Answers to important questions:
Q: What happens in the mind when attention returns after being distracted?
A: Coherent rotational waves move through the cortex, causing neurons to enter a focused state.
Q: What do these rotations have to do with behavior?
A: Once the rotation is complete, performance improves. Incomplete rotations result in errors or slow responses.
Q: Why is it important to understand how the brain works?
A: It shows that the brain uses analog traveling waves – an efficient mechanism – to restore attention and process information.
Summary: Neuroscientists have discovered that coherent waves of neural activity that circulate when the brain is distracted help the brain refocus. Using electrical measurements in animals, the team found that neurons in the prefrontal cortex synchronize in circular patterns — like stars in flight — to recover from cognitive disruptions.
When this rotation completed a full circle, performance was faster. When it didn’t, errors occurred. The results suggest that the brain uses these low-energy traveling waves as a natural analog computing system to refocus after interruptions.
Key data
- Circulatory recovery: Circulatory nerve waves in the prefrontal cortex help the brain recover after distraction.
- Predictability: Complete circular rotations result in accurate task performance. Incomplete rotations predict errors.
- Analog Performance: Research shows that the brain uses analog traveling waves to perform calculations efficiently.
Source: MIT Pecor Institute
Just as the brain is sensitive to distractions, it can also redirect attention to the task at hand.
A new animal study by scientists at MIT’s Picower Institute for Learning and Memory shows how this happens: Coordinated neural activity in the form of circulating brain waves gets thinking back on track.
Earl K. Miller, the study’s lead researcher and the Picower Professor at the Picower Institute and professor in the Department of Brain and Cognitive Sciences at MIT, provided an evocative description of the neural process: he stated that rotating waves function similarly to “shepherds”.
He further explained that their role is to guide the cortex into the correct computational path. This analogy suggests that the rhythmic, traveling nature of the rotating waves serves a critical, organizational function in directing the brain’s processing during tasks.
He is the lead author of the study, published in the Journal of Cognitive Neuroscience .
Mathematical ‘twist’…
In the study, animals were given a visual working memory task, but occasionally they were exposed to two different types of distractions while trying to remember something they saw.
As expected, distractions affected the animals’ performance on the task. Sometimes they made mistakes, but other times their reaction times slowed down when the task required them to act.
Meanwhile, the researchers monitored the electrical activity of hundreds of neurons in the prefrontal cortex, a region of the brain responsible for higher cognition.
To analyze the variations in neural activity across hundreds of experimental sessions—including trials with and without distractions, and those where animals performed successfully or poorly—the researchers employed a specific mathematical method.
This method incorporated the concept of “subspatial coding,” which measures the degree of coherence over time in neural signals. The underlying suggestion of subspatial coding is that the activity patterns of cortical neurons are highly coordinated rather than random or independent.
“It’s like the stars are murmuring in the sky,” Miller said.

After the distraction, there was a circular movement in the subspace, as if the “birds” were regrouping in circles after their formation was interrupted. In other words, according to Miller, the circling seems to be a sign of their restoration to an active state after the distraction.
The rotations effectively predicted the animals’ performance on the task. In cases where the distraction did not cause impairment, the neural data showed a complete circle, indicating that recovery was complete.
In cases where animals made errors due to distraction, the speed was less than the full circle (average 30 degrees). During the error sessions, the speed showed a lower speed, which may explain the lack of recovery after distraction.
A related finding was that animals recovered better when there was more time between the distraction and the need to act. The data showed that the brain needed this much time to mathematically complete the cycle and resume normal behavior.
The subcoding data suggested that the neurons function in a highly coordinated manner and that this circular organization helps them maintain attention. Surprisingly, the rotations occurred only when there was a distraction (both types of stimuli activated them) that the animals tried to ignore. The rotations did not occur spontaneously.
Reflect physical rotations.
Subspace coding is simply an abstract mathematical representation of neural activity over time. But when researchers analyzed direct physical measurements of neural activity, they discovered that it actually reflects a real traveling wave moving through the cortex.
Various measurements showed that neuronal activity exhibits a spatial arrangement with constantly changing angles, which is consistent with the wave of activity circulating through the cortical electrodes. In fact, the actual wave rotates at the same speed as the wave mathematically represented in the subspatial encoding.
“Miller points out that, in principle, there is no inherent reason why the rotation occurring within this mathematical subspace should directly align with the rotational movement observed at the Earth’s surface crust.
This highlights a key disconnect, suggesting that geophysical models attempting to link subsurface dynamics to crustal rotation must account for the fact that a theoretical rotation in an abstract mathematical domain is not guaranteed to correspond to the physical, measurable rotation of the planet’s outer layer.
But it works. This suggests to me that the brain uses these traveling waves to perform analog calculations. Analog calculations are much more energy efficient than digital ones, and biology favors energy-efficient solutions. It’s a different and more natural way to think about neural calculations.
In addition to Miller and Batbial, Scott Brinkett, Jacob Donoghue, Mikael Lundquist, and Meredith Mahnke also contributed to the article.
Funding: This study was funded by the Office of Naval Research, the Simon Center for the Social Brain, the Freedom Together Foundation, and the Pecor Institute for Learning and Memory.
About this neuroscience research news
Author: David Orenstein
Source: Picower Institute at MIT
Contact: David Orenstein – Picower Institute at MIT
Image: The image is credited to StackZone Neuro
Original Research: Open access.
“State–Space Trajectories and Traveling Waves Following Distraction” by Earl K. Miller et al. Journal of Cognitive Neuroscience
Abstract
Traveling waves after velocity and derivation in state space.
Cortical activity reflects the ability to recover from a distraction. We analyzed neural activity in the prefrontal cortex of monkeys performing working memory tasks with distractions (a guided gaze shift or irrelevant visual input) during the intermediate phase of memory acquisition.
After the perturbation, a state-space rotation dynamic emerged, returning to the population patterns before the perturbation. In fact, rotations were more complete when the task was performed correctly than when errors occurred.
We found a correspondence between state space rotations and waves traveling on the PFC surface.
This suggests that emergent dynamics, such as state space rotation and traveling waves, play a role in recovery from perturbations.

