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Experiment Note
A V2 ablation removed variable identity while retaining regional adaptation. This tested whether the joint variable-region representation added value beyond regional control alone.
The final cavity analysis found that full VARA won 22 of 39 selected quantities against the no-variable controller, with an average improvement of 1.6 percent. The gap was smaller than the gap against vanilla, implying that regional guarded allocation explained most of the effect while variable identity added a smaller multi-field benefit.
Technical Essay
This ablation refined the novelty claim. It would have been tempting to attribute all gains to variable awareness. The evidence did not support such a broad statement. On a scalar PDE such as Allen-Cahn, removing variable awareness is structurally inactive because there is only one output channel; the repository correctly preserved the numerically identical result instead of forcing a difference. In multi-field cavity flow, variable identity had measurable but secondary value.
Reading Note
Ablation design should remove exactly one mechanism while holding architecture, data, optimizer, seed, and budget fixed. Otherwise an apparent mechanism result is only another method comparison. This principle guided the later sampling- only, local-loss-only, no-guard, and no-variable experiments.
Progress Update
The project obtained a more precise explanation: regional allocation was the dominant mechanism; variable identity mattered most when multiple physical fields could compete.