From Preimage Search To Source-Grounded Feature Inversion

Interpreting a neural network requires understanding what its internal features extract from a particular input. Feature inversion seeks to express a selected feature in the input domain, but canonical iterative methods search for an input whose re-encoded representation matches the target. Because many inputs can satisfy this constraint, target matching alone does not specify the inverse associated with the sample that generated the feature. We formulate source-grounded feature inversion by conditioning the inverse on the source-local network geometry at the target-generating input. At each boundary of the computational DAG, backpropagation provides the correct reverse dependencies but transports an adjoint signal rather than an upstream-state estimate. We locally repair this signal with a closed-form matrix Wiener map from a mean-seed VJP to the upstream state, followed by a second Wiener map for the JVP forward-consistency residual, and compose the repaired states through the same DAG in one finite reverse pass. One calibrated zero-intercept map family supports new inputs, depths, channels, and channel groups across diverse CNN and Transformer architectures, tensor components, and visual distributions without query-specific optimisation. Matched target and source controls verify that each inverse depends on the selected feature and the local operators of the sample being explained, rather than a target-independent image template. Prediction-conditioned feature atlases align these visualisations with independent interventions on the corresponding internal features. Together, source-grounded feature inversion opens the model's hidden feature hierarchy to inspection at the level of individual layers and channels, linking what the network extracts from an input to the internal evidence that shapes its decision.

Spatial Information Bottleneck for Interpretable Visual Recognition

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.