Above are papers related to the following paper: [Paper_ID] Paper #1140548. 	[Title] Lending Direction to Neural Networks [Abstract] We present a general formulation for a network of stochastic directional units. This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values on a cyclic range, between 0 and 2 radians. This measure is appropriate to many domains, representing cyclic or angular values, e.g., wind direction, days of the week, phases of the moon. The state of each unit in a Directional-Unit Boltzmann Machine (DUBM) is described by a complex variable, where the phase component specifies a direction; the weights are also complex variables. We associate a quadratic energy function, and corresponding probability, with each DUBM configuration. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. In a mean-field approximation to a stochastic dubm, the phase component of a unit's state represents its mean direction, and the magnitude component specifies the degree of certainty associated with this direction. This combination of a value and a certainty provides additional representational power in a unit. We present a proof that the settling dynamics for a mean-field DUBM cause convergence to a free energy minimum. Finally, we describe a learning algorithm and simulations that demonstrate a mean-field DUBM's ability to learn interesting mappings. fl To appear in: Neural Networks. Please summarise all the given information.

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Paper #1140548 has the title `Lending Direction to Neural Networks  
` and the abstract `We present a general formulation for a network of stochastic directional units. This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values on a cyclic range, between 0 and 2 radians. This measure is appropriate to many domains, representing cyclic or angular values, e.g., wind direction, days of the week, phases of the moon. The state of each unit in a Directional-Unit Boltzmann Machine (DUBM) is described by a complex variable, where the phase component specifies a direction; the weights are also complex variables. We associate a quadratic energy function, and corresponding probability, with each DUBM configuration. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. In a mean-field approximation to a stochastic dubm, the phase component of a unit's state represents its mean direction, and the magnitude component specifies the degree of certainty associated with this direction. This combination of a value and a certainty provides additional representational power in a unit. We present a proof that the settling dynamics for a mean-field DUBM cause convergence to a free energy minimum. Finally, we describe a learning algorithm and simulations that demonstrate a mean-field DUBM's ability to learn interesting mappings. fl To appear in: Neural Networks.
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Question: Which category should Paper #1140548 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1140548 has the title `Lending Direction to Neural Networks  
` and the abstract `We present a general formulation for a network of stochastic directional units. This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values on a cyclic range, between 0 and 2 radians. This measure is appropriate to many domains, representing cyclic or angular values, e.g., wind direction, days of the week, phases of the moon. The state of each unit in a Directional-Unit Boltzmann Machine (DUBM) is described by a complex variable, where the phase component specifies a direction; the weights are also complex variables. We associate a quadratic energy function, and corresponding probability, with each DUBM configuration. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. In a mean-field approximation to a stochastic dubm, the phase component of a unit's state represents its mean direction, and the magnitude component specifies the degree of certainty associated with this direction. This combination of a value and a certainty provides additional representational power in a unit. We present a proof that the settling dynamics for a mean-field DUBM cause convergence to a free energy minimum. Finally, we describe a learning algorithm and simulations that demonstrate a mean-field DUBM's ability to learn interesting mappings. fl To appear in: Neural Networks.
`.
Question: Which category should Paper #1140548 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks