Jun Lee

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or Lp function with the widths dx+dy+2 and \maxdx+1,dy, respectively, where the target function maps a finite sequence of vectors in \mathbbRdx to a finite sequence of vectors in \mathbbRdy. We also compute the additional width required if the activation function is \tanh or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs.

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or Lp function with the widths dx+dy+2 and \maxdx+1,dy, respectively, where the target function maps a finite sequence of vectors in \mathbbRdx to a finite sequence of vectors in \mathbbRdy. We also compute the additional width required if the activation function is \tanh or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs.

This study investigates the impact of cheap talk on price and participant profits using a repeated Bertrand oligopoly experiment. During the first 10 rounds, participants are not allowed to communicate with each other. Twenty additional rounds are then played in which the participants can text with one another using an instant message system. Some groups are allowed to text before every round, some before every other round, some every third round, some every fourth round, and others only every fifth round. On average, when texting is allowed, groups attempt to collude to raise the price after being allowed to text. In summary, success in collusion with cheap talk is correlated with a combination of how often participants can text, the subject of their texts, and whether participants actually text when they can.

As modern epics of radical modernism, the major novels of John Dos Passos portray the history of modern American capitalism by means of their narrative politics of dialectical totalization, while giving rise to a utopian impulse. In other words, his novels are designed to present the historical portrayal of American capitalism as a whole by the dialectical totalization of their narrative politics and, at the same time, they articulate dialectically a utopian impulse in their sentiments of despair and disillusion. Thus, the theoretical perspective of my dissertation is based on the dialectical totality of history and its utopian impulse. As a modernist, Dos Passos employs the innovative forms and techniques of modernism for his epic-scale project of fictionalizing American capitalism during the early twentieth century. Moreover, he articulates the spirit of political radicalism with the dialectical form of utopian disillusion in his novels. After all, the dialectic as a philosophical method is an open window through which a glimpse of the utopian future flickers, not a closed, totalitarian conspiracy of which postmodernists unfairly accuse it. Therefore, it is indispensable for my study to discuss the tripartite mediation involving the innovative aesthetic forms and revolutionary spirit of radical modernism, the historical aspects of modern American capitalism, and the perspective of the dialectical totality of history and its immanent impulse toward a utopia. ;The major novels of Dos Passos attempt to portray the various historical frontiers of American capitalism through their narrative politics of dialectical totality. Three Soldiers represents the panoramic totality of World War I by its narrative style of contrast and juxtaposition, while Manhattan Transfer describes the metropolis, New York, as the physiognomy of high capitalism by its montage-shape narrative structure. However, it is the U.S.A. trilogy that fully realizes the utopian logic of the dialectical totality of history in its narrative politics. Through the dialectical politics of the four modernist narrative modes, the trilogy portrays the history of American capitalism during the first three decades of the twentieth century as dialectical totality. In consequence, U.S.A. is neither an elegy nor an epitaph for the ideals of the American past, but it is a radical hymn of faith that inspires in the reader the utopian resolution of American history by way of presenting entropic despair and disillusion