Though not an official term, Jedi Aberrants can be considered Jedi who deviate notably in one way or another from the standard teachings of the Jedi Order. They can wield a variety of lightsaber colors, but orange is the color that seems to most characteristically represent them.
Frequently, Jedi Aberrants were Jedi Consulars whose philosophies evolved over time, such that they came to disagree with certain teachings of the Jedi Order. Like Consulars, they were often regarded as mysterious by their fellow Jedi given their unique and varying perspectives of the Force. Unlike Consulars however, they often studied both Jedi and Sith prophecies even interacting with the Dark Side of the Force to do so; a practice which was looked upon with disdain by the Jedi High Council.
While it was not uncommon for a Jedi Aberrant to become so conflicted with the Order that they would leave it entirely (such as in the case of The Lost Twenty), many also remained within the Jedi Order and provided valuable and unique insight to resolving local and galactic issues, as well as uncovering mysteries of the Force.
Besides prophecies, many Jedi Aberrants traveled the galaxy studying ancient Sith and Jedi relics. They were often well-versed in ancient writings and cultures and some discovered hidden Jedi Temples that had been long-lost or forgotten. The Order 66 survivor, Baylan Skoll, adhered to these forms of thought, searching for the answers to an ancient legend that was said to exist outside of the known galaxy.
Important Jedi Aberrant Qualities: Mystery, defiance, curiosity, divergence
Prominent Examples: Baylan Skoll, Shin Hati