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RefineStat: Efficient Exploration for Probabilistic Program Synthesis

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
Probabilistic ProgrammingConstrained Generation
Abstract:

Probabilistic programming offers a powerful framework for modeling uncertainty, yet statistical model discovery in this domain entails navigating an immense search space under strict domain‐specific constraints. When small language models are tasked with generating probabilistic programs, they frequently produce outputs that suffer from both syntactic, and semantic errors, such as flawed inference constructs. Motivated by probabilistic programmers’ domain expertise and debugging strategies, we introduce RefineStat, a language model–driven framework that enforces semantic constraints ensuring synthesized programs contain valid distributions, well‐formed parameters, and then applies diagnostic‐aware refinement by resampling prior or likelihood components whenever reliability checks fail. We evaluate RefineStat on multiple probabilistic-programming code-generation tasks using smaller language models (SLMs) and find that it produces programs that are both syntactically sound and statistically reliable, often matching or surpassing those from closed-source large language models (e.g., OpenAI o3).

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces RefineStat, a framework for generating syntactically and semantically valid probabilistic programs using smaller language models. It resides in the 'Diagnostic-Aware Refinement for Probabilistic Program Generation' leaf, which currently contains only this work as its sole member. This leaf sits within the broader 'Language Model-Guided Program Synthesis and Search' branch, which includes three distinct approaches: LLM-guided enumerative synthesis with formal specifications, sequential Monte Carlo steering of language models, and the diagnostic-aware refinement category. The sparsity of this specific leaf suggests the diagnostic-driven refinement approach for probabilistic programs represents a relatively unexplored direction within the field.

The taxonomy reveals neighboring work in adjacent leaves that tackle related but distinct challenges. Sequential Monte Carlo steering methods enforce syntactic and semantic constraints at inference time through posterior inference mechanisms, while LLM-guided enumerative synthesis integrates language models into weighted search algorithms for formal specifications. The 'Natural Language to Probabilistic Program Translation' branch addresses specification-to-code conversion rather than data-driven synthesis, and 'Amortized and Learned Inference' focuses on accelerating inference within existing programs rather than generating new ones. RefineStat's diagnostic-aware approach bridges neural generation with symbolic verification, distinguishing it from these neighboring directions by emphasizing iterative repair guided by statistical test failures.

Among the 27 candidate papers examined through semantic search and citation expansion, none clearly refute any of RefineStat's three core contributions. The REFINESTAT framework contribution examined 10 candidates with zero refutable matches, semantic constrained decoding examined 7 candidates with zero refutations, and the diagnostic-aware iterative refinement procedure examined 10 candidates with zero refutations. This limited search scope suggests that within the top-30 semantically similar papers, the specific combination of semantic constraint enforcement and diagnostic-driven resampling for probabilistic program generation appears novel. However, the analysis does not claim exhaustive coverage of all potentially relevant prior work beyond these examined candidates.

The assessment reflects a focused literature search rather than comprehensive field coverage. The taxonomy structure indicates RefineStat occupies a sparse research direction, with no sibling papers in its immediate leaf and limited overlap detected among examined candidates. The framework's integration of domain-specific constraints with diagnostic feedback for probabilistic programs appears distinctive within the analyzed scope, though broader searches or domain-specific venues might reveal additional related work not captured in this top-K semantic retrieval.

Taxonomy

Core-task Taxonomy Papers
41
3
Claimed Contributions
27
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Probabilistic program synthesis from data using language models. This field sits at the intersection of probabilistic reasoning and neural program generation, aiming to produce executable probabilistic programs that capture uncertainty and structure from observed data. The taxonomy reveals several complementary directions: Neural-Symbolic Integration explores how to embed probabilistic logic within differentiable architectures (e.g., DeepProbLog[6], DeepStochLog[19]), enabling end-to-end learning of symbolic rules with neural components. Language Model-Guided Program Synthesis and Search leverages pretrained models to propose candidate programs, often combining enumeration with learned heuristics (Guiding Enumerative Synthesis[1], Thinksum[3]). Natural Language to Probabilistic Program Translation focuses on converting informal specifications into formal probabilistic code (ScenicNL[2], Generating Scenario Programs[16]), while Amortized and Learned Inference develops neural approximations to posterior inference in probabilistic programs (Inference Compilation[31], Deep Amortized Inference[27]). Compositional and Modular Program Generation emphasizes building complex programs from reusable components (Compositional Program Generation[22]), and Domain-Specific Applications demonstrate synthesis in areas like robotics (Robot Learning Synthesis[8]) and supply chain optimization (Supply Chain Optimization[36]). Theoretical Foundations provide comparative analyses across paradigms (Program Synthesis Paradigms[26]). A particularly active line of work explores how language models can iteratively refine candidate programs using execution feedback and diagnostic signals, balancing exploration with targeted repair. RefineStat[0] exemplifies this diagnostic-aware refinement approach within the Language Model-Guided branch, using statistical test failures to guide revision of probabilistic programs. This contrasts with more enumerative methods like Guiding Enumerative Synthesis[1], which prioritizes search efficiency through learned scoring, and differs from natural-language-first approaches such as ScenicNL[2], which emphasizes translating informal scenario descriptions. Meanwhile, works like Thinksum[3] and General Pattern Machines[4] highlight alternative strategies—Thinksum[3] focuses on reasoning chains for mathematical problem solving, while General Pattern Machines[4] explores meta-learning over program spaces. The central tension across these branches involves trade-offs between sample efficiency, interpretability of generated programs, and the ability to incorporate domain-specific constraints or probabilistic semantics, with RefineStat[0] contributing a feedback-driven refinement mechanism that bridges neural generation and symbolic verification.

Claimed Contributions

REFINESTAT framework for probabilistic program synthesis

A novel framework that uses small language models to generate probabilistic programs by enforcing semantic constraints during generation and applying diagnostic-aware refinement to ensure statistical reliability according to Bayesian workflow standards.

10 retrieved papers
Semantic constrained decoding for probabilistic programs

A constrained decoding approach that enforces validity predicates including distribution validity, parameter validity, dependency validity, support validity, and type validity to ensure generated probabilistic programs are both syntactically and semantically correct.

7 retrieved papers
Diagnostic-aware iterative refinement procedure

An iterative search procedure that systematically resamples prior or likelihood components when Bayesian workflow reliability checks fail, enabling a single small language model to produce statistically reliable programs without requiring multiple model instances.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

REFINESTAT framework for probabilistic program synthesis

A novel framework that uses small language models to generate probabilistic programs by enforcing semantic constraints during generation and applying diagnostic-aware refinement to ensure statistical reliability according to Bayesian workflow standards.

Contribution

Semantic constrained decoding for probabilistic programs

A constrained decoding approach that enforces validity predicates including distribution validity, parameter validity, dependency validity, support validity, and type validity to ensure generated probabilistic programs are both syntactically and semantically correct.

Contribution

Diagnostic-aware iterative refinement procedure

An iterative search procedure that systematically resamples prior or likelihood components when Bayesian workflow reliability checks fail, enabling a single small language model to produce statistically reliable programs without requiring multiple model instances.

Table of Contents