Categorization is a cornerstone of perception and cognition. Computationally, categorization amounts to applying decision boundaries in the space of stimulus features. We designed a visual categorization task in which optimal performance requires observers to incorporate trial-to-trial knowledge of the level of sensory uncertainty when setting their decision boundaries. We found that humans and monkeys did adjust their decision boundaries from trial to trial as the level of sensory noise varied, with some subjects performing near optimally. We constructed a neural network that implements uncertainty-based, near-optimal adjustment of decision boundaries. Divisive normalization emerges automatically as a key neural operation in this network. Our results offer an integrated computational and mechanistic framework for categorization under uncertainty.Bayesian inference | vision | decision-making | optimality I magine a woman is approaching you from a distance and you are trying to determine whether or not she is the friend you are waiting for. Because of various sources of noise, your observations of her facial features, hair color, etc. will be uncertain. A sensible strategy would be to be more tolerant to deviations between your observations and your knowledge of your friend's looks when she is far away than when she is close by and your observations are less uncertain. In this categorization problem, you are determining whether the image of the approaching woman falls into the narrow category of images of your friend or the wide category of images of all other people. Categorization can be modeled as a process of applying one or more decision boundaries to a noisy measurement in a space of stimulus features (1-7). The example suggests that adjusting such decision boundaries based on the current level of sensory uncertainty might be a better strategy than using uncertainty-independent decision boundaries.Previous studies have not addressed whether organisms adjust their decision boundaries from trial to trial according to the level of sensory uncertainty. Perceptual studies of categorization under sensory uncertainty have typically used category distributions for which the level of uncertainty was irrelevant for optimal behavior (2,3,6,8). For example, in a classic task, observers categorize the direction of motion of a set of dots coherently moving to the left or to the right, in the presence of distractor dots moving in random directions (8). Regardless of the level of sensory noise corrupting the brain's measurement of the net motion direction, the optimal decision is simply to report whether this measurement was to the right or to the left. In other words, applying a fixed decision boundary to a scalar estimate is optimal in this task; no knowledge of uncertainty about motion direction is needed. In cognitive models of categorization, dynamic decision boundaries have been invoked to explain a broad range of phenomenona, including sequential effects (9, 10), context effects (11), and generalization (12). Howeve...