相关论文: Parallel Identity Testing for Skew Circuits with B…

The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what…

The isolation lemma of Mulmuley et al \cite{MVV87} is an important tool in the design of randomized algorithms and has played an important role in several nontrivial complexity upper bounds. On the other hand, polynomial identity testing is…

Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…

Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the…

Zero-knowledge circuits are sets of equality constraints over arithmetic expressions interpreted in a prime field; they are used to encode computations in cryptographic zero-knowledge proofs. We make the following contributions to the…

The assumed hardness of the Linear Code Equivalence problem (LCE) lies at the core of the security of the LESS signature scheme and other signature schemes with advanced functionalities. The LCE problem asks to determine whether two linear…

We study the long-standing open problem of efficiently testing rectilinear planarity of series-parallel graphs (SP-graphs) in the variable embedding setting. A key ingredient behind the design of a linear-time testing algorithm for…

Checking whether two quantum circuits are equivalent is important for the design and optimization of quantum-computer applications with real-world devices. We consider quantum circuits consisting of Clifford gates, a practically-relevant…

Parallel thinking has emerged as a promising paradigm for reasoning, yet it imposes significant computational burdens. Existing efficiency methods primarily rely on local, per-trajectory signals and lack principled mechanisms to exploit…

Operations typically used in machine learning al-gorithms (e.g. adds and soft max) can be implemented bycompact analog circuits. Analog Application-Specific Integrated Circuit (ASIC) designs that implement these algorithms using techniques…

This paper considers the asymptotic power of likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n. The asymptotic distribution of LRT under alternatives is given and an explicit…

Read-$k$ oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs). In this work, we give an exponential lower bound of $\exp(n/k^{O(k)})$ on…

We introduce the polynomial coefficient matrix and identify maximum rank of this matrix under variable substitution as a complexity measure for multivariate polynomials. We use our techniques to prove super-polynomial lower bounds against…

Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen…

In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets,…

The circuit equivalence problem of a finite algebra $\mathbf A$ is the computational problem of deciding whether two circuits over $\mathbf A$ define the same function or not. This problem not just generalises the equivalence problem for…

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

This work studies skew polycyclic codes over finite chain rings defined by central trinomials. For this class of codes, we investigate Hamming equivalence in the non-commutative (skew) setting. We introduce an equivalence relation on the…

This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…

We characterize skew polynomial rings and skew power series rings that are reduced and right or left Archimedean.