ReForm: Reflective Autoformalization with Prospective Bounded Sequence
  Optimization
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.
69017aff646208eac0d1f3cb
Guoxin Chen
claimed_verified
2025-10-29T12:45:10.856Z
63f06116f1a47aaea5bd497b
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Guoxin Chen
GuoxinChen
user
GuoxinChen
69017aff646208eac0d1f3cc
Jing Wu
69017aff646208eac0d1f3cd
Xinjie Chen
69017aff646208eac0d1f3ce
Wayne Xin Zhao
69017aff646208eac0d1f3cf
Ruihua Song
69017aff646208eac0d1f3d0
Chengxi Li
claimed_verified
2025-12-25T20:54:26.992Z
6486e362c9d77c91be1ee2bf
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Chengxi Li
MrZixi
user
MrZixi
69017aff646208eac0d1f3d1
Kai Fan
69017aff646208eac0d1f3d2
Dayiheng Liu
69017aff646208eac0d1f3d3
Minpeng Liao
ReForm: Reflective Autoformalization with Prospective Bounded Sequence
  Optimization
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.
ReForm, a reflective autoformalization method, improves the semantic accuracy of formal statements generated from natural language mathematics through iterative refinement and semantic consistency evaluation.
autoformalization Large Language Models semantic consistency evaluation iterative refinement Prospective Bounded Sequence Optimization PBSO ConsistencyCheck