Dysarthria Normalization via Local Lie Group Transformations for Robust ASR

We present a geometry-driven method for normalizing dysarthric speech using local Lie group transformations of spectrograms. Time, frequency, and amplitude distortions are modeled as smooth, invertible deformations, parameterized by scalar fields and applied via exponential maps. A neural network is trained to infer these fields from synthetic distortions of typical speech-without using any pathological data. At test time, the model applies an approximate inverse to real dysarthric inputs. Despite zero-shot generalization, we observe substantial ASR gains, including up to 16 percentage points WER reduction on challenging TORGO samples, with no degradation on clean speech. This work introduces a principled, interpretable approach for robust speech recognition under motor speech disorders