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In the theory of artificial neural networks winnertakeall networks are a case of competitive learning in recurrent neural networks. Output nodes in the network mutually inhibit each other, while simultaneously activating themselves through reflexive connections. After some time, only one node in the output layer will be active, namely the one corresponding to the strongest input. Thus the network uses nonlinear inhibition to pick out the largest of a set of inputs. Winnertakeall is a general computational primitive that can be implemented using different types of neural network models, including both continuoustime and spiking networks (Grossberg, 1973; Oster et al. 2009).
Winnertakeall networks are commonly used in computational models of the brain, particularly for distributed decisionmaking in the cortex. Important examples include hierarchical models of vision (Riesenhuber et al. 1999), and models of selective attention and recognition (Carpenter and Grossberg, 1987; Itti et al. 1998). They are also common in artificial neural networks and neuromorphic analog VLSI circuits. It has been formally proven that the winnertakeall operation is computationally powerful compared to other nonlinear operations, such as thresholding (Maass 2000).
A simple, but popular CMOS winnertakeall circuit is shown on the right. This circuit was originally proposed by Lazzaro et al. (1989) using MOS transistors biased to operate in the weakinversion or subthreshold regime. In the particular case shown there are only two inputs (I_{IN,1} and I_{IN,2}), but the circuit can be easily extended to multiple inputs in a straightforward way. It operates on continuoustime input signals (currents) in parallel, using only two transistors per input. In addition, the bias current I_{BIAS} is set by a single global transistor that is common to all the inputs.
The largest of the input currents sets the common potential V_{C}. As a result, the corresponding output carries almost all the bias current, while the other outputs have currents that are close to zero. Thus, the circuit selects the larger of the two input currents, i.e., if I_{IN,1} > I_{IN,2}, we get I_{OUT,1} = I_{BIAS} and I_{OUT,2} = 0. Similarly, if I_{IN,2} > I_{IN,1}, we get I_{OUT,1} = 0 and I_{OUT,2} = I_{BIAS}.
A SPICEbased DC simulation of the CMOS winnertakeall circuit in the twoinput case is shown on the right. As shown in the top subplot, the input I_{IN,1} was fixed at 6nA, while I_{IN,2} was linearly increased from 0 to 10nA. The bottom subplot shows the two output currents. As expected, the output corresponding to the larger of the two inputs carries the entire bias current (10nA in this case), forcing the other output current nearly to zero.
In stereo matching algorithms, following the taxonomy proposed by Scharstein et al. (IJCV 2002), winnertakeall is a local method for disparity computation. Adopting a winnertakeall strategy, the disparity associated with the minimum or maximum cost value is selected at each pixel.
It is axiomatic that in the electronic commerce market, early dominant players such as AOL or Yahoo! get most of the rewards. By 1998, one study found the top 5% of all web sites garnered more than 74% of all traffic.
The winner take all hypothesis suggests that once a technology or a firm gets ahead, it will do better and better over time, whereas lagging technology and firms will fall further behind.
