Here is an example of a research paper that investigates the use of neural networks to discover classical algorithms:
"Neural Combinatorial Optimization with Reinforcement Learning" (Bello et al., 2016)
In this paper, the authors propose a method for using reinforcement learning to train a neural network to discover efficient algorithms for combinatorial optimization problems. The neural network is trained to solve a particular optimization problem by generating a sequence of actions, which are then executed by a virtual machine to find the optimal solution. The authors show that this approach can discover a variety of classical algorithms, such as the Knapsack algorithm and the Traveling Salesman algorithm, and can achieve similar or better performance compared to the original algorithms.