All reports by Author Michael Schmitt:

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TR04-075
| 21st July 2004
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Michael Schmitt#### Some dichotomy theorems for neural learning problems

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TR04-033
| 23rd January 2004
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Michael Schmitt#### On the sample complexity of learning for networks of spiking neurons with nonlinear synaptic interactions

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TR01-045
| 26th April 2001
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Michael Schmitt#### Neural Networks with Local Receptive Fields and Superlinear VC Dimension

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TR00-086
| 26th September 2000
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Michael Schmitt#### On the Complexity of Computing and Learning with Multiplicative Neural Networks

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TR00-002
| 23rd December 1999
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Michael Schmitt#### Lower Bounds on the Complexity of Approximating Continuous Functions by Sigmoidal Neural Networks

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TR99-005
| 21st December 1998
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Michael Schmitt#### On the Sample Complexity for Nonoverlapping Neural Networks

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TR97-049
| 22nd October 1997
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Michael Schmitt#### On the Complexity of Learning for Spiking Neurons with Temporal Coding

Michael Schmitt

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.

...
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Michael Schmitt

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 ...
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Michael Schmitt

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 ...
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Michael Schmitt

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 ...
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Michael Schmitt

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 ...
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Michael Schmitt

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. ...
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Michael Schmitt

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 ...
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