Deep neural networks (DNNs) could be very useful in blockchain applications such as DeFi and NFT trading. However, training / running large-scale DNNs as part of a smart contract is infeasible on todays blockchain platforms, due to two fundamental design issues of these platforms. First, blockchains nowadays typically require that each node maintain the complete world state at any time, meaning that the node must execute all transactions in every block. This is prohibitively expensive for computationally intensive smart contracts involving DNNs. Second, existing blockchain platforms expect smart contract transactions to have deterministic, reproducible results and effects. In contrast, DNNs are usually trained / run lock-free on massively parallel computing devices such as GPUs, TPUs and / or computing clusters, which often do not yield deterministic results. This paper proposes novel platform designs, collectively called A New Hope (ANH), that address the above issues. The main ideas are (i) computing-intensive smart contract transactions are only executed by nodes who need their results, or by specialized serviced providers, and (ii) a non-deterministic smart contract transaction leads to uncertain results, which can still be validated, though at a relatively high cost; specifically for DNNs, the validation cost can often be reduced by verifying properties of the results instead of their exact values. In addition, we discuss various implications of ANH, including its effects on token fungibility, sharding, private transactions, and the fundamental meaning of a smart contract.