This repository contains the grammar variational autoencoder used by SIGS, Neuro-Symbolic AI for Analytical Solutions of Differential Equations (Oikonomou et al., ICML 2026).

Model description

SIGS embeds syntactically valid mathematical expressions into a continuous latent space and decodes latent vectors under a context-free grammar. The wider SIGS pipeline searches that space for closed-form candidates and then refines their constants against differential-equation residuals.

This is a grammar model, not a natural-language model. Its inputs are one-hot grammar-production sequences with shape [batch, productions, sequence_length].

Loading

Install SIGS with its Hugging Face dependencies, then load the checkpoint:

python

from sigs.huggingface import SIGSModel

model = SIGSModel.from_pretrained("oroikono/sigs-icml-2026")

The associated production-sequence corpus can be represented with Hugging Face Datasets, and examples/train_with_accelerate.py provides a distributed training entry point.

Intended use

Research on grammar-guided symbolic generation.
Reproducing the symbolic proposal component of SIGS.
Closed-form differential-equation solution discovery with the wider SIGS search and residual-refinement pipeline.

Limitations

Generated candidates are restricted to the published grammar and maximum production-sequence length.
The model alone does not certify that an expression solves a differential equation; residual, initial-condition, and boundary-condition checks remain necessary.
Performance outside the PDE families and expression corpus reported in the paper has not been established.

Citation

bibtex

@misc{oikonomou2026neurosymbolic,
  title={Neuro-Symbolic AI for Analytical Solutions of Differential Equations},
  author={Oikonomou, Orestis and Lingsch, Levi and Grund, Dana and Mishra, Siddhartha and Kissas, Georgios},
  year={2026},
  eprint={2502.01476},
  archivePrefix={arXiv},
  primaryClass={cs.LG}
}