Storage capacity in symmetric binary perceptrons
Storage capacity in symmetric binary perceptrons
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DOI：
10.1088/1751-8121/ab227a
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发表时间：
2019-07-19
影响因子：
2.1
通讯作者：
Zdeborova, Lenka
中科院分区：
文献类型：
--
作者：
Aubin, Benjamin;Perkins, Will;Zdeborova, Lenka
我们研究的问题，确定的二进制感知器的两个变种的问题，相应的约束是对称的能力。我们称这些变体为矩形二进制感知器（RPB）和u函数二进制感知器（UBP）。我们表明，与通常的阶跃函数二进制感知器不同，在这些对称情况下的临界容量由参数空间的大区域中的退火计算给出（对于所有矩形约束和足够窄的u函数约束，K < K*）。我们证明了这一事实（在两个自然的假设下）使用第一和第二时刻的方法。我们进一步使用二阶矩方法来推测，对称二进制感知器的解决方案是组织在一个所谓的冻结IRSB结构，而不使用副本的方法。然后，我们使用副本方法来估计UBP情况下的容量阈值时，u函数是宽K > K*。我们的结论是，完整的步骤复制对称性破缺将不得不进行评估，以获得在这种情况下的确切容量。
We study the problem of determining the capacity of the binary perceptron for two variants of the problem where the corresponding constraint is symmetric. We call these variants the rectangle-binary-perceptron (RPB) and the u-function-binary-perceptron (UBP). We show that, unlike for the usual stepfunction-binary-perceptron, the critical capacity in these symmetric cases is given by the annealed computation in a large region of parameter space (for all rectangular constraints and for narrow enough u-function constraints, K < K*). We prove this fact (under two natural assumptions) using the first and second moment methods. We further use the second moment method to conjecture that solutions of the symmetric binary perceptrons are organized in a so-called frozen- IRSB structure, without using the replica method. We then use the replica method to estimate the capacity threshold for the UBP case when the u-function is wide K > K*. We conclude that full-step-replica-symmetry breaking would have to be evaluated in order to obtain the exact capacity in this case.