The human brain is often described in the language of tipping points: It toes a careful line between high and low activity, between dense and sparse networks, between order and disorder. Now, by analyzing firing patterns from a record number of neurons, researchers have uncovered yet another tipping point — this time, in the neural code, the mathematical relationship between incoming sensory information and the brain’s neural representation of that information. Their findings, published in Nature in June, suggest that the brain strikes a balance between encoding as much information as possible and responding flexibly to noise, which allows it to prioritize the most significant features of a stimulus rather than endlessly cataloging smaller details. The way it accomplishes this feat could offer fresh insights into how artificial intelligence systems might work, too.

A balancing act is not what the scientists initially set out to find. Their work began with a simpler question: Does the visual cortex represent various stimuli with many different response patterns, or does it use similar patterns over and over again? Researchers refer to the neural activity in the latter scenario as low-dimensional: The neural code associated with it would have a very limited vocabulary, but it would also be resilient to small perturbations in sensory inputs. Imagine a one-dimensional code in which a stimulus is simply represented as either good or bad. The amount of firing by individual neurons might vary with the input, but the neurons as a population would be highly correlated, their firing patterns always either increasing or decreasing together in the same overall arrangement. Even if some neurons misfired, a stimulus would most likely still get correctly labeled.

At the other extreme, high-dimensional neural activity is far less correlated. Since information can be graphed or distributed across many dimensions, not just along a few axes like “good-bad,” the system can encode far more detail about a stimulus. The trade-off is that there’s less redundancy in such a system — you can’t deduce the overall state from any individual value — which makes it easier for the system to get thrown off.

For the past couple of decades, research indicated that neural systems generally favored low-dimensional representations. Although the natural world contains an absolutely massive amount of information, the brain seemed to be discarding much of that in favor of simpler neural descriptions. But later analyses showed that this conclusion could be chalked up to weaknesses in the experiments themselves: The lab animals were presented with only a few stimuli, or very simple stimuli, and researchers could only record from a limited number of neurons at a time. “Of course those experiments gave those results,” said Kenneth Harris, a neuroscientist at University College London. “They couldn’t do anything different.”

So Harris and his colleagues revisited the problem, after creating a new technique for recording from 10,000 neurons simultaneously. As they showed mice nearly 3,000 images of natural scenes, they monitored the responses in the animals’ visual cortex and found a range of patterns that fit with a higher-dimensional picture of neural activity.

But the researchers also discovered something puzzling about that activity. The neurons didn’t care about all the dimensions equally: A few dimensions, or firing patterns, captured most of the neural responses to the visual stimuli. Adding other dimensions further increased that predictive power only by smaller and smaller increments. This decay followed what’s known as a power law, a special mathematical relationship “that’s been found almost everywhere people look for it,” said Jakob Macke, a computational neuroscientist at the Technical University of Munich who did not participate in the study.

Harris and his colleagues were stumped about what it might signify. Although recent studies have called the relevance (and even prevalence) of power laws into question — Harris quipped that even “the distribution of the number of exclamation marks in tweets from Donald Trump follows a power law” — there was something special about this one. It consistently had a particular slope, an exponent that couldn’t be explained by the mathematical structure of the stimuli.

“This sort of thing, this quantitative regularity in the data,” Harris said, “just doesn’t happen in biology. … We had absolutely no idea what it meant” — but it seemed to mean something.

In search of an explanation, they turned to previous mathematical work on the differentiability of functions. They found that if the power law mapping input to output decayed any slower, small changes in input would be able to generate large changes in output. The researchers referred to this as a breakdown in smoothness: The outputs produced by the underlying code were not always continuous.

It’s like being on the border of fractality, according to the co-leaders of the study, Carsen Stringer and Marius Pachitariu, both of whom worked in Harris’s lab and are now researchers at the Howard Hughes Medical Institute’s Janelia Research Campus in Virginia. “If you think of a fractal like the coastline of England,” Stringer said, “if you’re moving just a little bit along that coastline, you’re going to be changing very quickly, because there’s lots of jagged edges.”

In brain terms, that meant two very similar images could be represented by very different neural activity. “And that’s problematic,” she added. “If just one pixel changes, or if the image moves a bit, you don’t want your representation to totally change.”

Conversely, if the power law decayed any faster, the neural representations would become lower-dimensional. They would encode less information, emphasizing some key dimensions while ignoring the rest.

Taken together, those principles implied that the representations were as detailed and high-dimensional as they could get while still remaining smooth.

According to Harris, one way to interpret the finding is that with a slower decay, too much emphasis would be placed on less important dimensions (because if the curve relating neural activity to dimension were to get flatter, it would indicate that neural populations cared about all the dimensions more equally). Representations of the finer details in a stimulus would swamp the representation of the bigger features: The visual cortex would always be hypersensitive to certain trivial details, which would in turn make it difficult to formulate coherent perceptions and decisions. Meanwhile, with a faster decay, more weight than necessary would be placed on the larger features, overwhelming smaller features that might be relevant, too.