Stanford professor Thomas Icard is advancing mechanistic interpretability by applying causal abstraction — tools from causality theory — to understand how large language models implement algorithms at higher levels of abstraction. The central question is whether neural networks merely mimic reasoning or internally construct logical reasoning systems. Icard's framework makes precise what it means for a neural network to implement an algorithm beyond low-level matrix multiplications, searching for interpretable concepts from cognitive science and logic.

In a 2021 study led by then-Ph.D. student Atticus Geiger, now at Goodfire AI, researchers showed a BERT-based model internally implements elements of a logical reasoning system, learning algorithms for complex inferences involving quantifiers and negation. More recently, Goodfire AI's "Arithmetic in the Wild" paper revealed a Llama-based model reasons about cyclic concepts — months, weekdays, clock time — by first performing decimal addition (treating August as month 8, calculating 8+6=14) then applying modulo arithmetic (14=12+2, yielding February). The model applies this same general calculation strategy across different cyclic domains without explicit instruction.

Academic researchers are constrained to open-source models like Llama and OLMo at around ten billion parameters, while companies including Anthropic and Google DeepMind maintain internal interpretability teams. Current goals include making models safer, more reliable, efficient, and less biased. Major challenges remain in scaling techniques to larger models and automating interpretability processes that still depend heavily on human insight. Icard concludes mechanistic interpretability will not reduce LLMs to simple equations but may gradually turn deep neural networks into systems whose hidden algorithms can be partly understood.