Overcoming Catastrophic Forgetting in Continual Learning by Exploring Eigenvalues of Hessian Matrix

Area of Science:

• Artificial Intelligence
• Machine Learning
• Deep Learning

Background:

• Neural networks face performance degradation on prior tasks when trained sequentially without access to past data, a phenomenon known as catastrophic forgetting.
• Catastrophic forgetting is a major obstacle in continual learning (CL), limiting the ability of models to learn new information without compromising existing knowledge.
• Regularization-based CL methods attempt to mitigate forgetting by adding a penalty term to the loss function, approximating previous tasks' loss.

Purpose of the Study:

• To provide a rigorous theoretical analysis of the forgetting and convergence properties of regularization-based continual learning methods.
• To identify the relationship between the upper bound of forgetting and the maximum eigenvalue of the Hessian matrix.
• To propose a novel method, GEAR, that leverages these theoretical insights to reduce catastrophic forgetting.

Main Methods:

• Theoretical analysis of regularization-based methods in continual learning, focusing on forgetting and convergence.
• Derivation of the relationship between forgetting upper bound and the maximum eigenvalue of the Hessian matrix.
• Development of the eiGenvalues ExplorAtion Regularization-based (GEAR) method, which explores geometric properties of prior task loss approximations concerning the maximum eigenvalue.

Main Results:

• Theoretical analysis reveals that the upper bound of forgetting is directly related to the maximum eigenvalue of the Hessian matrix.
• The proposed GEAR method effectively utilizes this relationship to decrease the forgetting upper bound by exploring eigenvalue properties.
• Extensive experiments confirm that GEAR significantly mitigates catastrophic forgetting and achieves superior performance compared to existing regularization-based methods.

Conclusions:

• The theoretical framework provides a deeper understanding of forgetting in regularization-based continual learning.
• GEAR offers an effective strategy to combat catastrophic forgetting by optimizing based on eigenvalue analysis.
• The findings suggest a promising direction for developing more robust and efficient continual learning systems.