Be Persistent: Towards a Unified Solution for Mitigating Shortcuts in Deep Learning

TL;DR

This work addresses shortcut learning in deep neural networks by proposing a unified framework based on persistent homology (PH) to detect and mitigate spurious decision rules. By constructing Vietoris–Rips filtrations over neural activation graphs and analyzing 0D/1D persistence diagrams, the approach reveals topological signatures of shortcut trajectories. The authors demonstrate two key case studies—unlearnable examples and bias/fairness—showing statistically significant topological differences between benign and affected models, and discuss extensions to backdoor attacks. The results motivate a roadmap for integrating PH into data preprocessing, fairness assessment, and regularization, aiming to generalize to a broad class of shortcut-related failures in DNNs.

Abstract

Deep neural networks (DNNs) are vulnerable to shortcut learning: rather than learning the intended task, they tend to draw inconclusive relationships between their inputs and outputs. Shortcut learning is ubiquitous among many failure cases of neural networks, and traces of this phenomenon can be seen in their generalizability issues, domain shift, adversarial vulnerability, and even bias towards majority groups. In this paper, we argue that this commonality in the cause of various DNN issues creates a significant opportunity that should be leveraged to find a unified solution for shortcut learning. To this end, we outline the recent advances in topological data analysis (TDA), and persistent homology (PH) in particular, to sketch a unified roadmap for detecting shortcuts in deep learning. We demonstrate our arguments by investigating the topological features of computational graphs in DNNs using two cases of unlearnable examples and bias in decision-making as our test studies. Our analysis of these two failure cases of DNNs reveals that finding a unified solution for shortcut learning in DNNs is not out of reach, and TDA can play a significant role in forming such a framework.

Figures (10)

• Figure 1: Neural networks exhibit spurious correlations, which is a special case of shortcut learning. For instance, DNN trained over data that depicted cows exclusively over grass has created a spurious correlation where cows are only detected in the presence of grass beery2018cows.
• Figure 2: A $k$-Simplex can be regarded as the convex hull of $k+1$ points. A simplicial complex is a union of such simplices.
• Figure 3: An example of computing the VR complex for a set of points in the Euclidean space. As the threshold increases, the $0$-simplices gradually vanish. In the end, we would have only one connected component that lives forever.
• Figure 4: The distribution of average persistence of 1D homology groups for ResNet-18 models trained with different versions of unlearnable CIFAR-10 datasets. Each histogram summarizes the result of 70 independent training runs for each dataset. The p-value of the T-test has also been shown in each figure.
• Figure 5: Top-3 persistent cycles for one instance of ResNet-18 models trained with different versions of unlearnable CIFAR-10 datasets. Each node denotes a single neuron within the model. Note that due to the high number of neurons, we show a downsampled version of the original model.