IBM Patented Euler's 200 Year Old Math Technique for 'AI Interpretability'

Summary

LeetArxiv is a successor to Papers With Code after the latter shutdown. Quick SummaryIBM owns the patent to the use of derivatives to find the convergents of a generalized continued fraction.Here’s the bizarre thing: all they did was implement a number theory technique by Gauss, Euler and Ramanujan in PyTorch and call backward() on the computation graph.Now IBM’s patent trolls can charge rent on a math technique that’s existed for over 200 years. As always, code is available on Google Colab and GitHub.The 2021 paper CoFrNets: Interpretable Neural Architecture Inspired by Continued Fractions (Puri et al., 2021) investigates the use of continued fractions in neural network design.The paper takes 13 pages to assert: continued fractions (just like mlps) are universal approximators.The authors reinvent the wheel countless times: They rebrand continued fractions to ‘ladders’.They label basic division ‘The 1/z nonlinearity’.Ultimately, they take the well-defined concept of Generalized Continued Fractions and call them CoFrNets.Authors rename generalized continued fractions. Taken from page 2 of (Puri et al., 2021)Honestly, the paper is full of pretentious nonsense like this:The authors crack jokes while collecting rent on 200 years of math knowledge. Taken from page 2Simple continued fractions are mathematical expressions of the form:where pn / qn is the nth convergent (Cook, 2022).Continued fractions have been used by mathematicians to:Approximate Pi (MJD, 2014).Design gear systems (Brocot, 1861)Even Ramanujan’s math tricks utilised continued fractions (Barrow, 2000)Continued fractions are well-studied and previous LeetArxiv guides include (Lehmer, 1931) : The Continued Fraction Factorization Method and Stern-Brocot Fractions as a floating-point alternative.If your background is in AI, a continued fraction looks exactly like a linear layer but the bias term is replaced with another linear layer.(Jones, 1980) defines generalized continued fractions as expressions of the fo...