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We propose a novel method for approximate hardware implementation of univariate math functions with significantly fewer hardware resources compared to previous approaches. Examples of such functions include exp(x) and the activation function GELU(x), both used in transformer networks, gamma(x), which is used in image processing, and other functions such as tanh(x), cosh(x), sq(x), and sqrt(x). The method builds on previous works on hybrid binary-unary computing. The novelty in our approach is that we break a function into a number of sub-functions such that implementing each sub-function becomes cheap, and converting the output of the sub-functions to binary becomes almost trivial. Our method also uses self-similarity in functions to further reduce the cost. We compare our method to the conventional binary, previous stochastic computing, and hybrid binary-unary methods on several functions at 8-, 12-, and 16-bit resolutions. While preserving high accuracy, our method outperforms previous works in terms of hardware cost, e.g., tolerating less than 0.01 mean absolute error, our method reduces the (area x latency) cost on average by 5, 7, and 2 orders of magnitude, compared to the conventional binary, stochastic computing, and hybrid binary-unary methods, respectively. Ultimately, we demonstrate the potential benefits of our method for natural language processing and image processing applications. We deploy our method to implement major blocks in an encoding layer of BERT language model, and also the Roberts Cross edge detection algorithm. Both include non-linear functions.
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This content will become publicly available on May 1, 2026
Automatically Mitigating Vulnerabilities in Binary Programs via Partially Recompilable Decompilation
PRD lifts suspect binary functions to source, available for analysis, revision, or review, and creates a patched binary using source- and binary-level techniques. Al- though decompilation and recompilation do not typically succeed on an entire binary, our approach does because it is limited to a few functions, such as those identified by our binary fault localization.
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- PAR ID:
- 10624964
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Dependable and Secure Computing
- Volume:
- 22
- Issue:
- 3
- ISSN:
- 1545-5971
- Page Range / eLocation ID:
- 2270 to 2282
- Subject(s) / Keyword(s):
- Software engineering software maintenance
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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