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Nabil H. Farhat, Ph.D.

Professor, Dept of Electrical Engineering
School of Engineering and Applied Science
200 South 33rd Street/6390
Phila., PA 19104-6390
(215) 898-5882 FAX: (215) 573-2068
email:   farhat@ee.upenn.edu

Click here for selected publications since Dr. Farhat's arrival at Penn

RESEARCH INTERESTS

The focus of my research is in Corticonics* where I am applying concepts and tools from nonlinear dynamics, bifurcation theory, self-organized criticality, complexity, and chaos to the modeling and study of the cortex. The cortex is the seat of all higher-level intelligence and understanding its workings is crucial for elucidating the mind-body problem, questions of awareness and consciousness, neuroprosthesis, and for the ultimate development of machines with brain-like intelligence. The findings in corticonics are useful not only for understanding the cortex and higher brain function but also for other complex adaptive systems. In corticonics I am concerned with developing a dynamical approach to understanding the cortex and its collective codes for information processing. This includes: (a) Identifying salient features of cortical organization on both the morphological and physiological level to be abstracted and used in designing powerful new models of the cortex that circumvent the complexity of cortical tissue on the microscopic (neuronal circuit) level and yet have predictive, synthesizing, and explanationary power; (b) Dynamical computing with diverse attractors and the role of synchronicity (coherence) bifurcation, and chaos in biologically inspired paradigms of information processing and learning; (c) Corticonic systems for autonomous learning, distortion invariant recognition, and complex motor control with application to automated iterative object recognition in radar, sonar, and machine vision; (d) Photonic hardware realization of bifurcation processing elements for use in the development of corticonic systems (networks) with capabilities surpassing anything offered by present-day neural net and connectionist models.

Other: Microwave diversity imaging and optical information processing employing spectral, angular and polarization degrees of freedom; Image understanding, holography, and tomography; Stochastic learning and optical Boltzmann machines. Stochastic resonance and hypersensitive sensory mechanism in living organisms. Enabling technologies for the realization of neuromorphic systems.

RESEARCH TECHNIQUES

RESEARCH SUMMARY

In Corticonics, one is concerned with identifying salient anatomical and physiological attributes of cortical organization to be abstracted and used in the development of computational models of the cortex and related signal processing algorithms that are more powerful than what is offered today by neural net and connectionist models. Present day neural net and connectionist models of the cortex have not been effective in duplicating higher-level brain function and specially the ability of the cortex/brain to process dynamic input patterns (e.g., the spatio-temporal signals furnished by sensory organs under the influence of a complex uncontrolled and dynamic environment or alternately due to deliberate dynamic exploration of a stationary environment or its reflexive exploration as by fast saccadic eye movement or touch): We believe the reason for this failure is the simplistic transfer-function description of processing elements and the stimulus-response paradigm used in most present day neural net and connectionist models which do not accurately represent the way the cortex reacts to sensory information. The cortex is the seat of all higher-level brain function such as cognition, thought, language, memory and learning, control of complex motor function and possibly the more esoteric attributes of attention, awareness and consciousness. Better understanding of cortical dynamics can have profound scientific, technological and economical implications not to mention clinical benefits.

In my research I am seeking, with my graduate students, to develop and demonstrate the advantages and effectiveness of a novel approach to modeling the cortex which relies on a different paradigm than that used in the conventional models. We are doing this by adopting a distinctly different view- point than the transfer-function and stimulus-response paradigm, namely that the cortex is a high-dimensional nonlinear dynamical system that is continually active because of extensive feedback and reentrant signalling [V. Braitenberg, Vehicles, MIT Press, 1984] and that the effect of extrinsic (sensory) input patterns, which are usually dynamic, is to alter the system's state-space picture leading to behavioral changes and to adaptation and learning. Accordingly the behavior of the cortex is viewed as determined by "conjugation" of the extrinsic stimulus with the internal dynamics of the system that serve to furnish the context within which the sensory input gets processed and interpreted. It is clear that this paradigm and that used in conventional neural networks are quite distinct and one may therefore expect it to lead to systems with distinctly different capabilities. Our work gives evidence supporting this expectation (see below) and explains in more detail the motive for this approach. For the dynamic theorist, the new paradigm advocated here, together with the results described below, would conjure an environment in which a dissipative high-dimensional nonlinear dynamical system, such as the cortex, "floats" in its state-space carrying out the representation, encoding, learning and interpretation of extrinsic sensory patterns rapidly and efficiently in distinctly different way than that used in present day neural net models.

