# Holographic Neural PCFG for Unsupervised Parsing

arXiv: https://arxiv.org/abs/2607.08063 · HTML: https://mlsanity.com/paper/2607.08063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Ordered Neurons: Integrating Tree Structures into Recurrent Neural Networks](https://mlsanity.com/paper/1810.09536/) (2018)
- [Compound Probabilistic Context-Free Grammars for Grammar Induction](https://mlsanity.com/paper/1906.10225/) (2019)
- [Unsupervised Latent Tree Induction with Deep Inside-Outside Recursive Autoencoders](https://mlsanity.com/paper/1904.02142/) (2019)
- [A Minimal Span-Based Neural Constituency Parser](https://mlsanity.com/paper/1705.03919/) (2017)
- [Neural Language Modeling by Jointly Learning Syntax and Lexicon](https://mlsanity.com/paper/1711.02013/) (2017)
- [Unsupervised Recurrent Neural Network Grammars](https://mlsanity.com/paper/1904.03746/) (2019)
- [Visually Grounded Compound PCFGs](https://mlsanity.com/paper/2009.12404/) (2020)
- [StructFormer: Joint Unsupervised Induction of Dependency and Constituency Structure from Masked Language Modeling](https://mlsanity.com/paper/2012.00857/) (2020)
- [Unsupervised Parsing via Constituency Tests](https://mlsanity.com/paper/2010.03146/) (2020)
- [PCFGs Can Do Better: Inducing Probabilistic Context-Free Grammars with Many Symbols](https://mlsanity.com/paper/2104.13727/) (2021)
- [The Return of Lexical Dependencies: Neural Lexicalized PCFGs](https://mlsanity.com/paper/2007.15135/) (2020)
- [Neural Bi-Lexicalized PCFG Induction](https://mlsanity.com/paper/2105.15021/) (2021)
- [Fast-R2D2: A Pretrained Recursive Neural Network based on Pruned CKY for Grammar Induction and Text Representation](https://mlsanity.com/paper/2203.00281/) (2022)
- [Dynamic Programming in Rank Space: Scaling Structured Inference with Low-Rank HMMs and PCFGs](https://mlsanity.com/paper/2205.00484/) (2022)
- [Unsupervised Discontinuous Constituency Parsing with Mildly Context-Sensitive Grammars](https://mlsanity.com/paper/2212.09140/) (2022)
- [Contextual Distortion Reveals Constituency: Masked Language Models are Implicit Parsers](https://mlsanity.com/paper/2306.00645/) (2023)
- [Simple Hardware-Efficient PCFGs with Independent Left and Right Productions](https://mlsanity.com/paper/2310.14997/) (2023)
- [Unsupervised Parsing by Searching for Frequent Word Sequences among Sentences with Equivalent Predicate-Argument Structures](https://mlsanity.com/paper/2404.12059/) (2024)
- [Improving Unsupervised Constituency Parsing via Maximizing Semantic Information](https://mlsanity.com/paper/2410.02558/) (2024)

## Abstract (arXiv)

Unsupervised constituency parsing aims to accurately induce latent tree structures from raw text alone. Recent neural parameterizations of PCFGs achieve strong performance in both supervised and unsupervised parsing, yet rely on high-capacity black-box networks for rule scoring -- as exemplified by the Neural PCFG family -- leaving rule probabilities without an interpretable mathematical form. In this paper, we propose Holographic Neural PCFG (Hol-PCFG), which recasts PCFG rule scoring as algebraic relation modeling among grammar-symbol embeddings. Hol-PCFG adapts Holographic Embeddings (Nickel et al., 2016), which scores knowledge-graph triples via circular correlation, to the left-child, right-child, and lexical-emission relations over torus-constrained embeddings, giving every rule probability a closed form that carries the intrinsic structure of grammar rules by construction. Hol-PCFG achieves state-of-the-art parsing performance in six languages while cutting rule-scoring parameters by 99.94% relative to the baseline model and training more stably. Additionally, we demonstrate that Hol-PCFG can parse Japanese directly from characters without any morphological segmentation, retaining nearly the same morpheme-level performance.