26,079 research outputs found
Teaching "Symmetry" in the Introductory Physics Curriculum
Modern physics is largely defined by fundamental symmetry principles and
Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning
students, thus missing an opportunity to reveal that the subject of physics is
as lively and contemporary as molecular biology, and as beautiful as the arts.
We prescribe a symmetry module to insert into the curriculum, of a week's
length.Comment: 15 pages, 4 figure
Building high-level features using large scale unsupervised learning
We consider the problem of building high-level, class-specific feature
detectors from only unlabeled data. For example, is it possible to learn a face
detector using only unlabeled images? To answer this, we train a 9-layered
locally connected sparse autoencoder with pooling and local contrast
normalization on a large dataset of images (the model has 1 billion
connections, the dataset has 10 million 200x200 pixel images downloaded from
the Internet). We train this network using model parallelism and asynchronous
SGD on a cluster with 1,000 machines (16,000 cores) for three days. Contrary to
what appears to be a widely-held intuition, our experimental results reveal
that it is possible to train a face detector without having to label images as
containing a face or not. Control experiments show that this feature detector
is robust not only to translation but also to scaling and out-of-plane
rotation. We also find that the same network is sensitive to other high-level
concepts such as cat faces and human bodies. Starting with these learned
features, we trained our network to obtain 15.8% accuracy in recognizing 20,000
object categories from ImageNet, a leap of 70% relative improvement over the
previous state-of-the-art
Interpretable Transformations with Encoder-Decoder Networks
Deep feature spaces have the capacity to encode complex transformations of
their input data. However, understanding the relative feature-space
relationship between two transformed encoded images is difficult. For instance,
what is the relative feature space relationship between two rotated images?
What is decoded when we interpolate in feature space? Ideally, we want to
disentangle confounding factors, such as pose, appearance, and illumination,
from object identity. Disentangling these is difficult because they interact in
very nonlinear ways. We propose a simple method to construct a deep feature
space, with explicitly disentangled representations of several known
transformations. A person or algorithm can then manipulate the disentangled
representation, for example, to re-render an image with explicit control over
parameterized degrees of freedom. The feature space is constructed using a
transforming encoder-decoder network with a custom feature transform layer,
acting on the hidden representations. We demonstrate the advantages of explicit
disentangling on a variety of datasets and transformations, and as an aid for
traditional tasks, such as classification.Comment: Accepted at ICCV 201
Learning with Algebraic Invariances, and the Invariant Kernel Trick
When solving data analysis problems it is important to integrate prior
knowledge and/or structural invariances. This paper contributes by a novel
framework for incorporating algebraic invariance structure into kernels. In
particular, we show that algebraic properties such as sign symmetries in data,
phase independence, scaling etc. can be included easily by essentially
performing the kernel trick twice. We demonstrate the usefulness of our theory
in simulations on selected applications such as sign-invariant spectral
clustering and underdetermined ICA
Crosslingual Document Embedding as Reduced-Rank Ridge Regression
There has recently been much interest in extending vector-based word
representations to multiple languages, such that words can be compared across
languages. In this paper, we shift the focus from words to documents and
introduce a method for embedding documents written in any language into a
single, language-independent vector space. For training, our approach leverages
a multilingual corpus where the same concept is covered in multiple languages
(but not necessarily via exact translations), such as Wikipedia. Our method,
Cr5 (Crosslingual reduced-rank ridge regression), starts by training a
ridge-regression-based classifier that uses language-specific bag-of-word
features in order to predict the concept that a given document is about. We
show that, when constraining the learned weight matrix to be of low rank, it
can be factored to obtain the desired mappings from language-specific
bags-of-words to language-independent embeddings. As opposed to most prior
methods, which use pretrained monolingual word vectors, postprocess them to
make them crosslingual, and finally average word vectors to obtain document
vectors, Cr5 is trained end-to-end and is thus natively crosslingual as well as
document-level. Moreover, since our algorithm uses the singular value
decomposition as its core operation, it is highly scalable. Experiments show
that our method achieves state-of-the-art performance on a crosslingual
document retrieval task. Finally, although not trained for embedding sentences
and words, it also achieves competitive performance on crosslingual sentence
and word retrieval tasks.Comment: In The Twelfth ACM International Conference on Web Search and Data
Mining (WSDM '19
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