Physics of Neural Networks – serie

Since the appearance of Vol. 1 of Models of Neural Networks in 1991, the theory of neural nets has focused on two paradigms: information coding through coherent firing of the neurons and functional feedback. Information coding through coherent neuronal firing exploits time as a cardinal degree of freedom. This capacity of a neural network rests on the fact that the neuronal action potential is a short, say 1 ms, spike, localized in space and time. Spatial as well as temporal correlations of activity may represent different states of a network. In particular, temporal correlations of activity may express that neurons process the same "object" of, for example, a visual scene by spiking at the very same time. The traditional description of a neural network through a firing rate, the famous S-shaped curve, presupposes a wide time window of, say, at least 100 ms. It thus fails to exploit the capacity to "bind" sets of coherently firing neurons for the purpose of both scene segmentation and figure-ground segregation. Feedback is a dominant feature of the structural organization of the brain. Recurrent neural networks have been studied extensively in the physical literature, starting with the ground breaking work of John Hop­ field (1982).

One of the most challenging and fascinating problems of the theory of neural nets is that of asymptotic behavior, of how a system behaves as time proceeds. This is of particular relevance to many practical applications. Here we focus on association, generalization, and representation. We turn to the last topic first. The introductory chapter, "Global Analysis of Recurrent Neural Net­ works," by Andreas Herz presents an in-depth analysis of how to construct a Lyapunov function for various types of dynamics and neural coding. It includes a review of the recent work with John Hopfield on integrate-and­ fire neurons with local interactions. The chapter, "Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns" by Ken Miller, explains how the primary visual cortex may asymptotically gain its specific structure through a self-organization process based on Hebbian learning. His argu­ ment since has been shown to be rather susceptible to generalization.

Close this book for a moment and look around you. You scan the scene by directing your attention, and gaze, at certain specific objects. Despite the background, you discern them. The process is partially intentional and partially preattentive. How all this can be done is described in the fourth volume of Models of Neural Networks devoted to Early Vision and Atten­ tion that you are holding in your hands. Early vision comprises the first stages of visual information processing. It is as such a scientific challenge whose clarification calls for a penetrating review. Here you see the result. The Heraeus Foundation (Hanau) is to be thanked for its support during the initial phase of this project. John Hertz, who has extensive experience in both computational and ex­ perimental neuroscience, provides in "Neurons, Networks, and Cognition" to neural modeling. John Van Opstal explains in a theoretical introduction "The Gaze Control System" how the eye's gaze control is performed and presents a novel theoretical description incorporating recent experimental results. We then turn to the relay stations thereafter, the lateral genicu­ late nucleus (LGN) and the primary visual cortex. Their anatomy, phys­ iology, functional relations, and ensuing response properties are carefully analyzed by Klaus Funke et al. in "Integrating Anatomy and Physiology of the Primary Visual Pathway: From LGN to Cortex", one of the most comprehensive reviews that is available at the moment.

Close this book for a moment and look around you. You scan the scene by directing your attention, and gaze, at certain specific objects. Despite the background, you discern them. The process is partially intentional and partially preattentive. How all this can be done is described in the fourth volume of Models of Neural Networks devoted to Early Vision and Atten­ tion that you are holding in your hands. Early vision comprises the first stages of visual information processing. It is as such a scientific challenge whose clarification calls for a penetrating review. Here you see the result. The Heraeus Foundation (Hanau) is to be thanked for its support during the initial phase of this project. John Hertz, who has extensive experience in both computational and ex­ perimental neuroscience, provides in "Neurons, Networks, and Cognition" to neural modeling. John Van Opstal explains in a theoretical introduction "The Gaze Control System" how the eye's gaze control is performed and presents a novel theoretical description incorporating recent experimental results. We then turn to the relay stations thereafter, the lateral genicu­ late nucleus (LGN) and the primary visual cortex. Their anatomy, phys­ iology, functional relations, and ensuing response properties are carefully analyzed by Klaus Funke et al. in "Integrating Anatomy and Physiology of the Primary Visual Pathway: From LGN to Cortex", one of the most comprehensive reviews that is available at the moment.

One of the most challenging and fascinating problems of the theory of neural nets is that of asymptotic behavior, of how a system behaves as time proceeds. This is of particular relevance to many practical applications. Here we focus on association, generalization, and representation. We turn to the last topic first. The introductory chapter, "Global Analysis of Recurrent Neural Net­ works," by Andreas Herz presents an in-depth analysis of how to construct a Lyapunov function for various types of dynamics and neural coding. It includes a review of the recent work with John Hopfield on integrate-and­ fire neurons with local interactions. The chapter, "Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns" by Ken Miller, explains how the primary visual cortex may asymptotically gain its specific structure through a self-organization process based on Hebbian learning. His argu­ ment since has been shown to be rather susceptible to generalization.

Since the appearance of Vol. 1 of Models of Neural Networks in 1991, the theory of neural nets has focused on two paradigms: information coding through coherent firing of the neurons and functional feedback. Information coding through coherent neuronal firing exploits time as a cardinal degree of freedom. This capacity of a neural network rests on the fact that the neuronal action potential is a short, say 1 ms, spike, localized in space and time. Spatial as well as temporal correlations of activity may represent different states of a network. In particular, temporal correlations of activity may express that neurons process the same "object" of, for example, a visual scene by spiking at the very same time. The traditional description of a neural network through a firing rate, the famous S-shaped curve, presupposes a wide time window of, say, at least 100 ms. It thus fails to exploit the capacity to "bind" sets of coherently firing neurons for the purpose of both scene segmentation and figure-ground segregation. Feedback is a dominant feature of the structural organization of the brain. Recurrent neural networks have been studied extensively in the physical literature, starting with the ground breaking work of John Hop­ field (1982).

Neural Networks presents concepts of neural-network models and techniques of parallel distributed processing in a three-step approach: - A brief overview of the neural structure of the brain and the history of neural-network modeling introduces to associative memory, preceptrons, feature-sensitive networks, learning strategies, and practical applications. - The second part covers subjects like statistical physics of spin glasses, the mean-field theory of the Hopfield model, and the "space of interactions" approach to the storage capacity of neural networks. - The final part discusses nine programs with practical demonstrations of neural-network models. The software and source code in C are on a 3 1/2" MS-DOS diskette can be run with Microsoft, Borland, Turbo-C, or compatible compilers.