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Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial…

Computational Complexity · Computer Science 2021-07-26 Subhamoy Maitra , Chandra Sekhar Mukherjee , Pantelimon Stanica , Deng Tang

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…

Computational Complexity · Computer Science 2014-10-31 Eric Blais , Clément L. Canonne , Igor C. Oliveira , Rocco A. Servedio , Li-Yang Tan

With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known…

Machine Learning · Computer Science 2020-05-18 Mahum Naseer , Mishal Fatima Minhas , Faiq Khalid , Muhammad Abdullah Hanif , Osman Hasan , Muhammad Shafique

Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…

Probability · Mathematics 2017-10-25 Elchanan Mossel

We show strong (and surprisingly simple) lower bounds for weakly learning intersections of halfspaces in the improper setting. Strikingly little is known about this problem. For instance, it is not even known if there is a polynomial-time…

Computational Complexity · Computer Science 2026-05-06 Stefan Tiegel

In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions…

Probability · Mathematics 2007-05-23 Elchanan Mossel , Ryan O'Donnell , Krzysztof Oleszkiewicz

To discover intrinsic inter-class transition probabilities underlying data, learning with noise transition has become an important approach for robust deep learning on corrupted labels. Prior methods attempt to achieve such transition…

Machine Learning · Computer Science 2020-06-15 Jun Shu , Qian Zhao , Zongben Xu , Deyu Meng

Hierarchical quantum classifiers, such as quantum convolutional neural networks (QCNNs), represent recent progress toward designing effective and feasible architectures for quantum classification. However, their performance on near-term…

Quantum Physics · Physics 2026-02-26 Taehyun Kim , Israel F. Araujo , Daniel K. Park

We study the task of learning Multi-Index Models (MIMs) with label noise under the Gaussian distribution. A $K$-MIM is any function $f$ that only depends on a $K$-dimensional subspace. We focus on well-behaved MIMs with finite ranges that…

Machine Learning · Computer Science 2025-04-15 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Nikos Zarifis

We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \in \mathbb{Z}^+$ and $\varepsilon > 0$, it is NP-hard…

Computational Complexity · Computer Science 2017-07-07 Arnab Bhattacharyya , Suprovat Ghoshal , Rishi Saket

A high efficiency hardware integration of neural networks benefits from realizing nonlinearity, network connectivity and learning fully in a physical substrate. Multiple systems have recently implemented some or all of these operations, yet…

Neural and Evolutionary Computing · Computer Science 2021-06-28 Louis Andreoli , Xavier Porte , Stéphane Chrétien , Maxime Jacquot , Laurent Larger , Daniel Brunner

A generalization of the coherent-noise models [M. E. J. Newman and K. Sneppen, Phys. Rev. E{\bf54}, 6226 (1996)] is presented where the agents in the model are subjected to a multitude of stresses, generated in a hierarchy of different…

Data Analysis, Statistics and Probability · Physics 2009-10-31 Claus Wilke , Thomas Martinetz

Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to…

Machine Learning · Computer Science 2026-02-10 Themistoklis Haris , Zihan Zhang , Yuichi Yoshida

Complete characterization of a noisy multipartite quantum state in terms of entanglement requires full knowledge of how the entanglement content in the state is affected by the spatial distribution of noise in the state. Specifically, we…

Quantum Physics · Physics 2020-03-05 Ratul Banerjee , Amit Kumar Pal , Aditi Sen De

This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise…

Machine Learning · Statistics 2020-10-20 Ioannis Anagnostides , Themis Gouleakis , Ali Marashian

Natural target functions and tasks typically exhibit hierarchical modularity -- they can be broken down into simpler sub-functions that are organized in a hierarchy. Such sub-functions have two important features: they have a distinct set…

Machine Learning · Computer Science 2023-10-31 Shreyas Malakarjun Patil , Loizos Michael , Constantine Dovrolis

We study quantum-classical separations between classical and quantum supervised learning models based on constant depth (i.e., shallow) circuits, in scenarios with and without noises. We construct a classification problem defined by a…

Quantum Physics · Physics 2024-05-03 Zhihan Zhang , Weiyuan Gong , Weikang Li , Dong-Ling Deng

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Machine Learning · Computer Science 2023-07-18 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Puqian Wang , Nikos Zarifis

We study the problem of PAC learning a single neuron in the presence of Massart noise. Specifically, for a known activation function $f: \mathbb{R} \to \mathbb{R}$, the learner is given access to labeled examples $(\mathbf{x}, y) \in…

Machine Learning · Computer Science 2022-10-19 Ilias Diakonikolas , Daniel M. Kane , Lisheng Ren , Yuxin Sun

Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model…

Machine Learning · Computer Science 2024-02-14 Xingjian Li , Pengkun Yang , Yangcheng Gu , Xueying Zhan , Tianyang Wang , Min Xu , Chengzhong Xu