M.J. Healy

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M.J. verified their affiliation via an institutional email.

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• MS
• Researcher at University of New Mexico

We propose a new model of episodic memory. It consists of a hierarchy of partial sequences of events, blended for consistency across space and time by feedforward/feedback links to concepts expressing their shared information. This blended concept hierarchy is acquired and represented incrementally through synaptic or connection-weighted adaptation...

An issue in the representation by a neural network of objects detected by its sensors is whether such representations are based at a single neural cell or require a distributed subnetwork. We perform an analysis near the sensor level of a simple geometric shape and show that given the appropriate mathematical structure, representations can be both...

We introduce a category-theoretic account of episodic memory as an outgrowth of an existing mathematical theory of the semantics of neural networks. We propose that neural systems which can be said to have episodic memory represent sequences of events and their associated information within a hierarchy of concepts, represented in their neural netwo...

This report presents a mathematical model of the semantics, or meaning, of the connection-ist structure and stimulus activity of a neural network, whether artificial or biological. The mathematical model associates concepts about sensed objects with the neuron-like nodes in a neural network and composable concept relationships with the connection p...

Aphasic Compressed Representations: A Functorial Semantic Design Principle for Coupled ART Networks Supervised ART networks consist of interconnected subnetworks, a, b, and possibly also a map field. The a and b subnetworks have separate input representations for inputs and associated outputs. A categorical semantic analysis suggests that each in...

Distal reward refers to a class of problems where reward is temporally distal from actions that lead to reward. The difficulty for any biological neural system is that the neural activations that caused an agent to achieve reward may no longer be present when the reward is experienced. Therefore in addition to the usual reward assignment problem, t...

This paper presents a new semi-supervised neural architecture that learns to classify objects at a distance through experience. It utilizes Fuzzy LAPART extended with two temporal integrator subnetworks to create time-stamped perceptual memory codes in an unsupervised manner during object approach, and to retrospectively learn class code inferences...

Controversy exists regarding the optimal dosing regimen of radioactive iodine (RAI) for the treatment of hyperthyroidism. The dose of RAI was individualised, based on the size of the thyroid gland and 24-h RAI uptake. We performed a 10-year retrospective analysis of patients with hyperthyroidism treated with variable dose RAI, with a cure defined a...

Category theory is discussed as an appropriate mathematical basis for the formalization and study of ontologies. It is based upon the notion of the structure manifest in systems of compositional relations and through mappings between systems that preserve composition. With one or two important exceptions, the basic concepts of category theory neede...

Ontology was once understood to be the philosophical inquiry into the structure of reality: the analysis and categorization of 'what there is'. Recently, however, a field called 'ontology' has become part of the rapidly growing research industry in information technology. The two fields have more in common than just their name. Theory and Applicati...

Abstract A recently-developed mathematical semantic theory explains the relationship be- tween knowledge and its representation in connectionist systems. The semantic theory is based upon category theory, the mathematical theory of structure. A product of its explanatory capability is a set of principles to guide the design of future neural archite...

An application of nonlinear programming to the problem of airplane preliminary design is presented. The main steps of the method are described and a sample case is shown to illustrate the procedure and related difficulties.

Encoding sensor observations across time is a critical component in the ability to model cognitive processes. All biological cognitive systems receive sensory stimuli as continuous streams of observed data over time. Therefore, the perceptual grounding of all biological cognitive processing is in temporal semantic encodings, where the particular gr...

A category-theoretic account of neural network semantics has been used to characterize concept representation in neural memory. This involves categories of objects and morphisms representing the activity in connectionist structures at different stages of weight adaptation. The definition used in this previous work for the notion of a neural morphis...

We propose a neurologically plausible computational architecture to model human episodic memory and recall based on cortical-hippocampal structure and function. The model design is inspired by neuroscience findings and categorical neural semantic theory. Fuzzy Adaptive Resonance Theory (ART) and temporal integration are used to form episodic repres...

A recent neural network semantic theory provides the framework for mapping ontologies to neural networks. We use category theory, the mathematical theory of structure, to explore the concept representational abilities of select neural networks. Methodologies suggested by the semantic theory have been gainfully applied to specific applications. This...

The use of neural network architectures has historically presented a challenge to engineers. Problem domains could be "learned", but the acquired knowledge could be extracted only under limited circumstances. Healy and Caudell's application of category theory has been shown to improve both architecture design and performance. This paper reports on...

