论文标题
分段线性感知中非线性激发的扩散
Proliferation of non-linear excitations in the piecewise-linear perceptron
论文作者
论文摘要
我们研究了连续非convex优化问题的能源景观的本地最小值，带有分段线性成本功能的球形感知器，并表明它们至关重要，很稳定，并且略有稳定，并显示了一系列伪造，奇异性和非线性兴奋，它们的特性似乎在同一杂物式的包装中都很困难。分段线性的感知问题似乎是最近在[1]中研究的纯线性感知到纯线感知问题的演变。它的成本函数包含两个非分析点，其中衍生物具有跳跃。相应地，在非凸/玻璃相中，这两个点在力分布中产生了四个伪胶囊，这也诱导了间隙分布中的四个功率定律。此外，人们可以定义等速度的扩展概念，并表明在此阶段局部的最小值再次是同层。我们认为，随着成本函数中非分析点的数量的增加，我们的结果自然而然地概括为更复杂的病例，而非线性激发的泛滥数量增加。
We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.
