Is it possible to reduce the tail's file of accumulators for large data set
I've read a little about this area years ago. The naive example of an accumulator is simply multiplying primes together into the accumulator, which can then be checked for their presence simply by division. This obviously results in persistent growth of the accumulator.

I looked for an accumulator that addressed the endless growth issue, but I was never able to find one. However, I was more concerned about the increasing storage capacity required. It seems unlikely to me that one could exist, for they store information after all. It would be magical if it could continuously store information without growing in size.

However, as far as time complexity is concerned, it may be a different matter. The name of what you want would be something like "constant time cryptographic accumulator." For example, a bloom filter allows -- at increasing risk of false positives, but never with false negatives -- for O(1) membership querying on a set of recorded values, which means that time to (probabilistically) determine membership or (with certainty) a lack thereof doesn't grow with the number of elements added.

I would probably look for an accumulator built on a bloom filter if I were worried about time to query and could accept a small risk of false positives.