arXiv subjects

Qi Cheng

Publications and source records attributed to Qi Cheng.

At least 37 records · Page 2Linked to original sources

arXiv2025

Including Bloom Filters in Bottom-up Optimization

Bloom filters are used in query processing to perform early data reduction and improve query performance. The optimal query plan may be different when Bloom filters are used, indicating the need for Bloom filter-aware query optimization. To date, Bloom filter-aware query optimization has only been incorporated in a top-down query optimizer and limited to snowflake queries. In this paper, we show how Bloom filters can be incorporated in a bottom-up cost-based query optimizer. We highlight the challenges in limiting optimizer search space expansion, and offer an efficient solution. We show that including Bloom filters in cost-based optimization can lead to better join orders with effective predicate transfer between operators. On a 100 GB instance of the TPC-H database, our approach achieved a 32.8% further reduction in latency for queries involving Bloom filters, compared to the traditional approach of adding Bloom filters in a separate post-optimization step. Our method applies to all query types, and we provide several heuristics to balance limited increases in optimization time against improved query latency.

cs.DB↗

arXiv2024

A Construction of Evolving $3$-threshold Secret Sharing Scheme with Perfect Security and Smaller Share Size

The evolving $k$-threshold secret sharing scheme allows the dealer to distribute the secret to many participants such that only no less than $k$ shares together can restore the secret. In contrast to the conventional secret sharing scheme, the evolving scheme allows the number of participants to be uncertain and even ever-growing. In this paper, we consider the evolving secret sharing scheme with $k=3$. First, we point out that the prior approach has risks in the security. To solve this issue, we then propose a new evolving $3$-threshold scheme with perfect security. Given a $\ell$-bit secret, the $t$-th share of the proposed scheme has $\lceil\log_2 t\rceil +O({\lceil \log_4 \log_2 t\rceil}^2)+\log_2 p(2\lceil \log_4 \log_2 t\rceil-1)$ bits, where $p$ is a prime. Compared with the prior result $2 \lfloor\log_2 t\rfloor+O(\lfloor\log_2 t\rfloor)+\ell$, the proposed scheme reduces the leading constant from $2$ to $1$. Finally, we propose a conventional $3$-threshold secret sharing scheme over a finite field. Based on this model of the revised scheme and the proposed conventional $3$-threshold scheme, we present a brand-new and more concise evolving $3$-threshold secret sharing scheme.

cs.CR↗

arXiv2024

Learning Multimodal Cues of Children's Uncertainty

Understanding uncertainty plays a critical role in achieving common ground (Clark et al.,1983). This is especially important for multimodal AI systems that collaborate with users to solve a problem or guide the user through a challenging concept. In this work, for the first time, we present a dataset annotated in collaboration with developmental and cognitive psychologists for the purpose of studying nonverbal cues of uncertainty. We then present an analysis of the data, studying different roles of uncertainty and its relationship with task difficulty and performance. Lastly, we present a multimodal machine learning model that can predict uncertainty given a real-time video clip of a participant, which we find improves upon a baseline multimodal transformer model. This work informs research on cognitive coordination between human-human and human-AI and has broad implications for gesture understanding and generation. The anonymized version of our data and code will be publicly available upon the completion of the required consent forms and data sheets.

cs.CL↗

arXiv2024

Every Answer Matters: Evaluating Commonsense with Probabilistic Measures

Large language models have demonstrated impressive performance on commonsense tasks; however, these tasks are often posed as multiple-choice questions, allowing models to exploit systematic biases. Commonsense is also inherently probabilistic with multiple correct answers. The purpose of "boiling water" could be making tea and cooking, but it also could be killing germs. Existing tasks do not capture the probabilistic nature of common sense. To this end, we present commonsense frame completion (CFC), a new generative task that evaluates common sense via multiple open-ended generations. We also propose a method of probabilistic evaluation that strongly correlates with human judgments. Humans drastically outperform strong language model baselines on our dataset, indicating this approach is both a challenging and useful evaluation of machine common sense.

cs.CL↗

arXiv2024

A Construction of Evolving $k$-threshold Secret Sharing Scheme over A Polynomial Ring

