2,178 research outputs found
A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets
Results of Smale (1957) and Dugundji (1969) allow to compare the homotopy
groups of two topological spaces and whenever a map with
strong connectivity conditions on the fibers is given. We apply similar
techniques in o-minimal expansions of fields to compare the o-minimal homotopy
of a definable set with the homotopy of some of its bounded hyperdefinable
quotients . Under suitable assumption, we show that and . As a special case,
given a definably compact group, we obtain a new proof of Pillay's group
conjecture ")" largely independent of the
group structure of . We also obtain different proofs of various comparison
results between classical and o-minimal homotopy.Comment: 24 page
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
The Information Complexity of Learning Tasks, their Structure and their Distance
We introduce an asymmetric distance in the space of learning tasks, and a
framework to compute their complexity. These concepts are foundational for the
practice of transfer learning, whereby a parametric model is pre-trained for a
task, and then fine-tuned for another. The framework we develop is
non-asymptotic, captures the finite nature of the training dataset, and allows
distinguishing learning from memorization. It encompasses, as special cases,
classical notions from Kolmogorov complexity, Shannon, and Fisher Information.
However, unlike some of those frameworks, it can be applied to large-scale
models and real-world datasets. Our framework is the first to measure
complexity in a way that accounts for the effect of the optimization scheme,
which is critical in Deep Learning
Thromboprophylaxis in day surgery
AbstractMany patients undergoing day surgery are at low-risk of venous thromboembolic events. However, given that pulmonary embolism is the most common preventable cause of hospital death, the risk-benefit profile of thromboprophylaxis should be accurately balanced. In this narrative review, we will briefly discuss some topics of thromboprohylaxis in ambulatory surgical procedures: venous thromboembolic risk stratification, venous thromboembolic risk during laparoscopic surgery, use of antithrombotic drugs in case of neuraxial anesthesia/analgesia, American College of Chest Physicians recommendations for thromboprophylaxis
Critical Learning Periods for Multisensory Integration in Deep Networks
We show that the ability of a neural network to integrate information from
diverse sources hinges critically on being exposed to properly correlated
signals during the early phases of training. Interfering with the learning
process during this initial stage can permanently impair the development of a
skill, both in artificial and biological systems where the phenomenon is known
as critical learning period. We show that critical periods arise from the
complex and unstable early transient dynamics, which are decisive of final
performance of the trained system and their learned representations. This
evidence challenges the view, engendered by analysis of wide and shallow
networks, that early learning dynamics of neural networks are simple, akin to
those of a linear model. Indeed, we show that even deep linear networks exhibit
critical learning periods for multi-source integration, while shallow networks
do not. To better understand how the internal representations change according
to disturbances or sensory deficits, we introduce a new measure of source
sensitivity, which allows us to track the inhibition and integration of sources
during training. Our analysis of inhibition suggests cross-source
reconstruction as a natural auxiliary training objective, and indeed we show
that architectures trained with cross-sensor reconstruction objectives are
remarkably more resilient to critical periods. Our findings suggest that the
recent success in self-supervised multi-modal training compared to previous
supervised efforts may be in part due to more robust learning dynamics and not
solely due to better architectures and/or more data
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