The paper introduces the *query by committee* algorithm, which involves training a committee of students on the same dataset and selecting queries based on the principle of maximal disagreement. The algorithm is studied for two toy models: the high-low game and perceptron learning of another perceptron. As the number of queries approaches infinity, the committee algorithm yields asymptotically finite information gain, leading to an exponential decrease in generalization error. This contrasts with learning from randomly chosen inputs, where information gain approaches zero and generalization error decreases slowly. The authors suggest that asymptotically finite information gain may be a key characteristic of effective query algorithms. The paper also discusses the information content of a query and provides detailed mathematical derivations for both models, including replica calculations for the committee algorithm.The paper introduces the *query by committee* algorithm, which involves training a committee of students on the same dataset and selecting queries based on the principle of maximal disagreement. The algorithm is studied for two toy models: the high-low game and perceptron learning of another perceptron. As the number of queries approaches infinity, the committee algorithm yields asymptotically finite information gain, leading to an exponential decrease in generalization error. This contrasts with learning from randomly chosen inputs, where information gain approaches zero and generalization error decreases slowly. The authors suggest that asymptotically finite information gain may be a key characteristic of effective query algorithms. The paper also discusses the information content of a query and provides detailed mathematical derivations for both models, including replica calculations for the committee algorithm.