Measure adaptation cost.

This is the same reference used in Technical mode. Expand it whenever you need the exact numbers, assumptions or further explanation.

Compare the path to improvement

A new sensor may need calibration before its predictions are useful. Reporting only the final error hides whether one method needed two measurements and one update while another repeatedly processed the same data. Start with error before adaptation, then measure the curve at a declared evidence and compute budget.

The experiment uses three linear training tasks with slopes 0.5, 1 and 1.5 and intercepts −0.4, 0 and 0.4. They train a starting point. Four other task identities are excluded from those outer gradients: two linear tasks and two curved tasks. The curved family changes what the line predictor can represent, rather than merely changing the preferred coefficients.

Support teaches; query checks

Each task supplies two support measurements at x = ±0.75. Parameter updates use only these two measurements. Four distinct query inputs, −0.95, −0.25, 0.25 and 0.95, measure error after adaptation. Task identity, support membership and query membership have separate meanings; distinct x values alone would not establish a new task family.

The line predictor uses slope w and intercept b. Its support objective is mean half-squared error. With the symmetric support inputs, the slope curvature of this objective is 0.5625 and the intercept curvature is 1. One step at rate 0.4 therefore multiplies sensitivity to the preceding slope by 0.775 and sensitivity to the preceding intercept by 0.6.

The meta-gradient differentiates query loss through that actual support update, using those sensitivity factors. Forty outer updates at rate 0.5 build the starting point. This is a bounded two-parameter illustration of learning an initialization; it is not a reproduction of a large benchmark or a guarantee about every adaptation algorithm.

A matched comparison

Each displayed curve restarts from zero or the same trained starting point. It performs zero, one, two, five or ten support updates, then evaluates the query coordinates without fitting on them. Five updates mean ten support-row uses, but still only two supplied measurements. Meta-training and query computation are excluded from that fitting-row count and must be accounted for separately in a cost decision.

Read the zero-update row first. A starting point already closer to the linear family can have an advantage before seeing this task’s examples. Now compare changes from each initial error and the absolute errors after equal budgets. Finally compare the curved-family results: more fitting cannot remove the representational restriction to a line.

The graph uses a shared 0–4 MSE scale and counts clipped values. Its complete table shows both initializations at every budget, including failures. Do not interpret different axis limits as algorithmic improvement.

Preserve the role of exposed tasks

These task identities were excluded from meta-training, but the browser makes their outcomes public when opened. After using them to choose settings they are development evidence. Freezing later does not restore an untouched test. A larger study needs a predeclared new task family, task-level repeated runs, all-run reporting and independent replay.

Use the adaptation studio to record curves, source/configuration versions and costs. In Project 14, distinguish a claim about these four tasks from a claim about future tasks or real sensors.