Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...) in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

I address whether neural networks perform computations in the sense of computability theory and computer science. I explicate and defend
the following theses. (1) Many neural networks compute—they perform computations. (2) Some neural networks compute in a classical way.
Ordinary digital computers, which are very large networks of logic gates, belong in this class of neural networks. (3) Other neural networks
compute in a non-classical way. (4) Yet other neural networks do not perform computations. Brains may well (...) fall into this last class. (shrink)

Deep neural networks (DNNs) have found many useful applications in recent years. Of particular interest have been those instances where their successes imitate human cognition and many consider artificial intelligences to offer a lens for understanding human intelligence. Here, we criticize the underlying conflation between the predictive and explanatory power of DNNs by examining the goals of modeling.

Deep neural networks are said to be opaque, impeding the development of safe and trustworthy artificial intelligence, but where this opacity stems from is less clear. What are the sufficient properties for neural network opacity? Here, I discuss five common properties of deep neural networks and two different kinds of opacity. Which of these properties are sufficient for what type of opacity? I show how each kind of opacity stems from only one of these five properties, and (...) then discuss to what extent the two kinds of opacity can be mitigated by explainability methods. (shrink)

The ontology of social objects and facts remains a field of continued controversy. This situation complicates the life of social scientists who seek to make predictive models of social phenomena. For the purposes of modelling a social phenomenon, we would like to avoid having to make any controversial ontological commitments. The overwhelming majority of models in the social sciences, including statistical models, are built upon ontological assumptions that can be questioned. Recently, however, artificial neural networks have made their way (...) into the social sciences, raising the question whether they can avoid controversial ontological assumptions. ANNs are largely distinguished from other statistical and machine learning techniques by being a representation-learning technique. That is, researchers can let the neural networks select which features of the data to use for internal representation instead of imposing their preconceptions. On this basis, I argue that neural networks can avoid ontological assumptions to a greater degree than common statistical models in the social sciences. I then go on, however, to establish that ANNs are not ontologically innocent either. The use of ANNs in the social sciences introduces ontological assumptions typically in at least two ways, via the input and via the architecture. (shrink)

Computer simulations show that an unstructured neural-network model [Shultz, T. R., & Bale, A. C. (2001). Infancy, 2, 501–536] covers the essential features␣of infant learning of simple grammars in an artificial language [Marcus, G. F., Vijayan, S., Bandi Rao, S., & Vishton, P. M. (1999). Science, 283, 77–80], and generalizes to examples both outside and inside of the range of training sentences. Knowledge-representation analyses confirm that these networks discover that duplicate words in the sentences are nearly identical and that (...) they use this near-identity relation to distinguish sentences that are consistent or inconsistent with a familiar grammar. Recent simulations that were claimed to show that this model did not really learn these grammars [Vilcu, M., & Hadley, R. F. (2005). Minds and Machines, 15, 359–382] confounded syntactic types with speech sounds and did not perform standard statistical tests of results. (shrink)

An ideal vision model accounts for behavior and neurophysiology in both naturalistic conditions and designed lab experiments. Unlike psychological theories, artificial neural networks (ANNs) actually perform visual tasks and generate testable predictions for arbitrary inputs. These advantages enable ANNs to engage the entire spectrum of the evidence. Failures of particular models drive progress in a vibrant ANN research program of human vision.

Due to the excellent approximation ability, the neural networks based control method is used to achieve adaptive consensus of the fractional-order uncertain nonlinear multiagent systems with external disturbance. The unknown nonlinear term and the external disturbance term in the systems are compensated by using the radial basis function neural networks method, a corresponding fractional-order adaption law is designed to approach the ideal neural network weight matrix of the unknown nonlinear terms, and a control law is designed eventually. (...) According to the designed Lyapunov candidate function and the fractional theory, the systems stability is proved, and the adaptive consensus can be guaranteed by using the designed control law. Finally, two simulations are shown to illustrate the validity of the obtained results. (shrink)

