The ability of deep neural networks (DNNs) to represent phonotactic generalizations derived from lexical learning remains an open question. This study (1) investigates the lexically-invariant generalization capacity of generative convolutional neural networks (CNNs) trained on raw audio waveforms of lexical items and (2) explores the consequences of shrinking the fully-connected layer (FC) bottleneck from 1024 channels to 8 before training. Ultimately, a novel technique for probing a model's lexically-independent generalizations is proposed that works only under the narrow FC bottleneck: generating audio outputs by bypassing the FC and inputting randomized feature maps into the convolutional block. These outputs are equally biased by a phonotactic restriction in training as are outputs generated with the FC. This result shows that the convolutional layers can dynamically generalize phonetic dependencies beyond lexically-constrained configurations learned by the FC.