https://signal-and-syntax.com/tags/optimization/Recent content in Optimization on Signal & SyntaxHugoen-usWed, 08 Oct 2025 06:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-learn/Wed, 08 Oct 2025 06:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-learn/When you interact with a large language model (LLM) such as ChatGPT or Claude , the model seems to respond instantly relative to the question’s degree of difficulty. What’s easy to forget is that every word it predicts comes from a long history of learning where billions of gradient steps have slowly sculpted its understanding of language. Large language models don’t memorize text. They optimize it. Behind that optimization lies calculus.https://signal-and-syntax.com/posts/meeting-diet/Thu, 28 Aug 2025 05:00:00 -0700https://signal-and-syntax.com/posts/meeting-diet/Every week your calendar fills with more meeting invites than you can reasonably handle. Which ones are worth the time and energy, and which should you politely decline? What if there was a way to quantify that choice? The good news: math can help. By modeling your schedule as a 0/1 knapsack problem with two constraints ( Kellerer et al., 2004 ), you can treat meetings like items with value, time cost, and energy cost.https://signal-and-syntax.com/posts/three-d-packing/Wed, 20 Aug 2025 09:00:00 -0700https://signal-and-syntax.com/posts/three-d-packing/My first full-time programming job was for Holiday on Ice, an international ice show. While I focused mainly on back office systems such as accounting, itinerary, and box office reporting, I knew that one of the biggest technical challenges faced by the show’s crew was efficiently loading trucks for the next city. One day, the controller asked me if I could code a system that took, as input, the trucks’ 3D dimensions and the 3D dimensions (and weight) of every object to be packed.