Deep Neural Networks have achieved great success in some of the complex tasks that humans can do with ease. These include image recognition/classification, natural language processing, game playing etc. However, modern Neural Networks fail or perform poorly when trained on tasks that can be solved easily using backtracking and traditional algorithms. Therefore, we use the architecture of the Neuro Logic Machine (NLM) and extend its functionality to solve a 9X9 game of Sudoku. To expand the application of NLMs, we generate a random grid of cells from a dataset of solved games and assign up to 10 new empty cells. The goal of the game is then to find a target value ranging from 1 to 9 and fill in the remaining empty cells while maintaining a valid configuration. In our study, we showcase an NLM which is capable of obtaining 100% accuracy for solving a Sudoku with empty cells ranging from 3 to 10. The purpose of this study is to demonstrate that NLMs can also be used for solving complex problems and games like Sudoku. We also analyze the behaviour of NLMs with a backtracking algorithm by comparing the convergence time using a graph plot on the same problem. With this study we show that Neural Logic Machines can be trained on the tasks that traditional Deep Learning architectures fail using Reinforcement Learning. We also aim to propose the importance of symbolic learning in explaining the systematicity in the hybrid model of NLMs.

翻译：深度神经网络在人类可轻松完成的复杂任务中取得了巨大成功，包括图像识别/分类、自然语言处理、游戏博弈等。然而，当训练那些可通过回溯和传统算法轻松解决的任务时，现代神经网络往往失败或表现不佳。因此，我们采用神经逻辑机器（NLM）架构并扩展其功能，以求解9×9数独游戏。为拓展NLM的应用场景，我们从已解游戏数据集中生成随机网格，并分配至多10个新空格。游戏目标是在维持有效配置的前提下，寻找1至9之间的目标值并填充所有剩余空格。本研究表明，NLM能够对含3至10个空格的数独游戏实现100%的求解准确率。该研究旨在证明NLM同样可用于求解数独这类复杂问题与游戏。我们通过同一问题上的收敛时间图对比，分析了NLM与回溯算法的行为差异。通过本研究，我们证明了神经逻辑机器能在深度强化学习框架下，训练完成传统深度学习架构无法胜任的任务。同时，我们旨在阐明符号学习在解释NLM混合模型系统性中的重要意义。