WHY CAN'T TRANSFORMERS LEARN MULTIPLICATION? REVERSE-ENGINEERING REVEALS LONG-RANGE DEPENDENCY PITFALLS

Summary from the TLDR AI newsletter

Researchers reverse-engineered why language models fail at simple 4×4 multiplication and found successful models naturally built tree-like attention patterns that "cache" intermediate calculations then retrieve them later, like jotting down a thought on scratch paper. Standard training fails because models learn the easy outer digits first, but get stuck on the middle digits. By adding a simple auxiliary loss that forces the model to predict running totals at each step, models dramatically improve.