# CircuitSynth: Reliable Synthetic Data Generation

arXiv: https://arxiv.org/abs/2604.10114 · HTML: https://mlsanity.com/paper/2604.10114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Synthetic reasoning data and bootstrapping, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 11 Apr 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 13 of 13)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [DART: Open-Domain Structured Data Record to Text Generation](https://mlsanity.com/paper/2007.02871/) (2020)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [Guiding LLMs The Right Way: Fast, Non-Invasive Constrained Generation](https://mlsanity.com/paper/2403.06988/) (2024)
- [Scaling Up Probabilistic Circuits by Latent Variable Distillation](https://mlsanity.com/paper/2210.04398/) (2022)
- [Scaling Tractable Probabilistic Circuits: A Systems Perspective](https://mlsanity.com/paper/2406.00766/) (2024)
- [Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits](https://mlsanity.com/paper/2302.08086/) (2023)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [Building Expressive and Tractable Probabilistic Generative Models: A Review](https://mlsanity.com/paper/2402.00759/) (2024)
- [TreeSynth: Synthesizing Diverse Data from Scratch via Tree-Guided Subspace Partitioning](https://mlsanity.com/paper/2503.17195/) (2025)

## Built on by (most cited first, 1 of 1)

- [this-that-model-1.0: A typed decision model that decides in 30 ms, for a millionth of a cent](https://mlsanity.com/paper/2609.23886/) (2026)

## Abstract (arXiv)

The generation of high-fidelity synthetic data is a cornerstone of modern machine learning, yet Large Language Models (LLMs) frequently suffer from hallucinations, logical inconsistencies, and mode collapse when tasked with structured generation. Existing approaches, such as prompting or retrieval-augmented generation, lack the mechanisms to balance linguistic expressivity with formal guarantees regarding validity and coverage. To address this, we propose CircuitSynth, a novel neuro-symbolic framework that decouples semantic reasoning from surface realization. By distilling the reasoning capabilities of a Teacher LLM into a Probabilistic Sentential Decision Diagram (PSDD), CircuitSynth creates a tractable semantic prior that structurally enforces hard logical constraints. Furthermore, we introduce a convex optimization mechanism to rigorously satisfy soft distributional goals. Empirical evaluations across diverse benchmarks demonstrate that CircuitSynth achieves 100% Schema Validity even in complex logic puzzles where unconstrained baselines fail (12.4%) while significantly outperforming state-of-the-art methods in rare-combination coverage.