Related papers: Noise Sensitivity and Learning Lower Bounds for Hi…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…