The threshold secret sharing scheme allows the dealer to distribute the share to every participant such that the secret is correctly recovered from a certain amount of shares. The traditional $(k, n)$-threshold secret sharing scheme requests that the number of participants $n$ is known in advance. In contrast, the evolving secret sharing scheme allows that $n$ can be uncertain and even ever-growing. In this paper, we consider the evolving secret sharing scenario. Using the prefix codes and the properties of the polynomial ring, we propose a brand-new construction of evolving $k$-threshold secret sharing scheme for an $\ell$-bit secret over a polynomial ring, with correctness and perfect security. The proposed schemes establish the connection between prefix codes and the evolving schemes for $k\geq2$, and are also first evolving $k$-threshold secret sharing schemes by generalizing Shamir's scheme onto a polynomial ring. Specifically, the proposal also provides an unified mathematical decryption for prior evolving $2$-threshold secret sharing schemes. Besides, the analysis of the proposed schemes show that the size of the $t$-th share is $(k-1)(\ell_t-1)+\ell$ bits, where $\ell_t$ denotes the length of a binary prefix code of encoding integer $t$. In particular, when $δ$ code is chosen as the prefix code, the share size achieves $(k-1)\lfloor\lg t\rfloor+2(k-1)\lfloor\lg ({\lfloor\lg t\rfloor+1}) \rfloor+\ell$, which improves the prior best result $(k-1)\lg t+6k^4\ell\lg{\lg t}\cdot\lg{\lg {\lg t}}+ 7k^4\ell\lg k$, where $\lg$ denotes the binary logarithm. When $k=2$, the proposed scheme also achieves the minimal share size for single-bit secret, which is the same as the best known scheme.

cs.IT↗

arXiv2021

Mixture Model Framework for Traumatic Brain Injury Prognosis Using Heterogeneous Clinical and Outcome Data

Prognoses of Traumatic Brain Injury (TBI) outcomes are neither easily nor accurately determined from clinical indicators. This is due in part to the heterogeneity of damage inflicted to the brain, ultimately resulting in diverse and complex outcomes. Using a data-driven approach on many distinct data elements may be necessary to describe this large set of outcomes and thereby robustly depict the nuanced differences among TBI patients' recovery. In this work, we develop a method for modeling large heterogeneous data types relevant to TBI. Our approach is geared toward the probabilistic representation of mixed continuous and discrete variables with missing values. The model is trained on a dataset encompassing a variety of data types, including demographics, blood-based biomarkers, and imaging findings. In addition, it includes a set of clinical outcome assessments at 3, 6, and 12 months post-injury. The model is used to stratify patients into distinct groups in an unsupervised learning setting. We use the model to infer outcomes using input data, and show that the collection of input data reduces uncertainty of outcomes over a baseline approach. In addition, we quantify the performance of a likelihood scoring technique that can be used to self-evaluate the extrapolation risk of prognosis on unseen patients.

cs.LG↗

arXiv2021

On the ideal shortest vector problem over random rational primes

Any ideal in a number field can be factored into a product of prime ideals. In this paper we study the prime ideal shortest vector problem (SVP) in the ring $ \Z[x]/(x^{2^n} + 1) $, a popular choice in the design of ideal lattice based cryptosystems. We show that a majority of rational primes lie under prime ideals admitting a polynomial time algorithm for SVP. Although the shortest vector problem of ideal lattices underpins the security of Ring-LWE cryptosystem, this work does not break Ring-LWE, since the security reduction is from the worst case ideal SVP to the average case Ring-LWE, and it is one-way.

cs.CR↗

arXiv2020

Pulse Pileup Rejection Methods Using a Two-Component Gaussian Mixture Model for Fast Neutron Detection with Pulse Shape Discriminating Scintillator

Pulse shape discriminating scintillator materials in many cases allow the user to identify two basic kinds of pulses arising from two kinds of particles: neutrons and gammas. An uncomplicated solution for building a classifier consists of a two-component mixture model learned from a collection of pulses from neutrons and gammas at a range of energies. Depending on the conditions of data gathered to be classified, multiple classes of events besides neutrons and gammas may occur, most notably pileup events. All these kinds of events are anomalous and, in cases where the class of the particle is in doubt, it is preferable to remove them from the analysis. This study compares the performance of several machine learning and analytical methods for using the scores from the two-component model to identify anomalous events and in particular to remove pileup events. A specific outcome of this study is to propose a novel anomaly score, denoted G, from an unsupervised two-component model that is conveniently distributed on the interval [-1,1].

