1,426 research outputs found
Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back
We present an -time algorithm for
the maximum s-t flow and the minimum s-t cut problems in directed graphs with
unit capacities. This is the first improvement over the sparse-graph case of
the long-standing time bound due to Even and
Tarjan [EvenT75]. By well-known reductions, this also establishes an
-time algorithm for the maximum-cardinality bipartite
matching problem. That, in turn, gives an improvement over the celebrated
celebrated time bound of Hopcroft and Karp [HK73] whenever the
input graph is sufficiently sparse
Faster generation of random spanning trees
In this paper, we set forth a new algorithm for generating approximately
uniformly random spanning trees in undirected graphs. We show how to sample
from a distribution that is within a multiplicative of uniform in
expected time \TO(m\sqrt{n}\log 1/\delta). This improves the sparse graph
case of the best previously known worst-case bound of , which has stood for twenty years.
To achieve this goal, we exploit the connection between random walks on
graphs and electrical networks, and we use this to introduce a new approach to
the problem that integrates discrete random walk-based techniques with
continuous linear algebraic methods. We believe that our use of electrical
networks and sparse linear system solvers in conjunction with random walks and
combinatorial partitioning techniques is a useful paradigm that will find
further applications in algorithmic graph theory
Spectral Signatures in Backdoor Attacks
A recent line of work has uncovered a new form of data poisoning: so-called
\emph{backdoor} attacks. These attacks are particularly dangerous because they
do not affect a network's behavior on typical, benign data. Rather, the network
only deviates from its expected output when triggered by a perturbation planted
by an adversary.
In this paper, we identify a new property of all known backdoor attacks,
which we call \emph{spectral signatures}. This property allows us to utilize
tools from robust statistics to thwart the attacks. We demonstrate the efficacy
of these signatures in detecting and removing poisoned examples on real image
sets and state of the art neural network architectures. We believe that
understanding spectral signatures is a crucial first step towards designing ML
systems secure against such backdoor attacksComment: 16 pages, accepted to NIPS 201
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