The Missing Invariance Principle Found -- the Reciprocal Twin of Invariant Risk Minimization

Machine learning models often generalize poorly to out-of-distribution (OOD) data as a result of relying on features that are spuriously correlated with the label during training. Recently, the technique of Invariant Risk Minimization (IRM) was proposed to learn predictors that only use invariant features by conserving the feature-conditioned class expectation $\mathbb{E}_e[y|f(x)]$ across environments. However, more recent studies have demonstrated that IRM can fail in various task settings. Here, we identify a fundamental flaw of IRM formulation that causes the failure. We then introduce a complementary notion of invariance, MRI, that is based on conserving the class-conditioned feature expectation $\mathbb{E}_e[f(x)|y]$ across environments, that corrects for the flaw in IRM. Further, we introduce a simplified, practical version of the MRI formulation called as MRI-v1. We note that this constraint is convex which confers it with an advantage over the practical version of IRM, IRM-v1, which imposes non-convex constraints. We prove that in a general linear problem setting, MRI-v1 can guarantee invariant predictors given sufficient environments. We also empirically demonstrate that MRI strongly out-performs IRM and consistently achieves near-optimal OOD generalization in image-based nonlinear problems.

Combining Different V1 Brain Model Variants to Improve Robustness to Image Corruptions in CNNs

While some convolutional neural networks (CNNs) have surpassed human visual abilities in object classification, they often struggle to recognize objects in images corrupted with different types of common noise patterns, highlighting a major limitation of this family of models. Recently, it has been shown that simulating a primary visual cortex (V1) at the front of CNNs leads to small improvements in robustness to these image perturbations. In this study, we start with the observation that different variants of the V1 model show gains for specific corruption types. We then build a new model using an ensembling technique, which combines multiple individual models with different V1 front-end variants. The model ensemble leverages the strengths of each individual model, leading to significant improvements in robustness across all corruption categories and outperforming the base model by 38% on average. Finally, we show that using distillation, it is possible to partially compress the knowledge in the ensemble model into a single model with a V1 front-end. While the ensembling and distillation techniques used here are hardly biologically-plausible, the results presented here demonstrate that by combining the specific strengths of different neuronal circuits in V1 it is possible to improve the robustness of CNNs for a wide range of perturbations.