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 s prompting or retrieval-augmented generaon, 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.

The large language models offer a scaleable solution for the generation of synthetic data faced with a trade-off between maintaining the diversity of generation and achieving factually accurate results. This paper introduces Graphsynth, a framework which leverages a probabilistic factor graph modeling the universe of attributes. The framework leverages a high-level schema mapping compiled into efficient hard masks during the decoding phase for maintaining the syntactic truth and a span-synchronized verifier for dismissing logical contradictions at the decode time. The experiments conducted on biomedical, legal, and generic domains show that the method outperforms the state-of-the-art baselines with a structural integrity approaching perfection, a coverage of around 94% attributes on the factor graph solution, and a boost in performance on downstream tasks such as +17.9% on TruthfulQA.

Large language models (LLMs) have made significant advancements, but their increasing capabilities present serious risks of misuse, particularly in open-weight models where direct access to the model’s parameters is possible. Current safeguards, designed for closed-weight API models, are inadequate for open-weight models, as minimal fine-tuning can bypass these protections. Preserving the integrity of open-weight LLMs before deployment has thus become a critical challenge. We argue that these vulnerabilities stem from the overemphasis on maximizing the LLM’s log-likelihood during training, which amplifies data biases, especially with large datasets. To address these issues, we introduce Kahneman and Tversky’s Prospect Theoretic Integrity Preserving Alignment (KT-IPA), a framework that prioritizes maximizing generative utility rather than a singular optimization metric. This approach strengthens LLMs against misuse and weaponization while maintaining high performance, even after extensive fine-tuning. Our results demonstrate that integrating prospect theory into LLM training enhances robustness, security, and responsible innovation in this rapidly evolving field. Our codes are available on https://anonymous.4open.science/r/KT-IPA-40B7