Artificial intelligence
Query, Key, Value: The Foundation of Transformer Attention
Explains how QKV projections enable transformers to learn flexible attention patterns through specialized query, key, and value representations.

Michael Brenndoerfer
I work across AI, technology, and private equity.
Here, I share the ideas behind the work.
Books
Machine learning, language AI, and quantitative finance, explained from first principles.

The math, intuition, and Python behind the algorithms.
Free to read online
From classical NLP to transformers and modern language models.
In progress · Read available chapters

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Writing
Artificial intelligence
Explains how QKV projections enable transformers to learn flexible attention patterns through specialized query, key, and value representations.
Finance & markets
Market crashes erase quoted value rather than moving a fixed pool of cash. Covers forced selling, liquidity, wealth effects, price discovery, and recovery.
AI agents
AI agents combine a language model with tools, memory, and control logic. This article separates agents from workflows and multi-agent systems.
Finance & markets
Covers quadratic programming (QP) for portfolio optimization, including the mean-variance framework, efficient frontier construction.