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Relational Neurosymbolic Markov Models

AAAI 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Sparse concepts and hypothesis testing · 6 citations (OpenAlex)

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Introduces relational neurosymbolic Markov models (NeSy-MMs), differentiable sequential models whose states mix neural and relational-logic symbols, trained with a Rao-Blackwellised particle filter plus RLOO gradient estimation.

Problem

Sequential probabilistic models (e.g., transformers, HMMs) cannot guarantee logical constraints, while existing neurosymbolic systems scale exponentially with sequence length and cannot exploit Markov structure or handle neural transitions.

Approach

Model neurosymbolic states as (neural, relational symbolic) pairs with a Markov transition defined by relational logic plus neural networks; perform exact conditioning on finite parts via cluster factorisation and a Rao-Blackwellised particle filter, making the whole pipeline differentiable via RLOO gradient estimation instead of resampling.

Key results

• On the generative task with 5x5 grids, NeSy-MM reaches 97.17% reconstruction accuracy versus 91.39% for the variational transformer; on 10x10 it reaches 89.63% vs 30.62%.
• In the discriminative task, NeSy-MM achieves the best balanced accuracy in most out-of-distribution settings, e.g. 77.13% vs 41.54% for the transformer on N=15, T=20, E=2.
• VAEL fails to perform inference on a single length-10 sequence on a 3x3 grid within a 6h timeout, while NeSy-MM runs a forward and backward pass over a batch in about 0.25s.

Measured effects reported in the paper

Surprising findings

• The variational transformer achieves better reconstruction error than NeSy-MM on the 10x10 grid (2.23 vs 3.78), despite much lower reconstruction accuracy.
• The transformer is best in-distribution in the discriminative task (75.72 vs 64.45 balanced accuracy for NeSy-MM at N=10, T=10, E=1), so NeSy-MM does not dominate everywhere.

Limitations

• Discriminative experiments are limited to a custom NetHack-inspired simulator with only one or two enemies.
• Deep-HMM cannot be applied to larger grid sizes, and VAEL cannot scale to sequences of length 10 even on small grids.
• Requires exact conditioning of transition distributions on finite variables, which can still be costly; infinite variables rely on specialised gradient estimators.

Experimental setup

Datasets: MiniHack-based grid-world trajectories (generative) symbolic grid-world trajectories with enemies (discriminative)

Benchmarks: generative grid-world reconstruction (RE, RA) discriminative NetHack-inspired death prediction (balanced accuracy, F1)

Metrics: reconstruction error reconstruction accuracy balanced accuracy F1-score

Baselines: VAEL variational transformer Deep-HMM transformer

Builds on: DeepSeaProbLog VAEL RLOO Rao-Blackwellised particle filter weighted model integration

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• EM-NeSy: Expectation Maximization for Neurosymbolic Learning (NeurIPS 2026 · similarity 0.88)
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