13,055 research outputs found
Emergence of Invariance and Disentanglement in Deep Representations
Using established principles from Statistics and Information Theory, we show
that invariance to nuisance factors in a deep neural network is equivalent to
information minimality of the learned representation, and that stacking layers
and injecting noise during training naturally bias the network towards learning
invariant representations. We then decompose the cross-entropy loss used during
training and highlight the presence of an inherent overfitting term. We propose
regularizing the loss by bounding such a term in two equivalent ways: One with
a Kullbach-Leibler term, which relates to a PAC-Bayes perspective; the other
using the information in the weights as a measure of complexity of a learned
model, yielding a novel Information Bottleneck for the weights. Finally, we
show that invariance and independence of the components of the representation
learned by the network are bounded above and below by the information in the
weights, and therefore are implicitly optimized during training. The theory
enables us to quantify and predict sharp phase transitions between underfitting
and overfitting of random labels when using our regularized loss, which we
verify in experiments, and sheds light on the relation between the geometry of
the loss function, invariance properties of the learned representation, and
generalization error.Comment: Deep learning, neural network, representation, flat minima,
information bottleneck, overfitting, generalization, sufficiency, minimality,
sensitivity, information complexity, stochastic gradient descent,
regularization, total correlation, PAC-Baye
A commentary on "The now-or-never bottleneck: a fundamental constraint on language", by Christiansen and Chater (2016)
In a recent article, Christiansen and Chater (2016) present a fundamental
constraint on language, i.e. a now-or-never bottleneck that arises from our
fleeting memory, and explore its implications, e.g., chunk-and-pass processing,
outlining a framework that promises to unify different areas of research. Here
we explore additional support for this constraint and suggest further
connections from quantitative linguistics and information theory
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