Strong Turing Degrees for Additive BSS RAM's

For the additive real BSS machines using only constants 0 and 1 and order tests we consider the corresponding Turing reducibility and characterize some semi-decidable decision problems over the reals. In order to refine, step-by-step, a linear hierarchy of Turing degrees with respect to this model, we define several halting problems for classes of additive machines with different abilities and construct further suitable decision problems. In the construction we use methods of the classical recursion theory as well as techniques for proving bounds resulting from algebraic properties. In this way we extend a known hierarchy of problems below the halting problem for the additive machines using only equality tests and we present a further subhierarchy of semi-decidable problems between the halting problems for the additive machines using only equality tests and using order tests, respectively

Number Sequence Prediction Problems for Evaluating Computational Powers of Neural Networks

Inspired by number series tests to measure human intelligence, we suggest number sequence prediction tasks to assess neural network models' computational powers for solving algorithmic problems. We define the complexity and difficulty of a number sequence prediction task with the structure of the smallest automaton that can generate the sequence. We suggest two types of number sequence prediction problems: the number-level and the digit-level problems. The number-level problems format sequences as 2-dimensional grids of digits and the digit-level problems provide a single digit input per a time step. The complexity of a number-level sequence prediction can be defined with the depth of an equivalent combinatorial logic, and the complexity of a digit-level sequence prediction can be defined with an equivalent state automaton for the generation rule. Experiments with number-level sequences suggest that CNN models are capable of learning the compound operations of sequence generation rules, but the depths of the compound operations are limited. For the digit-level problems, simple GRU and LSTM models can solve some problems with the complexity of finite state automata. Memory augmented models such as Stack-RNN, Attention, and Neural Turing Machines can solve the reverse-order task which has the complexity of simple pushdown automaton. However, all of above cannot solve general Fibonacci, Arithmetic or Geometric sequence generation problems that represent the complexity of queue automata or Turing machines. The results show that our number sequence prediction problems effectively evaluate machine learning models' computational capabilities.Comment: Accepted to 2019 AAAI Conference on Artificial Intelligenc

Post-Turing Methodology: Breaking the Wall on the Way to Artificial General Intelligence

This article offers comprehensive criticism of the Turing test and develops quality criteria for new artificial general intelligence (AGI) assessment tests. It is shown that the prerequisites A. Turing drew upon when reducing personality and human consciousness to “suitable branches of thought” re-flected the engineering level of his time. In fact, the Turing “imitation game” employed only symbolic communication and ignored the physical world. This paper suggests that by restricting thinking ability to symbolic systems alone Turing unknowingly constructed “the wall” that excludes any possi-bility of transition from a complex observable phenomenon to an abstract image or concept. It is, therefore, sensible to factor in new requirements for AI (artificial intelligence) maturity assessment when approaching the Tu-ring test. Such AI must support all forms of communication with a human being, and it should be able to comprehend abstract images and specify con-cepts as well as participate in social practices

Machines will think: structure and interpretation of Alan Turing’s imitation game

Can machines think? I present a study of Alan Turing’s iconic imitation game or test and its central question. Seventy years of commentary has been produced about Turing’s 1950 proposal. The now legendary “Turing test” has grown a life of its own in the tradition of analytic philosophy with at best loose ties to the historical imitation tests (1948-1952) posed by Turing. I shall examine the historical and epistemological roots of Turing’s various versions of imitation game or test and make the case that they came out from within a dialogue, in fact a scientific controversy, most notably with physicist and computer pioneer Douglas Hartree, chemist and philosopher Michael Polanyi, and neurosurgeon Geoffrey Jefferson. Placing Turing’s views in their historical, social and cultural context, I shall reclaim their scientific and philosophical value for the sake of the discussion in the years to come. My study is organized according to three main philosophical problems whose analyses are backed by a subsidiary chronology of the concept of machine intelligence in Turing’s thought (1936-1952). The first problem I will address is the identification of Turing’s specific ambition which led him to announce that machines will think. War hero and brilliant mathematician, he challenged the conventional wisdom of what machines really were or could be and prophesized a future pervaded by intelligent machines which may be seen as a dystopia just as much as a utopia. I shall examine Turing’s profile and take special interest in the way he was seen by his contenders. In the second problem, over and above the mere proposal of a test for machine intelligence, I will study Turing’s proposition “machines can think” and its implied existential hypothesis — “there exists (will exist) a thinking machine” — from a point of view of the history of the philosophy of science. Unlike traditional readings of Turing, I found that Turing held a non-obvious realist attitude towards the existence of a mechanical mindbrain which he conjectured to frame the human and whose digital replica he intended to build in the machine. Turing’s 1950 paper has been acknowledged as a complex and multi-layered text. Opposing views can be identified in the literature relative to the question on whether or not Turing proposed his imitation test as an experiment to decide for machine intelligence. I shall call this the Turing test dilemma and address it as my third and main problem. My findings suggest that Turing cannot have proposed his imitation game as something other than a thought experiment. And yet its critical and heuristic functions within the mind-machine controversy are striking

Universal Intelligence: A Definition of Machine Intelligence

A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.Comment: 50 gentle page