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Mathematics and Computations

I find theoretical math and machine learning to be pretty fun. I think that good practical techniques that work well are derived from a theoretical root.

Optimization & Its Many Faces
Every Algorithm Is a Twitch on Taylor's Theorem Deriving everything we want in optimization from Taylor theory — and with small modifications to the assumptions, we get completely different families of algorithms. Constraints as Guidance, Not Hindrance All hard problems can be framed as a constraint-solving process if you look at them from a particular perspective — both in math and in life. If the Universe Is the Answer, What Is the Question? In the AI era the inner loop of optimization is solved; the hard part is choosing the objective and verifying what you found. A functional-optimization view of science, research, and life.
Probability & Statistics
Unfolding Stochasticity Sequentially Modeling interactions between stochasticity across time, sequentially, through the key representational example of the Random Walk. Lend It Some Confidence There are deep connections between statistics and probability, even on very basic statistics levels.
Graphs & Geometry
From Random Walks to Generating Molecules From random walks to graph transformers to hierarchical graph generation, tracing how the field learned to represent and generate graph-structured data. The Graph Hiding in the Ridges A graph can hide inside a cloud of points, in the ridges of the density it piles up into. Discrete Morse theory extracts those ridges as a skeleton, and persistence tells the real ones from noise.
Sequential Decision-Making
Optimism in the Face of Uncertainty From the multi-armed bandit problem to AlphaGo, deriving the Upper Confidence Bound and why the mathematically optimal strategy for minimizing regret is to explore the unknown. Walking Towards Singularity in All Reality From the Bellman equation to contraction mappings to Q-learning — how a simple recurrence converges to the singularity, the unique optimal value in the space of all possibilities.