Contextual Counting: A Mechanistic Study of Transformers on a Quantitative Task

This paper presents the contextual counting task, a novel benchmark to evaluate Transformers' quantitative and scientific reasoning abilities. It compares causal and non-causal architectures, with causal models generally outperforming non-causal ones. Positional encodings, like rotary embeddings (RoPE), are found to be competitive, while absolute positional embeddings (AbsPE) and some others yield less accurate results. The study highlights the importance of understanding Transformer decision-making, particularly in high-stakes applications, and links out-of-distribution performance to bias tokens. It also explores the role of encoder-decoder structures and the ability of models to learn regional context without explicit position markers. The contextual counting task serves as a test for generalization and the simulation of continuous computations in Transformers.