# Mastering Symbolic Operations: Augmenting Language Models with Compiled Neural Networks

arXiv: https://arxiv.org/abs/2304.01665 · HTML: https://mlsanity.com/paper/2304.01665/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 66 of its 78 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 66)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)

## Built on by (most cited first, 12 of 12)

- [DeepReview: Improving LLM-based Paper Review with Human-like Deep Thinking Process](https://mlsanity.com/paper/2503.08569/) (2025)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [DeepScientist: Advancing Frontier-Pushing Scientific Findings Progressively](https://mlsanity.com/paper/2509.26603/) (2025)
- [Personality Alignment of Large Language Models](https://mlsanity.com/paper/2408.11779/) (2024)
- [Locking Down the Finetuned LLMs Safety](https://mlsanity.com/paper/2410.10343/) (2024)
- [Large Language Models Need Holistically Thought in Medical Conversational QA](https://mlsanity.com/paper/2305.05410/) (2023)
- [LogiDebrief: A Signal-Temporal Logic based Automated Debriefing Approach with Large Language Models Integration](https://mlsanity.com/paper/2505.03985/) (2025)
- [ResearStudio: A Human-Intervenable Framework for Building Controllable Deep-Research Agents](https://mlsanity.com/paper/2510.12194/) (2025)
- [Algorithmic Language Models with Neurally Compiled Libraries](https://mlsanity.com/paper/2407.04899/) (2024)
- [Interacting with AI Reasoning Models: Harnessing "Thoughts" for AI-Driven Software Engineering](https://mlsanity.com/paper/2503.00483/) (2025)
- [Tracr-Injection: Distilling Algorithms into Pre-trained Language Models](https://mlsanity.com/paper/2505.10719/) (2025)
- [Empowering 9-1-1 Calltaking Training with Generative AI: Experiences and Lessons Learned](https://mlsanity.com/paper/2602.13241/) (2026)

## Abstract (arXiv)

Language models' (LMs) proficiency in handling deterministic symbolic reasoning and rule-based tasks remains limited due to their dependency implicit learning on textual data. To endow LMs with genuine rule comprehension abilities, we propose "Neural Comprehension" - a framework that synergistically integrates compiled neural networks (CoNNs) into the standard transformer architecture. CoNNs are neural modules designed to explicitly encode rules through artificially generated attention weights. By incorporating CoNN modules, the Neural Comprehension framework enables LMs to accurately and robustly execute rule-intensive symbolic tasks. Extensive experiments demonstrate the superiority of our approach over existing techniques in terms of length generalization, efficiency, and interpretability for symbolic operations. Furthermore, it can be applied to LMs across different model scales, outperforming tool-calling methods in arithmetic reasoning tasks while maintaining superior inference efficiency. Our work highlights the potential of seamlessly unifying explicit rule learning via CoNNs and implicit pattern learning in LMs, paving the way for true symbolic comprehension capabilities.