Related papers: RLWE and PLWE over cyclotomic fields are not equiv…

The linear code equivalence (LCE) problem is shown to be equivalent to the point set equivalence (PSE) problem, i.e., the problem to check whether two sets of points in a projective space over a finite field differ by a linear change of…

Pretrained language model (PLM) hidden states are frequently employed as contextual word embeddings (CWE): high-dimensional representations that encode semantic information given linguistic context. Across many areas of computational…

The shortest vector problem (SVP) over ideal lattices is closely related to the Ring-LWE problem, which is widely used to build post-quantum cryptosystems. Power-of-two cyclotomic fields are frequently adopted to instantiate Ring-LWE. Pan…

In analogy with the regularity lemma of Szemer\'edi, regularity lemmas for polynomials shown by Green and Tao (Contrib. Discrete Math. 2009) and by Kaufman and Lovett (FOCS 2008) modify a given collection of polynomials \calF =…

Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this paper, we extend the concept of polynomial-type exceptional…

In this work, we unveil an analogy between well-known lattice based learning with error problem and ill-posed inverse problems. We show that LWE problem is a structured inverse problem. Further, we propose a symmetric encryption scheme…

Arora & Ge introduced a noise-free polynomial system to compute the secret of a Learning With Errors (LWE) instance via linearization. Albrecht et al. later utilized the Arora-Ge polynomial model to study the complexity of Gr\"obner basis…

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training language models, but in practice, verifiers are rarely perfect. Recent theoretical work predicts that verifier noise affects the rate of…

The technique of $Q$-polinomials are used to derive the $w$- constraints in the two-matrix and Kontsevich-like model at finite $N$. These constraints are closed and form Lie algebra. They are associated with the matrices, $\lambda…

Most reinforcement learning (RL) methods for training large language models (LLMs) require ground-truth labels or task-specific verifiers, limiting scalability when correctness is ambiguous or expensive to obtain. We introduce Reinforcement…

The learning parity with noise (LPN) problem is a well-established computational challenge whose difficulty is critical to the security of several post-quantum cryptographic primitives such as HQC and Classic McEliece. Classically, the…

We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…

Recent work showed that ML-based attacks on Learning with Errors (LWE), a hard problem used in post-quantum cryptography, outperform classical algebraic attacks in certain settings. Although promising, ML attacks struggle to scale to more…

List-wise based learning to rank methods are generally supposed to have better performance than point- and pair-wise based. However, in real-world applications, state-of-the-art systems are not from list-wise based camp. In this paper, we…

Reinforcement Learning with Verifiable Rewards (RLVR) has become a prominent method for post-training Large Language Models (LLMs). However, verifiers are rarely error-free; even deterministic checks can be inaccurate, and the growing…

Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…

Despite rapid advances in speech recognition, current models remain brittle to superficial perturbations to their inputs. Small amounts of noise can destroy the performance of an otherwise state-of-the-art model. To harden models against…

Complexity problems associated with finite rings and finite semigroups, particularly semigroups of matrices over a field and the Rees matrix semigroups, are examined. Let M_nF be the ring of n x n matrices over the finite field F and let…

This paper presents a new semantic method for proving lower bounds in computational complexity. We use it to prove that maxflow, a PTIME complete problem, is not computable in polylogarithmic time on parallel random access machines (PRAMs)…

We explore further the hardness of the non-dual discrete variant of the Ring-LWE problem for various number rings, give improved attacks for certain rings satisfying some additional assumptions, construct a new family of vulnerable Galois…