Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent (2006.11942v4)

Abstract: In Continual Learning settings, deep neural networks are prone to Catastrophic Forgetting. Orthogonal Gradient Descent was proposed to tackle the challenge. However, no theoretical guarantees have been proven yet. We present a theoretical framework to study Continual Learning algorithms in the Neural Tangent Kernel regime. This framework comprises closed form expression of the model through tasks and proxies for Transfer Learning, generalisation and tasks similarity. In this framework, we prove that OGD is robust to Catastrophic Forgetting then derive the first generalisation bound for SGD and OGD for Continual Learning. Finally, we study the limits of this framework in practice for OGD and highlight the importance of the Neural Tangent Kernel variation for Continual Learning with OGD.

• The paper introduces a novel NTK-based framework that models continual learning as recursive kernel regression, capturing task similarity and transfer learning.
• The paper demonstrates that Orthogonal Gradient Descent reliably maintains performance across sequential tasks by mitigating catastrophic forgetting.
• The paper derives the first generalisation bounds for both SGD and OGD in continual learning, quantifying the influence of task similarity metrics.

Theoretical Framework and Generalisation Guarantees for Continual Learning with OGD

The research paper "Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent" provides an insightful examination into the mechanics of Continual Learning (CL) within the framework of the Neural Tangent Kernel (NTK) regime, particularly highlighting the orthogonal gradient descent (OGD) methodology's robustness against Catastrophic Forgetting. This paper stands out by offering a comprehensive theoretical foundation that delineates the convergence and generalisation properties of both stochastic gradient descent (SGD) and OGD in continual learning environments.

Key Contributions

1. Theoretical Framework in the NTK Regime: The authors introduce a novel theoretical structure to paper CL algorithms by leveraging the NTK regime insights. This framework characterizes CL as recursive kernel regression, integrating key concepts such as tasks similarity and transfer learning within the NTK context.
2. Orthogonal Gradient Descent Robustness: The paper formalizes the claim that OGD is inherently robust to forgetting, provided there is an infinite memory cache, allowing the agent to preserve performance across a sequence of tasks without degradation of learned knowledge.
3. Generalisation Bounds for Continual Learning: One of the most significant contributions is the derivation of the first generalisation bounds for both SGD and OGD in CL settings, elaborating on how task similarity affects learning and performance. These bounds highlight quantitative relationships and dependencies on the NTK-derived task similarity metrics.
4. Practical Implications and Limitations: The paper investigates the practical implications of the theoretical framework, uncovering that while OGD's theoretical guarantees hold under specific assumptions, real-world applications face challenges due to the variation in the NTK and memory constraints in non-overparameterized scenarios.

Insights and Implications

The paper's theoretical approach offers a fresh perspective on handling Catastrophic Forgetting, a notorious issue in CL. By integrating OGD within the NTK framework, the research affirms that, theoretically, OGD can maintain stability across a multitude of tasks by projecting gradient updates orthogonally relative to learned tasks' feature spaces. This insight suggests that OGD could be a plausible solution for achieving continual learning without extensive knowledge degradation over time.

Furthermore, the presented generalisation bounds underscore the importance of task similarity, elucidating how inherent task characteristics can influence the overall learning efficacy and retention in sequential learning processes. This underlines potential strategies for optimizing CL through careful task sequencing and similarity-based adjustments, indicative of a close relationship between transfer learning strategies and continual learning success.

Future Prospects in AI Development

This research opens avenues for further exploration into other theoretical frameworks that might apply to various CL architectures, potentially expanding beyond NTK. The insights regarding task similarity and generalisation may prompt future studies to develop advanced methods for quantifying and leveraging these elements in more dynamic learning environments.

The practical insights gained also highlight critical future work domains, such as addressing NTK variability and memory limitations in real-world applications and non-overparameterized settings. These pathways are crucial for realizing robust, scalable, and efficient CL systems that can adapt and perform optimally across evolving task sets without succumbing to catastrophic forgetting.

Conclusion

In essence, this paper marks a significant step in understanding and addressing the intricacies of continual learning through the lens of OGD and NTK. It delivers a rigorous exploration of theoretical underpinnings combined with practical evaluations, fostering deeper engagement with continual learning's challenges in digital cognition and autonomous system designs. As AI systems increasingly demand continuous learning capabilities, the insights from this research will undoubtedly contribute to refining such capabilities, ultimately enhancing the adaptability and longevity of intelligent systems in diverse domains.