Frozen Core Decomposition (FCD): An Architectural Approach to Continual Learning Without Catastrophic Forgetting

Catastrophic forgetting is a fundamental challenge in continual learning, where neural networks trained on sequential tasks lose previously acquired knowledge. This paper presents Frozen Core Decomposition (FCD), an architectural approach that provides hard isolation between tasks through Tucker-style tensor factorization. The method generates task-specific weights via Wt = U (S ×3 vt) V, where shared factors U, V and core tensor S are frozen after the first task, and only task-specific vectors vt are learned for subsequent tasks. This architectural constraint guarantees that previously learned representations remain unchanged. In the task-aware setting (task identity known at inference), evaluation is performed on Split MNIST, Permuted MNIST, and Split CIFAR-100. Results show forgetting below 1% across all benchmarks, with accuracy competitive or superior to existing methods. Ablation studies confirm that core freezing is the primary mechanism. Key Contributions:- An architectural approach to continual learning via Tucker-style factorization with task-specific coefficient vectors- A core freezing strategy that provides hard isolation between tasks, theoretically guaranteeing zero interference with frozen representations- Empirical validation on three benchmarks showing <1% forgetting in the task-aware setting- Extension to vision backbones (ResNet-18, custom CNN) and large language models (GPT-2) with FCD-LoRA