Transformers in Uniform TC$^0$
Abstract: Previous work has shown that the languages recognized by average-hard attention transformers (AHATs) and softmax-attention transformers (SMATs) are within the circuit complexity class TC$^0$. However, these results assume limited-precision arithmetic: using floating-point numbers with O(log n) bits (where n is the length of the input string), Strobl showed that AHATs can be approximated in L-uniform TC$^0$, and Merrill and Sabharwal showed that SMATs can be approximated in DLOGTIME-uniform TC$^0$. Here, we improve these results, showing that AHATs with no approximation, SMATs with O(poly(n)) bits of floating-point precision, and SMATs with at most $2^{−O(poly(n))}$ absolute error are all in DLOGTIME-uniform TC$^0$.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Colin_Raffel1
Submission Number: 3368
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