Artur Gorokh

Bharath Ramsundar, Roger Chen, Alok Vasudev et al.

We formalize the construction of decentralized data markets by introducing the mathematical construction of tokenized data structures, a new form of incentivized data structure. These structures both specialize and extend past work on token curated registries and distributed data structures. They provide a unified model for reasoning about complex data structures assembled by multiple agents with differing incentives. We introduce a number of examples of tokenized data structures and introduce a simple mathematical framework for analyzing their properties. We demonstrate how tokenized data structures can be used to instantiate a decentralized, tokenized data market, and conclude by discussing how such decentralized markets could prove fruitful for the further development of machine learning and AI.

Artur Gorokh, Yury Korolev, Tuomo Valkonen

Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, where errors are represented as bounds by means of the appropriate partial order. We apply the theory to Diffusion Tensor Imaging, where correct noise modelling is challenging: it involves the Rician distribution and the nonlinear Stejskal-Tanner equation. Linearisation of the latter in the statistical framework would complicate the noise model even further. We avoid this using the error bounds approach, which preserves simple error structure under monotone transformations.