We study the influence of a variable neuronal threshold on fixed points and convergence rates of an associative neural network in the presence of noise. We allow a random distribution in the activity levels of the patterns stored, and a modification to the standard Hebbian learning rule is proposed for this purpose. There is a threshold at which the retrieval ability, including the average final overlap and the convergence rate, is optimized for patterns with a particular activity level at a given noise level. This type of selective attention to one class of patterns with a certain activity level may be obtained at the cost of reducing the retrieval ability of the network for patterns with different activity levels. The effects of a constant threshold independent of noise, time, and pattern are discussed. For high-(low-) activity patterns, the average final overlap is shown to be increased at high noise levels and decreased at low noise levels by a negative (positive) constant threshold, whereas a positive (negative) threshold always reduces the final average overlap. When the magnitude of the constant threshold exceeds a critical value, there is no retrieval. Rates of convergence towards the stored pattern with negative (positive) thresholds are greater than those with positive (negative) thresholds. These results are related to (de)sensitization and anesthesia. For certain threshold values and patterns with certain activity levels, hysteresis appears in the plot of the average final overlap versus the noise level, even for first order interactions. We make the analogy between the pattern-dependent neuronal threshold proposed in the present paper and the "task-related" modulation in neuronal excitability determined by cognitive factors, such as the attentional state of a higher animal. A constant threshold is associated with overall changes in neuronal excitability caused, e.g., by various drugs and physical injuries. Neurophysiological evidence of a dynamically variable neuronal threshold, such as accommodation and potentiation, is presented.
Anesthesia Animals