# Assessing SATNet's Ability to Solve the Symbol Grounding Problem

arXiv: https://arxiv.org/abs/2312.11522 · HTML: https://mlsanity.com/paper/2312.11522/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 52 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Agent57: Outperforming the Atari Human Benchmark](https://mlsanity.com/paper/2003.13350/) (2020)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [RAVEN: A Dataset for Relational and Analogical Visual rEasoNing](https://mlsanity.com/paper/1903.02741/) (2019)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [The Microsoft 2017 Conversational Speech Recognition System](https://mlsanity.com/paper/1708.06073/) (2017)
- [Turning 30: New Ideas in Inductive Logic Programming](https://mlsanity.com/paper/2002.11002/) (2020)
- [TensorLog: A Differentiable Deductive Database](https://mlsanity.com/paper/1605.06523/) (2016)
- [A Hitchhiker's Guide to Statistical Comparisons of Reinforcement Learning Algorithms](https://mlsanity.com/paper/1904.06979/) (2019)
- [Reproducibility in Machine Learning for Health](https://mlsanity.com/paper/1907.01463/) (2019)
- [Differentiable Submodular Maximization](https://mlsanity.com/paper/1803.01785/) (2018)

## Built on by (most cited first, 10 of 10)

- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Learning Guided Automated Reasoning: A Brief Survey](https://mlsanity.com/paper/2403.04017/) (2024)
- [Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error](https://mlsanity.com/paper/2509.22023/) (2025)
- [Application of AI to formal methods - an analysis of current trends](https://mlsanity.com/paper/2411.14870/) (2024)
- [Symbol Correctness in Deep Neural Networks Containing Symbolic Layers](https://mlsanity.com/paper/2402.03663/) (2024)
- [Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible](https://mlsanity.com/paper/2503.12917/) (2025)
- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [Scaling Neuro-symbolic Problem Solving: Solver-Free Learning of Constraints and Objectives](https://mlsanity.com/paper/2508.20978/) (2025)
- [PARM: Pipeline-Adapted Reward Model](https://mlsanity.com/paper/2604.18327/) (2026)
- [Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integration](https://mlsanity.com/paper/2608.14569/) (2026)

## Abstract (arXiv)

SATNet is an award-winning MAXSAT solver that can be used to infer logical rules and integrated as a differentiable layer in a deep neural network. It had been shown to solve Sudoku puzzles visually from examples of puzzle digit images, and was heralded as an impressive achievement towards the longstanding AI goal of combining pattern recognition with logical reasoning. In this paper, we clarify SATNet's capabilities by showing that in the absence of intermediate labels that identify individual Sudoku digit images with their logical representations, SATNet completely fails at visual Sudoku (0% test accuracy). More generally, the failure can be pinpointed to its inability to learn to assign symbols to perceptual phenomena, also known as the symbol grounding problem, which has long been thought to be a prerequisite for intelligent agents to perform real-world logical reasoning. We propose an MNIST based test as an easy instance of the symbol grounding problem that can serve as a sanity check for differentiable symbolic solvers in general. Naive applications of SATNet on this test lead to performance worse than that of models without logical reasoning capabilities. We report on the causes of SATNet's failure and how to prevent them.