Understanding how the brain computes choice from sensory information is a central question in perceptual decision-making research. From a behavioral perspective, paradigms suitable to study perceptual decision-making condition choice on invariant properties of the stimuli, thus decoupling stimulus-specific information from decision-related variables. From a neural perspective, powerful tools for the dissection of brain circuits are needed, which suggests the mouse as a suitable animal model. However, whether and how mice can perform an invariant visual discrimination task has not yet been fully established. Here, we show that mice can solve a complex orientation discrimination task where the choices are decoupled from the orientation of individual stimuli. Moreover, we demonstrate a discrimination acuity of at least 6°, challenging the common belief that mice are poor visual discriminators. We reached these conclusions by introducing a novel probabilistic choice model that explained behavioral strategies in (n = 40) mice and identified unreported dimensions of variation associated with the circularity of the stimulus space. Furthermore, the model showed a dependence of history biases on task engagement, demonstrating behavioral sensitivity to the availability of cognitive resources. In conclusion, our results reveal that mice are capable of decoupling decision-relevant information from stimulus-specific information, thus demonstrating they are a useful animal model for studying neural representation of abstract learned categories in perceptual decision-making research.