Background

During the day, our brains acquire new memories; during sleep, they consolidate the important ones and discard the rest. Researchers have applied a similar principle to Hopfield networks, one of the classic models of artificial intelligence inspired by the brain. In 2025, Federico Ricci-Tersenghi and colleagues developed Daydreaming, an algorithm that combines learning new memories with eliminating spurious ones, dramatically improving network capacity. One limitation remained: these networks lose effectiveness on real-world data, which is rarely perfectly balanced — think very bright or very dark images, where white or black pixels overwhelmingly dominate.

A “classical” neural network

Hopfield networks, proposed by John Hopfield in 1982 (work that earned him the Nobel Prize in 2024), consist of artificial neurons connected to one another and are among the simplest models of associative memory. The simplest form can store a number of memories equal to only about 13% of its neuron count — the rest of its capacity is occupied by “false memories,” spurious configurations that mix elements of real memories and can lead the network into error.

Daydreaming, and its limits

“Dreaming” algorithms let a trained network explore its own memory and clean out spurious patterns, but cleaning for too long erases correct memories too — a problem called catastrophic forgetting. The 2025 Daydreaming algorithm solved this by learning and cleaning simultaneously, pushing network capacity up to the theoretical limit of one memory per neuron. But it still struggled with strongly imbalanced real-world data, where images become so similar to one another that the network has trouble telling which features actually distinguish one memory from another.

In a new study published in the Journal of Statistical Mechanics: Theory and Experiment, Ricci-Tersenghi and Japanese colleagues present “Centered Daydreaming,” a local modification that compares pixel differences from the average rather than absolute values. Using the example of face recognition, if all photos share a similar background, most pixels will be nearly identical across images, and that shared information can dominate learning; working instead from what differs from the average face lets the differences emerge clearly.

“It is much more realistic for each decision to be made locally. Biological neurons are connected to a limited number of other neurons and never communicate with the whole brain.”

Federico Ricci-Tersenghi, Sapienza University of Rome

In testing, Centered Daydreaming kept the network’s ability to retrieve memories almost unchanged even with strongly biased data, extending the algorithm to conditions closer to the real world without giving up the locally plausible learning rules. Ricci-Tersenghi said understanding how such brain-inspired models learn to distinguish what matters from what is irrelevant could eventually help build AI systems that are easier to understand and more energy-efficient.

Publication

The study, “Daydreaming algorithm for Biased Patterns,” was published in the Journal of Statistical Mechanics: Theory and Experiment on July 15, 2026. About the institution: Sissa Medialab.