Entropy landscape of solutions in the binary perceptron problem
Entropy landscape of solutions in the binary perceptron problem
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DOI：
10.1088/1751-8113/46/37/375002
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发表时间：
2013-04
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影响因子：
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通讯作者：
Haiping Huang;Haiping Huang;K. Y. Wong;Y. Kabashima
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文献类型：
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作者：
Haiping Huang;Haiping Huang;K. Y. Wong;Y. Kabashima
研究了二元感知器解空间的统计图像。二进制感知器通过一组二进制突触权重学习输入随机模式的随机分类。这种网络的学习是困难的，特别是当模式（约束）密度接近的容量，这应该是密切相关的解决方案空间的结构。的几何组织阐明的熵景观从一个参考配置和解决方案对分离的一个给定的汉明距离的解决方案空间。我们评估的熵在退火水平以及副本对称水平和平均场的结果证实了使用建议的消息传递算法的单实例的数值模拟。从第一个景观（随机配置作为参考），我们清楚地看到，随着更多的约束条件的添加，解决方案空间如何缩小。从解对的第二种景观出发，我们推导出解空间中聚集和冻结的共存。
The statistical picture of the solution space for a binary perceptron is studied. The binary perceptron learns a random classification of input random patterns by a set of binary synaptic weights. The learning of this network is difficult especially when the pattern (constraint) density is close to the capacity, which is supposed to be intimately related to the structure of the solution space. The geometrical organization is elucidated by the entropy landscape from a reference configuration and of solution-pairs separated by a given Hamming distance in the solution space. We evaluate the entropy at the annealed level as well as replica symmetric level and the mean field result is confirmed by the numerical simulations on single instances using the proposed message passing algorithms. From the first landscape (a random configuration as a reference), we see clearly how the solution space shrinks as more constraints are added. From the second landscape of solution-pairs, we deduce the coexistence of clustering and freezing in the solution space.