arXiv:2509.22335v3 Announce Type: replace Abstract: We investigate why deep neural networks suffer from loss of plasticity in continual learning, and thus fail to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. Analyzing a linearized ReLU network, we derive explicit $\epsilon$-rank conditions for successful training and prove that the loss-weighted Gram matrix is spectrally equivalent to the Generalized Gauss-Ne
This research is emerging as deep learning applications confront the practical challenges of continuous deployment and adaptation in real-world scenarios, where catastrophic forgetting is a major impediment.
Understanding the 'spectral collapse' of neural network plasticity provides a fundamental insight into a key limitation of current AI models, directly impacting the path to truly adaptive and general AI.
This research provides a theoretical framework and potential diagnostic for why deep learning models struggle with continual learning, shifting the focus towards architectural or algorithmic changes that preserve Hessian spectral properties.
- · AI research institutions specializing in foundational model robustness
- · Developers of meta-learning and adaptive AI algorithms
- · Hardware manufacturers whose products might better support dynamic model archite
- · Companies relying solely on static, re-trained deep learning models for evolving
- · AI development paradigms that do not account for plasticity loss
- · Approaches to continual learning that do not address spectral properties
This research will spur new architectural and algorithmic approaches for deep continual learning, focusing on maintaining model plasticity.
Improved continual learning capabilities could accelerate the development and deployment of robust AI agents and autonomous systems, reducing the need for costly re-training.
More adaptive AI models could lead to a proliferation of AI applications in dynamic environments, potentially transforming industries requiring continuous learning and adaptation.
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Read at arXiv cs.LG