The computational complexity of learning from binary examples is investigated for linear threshold neurons. We introduce combinatorial measures that create classes of infinitely many learning problems with sample restrictions. We analyze how the complexity of these problems depends on the values for the measures. The results are established as dichotomy ... more >>>

We study networks of spiking neurons that use the timing of pulses to encode information. Nonlinear interactions model the spatial groupings of synapses on the dendrites and describe the computations performed at local branches. We analyze the question of how many examples these networks must receive during learning to be ... more >>>

Local receptive field neurons comprise such well-known and widely used unit types as radial basis function neurons and neurons with center-surround receptive field. We study the Vapnik-Chervonenkis (VC) dimension of feedforward neural networks with one hidden layer of these units. For several variants of local receptive field neurons we show ... more >>>

In a great variety of neuron models neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks which contain units that multiply their inputs instead of summing them and, thus, allow inputs to interact nonlinearly. The class of multiplicative networks comprises such widely known ... more >>>

We calculate lower bounds on the size of sigmoidal neural networks that approximate continuous functions. In particular, we show that for the approximation of polynomials the network size has to grow as $\Omega((\log k)^{1/4})$ where $k$ is the degree of the polynomials. This bound is valid for any input dimension, ... more >>>

A neural network is said to be nonoverlapping if there is at most one edge outgoing from each node. We investigate the number of examples that a learning algorithm needs when using nonoverlapping neural networks as hypotheses. We derive bounds for this sample complexity in terms of the Vapnik-Chervonenkis dimension. ... more >>>

Spiking neurons are models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal pattern of their activity. In a network of spiking neurons a new set of parameters becomes relevant which has no counterpart in traditional neural network models: the ... more >>>