Given an orthographic transcription, forced alignment systems automatically determine boundaries between segments in speech, facilitating the use of large corpora. In the present paper, we introduce a neural network-based forced alignment system, the Mason-Alberta Phonetic Segmenter (MAPS). MAPS serves as a testbed for two possible improvements we pursue for forced alignment systems. The first is treating the acoustic model as a tagger, rather than a classifier, motivated by the common understanding that segments are not truly discrete and often overlap. The second is an interpolation technique to allow more precise boundaries than the typical 10 ms limit in modern systems. During testing, all system configurations we trained significantly outperformed the state-of-the-art Montreal Forced Aligner in the 10 ms boundary placement tolerance threshold. The greatest difference achieved was a 28.13 % relative performance increase. The Montreal Forced Aligner began to slightly outperform our models at around a 30 ms tolerance. We also reflect on the training process for acoustic modeling in forced alignment, highlighting how the output targets for these models do not match phoneticians' conception of similarity between phones and that reconciling this tension may require rethinking the task and output targets or how speech itself should be segmented.