Researchers Propose Local Linearization Method to Demystify Neural Network Decision-Making

Understanding how deep neural networks arrive at their predictions remains one of the field's central challenges. While these models excel across diverse applications, their opaque internal behavior has hindered real-world deployment in domains where interpretability matters—medicine, law, finance, and other high-stakes settings.

The Limitation of Current Approaches#

Existing interpretability methods typically rank features by importance, showing which inputs mattered to a given prediction. However, they often fail to explain the precise mechanism by which those features contribute to the outcome. This gap raises a fundamental question: are these methods actually highlighting the features a model genuinely used, or are they identifying spurious correlations?

The core obstacle is that neural networks are fundamentally non-linear systems. Their activation functions—ReLU, sigmoid, tanh—introduce kinks and discontinuities that resist straightforward analysis.

A Local Linearity Insight#

Researchers at arXiv (submitted October 2023, revised September 2026) propose a fresh angle: while neural networks are globally non-linear, any individual prediction operates under a fixed activation pattern. Put another way, for a given input, certain neurons fire and others don't, creating a locally linear computational path.

Building on this observation, the team introduces instance-wise linearization, which unfolds a neural network's layered convolution operations into a single linear transformation. The entire forward pass—no matter how deep or complex—reduces to the form:

F(x) = W · x + b

where W is a combined weight matrix and b is a bias term. This reformulation converts the black box into a white box for that specific input.

Applications and Implications#

Beyond feature attribution, this linearization approach enables direct calculation of how each feature contributes to a prediction. The researchers also demonstrate applications in supervised classification and unsupervised learning, including parametric t-SNE dimension reduction.

By making the internal computation transparent for individual examples, instance-wise linearization offers a path toward neural networks that practitioners can confidently interpret and defend—critical for deployment in regulated and safety-sensitive domains.