A static computational graph and a dynamic computational graph are two different approaches to implementing and executing computational graphs.

  A static computational graph is created and defined before the actual computation begins. It represents the flow of data and operations as a directed acyclic graph (DAG), where nodes represent operations and edges represent data dependencies between the operations. This graph is usually constructed using a graph-building API and is typically designed to be executed multiple times with different input data. The main advantage of a static computational graph is that it allows for optimizations and parallelization techniques to be applied to the graph structure. However, it lacks flexibility in handling variable-sized inputs or dynamic control flow.

  On the other hand, a dynamic computational graph is constructed and evaluated during runtime. It is more flexible and capable of handling variable-sized inputs and dynamic control flow. The graph is constructed incrementally as operations are executed and data dependencies are resolved. This approach allows for more efficient memory usage as the graph is built on the fly and only includes the necessary operations and data. The main advantage of a dynamic computational graph is its ability to handle dynamic situations, such as recurrent neural networks where the input size varies across time steps.

  Overall, the choice between static and dynamic computational graphs depends on the specific requirements of the problem at hand. Static graphs are useful for scenarios where efficiency and optimization are crucial, and the computation can be pre-defined and executed multiple times with fixed inputs. On the other hand, dynamic graphs are suitable for scenarios where flexibility and adaptability to changing inputs and control flow are important.