Recent posts:

• 28 Apr 2025 TPUs and Sharding

  While GPUs have long been popular for training and deploying AI models, Google's TPUs offer a compelling alternative, especially for large-scale applications. I recently had the chance to explore Google's TPUs on a fairly large scale. My impression is quite positive. They feel solid, fast, reliable, and cost-efficient. This post explores the basics of how they work.

  
  
• 20 Apr 2025 Exogeneous Growth

  Here we study the simplest economics growth model - the Solow model - by Robert Solow and Trevor Swan. It is the basis over which many other models build upon and is quite easy to analyze, while providing useful insights. For example, it asserts that changes in saving only matter for the economy's transition path, not for its permanent growth rate. Yet, savings obviously determine consumption. So should we save more or less? The model also introduces key questions such as whether poor countries grow faster than richer ones, or whether physical capital can explain big differences in output across space and time.

  
  
• 07 Apr 2025 Do States Need Territory?

  A state is an entity that holds a monopoly over the legitimate use of physical violence within a given territory. Classic international law doctrine, e.g. Franz Oppenheimer, has long held that “a state without territory is not possible”. Yet in modern times, globalization, digital networks, and unique political situations have prompted experiments in deterritorialized statehood. Can a state function without a fixed geographic base? And what would be the implication in terms of its fundamental characteristics?

  
  
• 29 Mar 2025 Data-Driven Structure From Motion

  Structure from motion (SFM) has come a long way. It started back in the 1950s when researchers painstakingly derived 3D structures from pairs of aerial photographs through precise geometric reasoning. The eight-point algorithm in 1981 was one of the first applications of mathematical rigour to the problem. In the late 1990s RANSAC enabled robust estimation in the presence of noise, while bundle adjustment greatly improved the reconstruction precision by jointly updating both the camera parameters and the scene geometry. In the next 10 years these solutions were scaled up and turned into products. Since then, deep learning has become the norm, with more of a focus on data-driven learning instead of explicit geometry modeling.

  
  
• 17 Mar 2025 Attempts to Solve a Market

  I was recently tinkering with some fairly realistic oligopolistic market simulations. Compared to textbook cases, where it is common to assume the market matches all buyers to all sellers simultaneously, in my case the simulation involved non-clearing markets, sequential search, and various computational constraints among the market participants. If you think about it, it gets quite hard to solve the market in this case. Analytic solutions are out of the question. One typically has to use numerical methods. Yet, I had the beautiful idea of tryin out multi-agent RL for finding the equilibria. It turned out to be a very nice bridge between the two disciplines - one providing the problem setting, and another providing the tool to solve it.