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Neural-Symbolic Recursive Machine for Systematic Generalization
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Proposes the Neural-Symbolic Recursive Machine (NSR), which induces a grounded symbol system from data via neural perception, dependency parsing and program induction, trained with a deduction-abduction algorithm, reaching near-perfect systematic generalization on SCAN, PCFG, HINT and a compositional translation task.
Problem
Systematic (compositional) generalization of learning models: learning compositional rules from limited data and extrapolating to novel combinations, without domain-specific knowledge or specialized curricula.
Approach
A Grounded Symbol System (directed tree of grounded input, abstract symbol, and semantic value) is induced from data by a modular stack of neural perception, a transition-based dependency parser, and functional program induction (DreamCoder-based), trained end-to-end via a deduction-abduction sampler that generates pseudo-supervision for the latent tree.
Key results
- NSR reaches 100% accuracy on all SCAN splits (Simple, Jump, Around Right, Length) and all PCFG splits (i.i.d., systematicity, productivity).
- On HINT with symbol input, NSR averages 90.1% versus 61.5% for the Transformer; with image input, 76.0% versus 53.1%.
- On compositional machine translation, NSR achieves 100% accuracy versus 14.4% for Transformer and 12.5% for Seq2Seq.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NSR instead of Transformer | SCAN Length · SCAN Length | accuracy: 20.0 -> 100.0 | Helped |
| Use NSR instead of Transformer | PCFG systematicity · PCFG systematicity | accuracy: 96 -> 100 | Helped |
| Use NSR instead of Transformer | PCFG productivity · PCFG productivity | accuracy: 85 -> 100 | Helped |
| Use NSR instead of Transformer with symbol input | HINT · HINT Avg. symbol input | accuracy: 61.5 -> 90.1 | Helped |
| Use NSR instead of Transformer with image input | HINT · HINT Avg. image input | accuracy: 53.1 -> 76.0 | Helped |
| Use NSR instead of Transformer on long expressions with image input | HINT · HINT LL image input | accuracy: 19.0 -> 58.2 | Helped |
| Use NSR instead of NeSS | PCFG · PCFG systematicity | accuracy: $\approx$0 -> 100 | Helped |
| Use NSR instead of NeSS | HINT · HINT symbol input Avg. | accuracy: $\approx$0 -> 90.1 | Helped |
| Use NSR instead of Seq2Seq | Compositional machine translation · Compositional machine translation | accuracy: 12.5 -> 100.0 | Helped |
Surprising findings
- NeSS achieves 100% on SCAN but fails (near 0%) on PCFG and HINT, indicating its domain-specific design does not transfer.
- Without category predictors, NeSS drops to about 20% on SCAN in 3 of 5 runs.
Limitations
- Scaling to real-world tasks may be hampered by noisy, abundant concepts enlarging the grounded symbol space and slowing training.
- Deterministic functional programs cannot represent probabilistic semantics such as multiple valid translations.
Experimental setup
Datasets: SCAN PCFG HINT compositional machine translation dataset (10,000 pairs)
Benchmarks: SCAN PCFG HINT compositional machine translation
Metrics: test accuracy
Baselines: Seq2Seq CNN Transformer equivariant Seq2seq NeSS GRU LSTM
Builds on: DreamCoder NeSS transition-based dependency parser REINFORCE
Closest papers by meaning
- Compositional Generalization via Neural-Symbolic Stack Machines (NeurIPS 2020 · similarity 0.90)
- NeSyCoCo: A Neuro-Symbolic Concept Composer for Compositional Generalization (AAAI 2025 · similarity 0.88)
- Mastering Symbolic Operations: Augmenting Language Models with Compiled Neural Networks (ICLR 2024 · similarity 0.87)
- Training Neural Networks as Recognizers of Formal Languages (ICLR 2025 · similarity 0.87)
- CraftFactory: A Conditioned Control Policy Benchmark for Compositional Generalization (AAAI 2025 · similarity 0.87)
- Emergent Symbolic Mechanisms Support Abstract Reasoning in Large Language Models (ICML 2025 · similarity 0.86)
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