The Mode of Computing

The Turing Machine is the paradigmatic case of computing machines, but there are others, such as Artificial Neural Networks, Table Computing, Relational-Indeterminate Computing and diverse forms of analogical computing, each of which based on a particular underlying intuition of the phenomenon of computing. This variety can be captured in terms of system levels, re-interpreting and generalizing Newell's hierarchy, which includes the knowledge level at the top and the symbol level immediately below it. In this re-interpretation the knowledge level consists of human knowledge and the symbol level is generalized into a new level that here is called The Mode of Computing. Natural computing performed by the brains of humans and non-human animals with a developed enough neural system should be understood in terms of a hierarchy of system levels too. By analogy from standard computing machinery there must be a system level above the neural circuitry levels and directly below the knowledge level that is named here The mode of Natural Computing. A central question for Cognition is the characterization of this mode. The Mode of Computing provides a novel perspective on the phenomena of computing, interpreting, the representational and non-representational views of cognition, and consciousness.Comment: 35 pages, 8 figure

Structured representations in a quantum probability model of similarity

Recently, Busemeyer et al. (2011) presented a model for how the conjunction fallacy (Tversky & Kahneman, 1983) emerges, based on the principles of quantum probability (QP) theory. Pothos et al. (2013) extended this model to account for the main similarity findings of Tversky (1977), which have served as a golden standard for testing novel theories of similarity. However, Tversky’s (1977) empirical findings did not address the now established insight that, in comparing two objects, overlap in matching parts of the objects tends to have a greater impact on their similarity, than overlap in non-matching parts. We show how the QP similarity model can be directly extended to accommodate structure in similarity comparisons. Smolensky’s et al.’s (2014) proposal for modeling structure in linguistic representations, with tensor products, can be adapted ‘as is’ with the QP similarity model. The formal properties of the extended QP similarity model are analyzed, some indicative fits are presented, and, finally, a novel prediction is developed

A Formal Model of Metaphor in Frame Semantics

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics

Knowledge transfer in cognitive systems theory: models, computation, and explanation

Knowledge transfer in cognitive systems can be explicated in terms of structure mapping and control. The structure of an effective model enables adaptive control for the system's intended domain of application. Knowledge is transferred by a system when control of a new domain is enabled by mapping the structure of a previously effective model. I advocate for a model-based view of computation which recognizes effective structure mapping at a low level. Artificial neural network systems are furthermore viewed as model-based, where effective models are learned through feedback. Thus, many of the most popular artificial neural network systems are best understood in light of the cybernetic tradition as error-controlled regulators. Knowledge transfer with pre-trained networks (transfer learning) can, when automated like other machine learning methods, be seen as an advancement towards artificial general intelligence. I argue this is convincing because it is akin to automating a general systems methodology of knowledge transfer in scientific reasoning. Analogical reasoning is typical in such a methodology, and some accounts view analogical cognition as the core of cognition which provides adaptive benefits through efficient knowledge transfer. I then discuss one modern example of analogical reasoning in physics, and how an extended Bayesian view might model confirmation given a structural mapping between two systems. In light of my account of knowledge transfer, I finally assess the case of quantum-like models in cognition, and whether the transfer of quantum principles is appropriate. I conclude by throwing my support behind a general systems philosophy of science framework which emphasizes the importance of structure, and which rejects a controversial view of scientific explanation in favor of a view of explanation as enabling control

A MDL-based Model of Gender Knowledge Acquisition

This paper presents an iterative model of\ud knowledge acquisition of gender information\ud associated with word endings in\ud French. Gender knowledge is represented\ud as a set of rules containing exceptions.\ud Our model takes noun-gender pairs as input\ud and constantly maintains a list of\ud rules and exceptions which is both coherent\ud with the input data and minimal with\ud respect to a minimum description length\ud criterion. This model was compared to\ud human data at various ages and showed a\ud good fit. We also compared the kind of\ud rules discovered by the model with rules\ud usually extracted by linguists and found\ud interesting discrepancies

How glassy are neural networks?

In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: Critical line, behavior of the principal thermodynamic observables and their fluctuations as well as overlap fluctuations are obtained and discussed. Then, we move further, extending such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and we show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two quenched spin-glass free energies even in the replica symmetric framework