Invariant Risk Minimization (IRM) is a learning paradigm that aims to enable out-of-distribution (OOD) generalization by learning invariant, causal predictors across multiple training environments. The paper addresses the problem of machine learning systems relying too heavily on spurious correlations in training data, which can lead to poor performance on new, unseen data distributions. The authors propose IRM as a method to identify and learn invariant features that are stable across different environments, thus improving generalization. The paper begins by discussing the limitations of traditional machine learning approaches, which often fail to generalize due to their reliance on training data biases. It introduces the concept of spurious correlations and their instability across environments, highlighting the need for methods that can identify true causal relationships. The authors then present IRM as a solution that minimizes the risk across environments while ensuring that the learned predictor remains invariant to changes in the data distribution. The paper outlines the theoretical foundations of IRM, showing how it can be used to find invariant predictors by minimizing the risk across training environments. It also discusses the challenges of learning invariant predictors, including the difficulty of finding features that are stable across different environments. The authors propose a constrained optimization problem that aims to find data representations that elicit invariant predictors, and they introduce IRMv1 as a practical implementation of this approach. The paper also explores the relationship between invariance, causation, and generalization, arguing that invariant predictors are closely related to causal explanations of the data. It discusses the theoretical underpinnings of IRM, including its connection to causal models and the conditions under which invariant predictors can be learned. The authors also address the practical implementation of IRM, including the use of gradient penalty terms to enforce invariance and the choice of linear classifiers for simplifying the optimization problem. The paper concludes with a discussion of the implications of IRM for machine learning, emphasizing its potential to improve generalization by learning invariant features that are stable across different environments. It also highlights the importance of understanding the relationship between invariance and causation in the development of more robust and generalizable machine learning models.Invariant Risk Minimization (IRM) is a learning paradigm that aims to enable out-of-distribution (OOD) generalization by learning invariant, causal predictors across multiple training environments. The paper addresses the problem of machine learning systems relying too heavily on spurious correlations in training data, which can lead to poor performance on new, unseen data distributions. The authors propose IRM as a method to identify and learn invariant features that are stable across different environments, thus improving generalization. The paper begins by discussing the limitations of traditional machine learning approaches, which often fail to generalize due to their reliance on training data biases. It introduces the concept of spurious correlations and their instability across environments, highlighting the need for methods that can identify true causal relationships. The authors then present IRM as a solution that minimizes the risk across environments while ensuring that the learned predictor remains invariant to changes in the data distribution. The paper outlines the theoretical foundations of IRM, showing how it can be used to find invariant predictors by minimizing the risk across training environments. It also discusses the challenges of learning invariant predictors, including the difficulty of finding features that are stable across different environments. The authors propose a constrained optimization problem that aims to find data representations that elicit invariant predictors, and they introduce IRMv1 as a practical implementation of this approach. The paper also explores the relationship between invariance, causation, and generalization, arguing that invariant predictors are closely related to causal explanations of the data. It discusses the theoretical underpinnings of IRM, including its connection to causal models and the conditions under which invariant predictors can be learned. The authors also address the practical implementation of IRM, including the use of gradient penalty terms to enforce invariance and the choice of linear classifiers for simplifying the optimization problem. The paper concludes with a discussion of the implications of IRM for machine learning, emphasizing its potential to improve generalization by learning invariant features that are stable across different environments. It also highlights the importance of understanding the relationship between invariance and causation in the development of more robust and generalizable machine learning models.