Heterogeneous self-couplings enable scale-invariant memory and cognitive flexibility without criticality

The human brain is a master of time. It can react to a sudden flash of light in a fraction of a second, yet it can also hold a complex thought in mind for minutes or weave a story that unfolds over years. This ability to operate across such vastly different speeds is not a bug; it is a fundamental feature of how we think, learn, and adapt. For decades, scientists have wondered how a network of billions of neurons manages to keep track of events from the distant past while still responding to the present moment. A leading theory suggested that the brain must constantly hover on a razor-thin edge between order and chaos, a state known as criticality, to achieve this flexibility. However, new research challenges this long-held view, proposing that the brain might achieve its remarkable timekeeping and adaptability through a simpler, more robust mechanism: a built-in diversity of speeds within its own circuits.

In a study published in October 2026, researchers Francesco Damiani, Gabriele Di Antonio, and their colleagues at Pompeu Fabra University and the Istituto Superiore di Sanità in Rome explored this possibility using a computer model of a neural network. They built a system that mimics the brain's structure but introduced a specific kind of variation: instead of every part of the network behaving exactly the same, they gave each unit a different strength of self-connection. In the language of the model, some units are tightly connected to themselves, making them slow to change their state, while others are loosely connected, allowing them to react quickly. The team found that this simple mix of fast and slow units was enough to create a system that remembers the past across a wide range of time scales, without needing to be tuned to a critical edge.

The researchers discovered that when these units are arranged with the right mix of self-connections, the network's memory does not fade away in a predictable, uniform way. Instead, the memory of past inputs decays slowly and steadily, following a pattern where information from the distant past still has a faint influence on the present. This is what scientists call scale-invariant memory. It means the system can handle information arriving at any speed, whether it is a rapid series of clicks or a slow, drawn-out conversation, without needing to be reconfigured. The model showed that this power-law decay of memory, often seen in real brain activity, can emerge naturally from the diversity of the network's internal connections, rather than requiring the entire system to be balanced precariously on the brink of chaos.

To test if this memory was actually useful, the team put their model through a series of mental challenges. First, they gave it a short-term memory task where it had to remember a sequence of six different signals presented at varying speeds. A standard network, where all parts are identical, struggled as the signals came faster or slower, quickly forgetting what it had seen. A network tuned to the edge of stability performed better but was fragile. In contrast, the model with diverse self-connections remembered the sequence robustly, regardless of the timing. It could hold onto the first signal just as well as the last, even when the gaps between them were twenty times longer than the speed of a single unit. This demonstrated that the mix of speeds allowed the network to maintain a stable record of the past without losing its ability to react to the now.

The researchers then took the test a step further, asking the model to solve a classic puzzle of cognitive flexibility known as the Wisconsin Card Sorting Test. In this task, a person must sort cards based on a rule, such as matching by color or by shape. The rule changes unexpectedly, and the person must figure out the new rule based on feedback, like an error signal. This requires holding the current context in mind while being ready to switch gears instantly. The model succeeded at this task by using its fast units to make immediate decisions based on the cards it saw, while its slow, self-connected units acted as a stable reservoir to hold the current rule in mind. When an error occurred, the network could shift its internal state to a new "attractor," effectively changing its rule without needing to rewire its entire structure. This ability to switch contexts smoothly and efficiently emerged directly from the network's internal diversity.

A crucial part of the study was comparing this approach to other ways of creating different speeds in a network. The team built a second model where the units had different speeds because they were built with different time constants, a common way to simulate diversity. While this second model could also solve the puzzle, it required much larger and more drastic changes to its connections to learn the rules. The model with diverse self-connections, however, learned the task with only tiny adjustments to its existing structure. This suggests that having a built-in landscape of different speeds and stable states is a more efficient way for a system to learn and adapt. It allows the network to recruit pre-existing capabilities rather than building new ones from scratch every time a situation changes.

The findings also shed light on a major debate in neuroscience regarding criticality. For years, many scientists believed that for a brain to be flexible and powerful, it must operate near a critical point, a state where it is perfectly balanced between being too rigid and too chaotic. The new simulations suggest that this is not strictly necessary. The researchers showed that their model remained in a stable, sub-critical state—meaning it was safely away from chaos—yet it still produced the complex, scale-free dynamics and flexible behavior that criticality was thought to be the only source of. This implies that the brain might not need to walk a tightrope to function well; instead, it can rely on the rich, varied dynamics created by its own structural diversity.

The study offers a new way to think about how the brain is organized. It suggests that the cortex might be a hierarchy of networks, where lower levels deal with fast, immediate sensory inputs and higher levels deal with slow, complex contexts. This hierarchy could arise simply because the strength of self-connections increases as you move up the brain's processing chain. The higher areas would naturally have more slow, stable units capable of holding onto abstract ideas and rules, while lower areas would have faster units for quick reactions. This single principle of varying self-connections could explain both the brain's ability to integrate information over long periods and its capacity for complex, abstract thought.

Ultimately, this work provides a compelling alternative to the idea that the brain's power comes from a delicate balance of chaos. Instead, it points to the strength of diversity. By simply having parts that move at different speeds and hold onto information for different lengths of time, a neural network can naturally develop the ability to remember the past, adapt to new rules, and process information across multiple time scales. The researchers' simulations show that this mechanism is robust, efficient, and capable of supporting the kind of flexible behavior that defines intelligent life, all without the need for the system to be tuned to a critical edge. The brain, it seems, may be less like a tightrope walker and more like a choir of voices, each singing at their own pace, creating a harmony that is both stable and endlessly adaptable.