# Stochastic Multivariate Universal-Radix Finite-State Machine: a Theoretically and Practically Elegant Nonlinear Function Approximator

arXiv: https://arxiv.org/abs/2405.02356 · HTML: https://mlsanity.com/paper/2405.02356/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 3 of 3)

- [Mutual Graph Learning for Camouflaged Object Detection](https://mlsanity.com/paper/2104.02613/) (2021)
- [Internal Language Model Estimation for Domain-Adaptive End-to-End Speech Recognition](https://mlsanity.com/paper/2011.01991/) (2020)
- [Stochastic Compositional Gradient Descent under Compositional Constraints](https://mlsanity.com/paper/2012.09400/) (2020)

## Abstract (arXiv)

Nonlinearities are crucial for capturing complex input-output relationships especially in deep neural networks. However, nonlinear functions often incur various hardware and compute overheads. Meanwhile, stochastic computing (SC) has emerged as a promising approach to tackle this challenge by trading output precision for hardware simplicity. To this end, this paper proposes a first-of-its-kind stochastic multivariate universal-radix finite-state machine (SMURF) that harnesses SC for hardware-simplistic multivariate nonlinear function generation at high accuracy. We present the finite-state machine (FSM) architecture for SMURF, as well as analytical derivations of sampling gate coefficients for accurately approximating generic nonlinear functions. Experiments demonstrate the superiority of SMURF, requiring only 16.07% area and 14.45% power consumption of Taylor-series approximation, and merely 2.22% area of look-up table (LUT) schemes.