ReForm: Reflective Autoformalization with Prospective Bounded Sequence
  Optimization
Authors: name: Guoxin Chen, name: Jing Wu, name: Xinjie Chen, name: Wayne Xin Zhao, name: Ruihua Song, name: Chengxi Li, name: Kai Fan, name: Dayiheng Liu, name: Minpeng Liao

Autoformalization, which translates natural language mathematics into
machine-verifiable formal statements, is critical for using formal mathematical
reasoning to solve math problems stated in natural language. While Large
Language Models can generate syntactically correct formal statements, they
often fail to preserve the original problem's semantic intent. This limitation
arises from the LLM approaches' treating autoformalization as a simplistic
translation task which lacks mechanisms for self-reflection and iterative
refinement that human experts naturally employ. To address these issues, we
propose ReForm, a Reflective Autoformalization method that tightly integrates
semantic consistency evaluation into the autoformalization process. This
enables the model to iteratively generate formal statements, assess its
semantic fidelity, and self-correct identified errors through progressive
refinement. To effectively train this reflective model, we introduce
Prospective Bounded Sequence Optimization (PBSO), which employs different
rewards at different sequence positions to ensure that the model develops both
accurate autoformalization and correct semantic validations, preventing
superficial critiques that would undermine the purpose of reflection. Extensive
experiments across four autoformalization benchmarks demonstrate that ReForm
achieves an average improvement of 17.2 percentage points over the strongest
baselines. To further ensure evaluation reliability, we introduce
ConsistencyCheck, a benchmark of 859 expert-annotated items that not only
validates LLMs as judges but also reveals that autoformalization is inherently
difficult: even human experts produce semantic errors in up to 38.5% of cases.