While learning algorithms have been used for astronomical data analysis, the vast majority of those algorithms have used supervised learning. In a continuation of the work described in Young et ah [18] we examine the use of unsupervised learning for this task with two types of Adaptive Resonance Theory (ART) neural networks. Using synthetic astrono...

We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to...

Data from neuroscience research has shown that the brain can be studied as a neural network. In view of the brain's seemingly infinite complexity, we organize the entire network into a series of sub-networks, each of whose functionalities combine to become the knowledge representation capability of the entire network. Thus, we look at the brain in...

The semantics of neural networks can be analyzed mathematically as a distributed system of knowledge and as systems of possible worlds expressed in the knowledge. Learning in a neural network can be analyzed as an attempt to acquire a representation of knowledge. We express the knowledge system, systems of possible worlds, and neural architectures...

Concepts have been expressed mathematically as propositions in a distributive lattice. A more comprehensive formulation is that of a generalized lattice, or category, in which the concepts are related in hierarchical fashion by lattice-like links called concept morphisms. A concept morphism describes how a more abstract concept is used within a mor...

Many studies have addressed the knowledge representation capability of neural networks. A recently-developed mathematical semantic theory explains the relationship between knowledge and its representation in connectionist systems. The theory yields design principles for neural networks whose behavioral repertoire expresses any desired capability th...

An unsupervised learning system, implemented as an autonomous agent is presented. A simulation of a challenging path planning problem is used to illustrate the agent design and demonstrate its problem solving ability. The agent, dubbed the ORG, employs fuzzy logic and clustering techniques to efficiently represent and retrieve knowledge and uses in...

We introduce a new architecture designed by applying a recently-developed mathematical model of neural network semantics using category theory. The new design has multiple subnetworks associated with different sensors and association regions. The subnetworks form individual, hierarchical representations of a body of knowledge. Subnetwork interconne...

Visualization is a useful method for understanding both learning and computation in artificial neural networks. There are a large number of parameters in a neural network. By viewing these parameters pictorially, a better understanding can be gained of how a network maps inputs to outputs. eLoom is an open source graph simulation tool, developed at...

eLoom is an open source graph simulation software tool, developed at the University of New Mexico (UNM), that enables users to specify and simulate neural network models. Its specification language and libraries enables users to construct and simulate arbitrary, potentially hierarchical network structures on serial and parallel processing systems....

Supervised ART networks consist of interconnected subnetworks, a, b, and possibly also a map field. The a and b subnetworks have separate input representations for inputs and associated outputs. A categorical semantic analysis suggests that each input field must have a compressed representation in the other subnetwork(s)

Presents an experimental study on the effects of sensorial representations, sensor fusion, control arbitration, and environmental configurations on the learning of a coupled simulated/physical robotic system using the LAPART-2 neural architecture

We apply a new semantic model for neural networks to the analysis of learned concept representations in ART networks. The new model is based upon the category theory, the mathematical theory of structure. It allows an unambiguous evaluation of the ability of an ART network to capture the hierarchical structure of interrelated symbolic concepts accu...

We deal with the performance bounding of fuzzy ARTMAP and other ART-based neural network architectures, such as boosted ARTMAP, according to the theory of structural risk minimization. Structural risk minimization research indicates a trade-off between training error and hypothesis complexity. This trade-off directly motivated boosted ARTMAP. In th...

Over the last two years, we have demonstrated the feasibility of applying category-theoretic methods in specifying, synthesizing, and maintaining industrial strength software systems. We have been using a first-of-its-kind tool for this purpose, Kestrel's SpecwareTM software development system. In this paper, we describe our experiences and give an...

We describe an alternative paradigm for software reuse that attempts to reuse software derivation knowledge at an appropriate level of abstraction. Sometimes that level is a domain theory that is involved in stating system requirements. Sometimes it is a design pattern. Sometimes it is a software component. Often it is a combination of the these. W...

In this chapter, we present the results of a study of a new version of the LAPART adaptive inferencing neural network [1], [2]. We will review the theoretical properties of this architecture, called LAPART-2, showing it to converge in at most two passes through a fixed training set of inputs during learning, and showing that it does not suffer from...

