Related papers: The Learning Stabilizers with Noise problem
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Many decision-making problems in engineering applications such as transportation, power system and operations research require repeatedly solving large-scale linear programming problems with a large number of different inputs. For example,…
While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…
Fine-tuning pre-trained language models such as BERT has become a common practice dominating leaderboards across various NLP tasks. Despite its recent success and wide adoption, this process is unstable when there are only a small number of…
Deep learning faces a formidable challenge when handling noisy labels, as models tend to overfit samples affected by label noise. This challenge is further compounded by the presence of instance-dependent noise (IDN), a realistic form of…
It's well-known that inverse problems are ill-posed and to solve them meaningfully, one has to employ regularization methods. Traditionally, popular regularization methods are the penalized Variational approaches. In recent years, the…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Randomized smoothing is a general technique for computing sample-dependent robustness guarantees against adversarial attacks for deep classifiers. Prior works on randomized smoothing against L_1 adversarial attacks use additive smoothing…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…
The advent of large-scale pre-trained language models has contributed greatly to the recent progress in natural language processing. Many state-of-the-art language models are first trained on a large text corpus and then fine-tuned on…
The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…
The concept of the smoothing parameter plays a crucial role in both lattice-based and code-based cryptography, primarily due to its effectiveness in achieving nearly uniform distributions through the addition of noise. Recent research by…
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 analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved.…
Due to the success of the Standard Model~(SM), it is reasonable to anticipate that the signal of new physics~(NP) beyond the SM is small. Consequently, future searches for NP and precision tests of the SM will require high luminosity…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…
Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be…
Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in…
Classical Random Neural Networks (RNNs) have demonstrated effective applications in decision making, signal processing, and image recognition tasks. However, their implementation has been limited to deterministic digital systems that output…