574 research outputs found
Constructing Kites to Integrate Mathematics and Arts Concepts
This article describes a tetrahedral kite activity that was implemented with grade 9 students (age 14-15). We detail how the three-part lesson provided opportunities to integrate mathematics and art concepts, with potential to also weave in science and engineering ideas. The first part primed students to consider tetrahedral kites, their cultural and historical significance, and the materials needed for constructing the kite. The second part had students create a prototype using nets of tissue paper decorated with mark making techniques. The third part had students create a tetrahedron kite containing cultural and geographical mark making techniques on the tissue paper sides before flying the kites at a community event. We conclude the article with recommendations to help other teachers integrate mathematics and visual arts topics through tetrahedral kites
Genuinely Distributed Byzantine Machine Learning
Machine Learning (ML) solutions are nowadays distributed, according to the
so-called server/worker architecture. One server holds the model parameters
while several workers train the model. Clearly, such architecture is prone to
various types of component failures, which can be all encompassed within the
spectrum of a Byzantine behavior. Several approaches have been proposed
recently to tolerate Byzantine workers. Yet all require trusting a central
parameter server. We initiate in this paper the study of the ``general''
Byzantine-resilient distributed machine learning problem where no individual
component is trusted.
We show that this problem can be solved in an asynchronous system, despite
the presence of Byzantine parameter servers and
Byzantine workers (which is optimal). We present a new algorithm, ByzSGD, which
solves the general Byzantine-resilient distributed machine learning problem by
relying on three major schemes. The first, Scatter/Gather, is a communication
scheme whose goal is to bound the maximum drift among models on correct
servers. The second, Distributed Median Contraction (DMC), leverages the
geometric properties of the median in high dimensional spaces to bring
parameters within the correct servers back close to each other, ensuring
learning convergence. The third, Minimum-Diameter Averaging (MDA), is a
statistically-robust gradient aggregation rule whose goal is to tolerate
Byzantine workers. MDA requires loose bound on the variance of non-Byzantine
gradient estimates, compared to existing alternatives (e.g., Krum).
Interestingly, ByzSGD ensures Byzantine resilience without adding communication
rounds (on a normal path), compared to vanilla non-Byzantine alternatives.
ByzSGD requires, however, a larger number of messages which, we show, can be
reduced if we assume synchrony.Comment: This is a merge of arXiv:1905.03853 and arXiv:1911.07537;
arXiv:1911.07537 will be retracte
Mitigating the Performance Impact of Network Failures in Public Clouds
Some faults in data center networks require hours to days to repair because
they may need reboots, re-imaging, or manual work by technicians. To reduce
traffic impact, cloud providers \textit{mitigate} the effect of faults, for
example, by steering traffic to alternate paths. The state-of-art in automatic
network mitigations uses simple safety checks and proxy metrics to determine
mitigations. SWARM, the approach described in this paper, can pick orders of
magnitude better mitigations by estimating end-to-end connection-level
performance (CLP) metrics. At its core is a scalable CLP estimator that quickly
ranks mitigations with high fidelity and, on failures observed at a large cloud
provider, outperforms the state-of-the-art by over 700 in some cases
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