Thus, using mathematics quite-different from that used in the transfer-function and stimulus-response approach to collective nonlinear processing used in conventional networks, we have adopted a novel approach to modeling the cortex that combines concepts and tools from nonlinear dynamics and information theory. This will offer a radically new way to process, classify/learn, recognize and display spatio-temporal signals of the kind encountered in numerous situations.

It is worth commenting that at first glance, the mixing of dynamical systems which can be chaotic and operating far-from-equilibrium, and the equilibrium thermodynamics on which information theory is based may be seen as incompatible. However, the results of our preliminary studies and simulation of corticonic networks indicates differently and gives evidence that much can in fact be gained from a judicial mix of the two. This evidence is given further credibility by a recent paper by E. Golf (Science, 7, 101-103, Jan. 2000) which shows that the macroscopic behavior of some far-from-equilibrium systems might be actually understood in terms of equilibrium statistical mechanics.

An important question about brain function, one can raise at this point in relation to the preceding discussion, concerns the role of attractors in cortical cognitive processes. The most obvious role for attractors is to make it possible to operate on or utilize the activity trace caused by a stimulus in the sensory cortices after it ceases to exist. Ultimately one may also ask: how can one compute with diverse attractors, is a particular attractor associated with the recognition of a particular object or stimulus? Is the settling of cortical activity into an attractor state synonymous with the recognition process? Is such persistent activity needed for the formation of memory? How do attractors conjure thoughts and mentation? Getting answers to these and other related questions via modeling and simulation, as is being done in our research, will also furnish a framework for understanding and harnessing complexity not only of the cortex but in complex adaptive systems in general including societal, and economical systems and will furnish important guidelines for the development of artificial intelligent machines.

More specifically, our plan consists of developing a macroscopic dynamical theory of the cortex in which groups of tightly coupled neurons form basic functional units, netlets or cortical columns, that are mathematically modeled by parametrically coupled logistic maps (PCLMs). Introducing the concept of PCLM has the advantage that instead of solving coupled systems of nonlinear differential equations representing the neurons in the netlet or column, we reduce the complex dynamics to a simple model, that of a PCLM, governed by a difference equation. This is computationally far more effective and opens the way for investigating the spatio-temporal dynamics of large assemblies of PCLMs in real-time and in particular to investigating the consequences of modeling the cortex with networks of (PCLMs). Plenty of evidence is available to justify this unusual approach, but the strongest comes from the results of exploratory computer simulations we carried out that give clear indication of its viability and promise despite the high-level of abstraction of cortical organization it represents. The supporting evidence obtained, shows that the examples of parametrically coupled logistic map networks (PCLMNs), studied so far, can exhibit remarkable corticomorphic behavior. This includes: the handling of dynamic i.e. spatio-temporal input patterns, self-organization and autonomous (unsupervised) learning from one exposure ("one-shot" learning) driven by mutual-information (MI) which is an information theoretic measure of the flow of information between elements of the network, memory formation with negligible cross-talk, emergence of stimulus (input) - specific isolated clusters of activity reminiscent to the hot spots of brain activity routinely pinpointed by functional magnetic resonance imaging (fMRI), automatic detection and reduction of redundancy in input patterns leading to sparse internal representations that boost storage capacity, provision of huge number of coexisting attractors available for input patterns to draw upon, computing with diverse attractors possessing basins of attraction that furnish a mechanism for learning with generalization, and a role for synchronicity, bifurcation, symmetry-breaking, and chaos in the operation of this new class of networks. The fact that a corticonic network, even one of modest size, has an immense number of coexisting attractors furnishes a clue as to how simple organisms with a modest nervous system manage to handle the immense variety of stimuli they are bound to encounter in a life-time of surviving in a complex unpredictable environment. Another intriguing feature of corticonic networks that is relevant to their hardware or software implementations, is the fact that every functional unit, i.e. the PCLM, is an emergent property of a netlet or neuronal group consisting of hundreds to thousands of neurons. The behavior of a corticonic network of size N is therefore equivalent to that of $(102-\; 103)$ x N neurons. Thus for example, if one can manage to build an array of 100x100 PCLMs with the required dynamic and adaptable connectivity in silicon, something which is not far fetched for modern semiconductor fabrication technologies, the resulting corticonic network would be effectively equivalent to a cortical patch of $106-107$ neurons, i.e. about one percent of the neurons in the human cortex.

