https://tomarcher.io/learningpaths/inside-the-transformer/Recent content in Inside the Transformer on Signal & SyntaxHugoen-usSat, 22 Aug 2026 06:00:00 -0700https://tomarcher.io/posts/inside-attention-part-1/Sat, 22 Aug 2026 06:00:00 -0700https://tomarcher.io/posts/inside-attention-part-1/The transformer architecture is composed of many repeating transformer layers, or blocks. Each block contains an attention sublayer followed by a feedforward sublayer, wrapped in residual connections and layer normalization. Positional information is added to the input so the model knows what order the tokens came in. The attention sublayer sets the table for the feedforward sublayer: it does the work of looking at other tokens and deciding what information to absorb from them.https://tomarcher.io/posts/discrete-math-in-large-language-models/Tue, 31 Mar 2026 06:00:00 -0700https://tomarcher.io/posts/discrete-math-in-large-language-models/A recent LinkedIn post from Michael Palmer described how discrete mathematics is the foundation for how computers reason about problems. That thread got me thinking about just how many discrete math concepts show up inside systems that seem purely statistical. LLMs are often described in terms of neural networks, gradient descent, and probability distributions. If you’ve taken discrete mathematics and wondered what it has to do with modern AI, the answer is: more than you’d expect.https://tomarcher.io/posts/how-large-language-models-think/Tue, 07 Oct 2025 06:00:00 -0700https://tomarcher.io/posts/how-large-language-models-think/When you enter a sentence into a Large Language Model (LLM) such as ChatGPT or Claude , the model does not process words as language. It represents them as numbers. Each word, phrase, and code token becomes a vector — a list of real-valued coordinates within a high-dimensional space. Relationships between meanings are captured not by grammar or logic but by geometry. The closer two vectors lie, the more similar their semantic roles appear to the model.