Willard L. Miranker

Simulated Apoptosis/Neurogenesis Regulates Learning and Memory Capabilities of Adaptive Neural Networks

Characterization of neuronal death and neurogenesis in the adult brain of birds, humans, and other mammals raises the possibility that neuronal turnover represents a special form of neuroplasticity associated with stress responses, cognition, and the pathophysiology and treatment of psychiatric disorders. Multilayer neural network models capable of learning alphabetic character representations via incremental synaptic connection strength changes were used to assess additional learning and memory effects incurred by simulation of coordinated apoptotic and neurogenic events in the middle layer. Using a consistent incremental learning capability across all neurons and experimental conditions, increasing the number of middle layer neurons undergoing turnover increased network learning capacity for new information, and increased forgetting of old information. Simulations also showed that specific patterns of neural turnover based on individual neuronal connection characteristics, or the temporal-spatial pattern of neurons chosen for turnover during new learning impacts new learning performance. These simulations predict that apoptotic and neurogenic events could act together to produce specific learning and memory effects beyond those provided by ongoing mechanisms of connection plasticity in neuronal populations. Regulation of rates as well as patterns of neuronal turnover may serve an important function in tuning the informatic properties of plastic networks according to novel informational demands. Analogous regulation in the hippocampus may provide for adaptive cognitive and emotional responses to novel and stressful contexts, or operate suboptimally as a basis for psychiatric disorders. The implications of these elementary simulations for future biological and neural modeling research on apoptosis and neurogenesis are discussed.

Apoptosis, neurogenesis, and information content in Hebbian networks

The functional significance of alternate forms of plasticity in the brain (such as apoptosis and neurogenesis) is not easily observable with biological methods. Employing Hebbian dynamics for synaptic weight development, a three-layer neural network model of the hippocampus is used to simulate nonsupervised (autonomous) learning in the context of apoptosis and neurogenesis. This learning is applied to the characters of a pair of related alphabets, first the Roman and then the Greek, resulting in a set of encodings endogenously developed by the network. The learning performance takes the form of a U-shaped curve, showing that apoptosis and neurogenesis favorably inform memory development. We also discover that networks that converge very quickly on the Roman alphabet take much longer to handle the Greek, while networks which converge over an extended timeframe can then adapt very quickly to the new language. We find that the effect becomes increasingly pronounced as the number of neurons in the dentate gyrus layer decreases, and identify a strong correlation between cases where the Roman alphabet is quickly learned and cases where a few neurons saturate many of their weights almost immediately, minimizing participation of other neurons. Cases where learning the Roman alphabet requires more time lead to larger numbers of neurons participating with a larger diversity in synaptic weights. We present an information-theoretic argument about why this implies a better, more flexible learning system and why it leads to faster subsequent correlated Greek alphabet learning, and propose that the reason that apoptosis and neurogenesis work is that they promote this effect

Mathematical foundations of consciousness

Abstract We employ the Zermelo–Frankel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo–Frankel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so-called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question.

Cortical memory dynamics

Abstract. Biological memories have a number of unique features, including (1) hierarchical, reciprocally interacting layers, (2) lateral inhibitory interactions within layers, and (3) Hebbian synaptic modifications. We incorporate these key features into a mathematical and computational model in which we derive and study Hebbian learning dynamics and recall dynamics. Introducing the construct of a feasible memory (a memory that formally responds correctly to a specified collection of noisy cues that are known in advance), we study stability and convergence of the two kinds of dynamics by both analytical and computational methods. A conservation law for memory feasibility under Hebbian dynamics is derived. An infomax net is one where the synaptic weights resolve the most uncertainty about a neural input based on knowledge of the output. The infomax notion is described and is used to grade memories and memory performance. We characterize the recall dynamics of the most favorable solutions from an infomax perspective. This characterization includes the dynamical behavior when the net is presented with external stimuli (noisy cues) and a description of the accuracy of recall. The observed richness of dynamical behavior, such as its initial state sensitivity, provides some hints for possible biological parallels to this model.

