Convolutional networks almost always incorporate some form of spatial pooling, and very often it is α × α max-pooling with α = 2. Max-pooling act on the hidden layers of the network, reducing their size by an integer multiplicative factor α. The amazing by-product of discarding 75% of your data is that you build into the network a degree of invariance with respect to translations and elastic distortions. However, if you simply alternate convolutional layers with max-pooling layers, performance is limited due to the rapid reduction in spatial size, and the disjoint nature of the pooling regions. We have formulated a fractional version of maxpooling where α is allowed to take non-integer values. Our version of max-pooling is stochastic as there are lots of different ways of constructing suitable pooling regions. We find that our form of fractional max-pooling reduces overfitting on a variety of datasets: for instance, we improve on the state of the art for CIFAR-100 without even using dropout.
Political powersharing arrangements serve three purposes: to give all relevant groups access to the most important political decisions; to partition the policy process, thereby granting groups autonomy in their own homeland and on issues of special concern; and to constrain political power-holders from abusing their authority at the expense of any group. We introduce a new global dataset on a broad range of political powersharing institutions, 1975-2010. As posited theoretically, we show that political powersharing statistically disaggregate into three component types: inclusive, dispersive, and constraining institutions. Existing literature associates powersharing with democracy as well as with civil conflict resolution. We find differences between the types of political powersharing institutions correlated with electoral democracy and those prevalent in post-conflict states. Inclusive powersharing institutions are common in post-conflict states but least strongly associated with electoral democracy. Conversely, constraining institutions, which are comparatively rare in states with current or recent civil conflicts, are highly correlated with electoral democracy.
Democracy is often fragile, especially in states recovering from civil conflict. To protect emerging democracies, many scholars and practitioners recommend political powersharing institutions, which aim to safeguard minority group interests. Yet there is little empirical research on whether powersharing promotes democratic survival, and some concern that it limits electoral accountability. To fill this gap, we differentiate between inclusive, dispersive, and constraining powersharing institutions and analyze their effects on democratic survival from 1975 to 2015 using a global dataset. We find sharp distinctions across types of powersharing and political context. Inclusive powersharing, such as ethnic quotas, promotes democratic survival only in post-conflict settings. In contrast, dispersive institutions such as federalism tend to destabilize post-conflict democracies. Only constraining powersharing consistently facilitates democratic survival regardless of recent conflict. Institution-builders and international organizations should therefore prioritize institutions that constrain leaders, including independent judiciaries, civilian control of the armed forces, and constitutional protections of individual and group rights.
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