One decade ago, Bitcoin was introduced, becoming the first cryptocurrency and establishing the concept of "blockchain" as a distributed ledger. As of today, there are many different implementations of cryptocurrencies working over a blockchain, with different approaches and philosophies. However, many of them share one common feature: they require proof-of-work to support the generation of blocks (mining) and, eventually, the generation of money. This proof-of-work scheme often consists in the resolution of a cryptography problem, most commonly breaking a hash value, which can only be achieved through brute-force. The main drawback of proof-of-work is that it requires ridiculously large amounts of energy which do not have any useful outcome beyond supporting the currency. In this paper, we present a theoretical proposal that introduces a proof-of-useful-work scheme to support a cryptocurrency running over a blockchain, which we named Coin.AI. In this system, the mining scheme requires training deep learning models, and a block is only mined when the performance of such model exceeds a threshold. The distributed system allows for nodes to verify the models delivered by miners in an easy way (certainly much more efficiently than the mining process itself), determining when a block is to be generated. Additionally, this paper presents a proof-of-storage scheme for rewarding users that provide storage for the deep learning models, as well as a theoretical dissertation on how the mechanics of the system could be articulated with the ultimate goal of democratizing access to artificial intelligence. Entropy 2019, 21, 723 2 of 17Additionally, in recent years many other cryptocurrencies have appeared whose workings are very similar to Bitcoin, although with some particularities and different philosophies. Probably, the most significant example is the Ether, the currency provided by the Ethereum platform, which was presented in 2013 by Buterin [7]. Again, this currency has seen its value increased significantly since it was born in July 2015, traded at about US$0.70 by August 2015 and with a value of more than US$220 by July 2019.Bitcoin, Ethereum, and many other cryptocurrencies of this kind work atop a technology commonly known as blockchain [8]. Blockchain technology allows to store transactions in blocks, which are placed sequentially, thus forming a chain. A cryptographic mechanism prevents the chain from being tampered, and the only operation that can alter the blockchain is appending a new block at the end of it. In other words, this mechanism avoids malicious activities that can try to alter or remove transactions that took place at some time in the past. Blockchains have been widely used with academic purposes, such as developing consensus protocols [9] or developing data exchange schemas for the internet of things [10]. Noticeably, they have also been used for not so honest purposes, and particularly some financial frauds, such as Ponzi schemes, have been detected in public networks [11].Although a blockchain can...