We study a minimal physical learner: a spring network trained on a continual stream of tasks. Learning progressively reduces its ability to acquire new tasks. The pattern echoes the synaptic homeostasis hypothesis, which proposes that sleep restores a capacity for plasticity that waking experience has used up (Tononi & Cirelli 2006).

The mechanical analogue of that saturation sits in the bonds. Learning drives each bond’s share of the load toward a limit, and a bond near either limit has less influence on the response to a new task. A conserved topological budget links this polarization to the decline in learning capacity, one for one. The polarization acts as a mechanical analogue of sleep pressure, the need for sleep that builds up during wake (Borbély et al. 2016).

Local random perturbations let each bond estimate its own load share and guide a restorative change in stiffness. Guided repair restores learning capacity at a cost to memory, with a better balance of acquisition and retention than repair that relaxes bonds blindly toward their rest stiffness. During learning, task activity biases those measurements toward weakening the bonds in use. Moving the repair offline avoids the interference. Offline repair improves continual learning compared with learning alone, and compared with learning and repair running together.

That bias also separates the two directions of repair. Strengthening can proceed during wake, while weakening waits for sleep, in parallel with firing-rate homeostasis in rat visual cortex (Hengen et al. 2016; Torrado Pacheco et al. 2021). Withholding repair increases the repair required later, in parallel with compensatory sleep after deprivation (Borbély et al. 2016). Sleep-like offline phases are needed when learning reduces adaptability and ongoing task activity distorts the measurements used for restoration.

In these simulations an external supervisor schedules wake and repair and sets the recovery target. Whether that offline phase can arise on its own is the next project, Emergence of sleep–wake rhythms.

This project follows Sleep without biology, with N. Pashine and J. M. Schwarz. There, continual learning creates a need for an offline phase, and an external supervisor decides when that phase happens. The paper on that project, “Why continual physical learners need sleep,” is coming out soon.

Living systems regulate that switch for themselves. They operate out of equilibrium, harvesting and dissipating energy to sense errors (Lan et al. 2012), revise their own structure, and decide when to disengage from the environment.

The aim is to find the energetic conditions under which an offline phase emerges on its own, and to see how an internal demand for repair can couple to environmental energy cycles and produce a sleep–wake rhythm.