Dean's Lecture: The Random Neural Network and Its Applications to Image Processing, Network Routing, and Cyberattack Detection
The Random Neural Network (RNN) is a mathematical model that Erol invented to mimic the behaviour of biological neurons and imitate the required «learning» ability of a neural network, since it is a universial approximator for continuous and bounded functions. In neural network terminology, it is a «recurrent» model in the sense that it can—in general—incorporate feedback loops, and yet still has a well-defined unique solution despite its non-linear computational structure. In essence, the RNN is a continuous time and discrete state-space multi-dimensional Markov chain whose states are the n-vectors {k}, of natural numbers, where each natural number represents the instantaneous «excitation level» or «discrete internal voltage» of each of the n neurons.
Erol will define the RNN model and derive its Chapman-Kolmogorov (differential-difference) equations that characterize the underlying Markov chain. He will show that under stability conditions, it has a unique stationary solution that is calculated from an «exact non-linear mean-field equation». Furthermore, similar to certain queueing networks (Jackson, BCMP) which have linear mean-field equations, the RNN has a Product Form Solution, and its stationary probability distribution is the product of the marginal probability distributions associated to each individual neuron. This analytical structure leads to an O(n^3) gradient-based deep learning algorithm, and to the use of other optimization techniques such as FISTA.
Based on these results, Erol will illustrate the use of the RNN for diverse applications, such as a patented tumor detection algorithm for Magnetic Resonance Images, color texture learning and generation, patented reinforcement learning for packet network routing, and the detection of Botnets and other cyberattacks.
About the Speaker
Erol Gelenbe FIEEE FACM FIFIP graduated from METU (Turkey), received his PhD from the NYU Tandon School of Engineering, and his Doctor of Mathematical Sciences from the Sorbonne. His career has included a tenure track position at the University of Michigan, a research directorship at INRIA, and professorships at the Universities of Liège (Belgium), Paris-Saclay, INRIA, Ecole Polytechnique, Duke University, University of Central Florida, and Imperial College, serving as a faculty member or Department Head. His diverse honors and awards include the Parlar Foundation Science Award (1994), Turkey, the Grand Prix France Télécom (1996), the UK Oliver Lodge Medal for Innovation, Imperial College Rector’s Research Award, the ACM SIGMETRICS Life-Time Achievement Award, the Mustafa Prize (2017), and Honorary Degrees from University of Roma II, Bogaziçi University (Istanbul), and the University of Liège.
Erol was elected to Academia Europaea, the French National Academy of Technologies, the Science Academies of Hungary, Poland, and Turkey, the Royal Academy of Sciences, Arts and Letters of Belgium, the Science Academy of the Organization of Islamic States, and to Foreign Fellowship of the Indian National Science Academy in 2025. He was awarded the Chevalier de la Légion d’Honneur and Commandeur de l’Ordre national du Mérite by the President of France, Commendatore al Merito della Repubblica and Grande Ufficiale della Stella d’Italia by the President of Italy, Commandeur de l’Ordre de la Couronne by the King of Belgium, and the Cross of Officer of Merit by the President of Poland.
Erol has graduated over 90 PhD students, including 25 women. Four of his former PhD students, including two women, were elected to the national academies of Canada and France. His recent election statement to the Indian National Science Academy states that he is a «pioneering researcher in Computer Systems and Networks. Using Markovian and semi-Markov methods, he obtained several seminal analytical results regarding the page fault rates in large classes of memory management algorithms, derived the stability and optimal control of the ALOHA communication system, and the load-dependent optimal values of checkpoints for databases. He invented new modeling and analysis methods, including the G-Network model. He invented the spiking random neural network and its deep learning, auto-associative, and reinforcement algorithms. His technological contributions include a patented optimal architecture for many-to-many communications, patented reinforcement learning routing for edge networks and the Internet, and the industrial simulation tool Flexsim.»