Continual Learning Evaluation › Intransigence

Intransigence measures the model's resistance to learning new tasks due to the inertia accumulated from prior training. Where forgetting asks "how much did the model lose from what it knew?", intransigence asks "how hard was it to learn new tasks given what the model already knew?". These are two distinct failure modes that must be measured separately.

The per-task intransigence for task $T_j$ is:

$$I_j = b_j - R_{j,j}$$

The aggregate intransigence averages over all tasks:

$$I = \frac{1}{N} \sum_{j=1}^{N} I_j$$

where:

• $b_j$ is the accuracy on task $T_j$ when trained from scratch in isolation (the best achievable performance without interference)
• $R_{j,j}$ is the accuracy on task $T_j$ when trained sequentially after tasks $T_1, \ldots, T_{j-1}$ (the model's result in the sequential setting)
• A positive value of $I_j$ means prior training hurt learning of task $T_j$
• A negative value of $I_j$ (though rare) would mean prior training helped

The relationship between intransigence and forward transfer is direct: intransigence is essentially the negative of FWT (with the average including the first task as well as subsequent ones). High intransigence corresponds to negative FWT: prior experience is making new learning harder, not easier. Low or negative intransigence corresponds to positive FWT: prior experience is a net benefit.

Intransigence is especially relevant when evaluating regularization-heavy methods. A method that penalizes all weight changes to protect prior tasks will show low forgetting but high intransigence: it cannot update weights freely enough to learn new tasks, so new-task accuracy stays well below what an unconstrained model would achieve. This is the fundamental tension in regularization-based approaches. Elastic Weight Consolidation (EWC), for example, adds a penalty term that slows down changes to weights deemed important for prior tasks. If the penalty coefficient is set too high, the model learns new tasks poorly, producing high intransigence. If set too low, forgetting is insufficiently controlled. Finding the right balance is one of the central practical challenges in deploying regularization-based continual learning.

High intransigence means the model's prior training makes it harder to absorb new information. This is the flip side of forgetting: forgetting measures damage to old knowledge while intransigence measures difficulty acquiring new knowledge. Both are failure modes in continual learning, and both must be monitored to understand a method's overall behavior. A complete evaluation should always report both, since a method that eliminates forgetting by making new learning impossible is not a useful solution.

There is a deeper conceptual reason why intransigence and forgetting both exist and why reducing one often exacerbates the other. The weights of a neural network must simultaneously encode representations for all tasks. When the representation space required by task $j+1$ overlaps significantly with the space required by tasks $1$ through $j$, there is room for the network to accommodate both without conflict, and intransigence is low. When the spaces conflict, any attempt to shift representations toward the new task will partially undo the old ones, and any attempt to freeze the old representations will block the new task from achieving its optimum. This geometric view of the plasticity-stability tradeoff explains why the problem is fundamentally hard and why the metrics of forgetting and intransigence together provide a more complete picture than either one alone.