One Hash Bloom Filters

Jim Calabro walks through how bloom filters work, how Bluesky moved from multiple hash functions to double hashing to cut contention, and then explores the one-hash bloom filter from Lu et al., which splits the bit array into partitions with pairwise coprime sizes so a single hash can stand in for k independent ones.

Tutorial · Algorithms · Data Structures · Performance · Programming

English: a vs anWhy vowel letters are the wrong rule for indefinite articles in generated text

Amit Patel (Red Blob Games) digs into when English wants “a” versus “an”: the rule tracks spoken vowel sounds, not written vowel letters, and only a small set of common words need exceptions for procedural text generation.

Tutorial · Programming · Writing · Algorithms · Education

Evaluating Polynomials Fast

Thomas Ahle presents a technique for evaluating polynomials in roughly half the multiplications that Horner's method requires, by preprocessing the coefficients offline. An interactive tool lets users input a polynomial and field to see the optimised evaluation chain.

Tutorial · Algorithms · Mathematics · Cryptography · Numerical Computing

Optimizing anamorphic sculptures

Thiago Cardoso walks through creating and optimizing anamorphic sculptures—images that resolve only from a specific vantage—using computational geometry techniques.

Tutorial · Programming · Algorithms · Design

Use 20x less peak RAM with dp_knapsack_sliding_hirschberg, a new activation memory budget solver for PyTorch

Jędrzej Maczan explains PyTorch's activation-checkpointing memory planner as a 0/1 knapsack problem and introduces dp_knapsack_sliding_hirschberg, a sliding-window DP with Hirschberg-style reconstruction that cuts peak RAM during memory planning by about 20x.

Tutorial · Machine Learning · Algorithms · Performance · Open Source

Reservoir SamplingOriginal article link with an AI-written directory summary

An interactive explanation of choosing a fair random sample from a stream of unknown length. Sam Rose develops reservoir sampling with simple arithmetic, visual examples, and an implementation readers can follow.

Tutorial · Algorithms · Probability

Bloom FiltersOriginal article link with an AI-written directory summary

A visual introduction to Bloom filters and their tradeoffs. Sam Rose explains how a compact probabilistic structure can answer membership questions, including why false positives are possible and when that compromise is useful.

Tutorial · Data Structures · Algorithms

Making Hybrid Images

Jeremy Kun explains hybrid images, pictures that read differently up close and from afar, using Fourier analysis: an intuitive tour of the discrete Fourier transform, low- and high-pass Gaussian filtering, and Python code that blends Marilyn Monroe and Albert Einstein into one image, with ideas for further experiments.

Tutorial · Mathematics · Python · Graphics · Algorithms