Our research program in corticonics seeks to consolidate, further understand, and extend these findings and observations. It is expected to lead to corticonic networks and computational models/algorithms that strive to imitate the following known functional traits of the cortex: (a) Ability to handle (accept, process, and autonomously learn to recognize) dynamic input patterns (spatio-temporal traces of sensory stimuli) evoked by a complex unpredictable environment, (b) ability to cope with the immense variety and number of sensory stimuli an organism is bound to encounter within its lifetime, (c) ability to deal with the plasticity-stability problem in memory formation? the brain self- organizes by changing its subtle connectivity with every act of perception; such plasticity is of course the basis for memory; if connection strengths are constantly changing by perception, how is it possible to form stable memories? All these capabilities are distinguishing features of cortical information processing that are beyond the reach of present day neural net and connectionist models of the association cortex and realizing them will have profound implication for the understanding, management, and control of complex adaptive systems.

It is envisioned that, as result of this research, corticonics and the dynamical systems approach will develop into: (a) A useful tool for understanding and modeling brain function by tracking results and findings from fMRI and other brain imaging techniques and correlating them with the results of computer simulations of corticonic networks. (b) Furnish the knowledge needed to design a new generation of machines with "brain-like" intelligence that will be tested in the context of "killer applications" (see below). (c) Furnish a rich source of topics for thesis and dissertations and senior design projects. (d) Would eventually be incorporated into engineering, physics, and systems neuroscience courses. Examples of course offerings in the EE department at the University of Pennsylvania that are benefiting from the ideas and research described here are: Neurodynamics and Neural Networks, and Chaotic Dynamics and Complexity in Electrical and Biological Systems.

Killer Application

As a killer-application, i.e. something useful that only a corticonic network can do or excel at, we are investigating a dynamic object recognition concept inspired by the sounding and recognition system, the sonar, of certain echo-locating mammals and specially that of the Dolphin. It is well known that the Dolphin uses sound not only to navigate and explore its environment, but also to achieve an uncanny ability to recognize objects in its environment. It has also been observed in controlled experiments reported in the literature [5], that slight changes occur in the emission, the click, waveform used by the Dolphin while it is engaging in a recognition task and that the click waveform stops changing, i.e. converges, once recognition seems to have been achieved. It is as if the Dolphin is changing its emissions to discern the object better. What is puzzling then, is how is it possible that the Dolphin succeeds to acquire more information about a scattering object by means of click waveforms that appear to change very little from click to click. This scenario suggests that the Dolphin is utilizing an iterative sounding and recognition "loop" that involves not only the object, but also its sound generation and sensing system and its auditory, motor, and other cortices. If the PCLMN and corticonic networks we are studying are viable models of the cortex, then they should be useful in modeling the cortex part of this echoing loop to help understand or explain the Dolphin's remarkable recognition abilities. Indeed, preliminary work being carried out in our Neuroengineering Laboratory seems to indicate this approach may be friuitful and may lead to ideas that will be useful in the design of a new generation of intelligent sonars and radars for automated object recognition.

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