arXiv:2512.05638cs.LGcs.AI2025-12被引 1

用模块化切片分析模型内部结构,区分可识别与伪似结构。

Modular Jets for Supervised Pipelines: Diagnosing Mirage vs Identifiability

  • 通过局部扰动响应建模模块行为,定义可识别性与幻象区
  • 在线性回归中证明:有模块级响应则分解唯一,仅凭损失无法区分
  • 提出MoJet算法,适用于线性与深度模型的可解释性诊断

传统监督学习主要通过保留数据上的预测风险评估模型,但这仅衡量函数在分布上的表现,未考察模型内部结构是否由数据和评估设计唯一确定。本文提出针对回归与分类流水线的「模块化切片」(Modular Jets)方法。给定任务流形(输入空间)、模块化分解及模块级表征,通过估计经验切片——即描述各模块对输入小规模结构性扰动的局部线性响应——来刻画内部机制。我们提出「幻象」(mirage)的实证概念:多个不同的模块分解产生不可区分的切片,因此观测上等价;而「可识别」(identifiable)情形下,观测到的切片能唯一确定分解(至自然对称性)。在线性双模块回归设定中,我们在弱秩假设下证明了切片可识别性定理:若具备模块级切片信息,则内部因子分解唯一;而仅依赖风险评估时,存在大量可实现相同输入-输出映射的幻象分解。随后我们提出用于经验切片估计与幻象诊断的算法(MoJet),并在线性与深度回归、流水线分类任务中进行了验证。

原文摘要 · Abstract (English)

Classical supervised learning evaluates models primarily via predictive risk on hold-out data. Such evaluations quantify how well a function behaves on a distribution, but they do not address whether the internal decomposition of a model is uniquely determined by the data and evaluation design. In this paper, we introduce \emph{Modular Jets} for regression and classification pipelines. Given a task manifold (input space), a modular decomposition, and access to module-level representations, we estimate empirical jets, which are local linear response maps that describe how each module reacts to small structured perturbations of the input. We propose an empirical notion of \emph{mirage} regimes, where multiple distinct modular decompositions induce indistinguishable jets and thus remain observationally equivalent, and contrast this with an \emph{identifiable} regime, where the observed jets single out a decomposition up to natural symmetries. In the setting of two-module linear regression pipelines we prove a jet-identifiability theorem. Under mild rank assumptions and access to module-level jets, the internal factorisation is uniquely determined, whereas risk-only evaluation admits a large family of mirage decompositions that implement the same input-to-output map. We then present an algorithm (MoJet) for empirical jet estimation and mirage diagnostics, and illustrate the framework using linear and deep regression as well as pipeline classification.

可解释性模型诊断模块化结构线性代数

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。