LLMs Don't Calculate - They Just Remember Everything

Explore the inner workings of large language models through a detailed mechanistic interpretability analysis that reveals how GPT-OSS-20B performs arithmetic operations. Discover through rigorous experimentation that LLMs don't actually compute mathematical operations but instead rely on sophisticated lookup tables stored in their neural networks. Learn how the researcher spent a week extracting and analyzing the model's arithmetic capabilities, uncovering that every mathematical operation uses completely separate neural pathways with zero overlap between different operations. Examine the surprising finding that addition and subtraction aren't mathematical opposites in the model's representation, sitting at 80 degrees apart rather than 180 degrees, and that single-digit and two-digit multiplication utilize entirely different neurons positioned 89 degrees apart. Understand how exact string matching affects performance, where "7*8=" produces correct results while "7*8" fails, and witness catastrophic out-of-distribution failure when models trained on digits 2-9 are tested on 1, 10, or 11. Follow the presentation of the first causal proof demonstrating how steering a single neuron can change whether the model looks up an answer or decomposes the problem, allowing you to observe intermediate computational steps appearing across different layers. Access reproducible findings with provided commands and tools including the Lazarus circuit extraction framework, while exploring six distinct strategies that are all variations of lookup operations rather than true mathematical computation.