Reuss, Arthur (2026) The Stability Gap as a Trajectory Problem: A Bent Descent Path, Its Overshoot, and One Gate in Two Designs. Bachelor's Thesis, Artificial Intelligence.
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BA Thesis-Arthur Reuß-s5582253-The Stability Gap as a Trajectory Problem - A Bent Descent Path, Its Overshoot, and One Gate in Two Designs.pdf Download (3MB) | Preview |
Abstract
Replay-based continual learning is usually judged by the accuracy it reaches after each task. Continual evaluation exposes what this view hides: the stability gap, a transient drop in past-task accuracy at the start of every new task. The gap persists even when the optimiser descends the exact joint loss, so at least part of its cause lies in the optimisation trajectory rather than the objective. This thesis explains the gap on two levels. The intended trajectory, the path exact gradient descent would take, bows out of the old task’s basin before returning; and the followed path overshoots the intended one through everything that vanishes with the step size: discrete updates, momentum, and gradient noise. We separate the two levels by measurement rather than by argument. Rescaling the step size is a reparametrisation of the same gradient flow, so a ladder of learning rates run at matched flow time from one frozen checkpoint discretises one and the same intended trajectory, and whatever survives η →0 is that trajectory. On rotated MNIST the ladder converges, and not on zero: of the 23 pp drop at the standard step size, roughly four fifths is discretisation overshoot, and a smooth arc of some four points remains that neither an exact replay gradient nor any further shortening of the step removes. Reaching that limit costs a hundred times the training, which sets the bar for a method: not lowering the gap, which a shorter step does with no method at all, but lowering it at the standard step size and in the standard number of steps. Written in a unified update rule, replay methods counter both levels with a single tool, a gate on the new-task gradient with the replay gradient restoring at full strength, and we build and compare the two pure gate designs: an adaptive λ-curriculum and asymmetric Fisher-preconditioned replay. The curriculum earns its keep only under momentum, and there it does not shallow the gap but removes it: the excursion’s area falls to a thirtieth of vanilla ER’s, the past task never dips far enough to register a recovery event, and the residual depth (3.7 pp against 15.9) is permanent forgetting rather than transient. It does this at vanilla accuracy, matches in one epoch what shortening the step reaches only in the limit, and carries to CIFAR-10 on a ResNet-18 at negligible overhead. The directional gate protects the past task at no measured plasticity cost but at far higher compute. Which gate is preferable is set by the momentum regime.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Ven, G.M. van de and Sabatelli, M. |
| Degree programme: | Artificial Intelligence |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 01 Sep 2026 07:01 |
| Last Modified: | 01 Sep 2026 07:01 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37549 |
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