The online incremental gradient (or backpropagation) algorithm is widely considered to be the fastest method for solving large-scale neural-network (NN) learning problems. In contrast, we show that an appropriately implemented iterative batch-mode (or block-mode) learning method can be much faster. For example, it is three times faster in the UCI letter classification problem (26 outputs, 16,000 data items, 6,066 parameters with a two-hidden-layer multilayer perceptron) and 353 times faster in a nonlinear regression problem arising in color recipe prediction (10 outputs, 1,000 data items, 2,210 parameters with a neuro-fuzzy modular network). The three principal innovative ingredients in our algorithm are the following: First, we use scaled trust-region regularization with inner-outer iteration to solve the associated "overdetermined" nonlinear least squares problem, where the inner iteration performs a truncated (or inexact) Newton method. Second, we employ Pearlmutter's implicit sparse Hessian matrix-vector multiply algorithm to construct the Krylov subspaces used to solve for the truncated Newton update. Third, we exploit sparsity (for preconditioning) in the matrices resulting from the NNs having many outputs.

Loopy belief propagation (BP) has been successfully used in a number of difficult graphical models to find the most probable configuration of the hidden variables. In applications ranging from protein folding to image analysis one would like to find not just the best configuration but rather the top M. While this problem has been solved using the junction tree formalism, in many real world problems the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations when exact inference is impossible. We start by developing a new exact inference algorithm for calculating the best configurations that uses only max-marginals. For approximate inference, we replace the max-marginals with the beliefs calculated using max-product BP and generalized BP. We show empirically that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.

Belief propagation on cyclic graphs is an efficient algorithm for computing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. In this paper we propose two new algorithms for approximating joint probabilities of arbitrary pairs of nodes and prove a number of desirable properties that these estimates fulfill. The first algorithm is a propagation algorithm which is shown to converge if belief propagation converges to a stable fixed point. The second algorithm is based on matrix inversion. Experiments compare a number of competing methods.

Spike timing plasticity (STDP) is a special form of synaptic plasticity where the relative timing of post-and presynaptic activity determines the change of the synaptic weight. On the postsynaptic side, active backpropagating spikes in dendrites seem to play a crucial role in the induction of spike timing dependent plasticity. We argue that postsynaptically the temporal change of the membrane potential determines the weight change. Coming from the presynaptic side induction of STDP is closely related to the activation of NMDA channels. Therefore, we will calculate analytically the change of the synaptic weight by correlating the derivative of the membrane potential with the activity of the NMDA channel.

The online incremental gradient (or backpropagation) algorithm is widely considered to be the fastest method for solving large-scale neural-network (NN) learning problems. In contrast, we show that an appropriately implemented iterative batch-mode (or block-mode) learning method can be much faster. For example, it is three times faster in the UCI letter classification problem (26 outputs, 16,000 data items, 6,066 parameters with a two-hidden-layer multilayer perceptron) and 353 times faster in a nonlinear regression problem arising in color recipe prediction (10 outputs, 1,000 data items, 2,210 parameters with a neuro-fuzzy modular network). The three principal innovative ingredients in our algorithm are the following: First, we use scaled trust-region regularization with inner-outer iteration to solve the associated "overdetermined" nonlinear least squares problem, where the inner iteration performs a truncated (or inexact) Newton method. Second, we employ Pearlmutter's implicit sparse Hessian matrix-vector multiply algorithm to construct the Krylov subspaces used to solve for the truncated Newton update. Third, we exploit sparsity (for preconditioning) in the matrices resulting from the NNs having many outputs.

Loopy belief propagation (BP) has been successfully used in a number of difficult graphical models to find the most probable configuration of the hidden variables. In applications ranging from protein folding to image analysis one would like to find not just the best configuration but rather the top M. While this problem has been solved using the junction tree formalism, in many real world problems the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations when exact inference is impossible. We start by developing a new exact inference algorithm for calculating the best configurations that uses only max-marginals. For approximate inference, we replace the max-marginals with the beliefs calculated using max-product BP and generalized BP. We show empirically that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.

Belief propagation on cyclic graphs is an efficient algorithm for computing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. In this paper we propose two new algorithms for approximating joint probabilities of arbitrary pairs of nodes and prove a number of desirable properties that these estimates fulfill. The first algorithm is a propagation algorithm which is shown to converge if belief propagation converges to a stable fixed point. The second algorithm is based on matrix inversion. Experiments compare a number of competing methods.

A mixed-signal image filtering VLSI has been developed aiming at real-time generation of edge-based image vectors for robust image recognition. A four-stage asynchronous median detection architecture based on analog digital mixed-signal circuits has been introduced to determine the threshold value of edge detection, the key processing parameter in vector generation. As a result, a fully seamless pipeline processing from threshold detection to edge feature map generation has been established. A prototype chip was designed in a 0.35-µm double-polysilicon three-metal-layer CMOS technology and the concept was verified by the fabricated chip. The chip generates a 64-dimension feature vector from a 64x64-pixel gray scale image every 80µsec.

Spike timing plasticity (STDP) is a special form of synaptic plasticity where the relative timing of post-and presynaptic activity determines the change of the synaptic weight. On the postsynaptic side, active backpropagating spikes in dendrites seem to play a crucial role in the induction of spike timing dependent plasticity. We argue that postsynaptically the temporal change of the membrane potential determines the weight change. Coming from the presynaptic side induction of STDP is closely related to the activation of NMDA channels. Therefore, we will calculate analytically the change of the synaptic weight by correlating the derivative of the membrane potential with the activity of the NMDA channel.

Significant progress in clustering has been achieved by algorithms that are based on pairwise affinities between the datapoints. In particular, spectral clustering methods have the advantage of being able to divide arbitrarily shaped clusters and are based on efficient eigenvector calculations. However, spectral methods lack a straightforward probabilistic interpretation which makes it difficult to automatically set parameters using training data. In this paper we use the previously proposed typical cut framework for pairwise clustering. We show an equivalence between calculating the typical cut and inference in an undirected graphical model. We show that for clustering problems with hundreds of datapoints exact inference may still be possible. For more complicated datasets, we show that loopy belief propagation (BP) and generalized belief propagation (GBP) can give excellent results on challenging clustering problems. We also use graphical models to derive a learning algorithm for affinity matrices based on labeled data.