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Mastering Symbolic Operations: Augmenting Language Models with Compiled Neural Networks
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Proposes Neural Comprehension, which plugs compiled neural networks (CoNNs, built via Tracr/RASP and an LLM-based AutoCoNN toolkit) into a pretrained LM with a gating scheme so that rule-based symbolic operations are executed exactly.
Problem
Language models struggle with deterministic symbolic operations and rule-based tasks (e.g., multi-digit addition, length generalization) because they learn rules implicitly from text statistics.
Approach
Integrate transformer modules whose attention weights are compiled from human-specified rules (CoNNs) into a standard LM, with a MoE-style gate that decides when a CoNN's one-hot output replaces the LM's token distribution, so the rule is executed without tools or interpreters.
Key results
- On GSM8K-Hard addition subset, NC reaches 21.2% average solve rate versus 20.8% for PAL and 18.8% for CoT across llama-2-7b, llama-2-70b and GLM-130B.
- With code-davinci-002 (GPT-3.5), CoT + NC gives 81.29% average versus 81.20% for CoT across five arithmetic datasets (small gain).
- CoNN parameter counts range from about 8.8K to 51.8M, roughly 1/3,000 to 1/20,000,000 of GPT-3, and latency rises only 1%-3% per the authors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| integrate Addition and Subtraction CoNNs | GPT-3 (175B) CoT · GSM8K | problem solve rate (%): 13.84 -> 13.95 (+0.11) | Helped |
| integrate Addition and Subtraction CoNNs | GPT-3 (175B) CoT · SingleEq | problem solve rate (%): 62.02 -> 62.83 (+0.81) | Helped |
| integrate Addition and Subtraction CoNNs | GPT-3 (175B) CoT · AddSub | problem solve rate (%): 57.22 -> 60.25 (+3.03) | Helped |
| integrate Addition and Subtraction CoNNs | GPT-3 (175B) CoT · MultiArith | problem solve rate (%): 45.85 -> 45.85 (+0.0) | No clear effect |
| integrate Addition and Subtraction CoNNs | GPT-3 (175B) CoT · SVAMP | problem solve rate (%): 38.42 -> 38.62 (+0.2) | Helped |
| integrate Addition and Subtraction CoNNs | GPT-3.5 (175B) CoT · SingleEq | problem solve rate (%): 91.01 -> 91.01 (+0.0) | No clear effect |
| integrate Addition and Subtraction CoNNs | GPT-3.5 (175B) CoT · GSM8K | problem solve rate (%): 60.20 -> 60.42 (+0.22) | Helped |
| use explicit operational instructions instead of Examples alone (ablation) | AutoCoNN · Parity CoNN generation | successful generations: 3/20 -> 7/20 | Helped |
| use explicit operational instructions instead of Examples alone (ablation) | AutoCoNN · Reverse CoNN generation | successful generations: 11/20 -> 16/20 | Helped |
| use explicit operational instructions instead of Examples alone (ablation) | AutoCoNN · Last Letter CoNN generation | successful generations: 10/20 -> 12/20 | Helped |
| use explicit operational instructions instead of Examples alone (ablation) | AutoCoNN · Copy CoNN generation | successful generations: 15/20 -> 17/20 | Helped |
| increase training data from 1 million to 15 million examples (ablation) | T5-large · symbolic operations OOD length generalization | OOD performance | No clear effect |
Surprising findings
- Adding CoNN modules to GPT-3.5 yields near-zero gains on standard arithmetic datasets (e.g., 0.0 on SingleEq and AddSub), which the authors attribute to limited CoNN coverage.
- AutoCoNN failed to generate working Addition or Subtraction CoNNs (0/20), though it produced working Parity, Reverse, Last Letter and Copy modules.
Limitations
- Gating is sparse and treats LM and CoNNs as separate modules rather than a dense integration.
- AutoCoNN fails on harder operations such as Addition and Subtraction; scalability to many CoNNs is untested (up to five stacked).
- Addition and Subtraction CoNNs only support natural numbers, with minuend greater than subtrahend for subtraction.
Experimental setup
Datasets: GSM8K AddSub SingleEq MultiArith SVAMP GSM8K-Hard
Benchmarks: GSM8K SingleEq AddSub MultiArith SVAMP GSM8K-Hard AddSub+ length generalization addition (1-40 digits)
Metrics: accuracy solve rate (%) inference latency
Baselines: Vanilla Fine-tune Vanilla Few-shot Scratchpad Algorithmic PAL CoT
Builds on: Tracr RASP Looped Transformers as Programmable Computers chain-of-thought PAL
Closest papers by meaning
- Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning (AAAI 2024 · similarity 0.88)
- Neural-Symbolic Recursive Machine for Systematic Generalization (ICLR 2024 · similarity 0.87)
- Large Language Models are Interpretable Learners (ICLR 2025 · similarity 0.87)
- Neural-Symbolic Collaborative Distillation: Advancing Small Language Models for Complex Reasoning Tasks (AAAI 2025 · similarity 0.86)
- Emergent Symbolic Mechanisms Support Abstract Reasoning in Large Language Models (ICML 2025 · similarity 0.86)
- Neuro-Symbolic Data Generation for Math Reasoning (NeurIPS 2024 · similarity 0.86)
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