CircuitSynth: Reliable Synthetic Data Generation

Zehua Cheng; Wei Dai; Jiahao Sun; Thomas Lukasiewicz

cs.CLApr 11, 2026

CircuitSynth: Reliable Synthetic Data Generation

Authors: Zehua Cheng, Wei Dai, Jiahao Sun, Thomas Lukasiewicz

Organizations: Department of Computer Science, University of Oxford · Institute of Logic and Computation, TU Wien

Abstract

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.

Figures & tables

Figure 1: The CircuitSynth Framework for Reliable Synthetic Data Generation. The architecture decouples semantic reasoning from surface realization1. (Left) The Project-and-Distill protocol uses a Teacher LLM to generate silver-standard semantic plans, which are distilled into a Probabilistic Sentential Decision Diagram (PSDD). (Center) The PSDD serves as the Semantic Prior ( $P_{\Theta}$ ); it structurally guarantees adherence to hard logical constraints ( $\Phi$ ) via logical compilation and satisfies soft distributional constraints via Convex Optimization (PGD). (Right) During generation, the optimized prior samples guaranteed-valid plans ( $z$ ), which drive a Student LLM (Neural Realizer) via Grammar-Constrained Decoding to produce high-fidelity, logically consistent text ( $x$ )

Dataset	Method	SV (%) $\uparrow$	Prec $\uparrow$	CE $\downarrow$	JS $\downarrow$	RCC (%) $\uparrow$	BPT $\downarrow$	PPL $\downarrow$
WebNLG (Standard)	Llama-3.1-8B	76.4	0.82	0.22	0.38	15.2	2.65	12.1
	Qwen 2.5 7B	79.1	0.84	0.20	0.35	16.8	2.58	11.5
	Evol-Instruct	82.5	0.79	0.18	0.31	19.4	2.71	12.8
	GraphRAG	91.2	0.89	0.15	0.25	26.5	2.38	10.9
	TreeSynth	96.8	0.91	0.14	0.21	35.2	2.29	9.8
	ND-PSDD	100.0	0.93	0.29	0.45	10.5	2.98	15.6

Table 1: Detailed Performance Comparison across WebNLG, DART, and ZebraLogic. SV: Schema Validity, Prec: Factuality, CE: Coverage Error (RMSE), JS: Jensen-Shannon, RCC: Rare-Combination Coverage, BPT: Bits-Per-Token. Best results are bolded .

Domain / Category	Source	Valid (Tree)	Valid (Ours)	Fact. (Tree)	Fact. (Ours)	JS (Tree)	JS (Ours)
Airport	WebNLG	98.1	100.0	0.91	0.98	0.12	0.05
Artist	WebNLG	96.5	100.0	0.89	0.97	0.15	0.06
Astronaut	WebNLG	97.2	100.0	0.92	0.99	0.14	0.04
Athlete	WebNLG	95.8	100.0	0.88	0.97	0.18	0.07
Building	WebNLG	94.4	100.0	0.85	0.96	0.21	0.08
CelestialBody	WebNLG	96.1	100.0	0.90	0.98	0.16	0.05

Table 2: Granular Performance Breakdown (Comparison with Strongest Baseline). Comparing TreeSynth (Baseline) vs. CircuitSynth (Ours).

Method Variant	CVR (%) $\downarrow$	KL $\downarrow$	Latency (ms)	Mechanism Responsible
Teacher (Oracle)	12.5	0.18	-	Pure Prompting
CS-NoConst	18.8	0.29	38	Distillation Only
CS-Strict	0.0	0.24	41	Distillation + PSDD
CS-MarginalOnly	14.2	0.08	40	Distillation + Optim
CircuitSynth (Full)	0.0	0.09	42	All Components

Table 3: Ablation of Neuro-Symbolic Components. CVR: Constraint Violation Rate (Hard), DD: Distributional Drift (Soft), Latency: ms/sample.

Synthetic Data Generation

Synthetic data generation creates artificial examples, simulations, and datasets to train, test, or protect machine-learning systems.

See all 609 papers

CasualSynth: Generating Structurally Sound Synthetic Data
May 17, 2026Zehua Cheng, Wei Dai, Jiahao Sun +1Structural Causal Models Synthetic Data Generation
Department of Computer Science, University of Oxford · FLock.io United Kingdom · Institute of Logic and Computation, TU Wien
MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis
Apr 13, 2026Zixiong Yu, Jun Rao, Guhan Chen +5Synthetic Data Generation Synthetic Data Generation for Language Models
Huawei Large Model Data Technology Lab · Tsinghua University · Harbin Institute of Technology, Shenzhen +1
ORACLE: Optimizing Reasoning Abilities of Large Language Models via Constraint-Led Synthetic Data Elicitation
Mar 22, 2026Zhuojie Yang, Wentao Wan, Keze WangSynthetic Data Generation for Language Models LLM Reasoning
School of Computer Science and Engineering, Sun Yat-sen University

May 17, 2026J/K move · Enter open · S save

CasualSynth: Generating Structurally Sound Synthetic Data

Zehua Cheng, Wei Dai, Jiahao Sun, Thomas Lukasiewicz

Department of Computer Science, University of Oxford · FLock.io United Kingdom · Institute of Logic and Computation, TU Wien

Structural Causal Models Synthetic Data Generation Causal Reasoning in Language Models Causal Inference Synthetic Data Evaluation

Open paper AskPDF arXiv

Large Language Models (LLMs) generate realistic synthetic data but offer no guarantee that their outputs respect the causal mechanisms governing the target domain. We introduce CausalSynth, a framework that decouples causal structure generation from semantic realization, yielding synthetic data that is both causally valid and linguistically rich. The framework operates in three phases. First, a Structural Causal Model (SCM) - a tuple of structural equations defined over a directed acyclic graph (DAG) generates causal skeletons, i.e., variable assignments that satisfy the Global Markov Property of the governing DAG, via ancestral sampling. Second, an LLM acts as a constrained realizer, a conditional translator that maps each skeleton to a high-dimensional observation such as a clinical note or a transaction log. Third, an Iterative Consistency Verification module detects structural violations through deterministic extraction and feeds targeted corrections back to the LLM, forming a closed-loop refinement process. We identify the Semantic Backdoor problem the systematic tendency of LLMs to override imposed causal facts with pre-training priors -- and prove that our iterative mechanism reduces the resulting selection bias relative to standard rejection sampling. On three causal benchmarks (ASIA, ALARM, and MIMIC-Struct), CausalSynth preserved conditional independencies with false-positive rates near the nominal

α=0.05

level and achieved realizability rates above 96% with 70B-parameter LLM backbones. The framework additionally supports principled interventional and counterfactual generation through noise retention and graph mutilation.

Abstract

Synthetic Data Generation

Explore similar work

CasualSynth: Generating Structurally Sound Synthetic Data

MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis

ORACLE: Optimizing Reasoning Abilities of Large Language Models via Constraint-Led Synthetic Data Elicitation