Abstract: Systems and methods are provided for using encoded representations of numbers in various applications. The encoded representations of numbers, also referred to as number embeddings, may be multi-element data structures (e.g., multi-dimensional vectors) in which each element is a real-numbered value. The values of a given number embedding collectively encode information from which properties of the number represented by the number embedding may be derived. Number embeddings may be compared or otherwise analyzed with respect to each other to identify patterns or similarities in the numbers represented by each number embedding.

Abstract: An automatic agent may be trained using reinforcement learning. A secret task may be obtained for a simulated user, and the secret task may be unknown to the automatic agent. At least one instruction to complete the secret task may be obtained from the simulated user according to at least one RL policy. At least one action may be generated by the automatic agent based on the at least one instruction and the at least one RL policy. Rewards may be determined for the simulated user and the automatic agent in response to determining that the at least one action successfully completes the secret task. The at least one RL policy may be adjusted based on the determined rewards.