The ability to group sensory stimuli into categories is crucial for efficient interaction with a rich and ever-changing environment. In olfaction, basic features of categorical representation of odors were observed as early as in the olfactory bulb (OB). Categorical representation was described in mitral cells (MCs) as sudden transitions in responses to odors that were morphed along a continuum. However, it remains unclear to what extent such response dynamics actually reflect perceptual categories and decisions therein. Here, we tested the role of learning on category formation in the mouse OB, using in vivo two-photon calcium imaging and behavior. We imaged MC responses in naive mice and in awake behaving mice as they learned two tasks with different classification logic. In one task, a one-decision-boundary task, animals learned to classify odor mixtures based on the dominant compound in the mixtures. As expected, categorical representation of odors, which was evident already in naive animals, further increased following learning. In a second task, a multi-decision-boundary task, animals learned to classify odors independent of their chemical similarity. Here, odor discrimination was based on the meaning ascribed to them (either rewarding or not). Following the multi-decision-boundary task, odor representations by MCs reorganized according to the odor value in the new category. This functional reorganization was also reflected as a shift from predominantly excitatory odor responses to predominantly inhibitory odor responses. Our data show that odor representations by MCs are flexible, are shaped by task demands, and carry category-related information.

There is a striking relationship between a three hundred years old Political Science theorem named "Condorcet's jury theorem" (1785), which states that majorities are more likely to choose correctly when individual votes are often correct and independent, and a modern Machine Learning concept called "Strength of Weak Learnability" (1990), which describes a method for converting a weak learning algorithm into one that achieves arbitrarily high accuracy and stands in the basis of Ensemble Learning. Albeit the intuitive statement of Condorcet's theorem, we could not find a compact and simple rigorous mathematical proof of the theorem neither in classical handbooks of Machine Learning nor in published papers. By all means we do not claim to discover or reinvent a theory nor a result. We humbly want to offer a more publicly available simple derivation of the theorem. We will find joy in seeing more teachers of introduction-to-machine-learning courses use the proof we provide here as an exercise to explain the motivation of ensemble learning.

The ability to group sensory stimuli into categories is crucial for efficient interaction with a rich and ever-changing environment. In olfaction, basic features of categorical representation of odours were observed as early as in the olfactory bulb (OB). Categorical representation was described in mitral cells (MCs) as sudden transitions in responses to odours that were morphed along a continuum. However, it remains unclear to what extent such response dynamics actually reflects perceptual categories and decisions therein. Here, we tested the role of learning on category formation in the mouse OB, using in vivo two-photon calcium imaging and behaviour. We imaged MCs responses in naïve mice and in awake behaving mice as they learned two tasks with different classification logic. In one task, a 1-decision boundary task, animals learned to classify odour mixtures based on the dominant compound in the mixtures. As expected, categorical representation of close by odours, which was evident already in naïve animals, further increased following learning. In a second task, a multi-decision boundary task, animals learned to classify odours independent of their chemical similarity. Rather, odour discrimination was based on the meaning ascribed to them (either rewarding or not). Following the second task, odour representations by MCs reorganized according to the odour value in the new category. This functional reorganization was also reflected as a shift from predominantly excitatory odour responses to predominantly inhibitory odour responses. Our data shows that odour representations by MCs is flexible, shaped by task demands, and carry category-related information.