This paper introduces a new framework for incremental learning (IL), called Riemannian Walk (RWalk), which addresses two key challenges: forgetting (catastrophic forgetting of previous knowledge) and intransigence (inability to update knowledge for new tasks). The authors propose two new metrics to quantify these issues and provide a theoretical foundation for their approach based on KL-divergence and Riemannian manifolds. RWalk is a generalization of EWC++ and Path Integral, combining their strengths to achieve better performance in terms of accuracy and the trade-off between forgetting and intransigence. The authors evaluate their method on MNIST and CIFAR-100 datasets, showing that RWalk outperforms existing IL algorithms in terms of accuracy and provides a better balance between forgetting and intransigence. They also introduce strategies to mitigate intransigence by storing representative samples from previous tasks. The paper highlights the importance of evaluating IL algorithms not only on accuracy but also on their ability to preserve and update knowledge, which is crucial for real-world applications where models must learn continuously. The authors argue that the proposed metrics and framework provide a more comprehensive understanding of IL algorithms and encourage further research in this area.This paper introduces a new framework for incremental learning (IL), called Riemannian Walk (RWalk), which addresses two key challenges: forgetting (catastrophic forgetting of previous knowledge) and intransigence (inability to update knowledge for new tasks). The authors propose two new metrics to quantify these issues and provide a theoretical foundation for their approach based on KL-divergence and Riemannian manifolds. RWalk is a generalization of EWC++ and Path Integral, combining their strengths to achieve better performance in terms of accuracy and the trade-off between forgetting and intransigence. The authors evaluate their method on MNIST and CIFAR-100 datasets, showing that RWalk outperforms existing IL algorithms in terms of accuracy and provides a better balance between forgetting and intransigence. They also introduce strategies to mitigate intransigence by storing representative samples from previous tasks. The paper highlights the importance of evaluating IL algorithms not only on accuracy but also on their ability to preserve and update knowledge, which is crucial for real-world applications where models must learn continuously. The authors argue that the proposed metrics and framework provide a more comprehensive understanding of IL algorithms and encourage further research in this area.