Cultural similarities and differences in facial expressions have been a controversial issue in the field of facial communications. A key step in addressing the debate regarding the cultural dependency of emotional expression is to characterize the visual features of specific facial expressions in individual cultures. Here we developed an image analysis framework for this purpose using convolutional neural networks that through training learned visual features critical for classification. We analyzed photographs of facial expressions derived from two databases, each developed (...) in a different country, in which corresponding emotion labels were available. While the CNNs reached high rates of correct results that were far above chance after training with each database, they showed many misclassifications when they analyzed faces from the database that was not used for training. These results suggest that facial features useful for classifying facial expressions differed between the databases. The selectivity of computational units in the CNNs to action units of the face varied across the facial expressions. Importantly, the AU selectivity often differed drastically between the CNNs trained with the different databases. Similarity and dissimilarity of these tuning profiles partly explained the pattern of misclassifications, suggesting that the AUs are important for characterizing the facial features and differ between the two countries. The AU tuning profiles, especially those reduced by principal component analysis, are compact summaries useful for comparisons across different databases, and thus might advance our understanding of universality vs. specificity of facial expressions across cultures. (shrink)

This work describes a mathematical concept of modelling field theory and its applications to a variety of problems, while offering a view of the relationships among mathematics, computational concepts in neural networks, semiotics, and concepts of mind in psychology and philosophy.

Engineers use neural networks to control systems too complex for conventional engineering solutions. To examine the behavior of individual hidden units would defeat the purpose of this approach because it would be largely uninterpretable. Yet neurophysiologists spend their careers doing just that! Hidden units contain bits and scraps of signals that yield only arcane hints about network function and no information about how its individual units process signals. Most literature on single-unit recordings attests to this grim fact. On the (...) other hand, knowing a system's function and describing it with elegant mathematics tell one very little about what to expect of interneuronal behavior. Examples of simple networks based on neurophysiology are taken from the oculomotor literature to suggest how single-unit interpretability might decrease with increasing task complexity. It is argued that trying to explain how any real neural network works on a cell-by-cell, reductionist basis is futile and we may have to be content with trying to understand the brain at higher levels of organization. (shrink)

Bowers et al. propose to use controlled behavioral experiments when evaluating deep neural networks as models of biological vision. We agree with the sentiment and draw parallels to the notion that “neuroscience needs behavior.” As a promising path forward, we suggest complementing image recognition tasks with increasingly realistic and well-controlled task environments that engage real-world object recognition behavior.

Cognitive science has evolved since early disputes between radical empiricism and radical nativism. The authors are reacting to the revival of radical empiricism spurred by recent successes in deep neural network (NN) models. We agree that language-like mental representations (language-of-thoughts [LoTs]) are part of the best game in town, but they cannot be understood independent of the other players.

The so-called Baldwin Effect generally says how learning, as a form of ontogenetic adaptation, can influence the process of phylogenetic adaptation, or evolution. This idea has also been taken into computation in which evolution and learning are used as computational metaphors, including evolving neural networks. This paper presents a technique called evolving self-taught neural networks – neural networks that can teach themselves without external supervision or reward. The self-taught neural network is intrinsically motivated. Moreover, the self-taught (...) neural network is the product of the interplay between evolution and learning. We simulate a multi-agent system in which neural networks are used to control autonomous agents. These agents have to forage for resources and compete for their own survival. Experimental results show that the interaction between evolution and the ability to teach oneself in self-taught neural networks outperform evolution and self-teaching alone. More specifically, the emergence of an intelligent foraging strategy is also demonstrated through that interaction. Indications for future work on evolving neural networks are also presented. (shrink)

A working hypothesis of computationalism is that Mind arises, not from the intrinsic nature of the causal properties of particular forms of matter, but from the organization of matter. If this hypothesis is correct, then a wide range of physical systems (e.g. optical, chemical, various hybrids, etc.) should support Mind, especially computers, since they have the capability to create/manipulate organizations of bits of arbitrarily complexity and dynamics. In any particular computer, these bit patterns are quite physical, but their particular physicality (...) is considered irrelevant (since they could be replaced by other physical substrata). (shrink)

