To build speech processing methods that can handle speech as naturally as humans, researchers have explored multiple ways of building an invertible mapping from speech to an interpretable space. The articulatory space is a promising inversion target, since this space captures the mechanics of speech production. To this end, we build an acoustic-to-articulatory inversion (AAI) model that leverages self-supervision to generalize to unseen speakers. Our approach obtains 0.784 correlation on an electromagnetic articulography (EMA) dataset, improving the state-of-the-art by 12.5\%. Additionally, we show the interpretability of these representations through directly comparing the behavior of estimated representations with speech production behavior. Finally, we propose a resynthesis-based AAI evaluation metric that does not rely on articulatory labels, demonstrating its efficacy with an 18-speaker dataset.