The fat-shattering dimension characterizes the uniform convergence property of real-valued functions. The state-of-the-art upper bounds feature a multiplicative squared logarithmic factor on the sample complexity, leaving an open gap with the existing lower bound. We provide an improved uniform convergence bound that closes this gap.

翻译：脂肪破碎维数刻画了实值函数的均匀收敛性质。目前最先进的上界在样本复杂度上包含一个乘性的平方对数因子，这与现有下界之间存在未解决的差距。我们提供了一个改进的均匀收敛界，填补了这一空白。