In an industrial research project, we have demonstrated the feasibility of applying category-theoretic methods to the specification, synthesis, and maintenance of industrial strength software systems. The demonstration used a first-of-its-kind tool for this purpose, Kestrel’s Specware™ software development system. We describe our experiences and di...

With the advent of intelligent computer aided design systems, companies such as Boeing are embarking on an era in which core competitive engineering knowledge and design rationale is being encoded in software systems. The promise of this technology is that this knowledge can be leveraged across many different designs, product families, and even dif...

Category theory can be applied to mathematically model the semantics of cognitive neural systems. Here, we employ colimits, functors and natural transformations to model the implementation of concept hierarchies in neural networks equipped with multiple sensors

In this paper, we describe an investigation into the reuse and application of an existing ontology for the purpose of specifying and formally developing software for aircraft design. Our goals were to clearly identify the processes involved in the task, and assess the cost-e#ectiveness of reuse. Our conclusions are that (re)using an ontology is far...

Abstract In an industrial research project, we have demonstrated the feasibility of applying category - theoretic methods to the specification, synthesis, and maintenance of industrial strength software systems The demonstration used a first - of - its - kind tool for this purpose, Kestrel's Specware software development system We describe our expe...

We present a modification to the Fuzzy ARTMAP neural network architecture for conducting classification in a probabilistic setting. We call this new architecture Hierarchical ARTMAP (HARTMAP). Performance comparisons with Fuzzy ARTMAP, Gaussian ARTMAP and Boosted ARTMAP on some simple two-class problems are discussed. Experimental results indicate...

Over the last two years, we have demonstrated the feasibility of applying category-theoretic methods in specifying, synthesizing, and maintaining industrial strength software systems. We have been using a first-of-its-kind tool for this purpose. Kestrel's Specware^TM software development system. In this paper, we describe our experiences...

An algorithm for adaptively controlling genetic algorithm parameter (GAP) coding using fuzzy rules is presented. The fuzzy GAP coding algorithm is compared to the dynamic parameter encoding scheme proposed by Schraudolph and Belew. The performance of the algorithm on a hydraulic brake emulator parameter identification problem is investigated. Fuzzy...

Rule extraction with neural networks is a subject of increasing interest. Research in this area could benefit from the availability of a formal model of the semantics of the rules. A model of this kind would express the relationship between the application data, the neural network learning model and the extracted rules with mathematical rigor, allo...

this article are of varying nature: position summaries, individual research summaries, historical accounts, discussion of controversial issues, etc. We have not attempted to connect the various pieces together, or to organize them within a coherent framework. Despite this, we think, the reader will find this collection useful.

This paper presents the results of a computer study of supervised learning and generalization in a new neural architecture that has extremely tight bounds on learning convergence. LAPART-2 is an extended version of the LAPART-1 introduced previously by the authors (1998). This paper explores the architectural generalisation through a series of nume...

We introduce a new kind of mathematics for neural network modeling and show its application in modeling a cognitive memory system. Category theory has found increasing use in formal semantics, the modeling of the concepts (or meaning) behind computations. Here, we apply it to derive a mathematical model of concept formation and recall in a neural n...

We present a modification to the fuzzy ARTMAP neural network architecture for conducting boosted learning in a probabilistic setting. We call this new architecture boosted ARTMAP (BARTMAP). Performance comparison with fuzzy ARTMAP, PROBART and ART-EMAP on some simple two-class problems is discussed. Experimental results indicate that BARTMAP gives...

We present a theoretical analysis of a version of the LAPART adaptive inferencing neural network. Our main result is a proof that the new architecture, called LAPART 2, converges in two passes through a fixed training set of inputs. We also prove that it does not suffer from template proliferation. For comparison, Georgiopoulos et al. (1994) have p...

This paper briefly describes our initial experiences in applied research of formal approaches to the generation and maintenance of software systems supporting structural engineering tasks. We describe the business context giving rise to this activity, and give an example of the type of engineering problem we have focused on. We briefly describe our...

In this paper we show how the stability of a LAPART neural network can be deduced as a result of a general theorem on the input/output stability of nonlinear systems. This result gives conditions on how to choose certain parameters in the LAPART network in order to guarantee stability, which has implications on LAPART's generalization properties an...