How might artificial neural networks (ANNs) inform cognitive science? Often cognitive scientists use ANNs but do not examine their internal structures. In this paper, we use ANNs to explore how cognition might represent musical properties. We train ANNs to classify musical chords, and we interpret network structure to determine what representations ANNs discover and use. We find connection weights between input units and hidden units can be described using Fourier phase spaces, a representation studied in musical set theory. We (...) find the total signal coming through these weighted connection weights is a measure of the similarity between two Fourier structures: the structure of the hidden unit's weights and the structure of the stimulus. This is surprising because neither of these Fourier structures is computed by the hidden unit. We then show how output units use such similarity measures to classify chords. However, we also find different types of units—units that use different activation functions—use this similarity measure very differently. This result, combined with other findings, indicates that while our networks are related to the Fourier analysis of musical sets, they do not perform Fourier analyses of the kind usually described in musical set theory. Our results show Fourier representations of music are not limited to musical set theory. Our results also suggest how cognitive psychologists might explore Fourier representations in musical cognition. Critically, such theoretical and empirical implications require researchers to understand how network structure converts stimuli into responses. (shrink)

This paper proposes an adaptive neural network control approach for a direct-current system with full state constraints. To guarantee that state constraints always remain in the asymmetric time-varying constraint regions, the asymmetric time-varying Barrier Lyapunov Function is employed to structure an adaptive NN controller. As we all know that the constant constraint is only a special case of the time-varying constraint, hence, the proposed control method is more general for dealing with constraint problem as compared with the existing works (...) on DC systems. As far as we know, this system is the first studied situations with time-varying constraints. Using Lyapunov analysis, all signals in the closed-loop system are proved to be bounded and the constraints are not violated. In this paper, the effectiveness of the control method is demonstrated by simulation results. (shrink)

Within the Hebbian paradigm the mechanism for integrating cell assemblies oscillating with different frequencies remains unclear. We hypothesize that such an integration may occur in cortical “interaction foci” that unite synchronously oscillated assemblies through hard-wired connections, synthesizing the information from various functional systems of the brain.

As an imitation of the biological nervous systems, neural networks, which have been characterized as powerful learning tools, are employed in a wide range of applications, such as control of complex nonlinear systems, optimization, system identification, and patterns recognition. This article aims to bring a brief review of the state-of-the-art NNs for the complex nonlinear systems by summarizing recent progress of NNs in both theory and practical applications. Specifically, this survey also reviews a number of NN based robot control (...) algorithms, including NN based manipulator control, NN based human-robot interaction, and NN based cognitive control. (shrink)

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human reasoning qualities. More recently, however, there has been an increasing interest in applying alternative approaches based on machine learning rather than logic-based formalisms to tackle this kind of tasks. Here, we make use of (...) state-of-the-art methods for training deep neural networks to devise a novel model that is closely coupled to symbolic reasoning methods, and thus able to learn how to effectively perform basic ontology reasoning. This term describes an important and at the same time very natural kind of problem settings where the rules for conducting reasoning are specified alongside with the actual information. Many problems in practice may be viewed as such reasoning tasks, which is why the presented approach is applicable to a plethora of important real-world problems. To demonstrate the effectiveness of the suggested method, we present the outcomes of several experiments that have been conducted on both toy datasets as well as real-world data, which show that our model learned to perform precise reasoning on a number of diverse inference tasks that require comprehensive deductive proficiencies. Furthermore, it turned out that the suggested model suffers much less from different obstacles that prohibit symbolic reasoning. (shrink)

