用递归逻辑解析神经网络，让模型可解释性更强
Recursive querying of neural networks via weighted structures
- 引入带权结构的递归查询语法，支持深层网络分析
- 提出多项式时间可解的简化逻辑，能表达多数实用查询
- 适合研究模型可解释性与逻辑推理的学者参考
对机器学习模型（视为一种有意向的数据）进行表达性强的查询，可通过声明式语言实现模型验证与解释，使数据的隐式表示更易理解。针对前馈神经网络的查询需求，我们研究了带权结构上的逻辑系统。由于神经网络深度无界，此类逻辑必须包含递归机制；为此我们重新审视了Grädel和Gurevich提出的函数不动点机制。采用类似Datalog的语法，将不动点逻辑的正规形式扩展至带权结构，并提出一种等价的‘宽松’不动点机制，允许归纳定义的权重函数被覆盖。我们提出一种‘标量’限制的函数不动点逻辑，具有多项式时间数据复杂度，并证明其可表达所有在权重多项式有界的简化网络上定义的PTIME模型无关查询。相反，我们证明某些极简的模型无关查询已是NP完全。最后，我们考察了通过迭代转换对带权结构进行变换的过程。
原文摘要 · Abstract (English)
Expressive querying of machine learning models - viewed as a form of intentional data - enables their verification and interpretation using declarative languages, thereby making learned representations of data more accessible. Motivated by the querying of feedforward neural networks, we investigate logics for weighted structures. In the absence of a bound on neural network depth, such logics must incorporate recursion; thereto we revisit the functional fixpoint mechanism proposed by Grädel and Gurevich. We adopt it in a Datalog-like syntax; we extend normal forms for fixpoint logics to weighted structures; and show an equivalent "loose" fixpoint mechanism that allows values of inductively defined weight functions to be overwritten. We propose a "scalar" restriction of functional fixpoint logic, of polynomial-time data complexity, and show it can express all PTIME model-agnostic queries over reduced networks with polynomially bounded weights. In contrast, we show that very simple model-agnostic queries are already NP-complete. Finally, we consider transformations of weighted structures by iterated transductions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。