The article further elaborates that this is particularly true when the function used is approximately associative. It uses the example of computing X = f(f(a,b) ,c) ~ f(a, f(b, c)) = Y. Depending on whether a,b finishes first or b,c finishes first, the computation could result in either X or Y. This variability increases with the number of values computed in parallel. Common computations like multiplication and addition fall into this category.
Key takeaways:
- The discussion is about why computing embeddings in the same way for a specific body yield different results.
- If f is approximately an associative function and you compute in parallel a,b,c with the goal of computing X = f(f(a,b) ,c) ~ f(a, f(b, c)) = Y, you may end up with different results depending on which computations finish first.
- The more values you compute in parallel, the more variations you may end up with.
- Some computations like multiplication, addition fall into this category where the order of operations can affect the outcome.