Rainer Malaka

Kinetic models of odor transduction implemented as artificial neural networks

We present a formal model of olfactory transduction corresponding to the biochemical reaction cascade found in chemosensory neurons. It assumes that odorants bind to receptor proteins which, in turn, activate transducer mechanisms corresponding to second messenger-mediated processes. The model is reformulated as a mathematically equivalent artificial neural network (ANN). To enable comparison of the computational power of our model, previously suggested models of chemosensory transduction are also presented in ANN versions. In ANNs, certain biological parameters, such as rate constants and affinities, are transformed into weights that can be fitted by training with a given experimental data set. After training, these weights do not necessarily equal the real biological parameters, but represent a set of values that is sufficient to simulate an experimental set of data. We used ANNs to simulate data recorded from bee subplacodes and compare the capacity of our model with ANN versions of other models. Receptor neurons of the nonpheromonal, general odor-processing subsystem of the honeybee are broadly tuned, have overlapping response spectra, and show highly nonlinear concentration dependencies and mixture interactions, i.e., synergistic and inhibitory effects. Our full model alone has the necessary complexity to simulate these complex response characteristics. To account for the complex response characteristics of honeybee receptor neurons, we suggest that several different receptor protein types and at least two second messenger systems are necessary that may interact at various levels of the transduction cascade and may eventually have opposing effects on receptor neuron excitability.

Real-time models of classical conditioning

Real-time models of classical conditioning simulate features of associative learning including its dependence on the timing of stimuli. We present the Sutton/Barto model, the TD model, the CP model, the drive-reinforcement model, and the SOP model in a framework of reinforcement learning rules. The role of eligibility and reinforcement is analyzed and the ability of the models to simulate time-dependent learning (e.g. inhibitory backward conditioning) and other conditioning phenomena is also compared. A new model is introduced, that is mathematically simple, and overcomes weaknesses of the other models. This model combines the two antagonistic US traces of the SOP model with the reinforcement term of the TD model.

Interactive Activation and Competition

Das Netzmodell Interactive Activation and Competition (IAC) geht auf McClelland und Rumelhart zuruck. Eine herausragende Anwendung von IAC ist die Modellierung der menschlichen Fahigkeit geschriebene Worter schneller zu erkennen als einzelne Buchstaben, und bekannte Worter schneller als unbekannte. IAC-Netze konnen jedoch nicht aus Beispielen lernen. Die Netztopologie und auch die Verbindungsgewichte zwischen den Neuronen mussen „von Hand“eingestellt werden.

Solving nonlinear optimization problems using networks of spiking neurons

Most artificial neural networks used in practical applications are based on simple neuron types in a multi-layer architecture. Here, we propose to solve optimization problems using a fully recurrent network of spiking neurons mimicking the response behavior of biological neurons. Such networks can compute a series of different solutions for a given problem and converge into a periodical sequence of such solutions. The goal of this paper is to prove that neural networks like the SRM (Spike Response Model) are able to solve nonlinear optimization problems. We demonstrate this for the traveling salesman problem. Our network model is able to compute multiple solutions and can use its dynamics to leave local minima in which classical models would be stuck. For adapting the model, we introduce a suitable network architecture and show how to encode the problem directly into the network weights.

Transformation of Neural Oscillators

In this paper we outline a method of model transformation for neural oscillators defined by a set of ordinary differential equations and a non-linearity. The transformation sets the parameters such that the transformed oscillators have the same phase and frequency in the state of harmonic balance. In simulations we show that these transformed neural oscillators not only behave equivalently in the state of harmonic balance of one single oscillator, but also mainly equivalent in stationary, oscillatory or chaotic activation states of networks of such elements.

Equivalent dynamics in different neural oscillator models

This paper introduces a method of model transformation for neural oscillators defined by a set of ordinary differential equations and a nonlinearity and gives an example for two popular neural oscillator models. The method finds the parameters of one oscillator model such that its dynamics are equivalent to that of another oscillator model. Although this equivalence is obtained using the assumption of harmonic oscillations, it can be shown in simulations that these transformed neural oscillators not only behave equivalently in the state of harmonic balance, but also mainly equivalent in stationary and chaotic activation states. Moreover, even networks consisting of those oscillators show equivalent dynamics under very different dynamic regimes.

Das symmetrische Hopfield-Modell

J. J. Hopfield schlug 1982 ein sehr popular gewordenes Modell eines neuronalen Assoziativspeichers vor. Dabei soll folgende Aufgabe gelost werden: In einem Netz sollen p vorgegebene Muster (N-stellige Binarvektoren uber {+1, -1}) gespeichert und wieder abgerufen werden. Dies soll auf fehlertolerante Art geschehen, d.h. ein verrauschtes oder unvollstandiges Muster soll immer moglichst gut wiedererkannt werden.

Optimieren mit neuronalen Netzen

Beim Optimieren mit neuronalen Netzen werden Probleme so in „Energie“-Funktionen kodiert, das deren Minimum gerade einer optimalen Losung entspricht. Solche Energiefunktionen haben wir bereits beim symmetrischen Hopfield-Modell kennengelernt. Beim Optimieren mit neuronalen Netzen soll jetzt versucht werden, anstelle von Mustern die Losungen von Optimierungsproblemen in die lokalen Minima der Energiefunktion eines neuronalen Netzes zu legen. Das hier verwendete Neuronenmodell ist ein vereinfachtes Hopfield-Tank-Modell. Das ursprungliche Modell wurde als analoges elektronisches Netz von J. J. Hopfield und D. W. Tank vorgeschlagen.

Assoziative Speicher - Palm-Netze

Bei assoziativer Speicherung wird nicht uber Adressen auf die gespeicherte Information zugegriffen, sondern diese uber eine Funktion berechnet, der man an bestimmten Stellen die Werte vorschreibt. Ahnlich wie bei der Interpolation eines Polynoms lernt der Speicher p Paare (x k,y k) von Schlusseln x k und Werten y k und baut dann eine Gesamtfunktion auf, die nach Moglichkeit zu jedem eingegebenen Schlussel x k die richtige Antwort y k findet. Man erwartet dabei, das nicht nur die gelernten Schlussel x k erkannt werden, sondern auch fur Schlussel x, die einem x k ahnlich sind, Ergebnisse geliefert werden, die zu y k ahnlich (interpolativ) oder nach Moglichkeit auch gleich sind (accretiv).