There is a growing body of work that leverages features extracted via<br>topological data analysis to train machine learning models. While this field,<br>sometimes known as topological machine learning (TML), has seen some notable<br>successes, an understanding of how the process of learning from topological<br>features differs from the process of learning from raw data is still limited.<br>In this work, we begin to address one component of this larger issue by asking<br>whether a model trained with topological features learns internal<br>representations of data that are fundamentally different than those learned by<br>a model trained with the original raw data. To quantify ``different'', we<br>exploit two popular metrics that can be used to measure the similarity of the<br>hidden representations of data within neural networks, neural stitching and<br>centered kernel alignment. From these we draw a range of conclusions about how<br>training with topological features does and does not change the representations<br>that a model learns. Perhaps unsurprisingly, we find that structurally, the<br>hidden representations of models trained and evaluated on topological features<br>differ substantially compared to those trained and evaluated on the<br>corresponding raw data. On the other hand, our experiments show that in some<br>cases, these representations can be reconciled (at least to the degree required<br>to solve the corresponding task) using a simple affine transformation. We<br>conjecture that this means that neural networks trained on raw data may extract<br>some limited topological features in the process of making predictions.