Latest Blog Posts

• Feb 9, 2026 Architectural and Mathematical Foundations of Machine Learning: A Rigorous Synthesis of Theory, Geometry, and Implementation
  

  A rigorous exploration of machine learning mathematics, from information theory and linear algebra to optimization dynamics and generative models, with correct implementations and theoretical connections.

• Jan 22, 2026 A Complete Guide to Neural Network Optimizers
  

  From SGD to Muon, explore how each optimizer builds on its predecessors to solve gradient descent challenges in deep learning.

• May 30, 2025 Essential Machine Learning Equations: A Reference Guide
  

  A reference guide to fundamental machine learning equations with correct implementations and clear explanations of how they connect to each other.

• May 30, 2025 Understanding Backpropagation in Deep Learning
  

  A highly technical yet understandable exploration of backpropagation, detailing its mechanics, mathematical foundations, and practical applications, making it accessible to those with a basic understanding of calculus and machine learning.

• Feb 24, 2025 The Energy Dilemma II (Post-COVID-19): Why N2N Isn't the Magic Bullet for America's Energy Future
  

  A post-COVID-19 critical review of Robert Bryce’s “Power Hungry: The Myths of 'Green' Energy and the Real Fuels of the Future.”

• Aug 2, 2024 Implementing a Recurrent Neural Network (RNN) From Scratch in Python: Character-Level Language Model Case Study
  

  In this blog post, we’ll dive deep into the implementation of a character-level language model using a vanilla Recurrent Neural Network (RNN). This type of model can learn to generate text one character at a time, capturing the patterns and structure of the language it’s trained on. We’ll walk through…

• Jul 15, 2024 Implementation of Karpathy's Neural Networks: Zero to Hero Lecture Series
  

  This blog post presents my detailed implementation of Andrej Karpathy’s Neural Networks: Zero to Hero YouTube lecture series and exercises in Jupyter Notebook. The articles go deeply from NNs to MLPs to CNNs to LLMs to ensure a thorough and robust understanding of neural networks.

• Sep 20, 2020 The Energy Dilemma I (Pre-COVID-19): Why N2N Isn't the Magic Bullet for America's Energy Future
  

  A pre-COVID-19 critical review of Robert Bryce’s “Power Hungry: The Myths of 'Green' Energy and the Real Fuels of the Future.”