The new paradigm of deep thinking of alternating "inference-erasure" (PENCIL ENables Context-efficient Inference and Learning, referred to as PENCIL) was proposed by Yang Chenxiao, a doctoral student at Toyota Technological University Chicago, and his team in March 2025. The relevant research results were published in the paper "PENCIL: Long Thoughts with Short Memory", this work has been included in ICML 2025.

PENCIL aims to allow large models to dynamically erase unnecessary intermediate results during the generation process until the final answer is obtained. Its design draws on the rewriting rule in logic and classical automatic theorem proving and the stack frame memory management in functional programming languages. PENCIL can perform general space-efficient computations by simulating Turing machines with optimal time and space complexity, thereby solving arbitrary computational tasks that are difficult to solve under context window constraints.