MonoQPM: Splitting Features into Concepts for Inherent Interpretability and Predictive Performance

Abstract: Alongside superposition, polysemanticity is one of the primary obstacles to achieving interpretable deep neural networks. While these phenomena are typically intrinsically linked, the Quadratic Programming Enhanced Model (QPM) naturally decouples them. By representing classes with a sparse binary assignment of very few features, QPM prevents superposition by design on its final features but still exhibits polysemanticity. However, measuring polysemanticity is an open problem. This work proposes a utility-focused approach to measuring polysemanticity by quantifying the decrease in interference-induced activation errors, which yields the practical utility of tighter prediction sets using Conformal Prediction (CP). We explicitly disentangle the polysemantic features of QPM into monosemantic concepts to create the Monosemantic QPM (MonoQPM). Because its features are disentangled, MonoQPM acts as a significantly more efficient Conformal Predictor. Additionally, we introduce CUBCars, a dataset providing ground truth information about shared concepts. Using this and other datasets, we demonstrate that polysemanticity emerges in QPM across all tested architectures, but is effectively alleviated by MonoQPM. For instance, MonoQPM guarantees 88% coverage using Adaptive Prediction Sets on ImageNet with just 66% of the frozen QPM’s set size.

Submission Type: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=QkkXIrfyYo

Changes Since Last Submission: The previous submission was desk-rejected due to a formatting issue (importing the times package, which overrode the default template font). In this resubmission, the LaTeX preamble has been corrected to strictly adhere to the standard TMLR template. The layout is adapted accordingly, and the abstract is slightly extended to make use of the additional space.

Assigned Action Editor: ~Quanshi_Zhang1

Submission Number: 8595