  A deep neural network of multiple nonlinear layers forms a large function
space, which can easily lead to overfitting when it encounters small-sample
data. To mitigate overfitting in small-sample classification, learning more
discriminative features from small-sample data is becoming a new trend. To this
end, this paper aims to find a subspace of neural networks that can facilitate
a large decision margin. Specifically, we propose the Orthogonal Softmax Layer
(OSL), which makes the weight vectors in the classification layer remain
orthogonal during both the training and test processes. The Rademacher
complexity of a network using the OSL is only $\frac{1}{K}$, where $K$ is the
number of classes, of that of a network using the fully connected
classification layer, leading to a tighter generalization error bound.
Experimental results demonstrate that the proposed OSL has better performance
than the methods used for comparison on four small-sample benchmark datasets,
as well as its applicability to large-sample datasets. Codes are available at:
https://github.com/dongliangchang/OSLNet.
