Artificial neural network reproduces gait patterns of four-legged animals

PROVIDENCE, R.I. [Brown University] - Imagine a horse stumbling on a rock. It regains momentum, then hits bumpier terrain and slows to a walk. Back on steady ground, the horse picks up its pace to catch up to the herd. How is the horse able to transition between these different gaits?

Researchers at Brown University's Carney Institute for Brain Science have developed an artificial neural network that shows how a four-legged creature may generate multiple distinct patterns in gait. Their work, published in Neural Computation, provides new insights into how the brain may process complex behaviors. It could also be useful in advancing the technology of quadruped robots, enabling them to perform complex dynamic movements more autonomously.

"We know the brain has to be able to flexibly and robustly maintain and change rhythms," said Carina Curto, a professor of applied mathematics at Brown. "By tapping into the rules of attractor networks, we have created an artificial neural network that hints at how biological brains might simultaneously encode and transition between different patterns and rhythms."

Attractor networks are a mathematical construct that can be used to explain neural activity patterns toward which the brain's dynamics naturally settle, Curto said. One type of attractor network, known as a Hopfield network, is used by neuroscientists to model "static" brain behaviors, or behaviors where neurons fire in a consistent pattern - such as retrieving stored information when recognizing someone's face.

The team's new research expands the attractor framework to create an efficient model for dynamic behaviors. Based on a streamlined and efficient network of 24 artificial neurons, the attractor-based network generates five distinct quadruped gaits (bounding, pacing, trotting, walking and a type of leap known as pronking), with the ability to capture fast transitions between these gaits, whether a sudden leap or the shift from a trot to a walk, without needing to adjust any of the model's parameters.

These findings suggest that attractor-based networks are more flexible and interpretable than other models, and provide a unified theoretical framework that can be used to study a range of brain behaviors.

The research team included collaborator Katherine Morrison, professor of mathematical sciences at the University of Northern Colorado, who worked with the team during a semester-long residency at ICERM, Brown's National Science Foundation-funded mathematics institute.

"This paper shows that you can expand attractor networks beyond the static to include the dynamic," said Juliana Londono Alvarez, a postdoctoral researcher at Brown and the study's lead author. "Once you do that, you can see how the same principles underlying memory encoding can also generate something dynamic, like these gaits."

The network could serve as inspiration for robotics, the researchers said. Quadruped robots already borrow behaviors from animals to perform tasks. However, the programs such robots run on tend to be expensive, massive and require that they be connected to the internet. A quadruped robot that took inspiration from the Curto lab's small and efficient neural network would be able to operate offline.

Londono Alvarez is currently in discussions with roboticists about adapting the network for their projects.

This work was supported by National Institutes of Health grants R01 EB022862, NSF DMS-1951165 and DMS-1951599. Part of this work was supported by National Science Foundation grant DMS-1929284 while the mathematicians were in residence at ICERM during the 2023 Math + Neuroscience program.