Fugu-MT 論文翻訳(概要): From Local Pseudorandom Generators to Hardness of Learning

論文の概要: From Local Pseudorandom Generators to Hardness of Learning

arxiv url: http://arxiv.org/abs/2101.08303v1
Date: Wed, 20 Jan 2021 20:07:47 GMT
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システム内更新日: 2021-03-22 01:33:23.547200
Title: From Local Pseudorandom Generators to Hardness of Learning
Title（参考訳）: 局所擬似乱数生成器から学習困難まで
Authors: Amit Daniely and Gal Vardi
Abstract要約: 局所擬似乱数発生器の存在に関する十分に研究された仮定の下で学習の硬度の結果を証明します。結果は以下のとおりである: $omega(1)$ halfspaces の交点を学習するハードネス、$omega(1)$ 項を持つ dnf 公式、および $omega(1)$ 隠れニューロンを持つ relu ネットワーク。
参考スコア（独自算出の注目度）: 43.47952928399709
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We prove hardness-of-learning results under a well-studied assumption on the existence of local pseudorandom generators. As we show, this assumption allows us to surpass the current state of the art, and prove hardness of various basic problems, with no hardness results to date. Our results include: hardness of learning shallow ReLU neural networks under the Gaussian distribution and other distributions; hardness of learning intersections of $\omega(1)$ halfspaces, DNF formulas with $\omega(1)$ terms, and ReLU networks with $\omega(1)$ hidden neurons; hardness of weakly learning deterministic finite automata under the uniform distribution; hardness of weakly learning depth-$3$ Boolean circuits under the uniform distribution, as well as distribution-specific hardness results for learning DNF formulas and intersections of halfspaces. We also establish lower bounds on the complexity of learning intersections of a constant number of halfspaces, and ReLU networks with a constant number of hidden neurons. Moreover, our results imply the hardness of virtually all improper PAC-learning problems (both distribution-free and distribution-specific) that were previously shown hard under other assumptions.
Abstract（参考訳）: 本研究では,ローカル擬似乱数生成器の存在を前提として,学習の難しさを実証する。我々が示すように、この仮定は、現在の芸術の状態を超越し、様々な基本的な問題の困難さを証明し、今日までハードネスの結果は得られない。 Our results include: hardness of learning shallow ReLU neural networks under the Gaussian distribution and other distributions; hardness of learning intersections of $\omega(1)$ halfspaces, DNF formulas with $\omega(1)$ terms, and ReLU networks with $\omega(1)$ hidden neurons; hardness of weakly learning deterministic finite automata under the uniform distribution; hardness of weakly learning depth-$3$ Boolean circuits under the uniform distribution, as well as distribution-specific hardness results for learning DNF formulas and intersections of halfspaces. また、一定の数のハーフスペースの学習交叉と、一定の数の隠れニューロンを持つReLUネットワークの複雑さの低い境界を確立する。さらに,本研究の結果は,これまで他の仮定では困難であった,事実上不適切なPAC学習問題(分布自由と分布特化の両方)の難しさを示唆している。