Distributive Thermometer: A New Unary Encoding for Weightless Neural Networks Alan T. L. Bacellar 1 , Zachary Susskind 2 , Luis A. Q. Villon 1 , Igor D. S. Miranda 3 , Leandro S. de Ara´ ujo 4 , Diego L. C. Dutra 1 , Mauricio Breternitz Jr. 5 , Lizy K. John 2 , Priscila M. V. Lima 1 and Felipe M. G. Fran¸ca 1, 6 * 1- UFRJ, Rio de Janeiro, Brazil, 2- UT Austin, Austin, USA, 3- UFRB, Cruz das Almas, Brazil, 4- UFF, Niter´ oi, Brazil, 5- ISTAR/ISCTE-IUL, Lisbon, Portugal, 6- Instituto de Telecomunica¸c˜ oes, Portugal Abstract. The binary encoding of real valued inputs is a crucial part of Weightless Neural Networks. The Linear Thermometer and its variations are the most prominent methods to determine binary encoding for input data but, as they make assumptions about the input distribution, the resulting encoding is sub-optimal and possibly wasteful when the assump- tion is incorrect. We propose a new thermometer approach that doesn’t require such assumptions. Our results show that it achieves similar or better accuracy when compared to a thermometer that correctly assumes the distribution, and accuracy gains up to 26.3% when other thermometer representations assume an unsound distribution. 1 Introduction Weightless neural networks (WNNs) are a type of neural model that utilizes a random access memory (RAM) to determine neuron activation, as opposed to weights and dot products commonly used in modern deep learning approaches. Because it only uses lookup tables, instead of multiply and accumulate operations which are comparably expensive, they can offer much lower latencies and energy costs [1], making them an attractive solution, especially for usage on edge, and it has been explored in various applications resulting in simple implementations and real-time performance [2, 3, 4, 5]. As using RAMs implicitly requires inputs to be binary, the encoding of real valued inputs is a crucial part of a WNN model and a naive approach can be detrimental to learning [6]. The literature presents many binary encoding techniques [6], with the linear thermometer [7] being the most prominent one. The linear thermometer works by encoding the real value inputs in unary code, under a uniform distribution assumption. A variation of the linear thermometer technique was proposed in [8], where different distributions were used as priors, such as a normal distribution, allowing for an increased resolution of information near the mean of the distribution, showing a significant increase in accuracy for the problem at hand. The major problem with this approach is the need to know * Acknowledgement: This study was financed in part by the Coordena¸c˜ao de Aper- fei¸coamento de Pessoal de N´ ıvel Superior - Brasil (CAPES) - Finance Code 001. This article was partially supported by Funda¸c˜ ao para a Ciˆ encia e a Tecnologia, I.P. (FCT) ISTAR Projects: UIDB/04466/2020 and UIDP/04466/2020; Project FLOYD: POCI-01-0247-FEDER-045912. 31 ESANN 2022 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium) and online event, 5-7 October 2022, i6doc.com publ., ISBN 978287587084-1. Available from http://www.i6doc.com/en/.