Fig. 10: Control Analyses.

The key distributed properties including A NRS representation, B NRS based distance effect, C NRS based \(\log\)-ratio effect, D MDS representations, E covariance between MDS dimension 1 and magnitude, and F covariance between MDS dimension 2 and mid-point anchor. These properties are all replicated for the three control analyses conducted, and in A–F the subplots show (a) Main: primary analysis based on accuracy reaching 99%+ levels; (b) Epoch 1: control for limited single epoch training where accuracy increases to 77%, similar to human accuracy levels; (c) RMS prop; control for change in training method from Adam optimizer to RMS propagation; and (d) SGD: control for change in training method from Adam optimizer to stochastic gradient descent. Source data are provided as a Source Data file.