5,920 research outputs found
Self-Paced Learning: an Implicit Regularization Perspective
Self-paced learning (SPL) mimics the cognitive mechanism of humans and
animals that gradually learns from easy to hard samples. One key issue in SPL
is to obtain better weighting strategy that is determined by minimizer
function. Existing methods usually pursue this by artificially designing the
explicit form of SPL regularizer. In this paper, we focus on the minimizer
function, and study a group of new regularizer, named self-paced implicit
regularizer that is deduced from robust loss function. Based on the convex
conjugacy theory, the minimizer function for self-paced implicit regularizer
can be directly learned from the latent loss function, while the analytic form
of the regularizer can be even known. A general framework (named SPL-IR) for
SPL is developed accordingly. We demonstrate that the learning procedure of
SPL-IR is associated with latent robust loss functions, thus can provide some
theoretical inspirations for its working mechanism. We further analyze the
relation between SPL-IR and half-quadratic optimization. Finally, we implement
SPL-IR to both supervised and unsupervised tasks, and experimental results
corroborate our ideas and demonstrate the correctness and effectiveness of
implicit regularizers.Comment: 12 pages, 3 figure
Curriculum Dropout
Dropout is a very effective way of regularizing neural networks.
Stochastically "dropping out" units with a certain probability discourages
over-specific co-adaptations of feature detectors, preventing overfitting and
improving network generalization. Besides, Dropout can be interpreted as an
approximate model aggregation technique, where an exponential number of smaller
networks are averaged in order to get a more powerful ensemble. In this paper,
we show that using a fixed dropout probability during training is a suboptimal
choice. We thus propose a time scheduling for the probability of retaining
neurons in the network. This induces an adaptive regularization scheme that
smoothly increases the difficulty of the optimization problem. This idea of
"starting easy" and adaptively increasing the difficulty of the learning
problem has its roots in curriculum learning and allows one to train better
models. Indeed, we prove that our optimization strategy implements a very
general curriculum scheme, by gradually adding noise to both the input and
intermediate feature representations within the network architecture.
Experiments on seven image classification datasets and different network
architectures show that our method, named Curriculum Dropout, frequently yields
to better generalization and, at worst, performs just as well as the standard
Dropout method.Comment: Accepted at ICCV (International Conference on Computer Vision) 201
Simple to Complex Cross-modal Learning to Rank
The heterogeneity-gap between different modalities brings a significant
challenge to multimedia information retrieval. Some studies formalize the
cross-modal retrieval tasks as a ranking problem and learn a shared multi-modal
embedding space to measure the cross-modality similarity. However, previous
methods often establish the shared embedding space based on linear mapping
functions which might not be sophisticated enough to reveal more complicated
inter-modal correspondences. Additionally, current studies assume that the
rankings are of equal importance, and thus all rankings are used
simultaneously, or a small number of rankings are selected randomly to train
the embedding space at each iteration. Such strategies, however, always suffer
from outliers as well as reduced generalization capability due to their lack of
insightful understanding of procedure of human cognition. In this paper, we
involve the self-paced learning theory with diversity into the cross-modal
learning to rank and learn an optimal multi-modal embedding space based on
non-linear mapping functions. This strategy enhances the model's robustness to
outliers and achieves better generalization via training the model gradually
from easy rankings by diverse queries to more complex ones. An efficient
alternative algorithm is exploited to solve the proposed challenging problem
with fast convergence in practice. Extensive experimental results on several
benchmark datasets indicate that the proposed method achieves significant
improvements over the state-of-the-arts in this literature.Comment: 14 pages; Accepted by Computer Vision and Image Understandin
Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions
This study investigates the optimization aspects of imposing hard inequality
constraints on the outputs of CNNs. In the context of deep networks,
constraints are commonly handled with penalties for their simplicity, and
despite their well-known limitations. Lagrangian-dual optimization has been
largely avoided, except for a few recent works, mainly due to the computational
complexity and stability/convergence issues caused by alternating explicit dual
updates/projections and stochastic optimization. Several studies showed that,
surprisingly for deep CNNs, the theoretical and practical advantages of
Lagrangian optimization over penalties do not materialize in practice. We
propose log-barrier extensions, which approximate Lagrangian optimization of
constrained-CNN problems with a sequence of unconstrained losses. Unlike
standard interior-point and log-barrier methods, our formulation does not need
an initial feasible solution. Furthermore, we provide a new technical result,
which shows that the proposed extensions yield an upper bound on the duality
gap. This generalizes the duality-gap result of standard log-barriers, yielding
sub-optimality certificates for feasible solutions. While sub-optimality is not
guaranteed for non-convex problems, our result shows that log-barrier
extensions are a principled way to approximate Lagrangian optimization for
constrained CNNs via implicit dual variables. We report comprehensive weakly
supervised segmentation experiments, with various constraints, showing that our
formulation outperforms substantially the existing constrained-CNN methods,
both in terms of accuracy, constraint satisfaction and training stability, more
so when dealing with a large number of constraints
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