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The theory of neural nets has two new paradigms: information coding through coherent firing of the neurons and structural feedback. As compared to traditional neural nets, spiking neurons provide an extra degree of freedom: time; this degree of freedom is realized by a coherent spiking of extensively many neurons in the network, a nonlinear phenomenon. The other paradigm, feedback, is a dominant feature of the structural organization of the brain. This volume provides an in-depth analysis of both paradigms starting with an extensive introduction to the ideas used in the subsequent chapters. In addition, one finds a detailed discussion of salient features such as coherent oscillations and their detection, associative binding and segregation, Hebbian learning, and sensory computations in the visual and olfactory cortex. The style and level of this book make it particularly useful for advanced students and researchers looking for an accessible survey of today's theory of neuronal networks.

This collection of articles by leading researchers in neural networks responds to the urgent need for timely and comprehensive reviews in a multidisciplinary, rapidly developing field of research. It continues the themes of the previous volume, but shifts its focus to more practical matters, such as data storage and retrieval, and the recognition of handwriting.

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).