SIGS-GrammarVAE

SIGS Grammar-VAE

SIGS is a grammar-guided neuro-symbolic system for discovering closed-form analytical solutions to ordinary and partial differential equations. This repository contains the trained Grammar-VAE state dictionary and its architecture configuration.

Model description

The model maps grammar production sequences into a 32-dimensional latent space using a one-dimensional convolutional encoder and reconstructs valid symbolic expressions with a GRU decoder. SIGS clusters the latent representations by the variables present in each expression and samples the relevant regions during PDE solution discovery.

This repository is part of the broader SIGS release:

• Source code
• Paper
• Expression dataset
• Interactive PDE Agent

Architecture

• Encoder: Conv1D channels 64, 128, and 256 with kernel sizes 2, 3, and 4
• Latent dimension: 32
• Decoder: one-layer GRU with hidden size 512
• Grammar production vocabulary: 53
• Maximum production-sequence length: 72

The exact training and topology settings are stored in config.yaml.

Loading the weights

The tensor names match sigs.training.GrammarVAEModel in the source repository:

import yaml
from safetensors.torch import load_file
from sigs.training import GrammarVAEModel

with open("config.yaml") as file:
    config = yaml.safe_load(file)

model = GrammarVAEModel(config)
model.load_state_dict(load_file("model.safetensors"), strict=True)
model.eval()

The published conversion was checked with strict loading: all 13 state entries matched the current architecture with no missing or unexpected keys.

Files

• model.safetensors — tensor-only state dictionary converted from the training checkpoint
• config.yaml — architecture and training configuration
• convert_checkpoint.py — reproducible conversion with source SHA-256 verification

The original checkpoint SHA-256 is 2c6834a9df30a5c189aeec073005b409f91d6596506cfaae698dacbbcfd16f7c.

Intended use

The model is intended for research in grammar-guided symbolic regression and analytical ODE/PDE solution discovery. It is not a general-purpose theorem prover, numerical PDE solver, or guarantee that a generated expression satisfies a differential equation.

Candidate expressions must be verified independently against the governing equation, initial conditions, and boundary conditions. The accompanying Space demonstrates residual verification for several reference PDEs.

Limitations

• The grammar covers a fixed set of arithmetic and elementary transcendental operations.
• Expression length is limited by the 72-step production representation.
• Latent sampling does not guarantee syntactic completion or physical validity.
• Reported results depend on the PDE residual, sampling budget, domain, and optimization procedure.
• The weights are released as a state dictionary; users must instantiate the architecture from the SIGS source repository and config.yaml.

Training data

The model was trained on 23,695 generated symbolic expressions. The Hub dataset includes the expressions, variable-presence labels, mathematical class, and 32-dimensional latent statistics.

Citation

@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}
}