4,559 research outputs found
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
A Survey of Quantum Learning Theory
This paper surveys quantum learning theory: the theoretical aspects of
machine learning using quantum computers. We describe the main results known
for three models of learning: exact learning from membership queries, and
Probably Approximately Correct (PAC) and agnostic learning from classical or
quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation.
This version will appear as Complexity Theory Column in SIGACT News in June
2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a
referenc
Genetic attack on neural cryptography
Different scaling properties for the complexity of bidirectional
synchronization and unidirectional learning are essential for the security of
neural cryptography. Incrementing the synaptic depth of the networks increases
the synchronization time only polynomially, but the success of the geometric
attack is reduced exponentially and it clearly fails in the limit of infinite
synaptic depth. This method is improved by adding a genetic algorithm, which
selects the fittest neural networks. The probability of a successful genetic
attack is calculated for different model parameters using numerical
simulations. The results show that scaling laws observed in the case of other
attacks hold for the improved algorithm, too. The number of networks needed for
an effective attack grows exponentially with increasing synaptic depth. In
addition, finite-size effects caused by Hebbian and anti-Hebbian learning are
analyzed. These learning rules converge to the random walk rule if the synaptic
depth is small compared to the square root of the system size.Comment: 8 pages, 12 figures; section 5 amended, typos correcte
What Can We Learn Privately?
Learning problems form an important category of computational tasks that
generalizes many of the computations researchers apply to large real-life data
sets. We ask: what concept classes can be learned privately, namely, by an
algorithm whose output does not depend too heavily on any one input or specific
training example? More precisely, we investigate learning algorithms that
satisfy differential privacy, a notion that provides strong confidentiality
guarantees in contexts where aggregate information is released about a database
containing sensitive information about individuals. We demonstrate that,
ignoring computational constraints, it is possible to privately agnostically
learn any concept class using a sample size approximately logarithmic in the
cardinality of the concept class. Therefore, almost anything learnable is
learnable privately: specifically, if a concept class is learnable by a
(non-private) algorithm with polynomial sample complexity and output size, then
it can be learned privately using a polynomial number of samples. We also
present a computationally efficient private PAC learner for the class of parity
functions. Local (or randomized response) algorithms are a practical class of
private algorithms that have received extensive investigation. We provide a
precise characterization of local private learning algorithms. We show that a
concept class is learnable by a local algorithm if and only if it is learnable
in the statistical query (SQ) model. Finally, we present a separation between
the power of interactive and noninteractive local learning algorithms.Comment: 35 pages, 2 figure
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