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.

Dense retrieval models usually adopt vectors from the last hidden layer of the document encoder to represent a document, which is in contrast to the fact that representations in different layers of a pre-trained language model usually contain different kinds of linguistic knowledge, and behave differently during fine-tuning. Therefore, we propose to investigate utilizing representations from multiple encoder layers to make up the representation of a document, which we denote Multi-layer Representations (MLR). We first investigate how representations in different layers affect MLR’s performance under the multi-vector retrieval setting, and then propose to leverage pooling strategies to reduce multi-vector models to single-vector ones to improve retrieval efficiency. Experiments demonstrate the effectiveness of MLR over dual encoder, ME-BERT and ColBERT in the single-vector retrieval setting, as well as demonstrate that it works well with other advanced training techniques such as retrieval-oriented pre-training and hard negative mining.