自我种植：在粗糙的景观中挖洞
Self-planting: digging holes in rough landscapes
摘要：
受经济学中潜在应用的启发，我们研究了一个简单的动态方案，以产生连续变量优化问题的种植解决方案。我们认为感知机模型作为一个原型模型。从随机输入模式和感知器权重开始，我们通过梯度下降找到局部最优的权重分配;然后删除错误分类的模式（如果有的话），并将其替换为新的随机提取的模式。这个“移除和替换”过程被迭代，直到实现完美的分类。我们称这个过程为“自我种植”，因为“种植”状态不是预先分配的，而是权重和模式共同进化的结果。我们发现一个算法的相变分离的区域中，自我种植有效地实现了从一个区域中，它需要在系统大小的指数时间。我们推测，这种转变可能存在于一个广泛的类类似的问题。
英文摘要：
Motivated by a potential application in economics, we investigate a simple dynamical scheme to produce planted solutions in optimization problems with continuous variables. We consider the perceptron model as a prototypical model. Starting from random input patterns and perceptron weights, we find a locally optimal assignment of weights by gradient descent; we then remove misclassified patterns (if any), and replace them by new, randomly extracted patterns. This "remove and replace" procedure is iterated until perfect classification is achieved. We call this procedure "self-planting" because the "planted" state is not pre-assigned but results from a co-evolution of weights and patterns. We find an algorithmic phase transition separating a region in which self-planting is efficiently achieved from a region in which it takes exponential time in the system size. We conjecture that this transition might exist in a broad class of similar problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
