Object Diagram

Focus

Shows the design or blueprint of the system

Shows real examples (objects) at a certain time

Representation

Shows classes, their properties, and actions

Shows objects, their values, and their connections

Static vs Dynamic

Static — stays the same while designing

Dynamic — changes depending on what's happening

Usage

Used to plan and design how the system should work

Used to see how things actually look while running

 


🧱 Defining Your Own Class

Creating a simple empty class:

Now create objects:

Assign attributes dynamically:

Or for s2:

You can even delete attributes:


πŸ”₯ Adding Methods to Classes

Let's make our class more powerful:

Usage:


🎯 Class Variables vs Object Variables

Aspect

Class Variable

Object Variable

Belongs To

Class itself

Individual Objects

Shared?

Yes

No

Example

name, roll


πŸ› ️ Special Methods: Magic Behind the Scenes

Python classes have special methods that control behavior:

Method

Purpose

Constructor

Pretty print

Developer representation

Operator overloading

Make objects callable

Example:


🧬 Real-World Example: 3D Vectors

Imagine building a physics engine or 3D model:

Use it like this:

πŸ—️ Applications: 

3D graphics, simulations, robotics, physics modeling!


πŸ”’ Public, Protected, and Private Variables

Modifier

Syntax

Access Level

Public

Anywhere

Protected

Within class and subclass

Private

Within class only

πŸ”΅ Flowchart:


🧩 Practice Exercises (With Hints! and solution)

1. Sphere Class

  • Hint:

2. Account Class

  • Hint: Withdraw only if balance ≥ amount!

3. Rationals Class

  • Hint:  methods.

4. Country Class

  • Hint: Calculate density as population/area.


🎯 Best Practices for Classes in Python

Example for clean class design:


Advanced Example: Singleton Class

⚠️ Common Mistakes Beginners Make

Forgetting self in method definitions

Using mutable default arguments

Fix:

Directly accessing private attributes

Instead, use getter/setter methods.


πŸ› ️ Want More? Advanced OOP Patterns Preview

  • πŸ”₯ Factory Pattern: Create objects dynamically without exposing the instantiation logic.
  • 🧠 Observer Pattern: Design systems where objects notify others about state changes.

πŸ‘‰ Coming soon in the next blog part! Stay tuned.


πŸ’¬ Let’s Connect!

I’d love to hear from you. πŸš€


πŸ”” Next Challenge Topic Preview:

" Exploring integers with SageMath

 

Comments

Popular posts from this blog

🌟 Illuminating Light: Waves, Mathematics, and the Secrets of the Universe

Spirals in Nature: The Beautiful Geometry of Life