298 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Public-Key Encryption, Local Pseudorandom Generators, and the Low-Degree Method
The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics.
We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis of a new public-key encryption scheme whose security is based on Goldreich\u27s pseudorandom generator. The scheme is a combination of two proposals of Applebaum, Barak, and Wigderson, and inherits desirable features from both
Provable Advantage of Curriculum Learning on Parity Targets with Mixed Inputs
Experimental results have shown that curriculum learning, i.e., presenting
simpler examples before more complex ones, can improve the efficiency of
learning. Some recent theoretical results also showed that changing the
sampling distribution can help neural networks learn parities, with formal
results only for large learning rates and one-step arguments. Here we show a
separation result in the number of training steps with standard (bounded)
learning rates on a common sample distribution: if the data distribution is a
mixture of sparse and dense inputs, there exists a regime in which a 2-layer
ReLU neural network trained by a curriculum noisy-GD (or SGD) algorithm that
uses sparse examples first, can learn parities of sufficiently large degree,
while any fully connected neural network of possibly larger width or depth
trained by noisy-GD on the unordered samples cannot learn without additional
steps. We also provide experimental results supporting the qualitative
separation beyond the specific regime of the theoretical results.Comment: 34 pages, 8 figure
Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach
Thesis elaborated from 2018 to 2023 at the Instituto de AstrofÃsica de AndalucÃa under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI :
With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels
Decoding algorithms for surface codes
Quantum technologies have the potential to solve computationally hard
problems that are intractable via classical means. Unfortunately, the unstable
nature of quantum information makes it prone to errors. For this reason,
quantum error correction is an invaluable tool to make quantum information
reliable and enable the ultimate goal of fault-tolerant quantum computing.
Surface codes currently stand as the most promising candidates to build error
corrected qubits given their two-dimensional architecture, a requirement of
only local operations, and high tolerance to quantum noise. Decoding algorithms
are an integral component of any error correction scheme, as they are tasked
with producing accurate estimates of the errors that affect quantum
information, so that it can subsequently be corrected. A critical aspect of
decoding algorithms is their speed, since the quantum state will suffer
additional errors with the passage of time. This poses a connundrum-like
tradeoff, where decoding performance is improved at the expense of complexity
and viceversa. In this review, a thorough discussion of state-of-the-art
surface code decoding algorithms is provided. The core operation of these
methods is described along with existing variants that show promise for
improved results. In addition, both the decoding performance, in terms of error
correction capability, and decoding complexity, are compared. A review of the
existing software tools regarding surface code decoding is also provided.Comment: 54 pages, 31 figure
Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms
Kearns' statistical query (SQ) oracle (STOC'93) lends a unifying perspective
for most classical machine learning algorithms. This ceases to be true in
quantum learning, where many settings do not admit, neither an SQ analog nor a
quantum statistical query (QSQ) analog. In this work, we take inspiration from
Kearns' SQ oracle and Valiant's weak evaluation oracle (TOCT'14) and establish
a unified perspective bridging the statistical and parametrized learning
paradigms in a novel way. We explore the problem of learning from an evaluation
oracle, which provides an estimate of function values, and introduce an
extensive yet intuitive framework that yields unconditional lower bounds for
learning from evaluation queries and characterizes the query complexity for
learning linear function classes. The framework is directly applicable to the
QSQ setting and virtually all algorithms based on loss function optimization.
Our first application is to extend prior results on the learnability of
output distributions of quantum circuits and Clifford unitaries from the SQ to
the (multi-copy) QSQ setting, implying exponential separations between learning
stabilizer states from (multi-copy) QSQs versus from quantum samples. Our
second application is to analyze some popular quantum machine learning (QML)
settings. We gain an intuitive picture of the hardness of many QML tasks which
goes beyond existing methods such as barren plateaus and the statistical
dimension, and contains crucial setting-dependent implications. Our framework
not only unifies the perspective of cost concentration with that of the
statistical dimension in a unified language but exposes their connectedness and
similarity.Comment: 97 Page
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Efficient Active Learning Halfspaces with Tsybakov Noise: A Non-convex Optimization Approach
We study the problem of computationally and label efficient PAC active
learning -dimensional halfspaces with Tsybakov
Noise~\citep{tsybakov2004optimal} under structured unlabeled data
distributions. Inspired by~\cite{diakonikolas2020learning}, we prove that any
approximate first-order stationary point of a smooth nonconvex loss function
yields a halfspace with a low excess error guarantee. In light of the above
structural result, we design a nonconvex optimization-based algorithm with a
label complexity of \footnote{In the main body
of this work, we use to hide factors
of the form \polylog(d, \frac{1}{\epsilon}, \frac{1}{\delta})}, under the
assumption that the Tsybakov noise parameter , which
narrows down the gap between the label complexities of the previously known
efficient passive or active
algorithms~\citep{diakonikolas2020polynomial,zhang2021improved} and the
information-theoretic lower bound in this setting.Comment: 29 page
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