Demonstrations

We model how a group decides when to flee a threat.

Each animal accumulates evidence about a threat and flees when its belief reaches a threshold. A neighbor’s flight is evidence for a threat, and its stillness is evidence against, a correction captured by one social discounting rate α (Kilpatrick, 2026).

We model how evidence accumulates to a commitment when the right answer can change.

We compare two observers of the same noisy evidence. One adds it all up; the other discounts the past at a rate set by how often the world changes.

The classical account of evidence accumulation is the drift-diffusion model, introduced by Ratcliff (1978) and developed through the random-dot motion work of the 1990s and 2000s, in which an observer integrates noisy evidence until it reaches a bound. Adding up every observation without discount is optimal there, and the paradigm assumes what makes it so: that the right answer holds still.

When the source can change, old evidence is not merely less useful but actively misleading, and an observer who has piled up belief without discounting it cannot be talked out of that belief. Glaze, Kable and Gold (2015) derived the normative alternative, in which the running belief is discounted by a nonlinear function of the assumed change rate, so confidence saturates instead of growing without bound. Much of our work asks what follows from that: how the change rate itself is learned, what the decision rule should be, and what people actually do.

We pair a model of a memory wandering on a continuous attractor with the delayed-estimation task that measures the wandering.

In the model, a localized activity bump wanders around a ring, and structure in the connectivity can anchor it near preferred locations.

Persistent neural activity was first characterized in the oculomotor delayed response (ODR) task of Funahashi, Bruce and Goldman-Rakic (1989). A monkey fixates while a cue flashes at one of several peripheral locations, holds that location through a delay of one to six seconds, then saccades to it. Neurons in dorsolateral prefrontal cortex turned out to have memory fields: elevated firing throughout the delay, tuned to a particular cue direction. Compte, Brunel, Goldman-Rakic and Wang (2000) showed that a recurrent network with local excitation and broad inhibition sustains exactly that pattern, as a localized bump of activity on a ring of cue directions. Because the bump sits on a continuous attractor, noise slides it along the ring at no energetic cost, so the remembered angle wanders, and error grows with the delay. That wandering is what this simulation shows.