论文标题
二元和三元神经网络的表现力
Expressive power of binary and ternary neural networks
论文作者
论文摘要
我们表明，具有三元重量的深度稀疏relu网络和具有二进制重量的深度relu网络可以在$ [0,1]^d $上近似$β$-Hölder的功能。另外，对于任何间隔$ [a，b）\ subset \ mathbb {r} $，$ [0,1]^d $上的连续函数可以通过depth $ 2 $的网络近似于具有二进制激活函数$ \ mathds $ \ mathds {1} _ {[a，b）} $。
We show that deep sparse ReLU networks with ternary weights and deep ReLU networks with binary weights can approximate $β$-Hölder functions on $[0,1]^d$. Also, for any interval $[a,b)\subset\mathbb{R}$, continuous functions on $[0,1]^d$ can be approximated by networks of depth $2$ with binary activation function $\mathds{1}_{[a,b)}$.
