Add parallel experiments via GNU parallel and geometric mean aggregation

Experiments across multiple inputs/seeds should be parallelized with
GNU parallel to reduce wall-clock time. Geometric mean is the default
summary statistic for aggregating multiple measurements.

Author: schulzchristian

AAE.md

@@ -123,6 +123,18 @@ Run the benchmark and collect results:
 - Extract the key metric(s) from the log.
 - If the run crashes, diagnose from the log tail.
 
+**Parallel runs**: When the benchmark must be run across multiple inputs, seeds, or configurations, use GNU `parallel` to execute them concurrently. For example:
+```bash
+parallel --jobs 4 --results run_results/ './bench.sh --input {} > logs/run_{}.log 2>&1' ::: input1 input2 input3 input4
+```
+This reduces wall-clock time per iteration significantly. Only parallelize when runs are independent and the system has sufficient resources (CPU cores, memory, GPU slots) to avoid contention that would distort measurements.
+
+**Aggregation**: When an experiment produces multiple measurements (e.g. across inputs or seeds), use the **geometric mean** as the default summary statistic. The geometric mean is appropriate for ratios and multiplicative quantities like speedups or normalized scores, and is less sensitive to outliers than the arithmetic mean. Compute it as:
+```
+geometric_mean = (x1 * x2 * ... * xn) ^ (1/n)
+```
+Use the arithmetic mean only when the metric is inherently additive (e.g. total time summed across phases) and the user explicitly requests it.
+
 ### 6. Evaluate (Keep or Discard)
 
 Compare the result to the current best: