Editing Continual Learning (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
The core problem: neural network weights encode knowledge through their specific values. When you train on Task B, gradient descent moves weights toward the minimum loss for Task B — often moving them away from the minimum for Task A. This is catastrophic forgetting: the gradient update for Task B destroys Task A's solution.

'''The stability-plasticity dilemma''': A model that never forgets (high stability) must also never change weights (low plasticity) — so it can't learn new things. A model that learns quickly (high plasticity) overwrites old knowledge. Managing this trade-off is the central challenge.

'''Three families of solutions''':

'''Regularization-based''': Add a penalty term to the loss that discourages large changes to parameters important for previous tasks. EWC computes the Fisher information matrix (how important each parameter is to Task A's performance) and uses it to weight the penalty: L = L''new + λ Σ''i F''i (θ''i - θ*_i)². Quadratic Penalties penalize based on simple L2 distance from previous parameters.

'''Memory-based (Replay)''': Keep a small buffer of past examples (coreset) and interleave them with new task data. This directly prevents forgetting by ensuring gradients for old tasks continue to appear. Gradient Episodic Memory (GEM) ensures new task gradients don't increase loss on stored examples.

'''Architecture-based''': Allocate different model capacity to different tasks — freeze old weights, expand the model for new tasks (Progressive Neural Networks), or use dynamic sparse masks per task (PackNet, HAT).
</div>

<div style="background-color: #8B0000; color: #FFFFFF; padding: 20px; border-radius: 8px; margin-bottom: 15px;">