Training-Target Spectra Induce Graded Shrinkage in Brain Decoder Predictions

Whether reconstruction from brain activity generalizes to subjective content a participant has not experienced during training can be governed by the composition of the training stimuli, the targets the decoder is trained to predict. The constraint the training targets place on prediction is known as output dimension collapse, but it is a binary one: it says only that what lies outside the subspace the training targets span is lost. We therefore introduce the directional prediction scale ratio, which measures the spread of the prediction along each eigendirection. In experiments on synthetic data, we observed that the scale ratio decays continuously toward directions with smaller target eigenvalues: the shrinkage of the prediction is graded rather than binary, with hard output-dimension collapse its zero-eigenvalue limit. The graded shrinkage persists even when the input carries no information about the features, and we observed the same gradient in features decoded from real brain activity. When the targets have cluster structure, the prediction lies close to the span of the cluster centers, and an unseen cluster inside that span is predictable. These results suggest that training data should be sampled so as to cover the feature variations one wants predicted.