Related papers: Learning with Errors over Group Rings Constructed …
We show a simple reduction which demonstrates the cryptographic hardness of learning a single periodic neuron over isotropic Gaussian distributions in the presence of noise. More precisely, our reduction shows that any polynomial-time…
In this paper, we investigate the computational complexity of isomorphism testing for finite groups and quasigroups, given by their multiplication tables. We crucially take advantage of their various decompositions to show the following: -…
We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…
Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test…
This study proposes post-quantum encrypted control systems based on dynamic-key Learning with Errors (LWE) encryption schemes. The proposed method develops update maps that simultaneously update the private key and ciphertexts within the…
AI-powered attacks on Learning with Errors (LWE), an important hard math problem in post-quantum cryptography, rival or outperform "classical" attacks on LWE under certain parameter settings. Despite the promise of this approach, a dearth…
We consider the hidden subgroup problem on the semi-direct product of cyclic groups $\Z_{N}\rtimes\Z_{p}$ with some restriction on $N$ and $p$. By using the homomorphic properties, we present a class of semi-direct product groups in which…
Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus,…
We study the problem of offline learning in automated decision systems under the contextual bandits model. We are given logged historical data consisting of contexts, (randomized) actions, and (nonnegative) rewards. A common goal is to…
We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\Gamma=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(\Gamma)$ with…
We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…
The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…
We study the last fall degrees of {\em semi-local} polynomial systems, and the computational complexity of solving such systems for closed-point and rational-point solutions, where the systems are defined over a finite field. A semi-local…
Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…
In this paper, we show new algorithms, hardness results and applications for $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the…
Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative…
We consider the regret minimization problem in reinforcement learning (RL) in the episodic setting. In many real-world RL environments, the state and action spaces are continuous or very large. Existing approaches establish regret…
While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the…
Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses…
Inverse reinforcement learning (IRL) is the task of finding a reward function that generates a desired optimal policy for a given Markov Decision Process (MDP). This paper develops an information-theoretic lower bound for the sample…