Modeling consciousness as an adaptive phenomenon

We start at the level of a bacterium where an observer feature associated with foraging measurements motivates introduction of a notion of awareness (a proto-consciousness) as a primitive, a dualist construct. The relative simplicity of Darwinian concepts at the level of a bacterial colony then leads to development of an analytic theory of perceptual consciousness that includes colonial notions of qualia. Results of simulations that verify the colonial principles developed are given. We extend this approach, first to a neuron and then to a neuronal assembly, each extension accompanied by a derived consciousness construct. For each construct (dualist or derived), a mathematical model in the form of a measurable quantity called a token is developed. The pairs, token and construct, permit the design of experiments that would validate the theory. Applications of the theory are developed, each based upon the analytic model (the tokens) and each explaining a familiar aspect of human consciousness in mathematical terminology.

Dynamics of mental activity

Abstract Motivated by neuronal modeling, our development of the mathematical foundations of consciousness in [W. Miranker, G. Zuckerman, Mathematical Foundations of Consciousness, J. Appl. Logic (2009)] (M-Z) was characterized by an axiomatic theory for consciousness operators that acted on the collection of all sets. Consciousness itself was modeled as emanating from the action of such operators on the labeled decoration of a graph, the latter set theoretic construct given the characterization of experience. Since mental activity (conscious and unconscious) is a time dependent process, we herein develop a discrete time dependent version of the theory. Specification of the relevant mental dynamics illuminates and expands the development of the mathematical framework in (M-Z) upon which our study of consciousness rests. This framework is an abstraction of neural net modeling. We review the Aczel theory for decorating labeled graphs, in particular that theorys application to the (M-Z) foundations. The relevant neuronal modeling concepts and terminology are also reviewed. A number of examples are presented. Then an extension of our considerations from graphs to multigraphs is made, since the latter represent a more accurate model of neuronal circuit connectivity. The dynamics are crafted for non-well-founded constructs by development of a hierarchy of systems, starting with the McCulloch–Pitts neuronal voltage input–output relations and building to a dynamics for the cognitive notions of memes and themata; these latter corresponding to aspects of decorations of labeled graphs associated with neural networks. We conclude with a summary and discussion of the semantics of the cognitive features of our development: memes, themata, qualia, consciousness operators, awareness field.

Introducing Affect into Competitive Game Play

A dynamic notion of affect (degree of satisfaction) that an agent acquires in competitive iterated game play is developed. Simulated play against both a random environment and a competitor agent is used to study the impact of affect on game playing strategies. For definiteness, the formulation is framed in terms of stock trading. Comments on how affect in game play informs a notion of consciousness along with simulations are given.

A Neural Network-Based Approach to Modeling the Allocation of Behaviors in Concurrent Schedule, Variable Interval Learning

In this paper we present a neural network-based model of the acquisition of choice behaviors. We employ a multi-layer perceptron, trained using backpropagation with a modified desired-output vector, to model behavior in concurrent-schedule, variable-interval, reinforcing learning situations. We show that our model can be used to describe and predict steady state behavior and learning patterns at the molar level.

The neural network as a renormalizer of information

We characterize the behavior of information in neural processing as the neuronal circuitry itself agglomerates into assemblies of increasing size and complexity. The basic synaptic stage of this processing is interpreted as the observer feature of a measurement process, a quality that extends up the assembly hierarchy. Renormalization techniques are employed, and they supply features of emergence to the information. Renormalization also supplies each observer feature with a measurable physical quantity called a token, the latter supplying quantitative aspects to the entire development. This development is used to frame an analytic theory of phenomenal consciousness, featuring emergent aspects. The tokens furnish the means for the various predictions and explanations of that theory to be subjected to measurement and experimental verification.

A Force Field Driven SOM for boundary detection

We will introduce a method to extract object boundaries from an image. This method utilizes a deformable curve based on the Self Organizing Map algorithm. The proposed SOM has some unique properties such as batch update and neuron insertion/deletion. These properties can make the SOM converge to object concavities as well as maintain a uniform distribution of neurons along the SOM. In comparison with other traditional active contour methods, this algorithm is less sensitive to initialization more flexible in noisy conditions. It outperforms the Gradient Vector Flow method.