Elliptic curves
- Associativity of the group law on an elliptic curve
- A toy elliptic curve over a finite field
- Pairings on elliptic curves: a toy example
- What does an elliptic curve look like near the point at infinity (the identity)?
Finite fields
- Construction of the finite fields (with exercises)
- The multiplicative group of a finite field is cyclic
FRI, Reed-Solomon codes & proofs of proximity
- FRI is a proof of proximity, not a low-degree test
- Building a polynomial commitment scheme from the FRI-IOPP
- From equivalences of Reed-Solomon codes to algebraic geometry codes
Programmable cryptography miscellany
- Consequences real & imaginary of “How to Prove False Statements: Practical Attacks on Fiat-Shamir”
- Understanding LogUp: A Royal Road
- Deep Differentiable Logic Gate Networks & their (potential) relevance to ZKML
- Efficient polynomial interpolation on $0, 1, 2, .. $ (the inverse Vandermonde on integer nodes)
- When is a polynomial determined by evaluations? Polynomial interpolation over commutative rings with unity.
Machine learning
- Controlled Experiments for Word Embeddings (arXiv)
- Skipgram isn’t Matrix Factorisation
- Hierarchical Softmax
- The limits of linear-time machine learning
- Minsky & Papert’s “Perceptrons”
- Expectation-Maximisation and Gaussian Mixture Models
- word2vec and GloVe
- Skip-gram word embeddings in hyperbolic space (arXiv) (also GitHub)
Optimization
- Convergence rate of gradient descent
- Softmax parameterisation and optimisation
- Projected Gradient Descent
Geometry (often meets optimization)
- Gradient descent in hyperbolic space (arXiv)
- Gradient optimisation on the Poincaré disc
- Graph embeddings in Hyperbolic Space
- Orthogonal transformations and gradient updates
- Parameterising the Mahalanobis distances for metric learning
- Visualising the set of 2×2 positive semidefinite matrices
Statistics
- Entropy of the Normal Distribution
- Shannon: averaging operations can only increase the entropy
- Perpendicularity and dimension
- Limiting Distributions of Markov Chains
- Marginal and Conditional Distributions of the Multivariate Gaussian
- Estimation Theory and the Bias-Variance Trade-Off
- Squared pair-wise differences estimate the variance
Complexity theory
Phylogenetics
Math odds and ends
- Matrix Factorisation and the Eigendecomposition of the Gram Matrix
- Eigendecomposition of real, symmetric matrices
- The mathematics of the discrete Fourier transform
- Short-time Fourier transform cheatsheet
- Factorisation of stochastic matrices
- Polynomials over a finite field vs polynomial functions on a finite field
Software
- HyperNaut: a navigator for the hyperbolic plane (see also article)
- Misc ML projects on Github (mostly optimization in hyperbolic space)
Representation theory
See Google Scholar.