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arXiv 2410.08025cs.AIcs.CCq-bio.NC
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面向内在可解释性的电路发现的计算复杂性

The Computational Complexity of Circuit Discovery for Inner Interpretability

ESI Neuroscience, Max-Planck Society & University of Bristol(ESI神经科学研究所、马克斯·普朗克学会与布里斯托尔大学);Goethe University Frankfurt(法兰克福大学);Memorial University of Newfoundland(纽芬兰纪念大学)

Federico Adolfi, Martina G. Vilas, Todd Wareham

AI总结:

本文利用经典与参数化计算复杂性理论研究神经网络的电路发现问题,揭示了多数查询难解且不可近似,同时证明了部分适度查询的易处理性,为内在可解释性的范围与限制提供了理论框架。

摘要:

神经网络在机器学习、认知/脑科学及社会中的许多拟议应用,取决于通过电路发现实现内在可解释性的可行性。这要求对可行的算法选项进行实证与理论探索。尽管在启发式方法的设计与测试上取得了进展,但在我们缺乏对所求解问题复杂性属性的理解时,对其可扩展性与忠实性仍存疑虑。为解决此问题,我们利用经典与参数化计算复杂性理论研究电路发现:(1) 我们描述了一个概念脚手架,以根据描述、解释、预测和控制的可供性来推理电路查找查询;(2) 我们形式化了一套用于机制解释的综合查询,并提出了一个用于分析它们的形式化框架;(3) 我们利用它解决了多层感知机上具有实际意义的许多查询变体与松弛的复杂性。我们的发现揭示了一个极具挑战性的复杂性图景。许多查询是难解的,相对于模型/电路特征保持固定参数难解,并且在加性、乘性和概率近似方案下是不可近似的。为导航该图景,我们证明存在转换以用理解更透彻的启发式方法处理其中一些困难问题,并证明了保留有用可供性的更适度查询的易处理性或固定参数易处理性。该框架使我们能够理解可解释性查询的范围与限制,探索可行选项,并比较它们在现有与未来架构上的资源需求。

英文摘要:

Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of viable algorithmic options. Despite advances in the design and testing of heuristics, there are concerns about their scalability and faithfulness at a time when we lack understanding of the complexity properties of the problems they are deployed to solve. To address this, we study circuit discovery with classical and parameterized computational complexity theory: (1) we describe a conceptual scaffolding to reason about circuit finding queries in terms of affordances for description, explanation, prediction and control; (2) we formalize a comprehensive set of queries for mechanistic explanation, and propose a formal framework for their analysis; (3) we use it to settle the complexity of many query variants and relaxations of practical interest on multi-layer perceptrons. Our findings reveal a challenging complexity landscape. Many queries are intractable, remain fixed-parameter intractable relative to model/circuit features, and inapproximable under additive, multiplicative, and probabilistic approximation schemes. To navigate this landscape, we prove there exist transformations to tackle some of these hard problems with better-understood heuristics, and prove the tractability or fixed-parameter tractability of more modest queries which retain useful affordances. This framework allows us to understand the scope and limits of interpretability queries, explore viable options, and compare their resource demands on existing and future architectures.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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