- 🛩️The Spectral Maximal Update Parameterization in Theory and PracticeDecember 1, 2025
A practitioner's guide to spectral μP: heuristic derivations for SGD, Adam, AdamW, depth, and Muon, plus how the spectral perspective resolves subtle coordinate-check failures.
- 0️⃣Why You Cannot Divide by ZeroJanuary 27, 2025
A short explanation of why dividing by zero is undefined, illustrated with the classic sinc function.
- 🛠️Accelerating PINN Experiments with n-TangentPropJanuary 2025
Standard autodiff produces exponentially large computational graphs for high-order derivatives. n-TangentProp exploits the recursive structure of neural networks and Faà di Bruno's formula to compute nth-order derivatives in a single forward pass, yielding 24x–65x speedups for PINN training.
- 🧲An Exact, Over-Compressive Shock Solution for the Brio-Hunter EquationsAugust 2024
We construct an explicit over-compressive shock solution to the Brio-Hunter-Freistuhler system — a non-strictly hyperbolic conservation law — by decoupling through Riemann invariants and solving the resulting Burgers equation exactly.
- 🪜Temporal Sequence Recognition with RNNsMarch 10, 2023
- 🧶Should You Multithread? An Experiment-Driven ApproachNovember 7, 2022
Spawning threads has overhead. We implement matrix multiplication in C, measure pthread creation cost, derive a closed-form break-even condition, and build a smart multiplier that chooses the faster path automatically.
- 📈Binance OHLC 1m DatasetSeptember 2022
- ⛪Solution of a Certain Nonlocal ODE by Reduction to a Riemann-Hilbert ProblemApril 2021
- 📏Measure Theory, Lebesgue Integration and $L^p$ SpacesApril 19, 2019
- 🧠Current State of Artificial Neural NetworksMarch 2016