[论文解读] The Neural Network Pushdown Automaton: Model, Stack and Learning Simulations

Guo-Zheng Sun, C. Lee Giles+2 more|arXiv (Cornell University)|Nov 15, 2017

Machine Learning and Algorithms被引用 15

一句话总结

该论文提出了一种神经网络下推自动机（NNPDA），通过将循环神经网络与连续、可微分的栈结合，以学习确定性上下文无关文法。通过梯度下降优化联合误差函数，模型同时训练网络与栈操作，随后通过量化提取离散PDA。关键结果是，提取的PDA能准确识别任意长度的未见过的字符串，如1^n0^n和回文串，且与源文法的PDA完全一致。

ABSTRACT

In order for neural networks to learn complex languages or grammars, they must have sufficient computational power or resources to recognize or generate such languages. Though many approaches have been discussed, one ob- vious approach to enhancing the processing power of a recurrent neural network is to couple it with an external stack memory - in effect creating a neural network pushdown automata (NNPDA). This paper discusses in detail this NNPDA - its construction, how it can be trained and how useful symbolic information can be extracted from the trained network. In order to couple the external stack to the neural network, an optimization method is developed which uses an error function that connects the learning of the state automaton of the neural network to the learning of the operation of the external stack. To minimize the error function using gradient descent learning, an analog stack is designed such that the action and storage of information in the stack are continuous. One interpretation of a continuous stack is the probabilistic storage of and action on data. After training on sample strings of an unknown source grammar, a quantization procedure extracts from the analog stack and neural network a discrete pushdown automata (PDA). Simulations show that in learning deterministic context-free grammars - the balanced parenthesis language, 1*n0*n, and the deterministic Palindrome - the extracted PDA is correct in the sense that it can correctly recognize unseen strings of arbitrary length. In addition, the extracted PDAs can be shown to be identical or equivalent to the PDAs of the source grammars which were used to generate the training strings.

研究动机与目标

• 通过集成外部栈扩展循环神经网络的计算能力，使其超越有限状态自动机的能力。
• 使神经网络能够学习并推断确定性上下文无关文法，如平衡括号和回文串。
• 开发一种可微分的栈机制，支持对压栈/弹栈操作的连续、基于梯度的学习。
• 从训练后的模拟网络与栈中提取离散、可解释的下推自动机（PDA），用于符号分析。
• 验证所推断的PDA与生成训练字符串的源文法PDA等价，即使对未见过的长字符串也成立。

提出的方法

• 提出一种混合NNPDA模型，结合有限循环神经网络与连续、可微分的栈内存。
• 设计一种模拟栈，其中栈操作（压栈、弹栈、无操作）为连续且可微分，支持基于梯度的学习。
• 定义一个联合误差函数，将神经网络状态转移的学习与栈操作学习耦合。
• 使用实时循环学习（RTRL）计算误差相对于网络权重与栈参数的梯度。
• 在学习完成后，应用量化过程将训练后的模拟栈与网络转换为离散PDA。
• 基于栈动力学与S型激活函数导数推导梯度更新，其近似在字符串长度较短或操作饱和时有效。

实验结果

研究问题

• RQ1 带有连续栈的神经网络能否学习确定性上下文无关文法，如1^n0^n和回文串？
• RQ2 能否在可微分栈上使用梯度下降实现神经网络状态与栈操作的联合训练？
• RQ3 能否从训练后的模拟NNPDA中可靠地提取出离散、可解释的PDA？
• RQ4 所提取的PDA能否正确识别目标文法生成的未见过的任意长度字符串？
• RQ5 所提取的PDA是否与生成训练字符串的源文法PDA等价？

主要发现

• NNPDA成功学习了确定性上下文无关文法，包括平衡括号语言1^n0^n和确定性回文串。
• 训练后，量化过程提取出的离散PDA能正确识别任意长度的未见字符串。
• 所提取的PDA与生成训练数据的源文法PDA完全相同或等价。
• 该模型对训练时未见过的更长字符串实现了正确泛化，表现出强鲁棒性。
• 基于梯度的训练结合可微分栈，实现了网络状态与栈操作的有效联合学习。
• 理论推导与近似（如式A-13）在字符串长度较短或操作值饱和的条件下得到验证。