Fig. 2: Performance-optimized neural network model of decision confidence.

a Model architecture. An image x, belonging to class y, was passed through a deep neural network (DNN) encoder f (the exact architecture of this encoder depended on the dataset, as detailed in “Encoder”), followed by two output layers: g_class generated a decision \(\hat{y}\) classifying the image, and g_conf generated a confidence score by predicting \(p\left(\hat{y}=y\right)\), the probability that the decision was correct. b The model was trained through supervised learning using the MNIST handwritten digits dataset and the CIFAR-10 object classification dataset. For these datasets, the classification layer was trained to label the class of the image, and the confidence layer was trained to output a target of 1 if the classification response was correct, and 0 if the classification response was incorrect. The model was also trained through reinforcement learning (RL) to perform an orientation discrimination task, in which, rather than generating an explicit confidence rating, the model had the option to opt-out of a decision and receive a small but guaranteed reward, allowing the use of the opt-out rate as an implicit measure of confidence. c To evaluate the relative influence of signal strength and noise on the model’s behavior, images were modified by manipulating both the contrast μ and the noise level σ.