44 research outputs found
LDMNet: Low Dimensional Manifold Regularized Neural Networks
Deep neural networks have proved very successful on archetypal tasks for
which large training sets are available, but when the training data are scarce,
their performance suffers from overfitting. Many existing methods of reducing
overfitting are data-independent, and their efficacy is often limited when the
training set is very small. Data-dependent regularizations are mostly motivated
by the observation that data of interest lie close to a manifold, which is
typically hard to parametrize explicitly and often requires human input of
tangent vectors. These methods typically only focus on the geometry of the
input data, and do not necessarily encourage the networks to produce
geometrically meaningful features. To resolve this, we propose a new framework,
the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which
incorporates a feature regularization method that focuses on the geometry of
both the input data and the output features. In LDMNet, we regularize the
network by encouraging the combination of the input data and the output
features to sample a collection of low dimensional manifolds, which are
searched efficiently without explicit parametrization. To achieve this, we
directly use the manifold dimension as a regularization term in a variational
functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami
equation over a point cloud, which is solved by the point integral method
without increasing the computational complexity. We demonstrate two benefits of
LDMNet in the experiments. First, we show that LDMNet significantly outperforms
widely-used network regularizers such as weight decay and DropOut. Second, we
show that LDMNet can be designed to extract common features of an object imaged
via different modalities, which proves to be very useful in real-world
applications such as cross-spectral face recognition