Beyond receptive fields: sequence-pooled normalization can supply most of a sequence labeler's context

What the math gives to ML

The paper isolates a concrete mechanism by which sequence-pooled normalization creates a global input-to-output dependency even when the convolutional receptive field is local. Its Jacobian gives an exact, task-independent test for whether distant positions can affect an output, while the normalized value exposes the global mean and variance as a low-cost sequence summary. This suggests replacing some expensive dilation or long-range convolution layers with channelwise sequence normalization when labels exhibit long runs, while using per-position statistics when strict locality is required. The same Jacobian can also serve as a diagnostic for measuring the true context of sequence models and avoiding misleading receptive-field ablations.