Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the permutation approaches.

Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the permutation approaches.

Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has gained considerable attention due to the intriguing observation that different solutions can be connected by a linear path in the parameter space while maintaining near-constant training and test losses. In this work, we introduce a stronger notion of linear connectivity, Layerwise Linear Feature Connectivity (LLFC), which says that the feature maps of every layer in different trained networks are also linearly connected. We provide comprehensive empirical evidence for LLFC across a wide range of settings, demonstrating that whenever two trained networks satisfy LMC (via either spawning or permutation methods), they also satisfy LLFC in nearly all the layers. Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the spawning and permutation approaches. The study of LLFC transcends and advances our understanding of LMC by adopting a feature-learning perspective.

This paper advocates against permute-and-predict (PaP) methods for interpreting black box functions. Methods such as the variable importance measures proposed for random forests, partial dependence plots, and individual conditional expectation plots remain popular because of their ability to provide model-agnostic measures that depend only on the pre-trained model output. However, numerous studies have found that these tools can produce diagnostics that are highly misleading, particularly when there is strong dependence among features. Rather than simply add to this growing literature by further demonstrating such issues, here we seek to provide an explanation for the observed behavior. In particular, we argue that breaking dependencies between features in hold-out data places undue emphasis on sparse regions of the feature space by forcing the original model to extrapolate to regions where there is little to no data. We explore these effects through various settings where a ground-truth is understood and find support for previous claims in the literature that PaP metrics tend to over-emphasize correlated features both in variable importance and partial dependence plots, even though applying permutation methods to the ground-truth models do not. As an alternative, we recommend more direct approaches that have proven successful in other settings: explicitly removing features, conditional permutations, or model distillation methods.