https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Miller (1956) summarized evidence that people can remember about seven chunks in short-term memory (STM) tasks. How- ever, that number was meant more as a rough estimate and a rhetorical device than as a real capacity limit. Others have since suggested that there is a more precise capacity limit, but that it is only three to five chunks. The present target article brings together a wide vari- ety of data on capacity limits suggesting that the smaller capacity limit is real. Capacity limits will be useful in analyses of information processing only if the boundary conditions for observing them can be carefully described. Four basic conditions in which chunks can be identified and capacity limits can accordingly be observed are: (1) when information overload limits chunks to individual stimulus items, (2) when other steps are taken specifically to block the recoding of stimulus items into larger chunks, (3) in performance discontinuities caused by the capacity limit, and (4) in various indirect effects of the capacity limit. Under these conditions, rehearsal and long-term memory cannot be used to combine stimulus items into chunks of an unknown size; nor can storage mechanisms that are not capacity- limited, such as sensory memory, allow the capacity-limited storage mechanism to be refilled during recall. A single, central capacity limit averaging about four chunks is implicated along with other, noncapacity-limited sources. The pure STM capacity limit expressed in chunks is distinguished from compound STM limits obtained when the number of separately held chunks is unclear. Reasons why pure capacity estimates fall within a narrow range are discussed and a capacity limit for the focus of attention is proposed.

/pdf/the-magical-number-4-in-short-term-memory-a-reconsideration-3704b9phuz.pdf

The magical number 4 in short-term memory: a reconsideration of mental storage capacity.

Introduction to support vector learning roadmap. Part 1 Theory: three remarks on the support vector method of function estimation, Vladimir Vapnik generalization performance of support vector machines and other pattern classifiers, Peter Bartlett and John Shawe-Taylor Bayesian voting schemes and large margin classifiers, Nello Cristianini and John Shawe-Taylor support vector machines, reproducing kernel Hilbert spaces, and randomized GACV, Grace Wahba geometry and invariance in kernel based methods, Christopher J.C. Burges on the annealed VC entropy for margin classifiers - a statistical mechanics study, Manfred Opper entropy numbers, operators and support vector kernels, Robert C. Williamson et al. Part 2 Implementations: solving the quadratic programming problem arising in support vector classification, Linda Kaufman making large-scale support vector machine learning practical, Thorsten Joachims fast training of support vector machines using sequential minimal optimization, John C. Platt. Part 3 Applications: support vector machines for dynamic reconstruction of a chaotic system, Davide Mattera and Simon Haykin using support vector machines for time series prediction, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel. Part 4 Extensions of the algorithm: reducing the run-time complexity in support vector machines, Edgar E. Osuna and Federico Girosi support vector regression with ANOVA decomposition kernels, Mark O. Stitson et al support vector density estimation, Jason Weston et al combining support vector and mathematical programming methods for classification, Bernhard Scholkopf et al.

Advances in kernel methods: support vector learning

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

Recurrence plots for the analysis of complex systems

Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.

Neural networks with dynamic synapses

It is shown that a topographic product P, first introduced in nonlinear dynamics, is an appropriate measure of the preservation or violation of neighborhood relations. It is sensitive to large-scale violations of the neighborhood ordering, but does not account for neighborhood ordering distortions caused by varying areal magnification factors. A vanishing value of the topographic product indicates a perfect neighborhood preservation; negative (positive) values indicate a too small (too large) output space dimensionality. In a simple example of maps from a 2D input space onto 1D, 2D, and 3D output spaces, it is demonstrated how the topographic product picks the correct output space dimensionality. In a second example, 19D speech data are mapped onto various output spaces and it is found that a 3D output space (instead of 2D) seems to be optimally suited to the data. This is an agreement with a recent speech recognition experiment on the same data set. >

Quantifying the neighborhood preservation of self-organizing feature maps

We derive return maps and phase diagrams to identify mechanisms of synchronization of pulse-coupled oscillators and emphasize the importance of temporal delays and inhibitory coupling. Optimum synchronization between two oscillators is obtained for inhibitory coupling, where delays give rise to stable in-phase synchronization; those with excitatory coupling only synchronize with a phase lag. In large ensembles of globally coupled oscillators the delayed interaction leads to new collective phenomena like synchronization in multistable clusters of common phases for inhibitory coupling; for excitatory coupling a mechanism of emerging and decaying synchronized clusters prevails.

Synchronization induced by temporal delays in pulse-coupled oscillators.

Guided by topological considerations, a new method is introduced to obtain optimal delay coordinates for data from chaotic dynamic systems. By determining simultaneously the minimal necessary embedding dimension as well as the proper delay time we achieve optimal reconstructions of attractors. This can be demonstrated, e.g., by reliable dimension estimations from limited data series.

Optimal Embeddings of Chaotic Attractors from Topological Considerations

We analyze the dynamics of pulse coupled oscillators depending on strength and delay of the interaction. For two oscillators, we derive return maps for subsequent phase differences, and construct phase diagrams for a broad range of parameters. In-phase synchronization proves stable for inhibitory coupling and unstable for excitatory coupling if the delay is not zero. If the coupling strength is high, additional regimes with marginally stable synchronization are found. Simulations with N@2 oscillators reveal a complex dynamics including spontaneous synchronization and desynchronization with excitatory coupling, and multistable phase clustering with inhibitory coupling. We simulate a continuous description of the system for N!‘ oscillators and demonstrate that these phenomena are independent of the size of the system. Phase clustering is shown to relate to stability and basins of attraction of fixed points in the return map of two oscillators. Our findings are generic in the sense that they qualitatively are robust with respect to modeling details. We demonstrate this using also pulses of finite rise time and the more realistic model by Hodgkin and Huxley which exhibits multistable synchronization as predicted from our analysis as well. @S1063-651X~98!09902-4#

Klaus Pawelzik

Papers

Neural networks with dynamic synapses

Quantifying the neighborhood preservation of self-organizing feature maps

Synchronization induced by temporal delays in pulse-coupled oscillators.

Optimal Embeddings of Chaotic Attractors from Topological Considerations

Delay-induced multistable synchronization of biological oscillators