3 "Optimization" Posts

How Large Language Models (LLMs) Learn: Calculus and the Search for Understanding

Exploring how gradient descent and partial derivatives teach models to think
What You'll Learn
  • How derivatives tell a model which direction will reduce its prediction error
  • How gradient descent turns billions of small corrections into learning
  • How backpropagation uses the chain rule to assign error across many layers
  • Why the learning rate controls the balance between fast progress and stable training
  • Why noisy mini-batch updates can help a model generalize instead of memorize
  • How transformers keep gradients stable while learning which patterns deserve attention

The Meeting Diet: An Optimization Approach to Your Calendar

How optimization can help you decide which meetings deserve your limited time and energy
What You'll Learn
  • How to turn meeting choices into a mathematical optimization problem
  • How time and mental energy can be modeled as separate constraints
  • How a 0/1 knapsack model chooses the most valuable combination of meetings
  • How Python and PuLP can solve a meeting schedule automatically
  • How AI can scaffold optimization code when you give it the right mathematical structure
  • How simulation and visualization can reveal which meetings are worth attending

From Ice Shows to Algorithms: Cracking the Truck-Packing Problem

Using Python, heuristics, and 3D visualization to tackle a real-world optimization problem
What You'll Learn
  • Why loading a truck efficiently is a difficult 3D optimization problem
  • Why NP-hard problems usually require practical heuristics instead of perfect solutions
  • How box dimensions, orientation, weight, and truck boundaries become constraints in a packing model
  • How a greedy Python algorithm can build a workable packing plan
  • How 3D visualization helps reveal overlaps, wasted space, and placement mistakes
  • How more advanced techniques can improve packing efficiency when simple heuristics are not enough