# Deep Reasoning Networks: Thinking Fast and Slow

arXiv: https://arxiv.org/abs/1906.00855 · HTML: https://mlsanity.com/paper/1906.00855/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2019.

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

- [SwiftSage: A Generative Agent with Fast and Slow Thinking for Complex Interactive Tasks](https://mlsanity.com/paper/2305.17390/) (2023)
- [Planning Like Human: A Dual-process Framework for Dialogue Planning](https://mlsanity.com/paper/2406.05374/) (2024)
- [Learning to Solve Constraint Satisfaction Problems with Recurrent Transformer](https://mlsanity.com/paper/2307.04895/) (2023)
- [Thinking Fast and Slow in AI: the Role of Metacognition](https://mlsanity.com/paper/2110.01834/) (2021)
- [A Neural-Symbolic Approach to Natural Language Understanding](https://mlsanity.com/paper/2203.10557/) (2022)
- [Towards Building Specialized Generalist AI with System 1 and System 2 Fusion](https://mlsanity.com/paper/2407.08642/) (2024)
- [NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learning](https://mlsanity.com/paper/2210.00973/) (2022)
- [Self-Supervised Transformers as Iterative Solution Improvers for Constraint Satisfaction](https://mlsanity.com/paper/2502.15794/) (2025)
- [Combining Fast and Slow Thinking for Human-like and Efficient Navigation in Constrained Environments](https://mlsanity.com/paper/2201.07050/) (2022)
- [Bridging Social Psychology and LLM Reasoning: Conflict-Aware Meta-Review Generation via Cognitive Alignment](https://mlsanity.com/paper/2503.13879/) (2025)
- [LabelKAN -- Kolmogorov-Arnold Networks for Inter-Label Learning: Avian Community Learning](https://mlsanity.com/paper/2601.18818/) (2026)
- [Hybrid Learners Do Not Forget: A Brain-Inspired Neuro-Symbolic Approach to Continual Learning](https://mlsanity.com/paper/2503.12635/) (2025)

## Abstract (arXiv)

We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with reasoning for solving complex tasks, typically in an unsupervised or weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining logic and constraint reasoning with stochastic-gradient-based neural network optimization. We illustrate the power of DRNets on de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku) and on a substantially more complex task in scientific discovery that concerns inferring crystal structures of materials from X-ray diffraction data under thermodynamic rules (Crystal-Structure-Phase-Mapping). At a high level, DRNets encode a structured latent space of the input data, which is constrained to adhere to prior knowledge by a reasoning module. The structured latent encoding is used by a generative decoder to generate the targeted output. Finally, an overall objective combines responses from the generative decoder (thinking fast) and the reasoning module (thinking slow), which is optimized using constraint-aware stochastic gradient descent. We show how to encode different tasks as DRNets and demonstrate DRNets' effectiveness with detailed experiments: DRNets significantly outperform the state of the art and experts' capabilities on Crystal-Structure-Phase-Mapping, recovering more precise and physically meaningful crystal structures. On Multi-MNIST-Sudoku, DRNets perfectly recovered the mixed Sudokus' digits, with 100% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. Finally, as a proof of concept, we also show how DRNets can solve standard combinatorial problems -- 9-by-9 Sudoku puzzles and Boolean satisfiability problems (SAT), outperforming other specialized deep learning models. DRNets are general and can be adapted and expanded to tackle other tasks.