Bounds on the number of training examples needed to guarantee a certain level of generalization performance in the ARTMAP architecture are derived. Conditions are derived under which ARTMAP can achieve a specific level of performance assuming any unknown, but fixed, probability distribution on the training data

Envisioning neural networks as systems that learn rules calls forth the verification issues already being studied in knowledge-based systems engineering, and complicates these with neural-network concepts such as nonlinear dynamics and distributed memories. We show that the issues can be clarified and the learned rules visualized symbolically by fo...

The logical neural architecture LAPART is used in a mode that allows through learning the easy creation and extraction of IF-THEN inference rules from data. This paper first describes ART1 and the complement coded stack input binary representations. Next, we present a more detailed discussion of LAPART. Then we show how rules are learned and extrac...

A complex neural architecture called the Encephalon is presented as an example of a network that makes extensive use of adaptive resonance theory (ART) networks. The Encephalon is a machine vision system that autonomously learns object classification inference rules, and makes extensive use of the interplay between the bottom-up and top-down flow o...

LAPART, a neural network architecture for logical inferencing and supervised learning is discussed. Emphasizing its use in recognizing familiar sequences of patterns by verifying pattern pairs inferred from prior experience. It consists of interconnected adaptive resonance theory (ART) networks. The interconnects enable LAPART to learn to infer one...

The authors describe a neural architecture for efficient recognition of invariant features placed arbitrarily in patterns of data. The architecture provides versatility in invariant selection with minimal computation and storage requirements. Operating in dumb mode, the architecture, called the big, dumb mass detector (BDMD), autonomously extracts...

The author discusses a neural network architecture for supervised learning with inherent stability properties. The architecture uses two ART 1 unsupervised systems with supervision through interconnects. The system will respond as trained under controlled operating conditions, and the use of adaptive resonance provides a means of addressing novel i...

Large and sparse convex quadratic programming problems are often generated in the course of solving large-scale optimization problems. An important class of these problems has the property that only a small number of constraints are at their bounds at a solution. We describe an implementation of a range-space method designed for efficient solution...

Summary form only given, as follows. Simplifying assumptions allow identification of the logical equivalent of the computations in a class of neural networks. Higher-order functions encapsulate the semantic content of patterns of signals and synaptic weights by forming formulas in a formal logic. This model was applied to capture the semantic conte...

The generalization properties of a class of neural architectures can be modelled mathematically. The model is a parallel predicate calculus based on pattern recognition and self-organization of long-term memory in a neural network. It may provide the basis for adaptive expert systems capable of inductive learning and rapid processing in a highly co...

Pending the availability of hardware implementations of artificial neural architectures, digital software algorithms for pattern recognition and machine learning developed from them may be useful in many applications. The extent to which these algorithms can preserve the natural parallelism in an application, and the effect of the host environment,...

A comprehensive engine/airframe screening methodology has been developed based on surface fitting and nonlinear optimization procedures. These procedures include the use of experimental design techniques, and a gradient-based method for nonlinear constrained minimization. The methodology has been programed for use on the CDC 6600 computer and has b...

Summary. Concepts have been expressed mathematically as propositions in a distributive lattice. A more comprehensive formulation is that of a generalized lattice, or category, in which the concepts are related in hierarchical fashion by lattice-like links called concept morphisms. A concept morphism describes how an abstract concept can be used wit...

Category theory can be applied to mathematically model the semantics of cognitive neural systems. We discuss semantics as a hierarchy of concepts, or symbolic descriptions of items sensed and represented in the connection weights distributed throughout a neural network. The hierarchy expresses subconcept relationships, and in a neural network it be...

This report is intended to be read easily by cognitive scientists, neuroscientists interested in cognition, engineers, and scientific investigators in other fields. Categorization and the judgement of similarity are fundamental in cognition. We propose that these and other activities are based upon an underlying structure of knowledge, or concept r...

A category-theoretic account of neural network semantics has been used to characterize incremental concept representation in neural memory. It involves a category of concepts and concept morphisms together with categories of objects and morphisms representing the activity in connectionist structures at different stages of weight adaptation. Colimit...

: The paper presents first phase results of an experimental development to establish a standardized method for evaluating crewstation geometry. The new evaluation technique determines whether any sized operator can perform required functions in any specified work station. A 23-pin-joint man-model is used for the development. Joint angular parameter...