Kaixiang Shu

Kaixiang Shu

A foundational assumption in CNN interpretability -- that deep encoders suppress background pixels while classifiers merely select from a cleaned feature pool (the Spatial Funnel Hypothesis) -- remains untested due to spatial hallucinations in existing visualization tools. We address this by introducing a hallucination-free inversion framework built on magnitude-phase decoupling and Local Adjoint Correctors. Our method mathematically guarantees that the spatial gradient support of every reconstruction stems strictly from genuinely active channels. Using this framework as a geometric probe, we uncover the first pixel-level evidence of strong superposition in vision encoders. We show that per-channel inversions are uniformly holographic: positive and negative weight reconstructions are visually and energetically indistinguishable. However, their algebraic sum sharply concentrates on the foreground. This proves classification operates via destructive interference -- classifier weights cancel a shared background direction in pixel space and constructively assemble class-discriminative residuals, directly falsifying the Spatial Funnel Hypothesis. This interference model identifies the volume of the admissible interference subspace as the geometric quantity governing channel requirements. We prove this volume is dual to the GAP covariance determinant, yielding a covariance-volume channel selection algorithm with a $(1-1/e)$ approximation guarantee. This algorithm mathematically reveals out-of-distribution (OOD) failure as a measurable collapse of the covariance volume essential for interference-based classification. Our framework extends seamlessly to attention-based heads without retraining.

Kaixiang Shu, Kai Meng, Junqin Luo

Deep neural networks typically learn spatially entangled representations that conflate discriminative foreground features with spurious background correlations, thereby undermining model interpretability and robustness. We propose a novel understanding framework for gradient-based attribution from an information-theoretic perspective. We prove that, under mild conditions, the Vector-Jacobian Products (VJP) computed during backpropagation form minimal sufficient statistics of input features with respect to class labels. Motivated by this finding, we propose an encoding-decoding perspective : forward propagation encodes inputs into class space, while VJP in backpropagation decodes this encoding back to feature space. Therefore, we propose Spatial Information Bottleneck (S-IB) to spatially disentangle information flow. By maximizing mutual information between foreground VJP and inputs while minimizing mutual information in background regions, S-IB encourages networks to encode information only in class-relevant spatial regions. Since post-hoc explanation methods fundamentally derive from VJP computations, directly optimizing VJP's spatial structure during training improves visualization quality across diverse explanation paradigms. Experiments on five benchmarks demonstrate universal improvements across six explanation methods, achieving better foreground concentration and background suppression without method-specific tuning, alongside consistent classification accuracy gains.