论文标题
用梯度方法学习单个神经元
Learning a Single Neuron with Gradient Methods
论文作者
论文摘要
我们考虑使用标准梯度方法学习单个神经元$ x \mapstoσ（w^\ top x）$的基本问题。与以前的作品相反，该作品考虑了特定的（且不总是现实的）输入分布和激活功能$σ（\ cdot）$，我们询问在较温和的假设下是否可以达到更一般的结果。一方面，我们证明了有关分布和激活函数的一些假设。另一方面，我们在轻度假设下证明了积极的保证，这超出了迄今为止文献所研究的假设。我们还指出并研究进一步加强和推广我们的结果的挑战。
We consider the fundamental problem of learning a single neuron $x \mapstoσ(w^\top x)$ using standard gradient methods. As opposed to previous works, which considered specific (and not always realistic) input distributions and activation functions $σ(\cdot)$, we ask whether a more general result is attainable, under milder assumptions. On the one hand, we show that some assumptions on the distribution and the activation function are necessary. On the other hand, we prove positive guarantees under mild assumptions, which go beyond those studied in the literature so far. We also point out and study the challenges in further strengthening and generalizing our results.
