Correlation of internal representations in feed-forward neural networks

Feed-forward multilayer neural networks implementing random input-output mappings develop characteristic correlations between the activity of their hidden nodes which are important for the understanding of the storage and generalization performance of the network. It is shown how these correlations can be calculated from the joint probability distribution of the aligning fields at the hidden units for arbitrary decoder function between hidden layer and output. Explicit results are given for the parity-, and-, and committee-machines with arbitrary number of hidden nodes near saturation.Comment: 6 pages, latex, 1 figur

Evidence for Indonesian Throughflow slowdown during Heinrich events 3-5

We present sea surface and upper thermocline temperature records (60-100 year temporal resolution) spanning marine isotope stage 3 (similar to 24-62 ka B. P.) from International Marine Global Change Study core MD01-2378 (121 degrees 47.27'E and 13 degrees 04.95'S; 1783 m water depth) located in the outflow area of the Indonesian Throughflow within the Timor Sea. Stable isotopes and Mg/Ca of the near-surface-dwelling planktonic foraminifer Globigerinoides ruber (white) and the upper thermocline-dwelling Pulleniatina obliquiloculata reveal rapid changes in the thermal structure of the upper ocean during Heinrich events. Thermocline warming and increased delta O-18(seawater) (P. obliquiloculata record) during Heinrich events 3, 4, and 5 reflect weakening of the relatively cool and fresh thermocline flow and reduced export of less saline water from the North Pacific and Indonesian Seas to the tropical Indian Ocean. Three main factors influenced Indonesian Throughflow variability during marine isotope stage 3: (1) global slowdown in thermohaline circulation during Heinrich events triggered by Northern Hemisphere cooling, (2) increased freshwater export from the Java Sea into the Indonesian Throughflow controlled by rising sea level from similar to 60 to 47 ka, and (3) insolation-related changes in the Australasian monsoon with associated migration of hydrological fronts between Indian Ocean- and Indonesian Throughflow-derived water masses at similar to 46-40 ka

A canonical ensemble approach to graded-response perceptrons

Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear and quadratic error measure, corresponding to the perceptron respectively the adaline learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated.Comment: 26 pages, 10 ps figure

Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks

The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical extremely diluted network. Capacity-gain parameter phase diagrams are obtained for the Q=3, Q=4 and $Q=\infty$ state networks with uniformly distributed patterns of low activity in order to search for the effects of a gradual dilution of the synapses. It is shown that enlarged regions of continuous changeover into a region of optimal performance are obtained for finite stochastic noise and small but finite connectivity. The de Almeida-Thouless lines of stability are obtained for arbitrary connectivity, and the resulting phase diagrams are used to draw conclusions on the behavior of symmetrically diluted networks with other pattern distributions of either high or low activity.Comment: 21 pages, revte