A.1 Experiment 1 A.1.1 Participants Experiment 1 recruited 21 participants (11 females, aged 18-25). All participants had provided informed consent before the experiment. Cover story Participants were told that they were apprentice magicians in a magical world. In this world, dangerous magic lava rocks were emitted from an unknown number of invisible volcano(es). On each trial, they observed past landing locations of lava rocks in a specific area (on the screen), and their job was to predict the probability density of future landing locations. More specifically, they were asked to draw a probability density by reporting, using click-and-drag mouse gestures, three key properties of the volcano(es), corresponding to the mean, the weight, and the standard deviation of a Gaussian component. They were told that their bonus payment depended on the accuracy of the reported predictive density.

Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space.

In addition, since only the binary failure can be obtained, the number of latent constraints is also unknown.

Work done as a master's student at the University of Chicago. One way to compute this optimum is to use EM. We then get the following (see e.g., Sec 4.2.4 of Murphy [2022] In this section we discuss the datasets in more detail. B.1 Colored MNIST We show some sample images in Figure 1. We show some sample images in Figure 2. We list all the target attributes in Table 1.