about me
research papers
Geometric structures in the residual stream
What are their statistical origins and computational roles?
5 minTowards an atlas of deep learning
We should coordinate our research expeditions to make layered scientific maps.
13 min
Deriving the DMFT cavity equation using the matrix block inverse formula
How to solve linear systems where one variable responds to constraints on the remaining.
15 minA visual derivation of the Sherman-Morrison formula
The inverse of a rank-one perturbation of M equals a rank-one perturbation of M⁻¹.
8 minDeriving the Nyquist theorem from the Eigenlearning framework
Nyquist-Shannon-style bandlimited signal recovery is really just linear regression.
10 minSolving the training dynamics of word2vec
Word embedding models learn interpretable topic-level concepts one at a time.
10 minLazy (NTK) and active (muP) training -- what gives?
There's only one degree of freedom in choosing how hyperparameters scale with network width.
6 minHow to take derivatives of matrix expressions
Using einsums for pen-and-paper matrix differentiation
8 minQuick n dirty derivation of Larmor radiation and gravitational waves
How to derive order-of-magnitude expressions for radiation formulas
4 minStatistical physics of signal propagation in deep neural networks
Using statistical physics to understand what makes a good activation function
7 minDetecting and tracking structures in protostellar outflows
My senior thesis won an award
1 minBlackbody radiation made simpler
The "cavity with a hole" is soo confusing.
10 min