adverb "synonym" for "whatever" — it doesn't matter, unrestricted

Question

It's possible to chain identical modules to operate on ________ly large inputs.

I want a word that means, the size of the input doesn't matter, it can be any size, it is unrestricted/unbounded/has no upper limit.

"Trivially", "unlimitedly", "ambiguously" have entered by head but are not what I am looking for (and "ambiguously" doesn't even make sense).

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It's possible to chain identical modules to operate on however-large inputs.

It's possible to chain identical modules to operate on whatever inputs.

Have the right kind of sentiment, but I feel like there's an idiomatic word ending in -ly that fits better.

Answer 1

I suggest arbitrarily. The word is often used in science when discussing a non-specific quantity that may be of any chosen or otherwise determined (perhaps random, or merely exemplary) value.

There is a useful discussion at

https://math.stackexchange.com/questions/775333/arbitrarys-meaning

Answer 2

An adverb which is commonly used for this (especially in technical contexts as suggested by your example sentence) is indefinitely.

It's possible to chain identical modules to operate on indefinitely large inputs.

Lexico:

indefinitely ADVERB
1.1 (as submodifier) To an unlimited or unspecified degree or extent.
‘an indefinitely large number of channels’