The literature on common pool resource (CPR) governance lists numerous factors that influence whether a given CPR system achieves ecological long-term sustainability. Up to now there is no comprehensive model to integrate these factors or to explain success within or across cases and sectors. Difficulties include the absence of large-N-studies (Poteete 2008), the incomparability of single case studies, and the interdependence of factors (Agrawal and Chhatre 2006). We propose (1) a synthesis of 24 success factors based on the current SES (...) framework and a literature review; (2) the application of neural networks on a database of CPR management case studies in an attempt to test the viability of this synthesis. This method allows us to obtain an implicit quantitative and rather precise model of the interdependencies in CPR systems. Given such a model, every success factor in each case can be manipulated separately, yielding different predictions for success. This could become be a fast and inexpensive way to analyze, predict and optimize performance for communities world-wide facing CPR challenges. Existing theoretical frameworks could be improved as well. (shrink)

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human reasoning qualities. More recently, however, there has been an increasing interest in applying alternative approaches based on machine learning rather than logic-based formalisms to tackle this kind of tasks. Here, we make use of (...) state-of-the-art methods for training deep neural networks to devise a novel model that is closely coupled to symbolic reasoning methods, and thus able to learn how to effectively perform basic ontology reasoning. This term describes an important and at the same time very natural kind of problem settings where the rules for conducting reasoning are specified alongside with the actual information. Many problems in practice may be viewed as such reasoning tasks, which is why the presented approach is applicable to a plethora of important real-world problems. To demonstrate the effectiveness of the suggested method, we present the outcomes of several experiments that have been conducted on both toy datasets as well as real-world data, which show that our model learned to perform precise reasoning on a number of diverse inference tasks that require comprehensive deductive proficiencies. Furthermore, it turned out that the suggested model suffers much less from different obstacles that prohibit symbolic reasoning. (shrink)

In this paper an Artificial Neural Network (ANN) model, for predicting the category of a tumor was developed and tested. Taking patients’ tests, a number of information gained that influence the classification of the tumor. Such information as age, sex, histologic-type, degree-of-diffe, status of bone, bone-marrow, lung, pleura, peritoneum, liver, brain, skin, neck, supraclavicular, axillar, mediastinum, and abdominal. They were used as input variables for the ANN model. A model based on the Multilayer Perceptron Topology was established and trained (...) using data set which its title is “primary tumor” and was obtained from the University Medical Centre, Institute of Oncology, Ljubljana, Yugoslavia Test data evaluation shows that the ANN model is able to correctly predict the tumor category with 76.67 % accuracy. (shrink)

There is a gap between two different modes of computation: the symbolic mode and the subsymbolic (neuron-like) mode. The aim of this paper is to overcome this gap by viewing symbolism as a high-level description of the properties of (a class of) neural networks. Combining methods of algebraic semantics and non-monotonic logic, the possibility of integrating both modes of viewing cognition is demonstrated. The main results are (a) that certain activities of connectionist networks can be interpreted as non-monotonic inferences, (...) and (b) that there is a strict correspondence between the coding of knowledge in Hopfield networks and the knowledge representation in weight-annotated Poole systems. These results show the usefulness of non-monotonic logic as a descriptive and analytic tool for analyzing emerging properties of connectionist networks. Assuming an exponential development of the weight function, the present account relates to optimality theory – a general framework that aims to integrate insights from symbolism and connectionism. The paper concludes with some speculations about extending the present ideas. (shrink)

Infertility is recognized as a major problem of modern society. Assisted Reproductive Technology is the one of many available treatment options to cure infertility. However, the efficiency of the ART treatment is still inadequate. Therefore, the procedure’s quality is constantly improving and there is a need to determine statistical predictors as well as contributing factors to the successful treatment. There is a concern over the application of adequate statistical analysis to clinical data: should classic statistical methods be used or would (...) it be more appropriate to apply advanced data mining technologies? By comparing two statistical models, Multivariable Logistic Regression analysis and Artificial Neural Network it has been demonstrated that Multivariable Logistic Regression analysis is more suitable for theoretical interest but the Artificial Neural Network method is more useful in clinical prediction. (shrink)