Related papers: Classical Hardness of Learning with Errors
Neural networks are nowadays highly successful despite strong hardness results. The existing hardness results focus on the network architecture, and assume that the network's weights are arbitrary. A natural approach to settle the…
Large language models (LLMs) excel in many tasks of software engineering, yet progress in leveraging them for vulnerability discovery has stalled in recent years. To understand this phenomenon, we investigate LLMs through the lens of…
In this work, we study the discrete logarithm problem in the context of TFNP - the complexity class of search problems with a syntactically guaranteed existence of a solution for all instances. Our main results establish that suitable…
Weaknesses in computer systems such as faults, bugs and errors in the architecture, design or implementation of software provide vulnerabilities that can be exploited by attackers to compromise the security of a system. Common Weakness…
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…
The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally…
We study the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass…
We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial-time bounded quantum device interacting with a classical polynomial-time verifier. In this model we propose solutions to two tasks - a…
An experimental cryptographic proof of quantumness will be a vital milestone in the progress of quantum information science. Error tolerance is a persistent challenge for implementing such tests: we need a test that not only can be passed…
In our recent work (Bubeck, Price, Razenshteyn, arXiv:1805.10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem. More precisely, we constructed a binary…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
While reinforcement learning (RL) holds great potential for decision making in the real world, it suffers from a number of unique difficulties which often need specific consideration. In particular: it is highly non-stationary; suffers from…
How many different binary classification problems a single learning algorithm can solve on a fixed data with exactly zero or at most a given number of cross-validation errors? While the number in the former case is known to be limited by…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
Effectively modeling time information and incorporating it into applications or models involving chronologically occurring events is crucial. Real-world scenarios often involve diverse and complex time patterns, which pose significant…
The widespread deployment of products powered by machine learning models is raising concerns around data privacy and information security worldwide. To address this issue, Federated Learning was first proposed as a privacy-preserving…
In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller…
Federated Learning (FL) is a collaborative method for training machine learning models while preserving the confidentiality of the participants' training data. Nevertheless, FL is vulnerable to reconstruction attacks that exploit shared…
The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability…
The paper provides results regarding the computational complexity of hybrid system identification. More precisely, we focus on the estimation of piecewise affine (PWA) maps from input-output data and analyze the complexity of computing a…