相关论文: On Learning Thresholds of Parities and Unions of R…

In recent years we see a rapidly growing line of research which shows learnability of various models via common neural network algorithms. Yet, besides a very few outliers, these results show learnability of models that can be learned using…

We give two results on PAC learning DNF formulas using membership queries in the challenging "distribution-free" learning framework, where learning algorithms must succeed for an arbitrary and unknown distribution over $\{0,1\}^n$. (1) We…

We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…

We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…

Neural networks (NNs) struggle to efficiently solve certain problems, such as learning parities, even when there are simple learning algorithms for those problems. Can NNs discover learning algorithms on their own? We exhibit a NN…

Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed…

Learning parity functions is a canonical problem in learning theory, which although computationally tractable, is not amenable to standard learning algorithms such as gradient-based methods. This hardness is usually explained via…

It is shown that a class of optical physical unclonable functions (PUFs) can be learned to arbitrary precision with arbitrarily high probability, even in the presence of noise, given access to polynomially many challenge-response pairs and…

We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\tilde{O}(s^{3}/\epsilon + s^{2}/\epsilon^{2})$, where $s$ is the size of DNF formula and $\epsilon$ is the PAC error…

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result…

Learning in uncertain, noisy, or adversarial environments is a challenging task for deep neural networks (DNNs). We propose a new theoretically grounded and efficient approach for robust learning that builds upon Bayesian estimation and…

Deep neural networks (DNNs) are vulnerable to adversarial noise. Their adversarial robustness can be improved by exploiting adversarial examples. However, given the continuously evolving attacks, models trained on seen types of adversarial…

Random walk neural networks (RWNNs) have emerged as a promising approach for graph representation learning, leveraging recent advances in sequence models to process random walks. However, under realistic sampling constraints, RWNNs often…

Parities have become a standard benchmark for evaluating learning algorithms. Recent works show that regular neural networks trained by gradient descent can efficiently learn degree $k$ parities on uniform inputs for constant $k$, but fail…

Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$…

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…

Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

Deep neural networks (DNNs) are increasingly deployed in different applications to achieve state-of-the-art performance. However, they are often applied as a black box with limited understanding of what knowledge the model has learned from…

Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of…