9,177 research outputs found
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
Interpreting Adversarially Trained Convolutional Neural Networks
We attempt to interpret how adversarially trained convolutional neural
networks (AT-CNNs) recognize objects. We design systematic approaches to
interpret AT-CNNs in both qualitative and quantitative ways and compare them
with normally trained models. Surprisingly, we find that adversarial training
alleviates the texture bias of standard CNNs when trained on object recognition
tasks, and helps CNNs learn a more shape-biased representation. We validate our
hypothesis from two aspects. First, we compare the salience maps of AT-CNNs and
standard CNNs on clean images and images under different transformations. The
comparison could visually show that the prediction of the two types of CNNs is
sensitive to dramatically different types of features. Second, to achieve
quantitative verification, we construct additional test datasets that destroy
either textures or shapes, such as style-transferred version of clean data,
saturated images and patch-shuffled ones, and then evaluate the classification
accuracy of AT-CNNs and normal CNNs on these datasets. Our findings shed some
light on why AT-CNNs are more robust than those normally trained ones and
contribute to a better understanding of adversarial training over CNNs from an
interpretation perspective.Comment: To apper in ICML1
Gabor frames and deep scattering networks in audio processing
This paper introduces Gabor scattering, a feature extractor based on Gabor
frames and Mallat's scattering transform. By using a simple signal model for
audio signals specific properties of Gabor scattering are studied. It is shown
that for each layer, specific invariances to certain signal characteristics
occur. Furthermore, deformation stability of the coefficient vector generated
by the feature extractor is derived by using a decoupling technique which
exploits the contractivity of general scattering networks. Deformations are
introduced as changes in spectral shape and frequency modulation. The
theoretical results are illustrated by numerical examples and experiments.
Numerical evidence is given by evaluation on a synthetic and a "real" data set,
that the invariances encoded by the Gabor scattering transform lead to higher
performance in comparison with just using Gabor transform, especially when few
training samples are available.Comment: 26 pages, 8 figures, 4 tables. Repository for reproducibility:
https://gitlab.com/hararticles/gs-gt . Keywords: machine learning; scattering
transform; Gabor transform; deep learning; time-frequency analysis; CNN.
Accepted and published after peer revisio
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
The success of deep convolutional architectures is often attributed in part
to their ability to learn multiscale and invariant representations of natural
signals. However, a precise study of these properties and how they affect
learning guarantees is still missing. In this paper, we consider deep
convolutional representations of signals; we study their invariance to
translations and to more general groups of transformations, their stability to
the action of diffeomorphisms, and their ability to preserve signal
information. This analysis is carried by introducing a multilayer kernel based
on convolutional kernel networks and by studying the geometry induced by the
kernel mapping. We then characterize the corresponding reproducing kernel
Hilbert space (RKHS), showing that it contains a large class of convolutional
neural networks with homogeneous activation functions. This analysis allows us
to separate data representation from learning, and to provide a canonical
measure of model complexity, the RKHS norm, which controls both stability and
generalization of any learned model. In addition to models in the constructed
RKHS, our stability analysis also applies to convolutional networks with
generic activations such as rectified linear units, and we discuss its
relationship with recent generalization bounds based on spectral norms
A Comparative Evaluation of Approximate Probabilistic Simulation and Deep Neural Networks as Accounts of Human Physical Scene Understanding
Humans demonstrate remarkable abilities to predict physical events in complex
scenes. Two classes of models for physical scene understanding have recently
been proposed: "Intuitive Physics Engines", or IPEs, which posit that people
make predictions by running approximate probabilistic simulations in causal
mental models similar in nature to video-game physics engines, and memory-based
models, which make judgments based on analogies to stored experiences of
previously encountered scenes and physical outcomes. Versions of the latter
have recently been instantiated in convolutional neural network (CNN)
architectures. Here we report four experiments that, to our knowledge, are the
first rigorous comparisons of simulation-based and CNN-based models, where both
approaches are concretely instantiated in algorithms that can run on raw image
inputs and produce as outputs physical judgments such as whether a stack of
blocks will fall. Both approaches can achieve super-human accuracy levels and
can quantitatively predict human judgments to a similar degree, but only the
simulation-based models generalize to novel situations in ways that people do,
and are qualitatively consistent with systematic perceptual illusions and
judgment asymmetries that people show.Comment: Accepted to CogSci 2016 as an oral presentatio
- …