KAN/H: Kolmogorov-Arnold Network using Haar-like bases

This paper proposes KAN/H, a variant of Kolmogorov-Arnold Network (KAN) that uses a Haar-variant basis system having both global and local bases instead of B-spline. The resulting algorithm is applied to function approximation problems and MNIST. We show that it does not require most of the problem-specific hyper-parameter tunings.

General-purpose Declarative Inductive Programming with Domain-Specific Background Knowledge for Data Wrangling Automation

Given one or two examples, humans are good at understanding how to solve a problem independently of its domain, because they are able to detect what the problem is and to choose the appropriate background knowledge according to the context. For instance, presented with the string "8/17/2017" to be transformed to "17th of August of 2017", humans will process this in two steps: (1) they recognise that it is a date and (2) they map the date to the 17th of August of 2017. Inductive Programming (IP) aims at learning declarative (functional or logic) programs from examples. Two key advantages of IP are the use of background knowledge and the ability to synthesise programs from a few input/output examples (as humans do). In this paper we propose to use IP as a means for automating repetitive data manipulation tasks, frequently presented during the process of {\em data wrangling} in many data manipulation problems. Here we show that with the use of general-purpose declarative (programming) languages jointly with generic IP systems and the definition of domain-specific knowledge, many specific data wrangling problems from different application domains can be automatically solved from very few examples. We also propose an integrated benchmark for data wrangling, which we share publicly for the community.

Computable Variants of AIXI which are More Powerful than AIXItl

This paper presents Unlimited Computable AI, or UCAI, that is a family of computable variants of AIXI. UCAI is more powerful than AIXItl, that is a conventional family of computable variants of AIXI, in the following ways: 1) UCAI supports models of terminating computation, including typed lambda calculus, while AIXItl only supports Turing machine with timeout t, which can be simulated by typed lambda calculus for any t; 2) unlike UCAI, AIXItl limits the program length to l.