Continual Learning is the machine learning paradigm focused on training neural networks on a sequence of tasks without catastrophic forgetting — where the network retains knowledge from previously learned tasks while acquiring new capabilities, addressing the fundamental limitation that standard neural network training on new data overwrites the weights encoding old knowledge.

Catastrophic Forgetting

When a neural network trained on Task A is subsequently fine-tuned on Task B, performance on Task A degrades dramatically — often to random-chance levels. This occurs because gradient descent moves weights to minimize the Task B loss without regard for the Task A loss surface. The weight configurations optimal for Task A and Task B may be incompatible, and training on B destroys A's solution.

Continual Learning Strategies

• Regularization-Based Methods:
• EWC (Elastic Weight Consolidation): Identifies weights important for previous tasks (via the Fisher Information Matrix) and adds a penalty for changing them when learning new tasks. Important weights are "elastic" — pulled back toward their old values. L_total = L_new + λ Σᵢ Fᵢ(θᵢ - θᵢ*)², where Fᵢ is the Fisher importance.
• SI (Synaptic Intelligence): Computes parameter importance online during training by tracking each parameter's contribution to the loss reduction.
• LwF (Learning without Forgetting): Uses knowledge distillation — the model's predictions on new task data (using old task outputs as soft targets) serve as a regularizer.

• Replay-Based Methods:
• Experience Replay: Store a small buffer of examples from previous tasks and interleave them during new task training. Simple but effective. Storage cost grows with number of tasks.
• Generative Replay: Instead of storing real examples, train a generative model to produce synthetic examples from previous task distributions.
• Dark Experience Replay (DER++): Store both examples and the model's logits (soft predictions) from when the example was first seen, combining replay with distillation.

• Architecture-Based Methods:
• Progressive Neural Networks: Add new columns (sub-networks) for each task with lateral connections to previous columns (which are frozen). No forgetting by design, but parameter count grows linearly with tasks.
• PackNet: Prune the network after each task and assign freed capacity to new tasks using binary masks per task.
• LoRA-based Continual Learning: Add separate LoRA adapters for each task while keeping the base model frozen. Task-specific adapters are loaded at inference based on the detected task.

Evaluation Protocols

• Task-Incremental: Task identity is known at test time (easier — model selects the right head).
• Class-Incremental: New classes are added over time; model must classify among all seen classes (harder — requires distinguishing old from new).
• Domain-Incremental: Same task but data distribution shifts (e.g., different hospitals, seasons).

Continual Learning is the pursuit of neural networks that accumulate knowledge rather than replace it — the missing capability that separates current AI systems (which are frozen after training) from biological intelligence (which learns continuously throughout life).