What are the benefits of using core.max_dim and core.min_dim in JAX

1. Delayed Inequality Comparison: These functions allow the comparison of symbolic dimensions to be delayed until compilation time, when shapes become known. This is useful because JAX can then evaluate inequalities involving symbolic dimensions more effectively, reducing errors related to inconclusive dimension operations[1].

2. Handling Conditional Statements: By using `core.max_dim` and `core.min_dim`, you can rewrite conditional statements in a way that is more compatible with JAX's compilation process. For example, instead of `d if d > 0 else 0`, you can write `core.max_dim(d, 0)`, which avoids explicit conditional logic and makes the code more amenable to optimization[1].

3. Improved Shape Polymorphism: These functions help in handling shape-polymorphic programs, which are crucial for creating models that can work with different input sizes. By expressing max and min operations symbolically, JAX can better handle batch-size-polymorphic programs, allowing a single SavedModel to work with various batch sizes[1].

4. Avoiding Integer Dependencies: By using `core.max_dim` and `core.min_dim`, you can avoid explicit integer conversions, which can make your code more flexible and less dependent on specific integer values. This is beneficial when working with symbolic dimensions that can be treated as integers for most arithmetic operations[1].

Overall, these functions enhance the expressiveness and flexibility of JAX programs, especially when dealing with symbolic dimensions and shape polymorphism.