# Stochastic Gradient Descent with integer arithmetics

Most implementations of stochastic gradient descent (SGD) rely on floating points. Is there implementations using infinite or finite precision integer arithmetics ?

• Is this question about the theory of stochastic gradient descent or about finding a suitable software package? – Lev Reyzin Jan 21 '12 at 4:32
• The former. I'm not looking for a software library for SGD but rather if there is a paper describing a variant of the algorithm using integer arithmetics. – Ghassen Hamrouni Jan 21 '12 at 17:34
• eh - representing floating point via ints causes all kinds of numerical problems. The "correct" approach is to use adaptively growing (or even infinite) precision as is done in many geometric questions. – Suresh Venkat Jan 25 '12 at 18:09
• I see. This reminds me why I never went into numerical analysis... – Lev Reyzin Jan 25 '12 at 19:31
• I am not sure I understand the point of your question. Why not just change the algorithm to use other representations? (like nested intervals?) – Kaveh Jan 28 '12 at 22:53

the general idea in various implementations is to represent/approximate real numbers $x \in[0..1]$ as integers in the form $x \cdot 10^m$ where $m$ is some integer exponent.