Shaw & Co.[5] Fiete completed her graduate studies in 2003, and moved across the country to hold an appointment as a postdoctoral fellow at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara from 2004 until 2006.

In 2006, Fiete and her colleagues described a framework to understand the computations of grid cells in the entorhinal cortex, and how they encode the positions of rats.

[10] After serving on the faculty for 10 years and founding the Center for Theoretical and Computational Neuroscience [11] there, in 2018 Fiete accepted an offer from the Massachusetts Institute of Technology and became an associate professor with tenure within the Department of Brain and Cognitive Sciences.

[12] Fiete and her colleagues at UT Austin were interested in exploring the neural computations underlying grid cells in the entorhinal cortex.

Fiete and her colleagues found that grid cell computations can emerge from a pattern formation process, and can be modelled by continuous attractor networks.

[14] With inputs signifying the velocity and heading direction of the animal, continuous attractor models can generate triangular grid responses that encode updated estimates of location in two-dimensional spaces.

[13] In 2013, Fiete and her colleagues used in vivo neural recordings as the basis for their computational investigation of the mechanisms underlying grid cell activity.

[15] Their model, relying on low-dimensional continuous attractor dynamics, reliably characterized grid cell responses in short duration, familiar enclosures.

[17] Using the grid cell system, which Fiete had extensively probed and serves as a good system for testing computational models, Fiete showed that the "distribution of relative phase shifts" model has the potential to reveal highly detailed cortical circuit mechanisms from sparse neural recordings.

[17] In 2019, once Fiete had arrived at MIT, she published a paper using topological modeling to transform the neural activity of large populations of neurons into a data cloud representing the shape of a ring.