Parallel Prisms

A Blog on Sparse Algorithms, AI, and Supercomputing Synergy

Cross-Entropy Is a Polynomial in a Trench Coat

How polynomial capacity connects softmax training, trace-power log-determinant estimation, and the complex zeros that limit Taylor series.

22 min read · September 16, 2026

2026 · machine-learning softmax cross-entropy polynomials posynomials log-sum-exp curvature optimization probability linear-algebra polynomial-capacity log-determinants complex-zeros information-theory · research
How Many Matrix Multiplications Do You Actually Need?

Faster Neumann series evaluation through smarter radix kernels - achieving ~25% fewer matrix products at the same accuracy.

15 min read · March 21, 2026

2026 · numerical-methods linear-algebra high-performance-computing matrix-computation preconditioning · research
Quantum Computers: The Key to Unlocking (or Breaking) the Simulation?

Exploring the Simulation Hypothesis and whether quantum computers like Google's Willow could reveal or even break our simulated reality.

6 min read · March 31, 2025

2025 · quantum-computing simulation-hypothesis google-willow philosophy technology physics · science technology speculation
The Multiplicative Effect of Good Collaboration in Mental Tasks

how good collaboration can have a multiplicative effect on productivity in certain mental tasks

4 min read · March 13, 2024

2024 · collaboration math-modelling productivity · research