ideasthesia

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Ryan Collison

I write about cool science and share it here.

Learning curve showing sudden jump from memorization to generalization

Grokking: When Neural Networks Suddenly Understand

Series: Mechanistic Interpretability | Part: 4 of 9 In 2021, researchers at OpenAI noticed something strange. They trained a small transformer on simple modular arithmetic—the kind of problem you learn in middle school. At first, the network memorized the training examples perfectly but failed completely on new ones. Standard overfitting

Induction head circuit diagram showing attention patterns

Circuits in Silicon Minds: How Neural Networks Compute

Series: Mechanistic Interpretability | Part: 3 of 9 In 2021, researchers at Anthropic discovered something remarkable: they could trace how GPT-2 completes simple patterns like “John is a man. Mary is a ___.” Not by probing thousands of neurons at once, but by following a specific computational pathway—a circuit—that

Overlapping feature vectors in neural network activation space

Superposition: How Neural Networks Pack More Concepts Than Neurons

Series: Mechanistic Interpretability | Part: 2 of 9 When researchers first opened the hood on GPT-2, they expected neural networks to work like filing cabinets. One neuron per concept. One drawer per category. What they found instead was more like the interference patterns in a hologram—every piece containing information

Neural network internals with interpretable circuits and features revealed

Reading the Mind of AI: The Mechanistic Interpretability Revolution

Series: Mechanistic Interpretability | Part: 1 of 9 In 2022, researchers at Anthropic made a discovery that should have terrified everyone paying attention. Inside a large language model, they found a single artificial neuron that activated for one specific concept: the Golden Gate Bridge. Not bridges in general. Not San Francisco

Synthesis of categorical structures—composition as geometric coherence

Synthesis: Category Theory as the Geometry of Composition

Series: Applied Category Theory | Part: 10 of 10 Throughout this series, we’ve explored how category theory provides the mathematical language for compositional systems—from neural networks to language to active inference. Now we close the loop: category theory isn’t just a tool for describing AToM’s coherence geometry.

Active inference diagram with categorical structure—Markov categories

Category Theory for Active Inference: The Mathematical Backbone

Series: Applied Category Theory | Part: 9 of 10 In 2022, a paper appeared that changed how computational neuroscientists think about brain architecture. Not because it introduced new experimental data, but because it showed that the Free Energy Principle—Karl Friston’s increasingly influential theory of how systems maintain themselves by

Operad tree structure with multiple inputs composing—algebra of operations

Operads and the Algebra of Composition: From Syntax to Semantics

Series: Applied Category Theory | Part: 8 of 10 Your brain builds sentences by composing words. Neural networks build representations by composing layers. Cells build organisms by composing signals. The question isn’t whether composition happens—it’s how to formalize the rules that make it work. This is what operads