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Monte Carlo Crash Course: Quasi-Monte Carlo

Monte Carlo Crash Course Quasi-Monte Carlo We’ve learned how to define and apply Monte Carlo integration—fundamentally, it’s the only tool we need. In the remaining chapters, we’ll explore ways to reduce variance and successfully sample difficult distributions. Variance & Correlation In chapter two, we determined that the variance of a Monte Carlo estimator is inversely proportional to its sample count. Empirically, we confirmed that our integrators’ expected error scaled with $$\frac{1}{\sq

The Ski Rental Problem

Ski Rental Problem The ski rental problem is a classic example problem in online algorithms. It feels like a small but interesting problem that can be explained relatively easily while some clever tricks can be applied to it. In this article, I took these lecture notes by Debmalya Panigrahi and Hangjie Ji and tried to rewrite them in a way that is easier to understand (at least for me). Formulation You are going skiing in the mountains but you are unsure about the weather reports and don't k

New AI architecture delivers 100x faster reasoning than LLMs with just 1,000 training examples

Want smarter insights in your inbox? Sign up for our weekly newsletters to get only what matters to enterprise AI, data, and security leaders. Subscribe Now Singapore-based AI startup Sapient Intelligence has developed a new AI architecture that can match, and in some cases vastly outperform, large language models (LLMs) on complex reasoning tasks, all while being significantly smaller and more data-efficient. The architecture, known as the Hierarchical Reasoning Model (HRM), is inspired by ho