Abnormal

The Deviant Type (奇行種), also known as an Aberrant or Abnormal Titan, is an uncommon type of Titan which possesses unusual intelligence and performs unpredictable actions.

Description
Unlike the typical Titan which attacks and devours humans on sight, Deviant Type Titans may choose to ignore humans and exhibit unpredictable behaviour; often resulting in them causing larger damage as they disrupt important strategic locations. Some of these uncommon behaviors are ignoring humans, walking fast or running, performing great jumps, or even speaking human language.

Battle of Trost District arc
During the 49th Expedition outside the Walls, Hange Zoë among other members of Levi's squad encounter a Deviant Type Titan that, after chasing Hange, suddenly turns around and heads back into the forest. Hange follows it deep into the forest and it stops within a field. After a brief delay, it begins banging its head of a tree within the centre of the field. Hange and company get off their horses and tries to ask it what's its purpose is but is interrupted when it swings at them. After using their Three Dimensional Maneuver Gear to escape to a tree, they again come down to the ground and try to talk to it before Oluo attempts to kill it. When Hange pleas him to stop he becomes distracted and is captured and almost eaten before Levi appears and cuts of its arm and then kills it. After Levi expresses his outrage towards Hange's incompetence for her team mates safety, Petra shockingly points out a decapitated corpse hidden within a hole in the tree. They then find a lost diary on the ground that belonged to Ilse Langnar before her death.

Hange reads the diary. It explains that after Ilse's entire flank was massacred, she fled to a nearby forest, heading north. After profuse running, she inadvertently runs into a Titan and writes in the diary, believing it to be her end. She remarks that instead of immediately eating her, it hesitates. It then addresses her, saying "Ymir's people" and "Ymir-sama", greeting her with deep respect, and bows. She is thoroughly confused that the Titan can form speech, and writes in her diary that she has attempted communication. She first questions it about what the Titans are, and building up blind sadness, fear and rage, she angrily yells why Titans eat humans and what their objective is. The Titan appears more and more frustrated as it moans and tears at its cheeks, ripping off flesh and spraying blood. Ilse attempts to flee but is caught by the Titan, who is rapidly crushing her skull, and Ilse writes down her last few notes about the experience before being decapitated. The Titan later stores her corpse in the tree. Nothing is known about the Titan's motive and actions, but Ilse's notes prove significantly useful to humanity.

After the breach caused by the Colossal Titan and subsequent invasion of Shiganshina District, a horde of Titans entered through the destroyed gate. They are notable for entering the district almost immediately after the breach, and it is theorized by Armin that they were somehow lured in.

As Eren Yeager's group was heading towards the middle guard in the Trost district, a Deviant Type Titan jumped out of nowhere and grabbed Thomas Wagner in its mouth. The rest of the group looked on, horrified, as the Titan swallowed him whole. The same Titan would later appear, where it would be killed by Eren in his Titan form.

Another Deviant Type appeared and charged straight towards the rear exit of Trost, where a group of citizens were gathered and trying to escape. It ran so fast that the elite guards stationed in that area couldn't keep up with it. Mikasa Ackerman appeared and sliced the nape of its neck to kill it, dulling her blades in the process.

The Female Titan arc
The Survey Corps went on its expedition outside Wall Rose and on the way, a Deviant Type suddenly appeared towards the right flank. It completely ignored the soldiers at the outer guard and charged straight towards the center of the formation. Armin Arlert watched as Luke Siss and Dita Ness attempted to kill it, cutting the tendons of its foot and making it fall, and successfully killing it. There is also a deviant type Titan which walks and runs on it's hands and feet and is capable of running to very high speeds. Its limbs are deformed giving it a spider like gait and it is subdued by a captain leading it into a tree, knocking it unconscious.

Clash of the Titans arc
Connie Springer encounters his mother's Titan form in Ragako village. It's arms and legs were shrunken and paralyzed, and it said "welcome home." It is later revealed that the Beast Titan is directly responsible for the humans-turned-Titans in the village.

When Mike Zacharius first encountered the Beast Titan, he believed it to be a Deviant Type Titan due to the mass amount of fur on its body.

After Eren and Ymir were kidnapped by Reiner and Bertolt, they stopped by in the Forest of Giant Trees between Wall Rose and Wall Maria. As they were resting atop the branches, a Deviant Type Titan was casually lying beneath them and appeared to be watching their every movement.

The Uprising Arc
After drinking the serum that turns a person into a titan, Rod Reiss turned into a gargantuan Titan twice as big as the Colossal Titan. He was so big that he could only crawl and his body generate enough heat to burn close trees.

This Titan turned out to be a Deviant type and it headed to the Orvud District, the nearest and most populated area, attracted by the amount of people in the city. It ignored completely the concentrated cannon fire against him and just kept going towards the city.

Trivia

 * Titan Shifters are considered to be Deviant Types, but are classified differently.