physics.ins-det↗

arXiv2020

Computing zeta functions of large polynomial systems over finite fields

In this paper, we improve the algorithms of Lauder-Wan \cite{LW} and Harvey \cite{Ha} to compute the zeta function of a system of $m$ polynomial equations in $n$ variables over the finite field $\FF_q$ of $q$ elements, for $m$ large. The dependence on $m$ in the original algorithms was exponential in $m$. Our main result is a reduction of the exponential dependence on $m$ to a polynomial dependence on $m$. As an application, we speed up a doubly exponential time algorithm from a software verification paper \cite{BJK} (on universal equivalence of programs over finite fields) to singly exponential time. One key new ingredient is an effective version of the classical Kronecker theorem which (set-theoretically) reduces the number of defining equations for a "large" polynomial system over $\FF_q$ when $q$ is suitably large.

math.NT↗

arXiv2017

Counting Roots of Polynomials Over Prime Power Rings

Suppose $p$ is a prime, $t$ is a positive integer, and $f\!\in\!\mathbb{Z}[x]$ is a univariate polynomial of degree $d$ with coefficients of absolute value $<\!p^t$. We show that for any fixed $t$, we can compute the number of roots in $\mathbb{Z}/(p^t)$ of $f$ in deterministic time $(d+\log p)^{O(1)}$. This fixed parameter tractability appears to be new for $t\!\geq\!3$. A consequence for arithmetic geometry is that we can efficiently compute Igusa zeta functions $Z$, for univariate polynomials, assuming the degree of $Z$ is fixed.

math.NT↗

arXiv2017

An Efficient Version of the Bombieri-Vaaler Lemma

In their celebrated paper "On Siegel's Lemma", Bombieri and Vaaler found an upper bound on the height of integer solutions of systems of linear Diophantine equations. Calculating the bound directly, however, requires exponential time. In this paper, we present the bound in a different form that can be computed in polynomial time. We also give an elementary (and arguably simpler) proof for the bound.

math.NT↗

arXiv2017

LWE from Non-commutative Group Rings

The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, and build cryptographic schemes based on this new primitive. One can regard the LWE on cyclotomic integers as a special case when the underlying group is cyclic, while our proposal utilizes non-commutative groups, which eliminates the weakness associated with the principal ideal lattices. In particular, we show how to build public key encryption schemes from dihedral group rings, which maintains the efficiency of the ring-LWE and improves its security.

cs.CR↗

arXiv2016

Sparse Univariate Polynomials with Many Roots Over Finite Fields

Suppose $q$ is a prime power and $f\in\mathbb{F}_q[x]$ is a univariate polynomial with exactly $t$ monomial terms and degree $<q-1$. To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) proved an upper bound of $2(q-1)^{\frac{t-2}{t-1}}$ on the number of cosets in $\mathbb{F}^*_q$ needed to cover the roots of $f$ in $\mathbb{F}^*_q$. Here, we give explicit $f$ with root structure approaching this bound: For $q$ a $(t-1)$-st power of a prime we give an explicit $t$-nomial vanishing on $q^{\frac{t-2}{t-1}}$ distinct cosets of $\mathbb{F}^*_q$. Over prime fields $\mathbb{F}_p$, computational data we provide suggests that it is harder to construct explicit sparse polynomials with many roots. Nevertheless, assuming the Generalized Riemann Hypothesis, we find explicit trinomials having $Ω\left(\frac{\log p}{\log \log p}\right)$ distinct roots in $\mathbb{F}_p$.

math.NT↗

arXiv2013

On Determining Deep Holes of Generalized Reed-Solomon Codes

For a linear code, deep holes are defined to be vectors that are further away from codewords than all other vectors. The problem of deciding whether a received word is a deep hole for generalized Reed-Solomon codes is proved to be co-NP-complete. For the extended Reed-Solomon codes $RS_q(\F_q,k)$, a conjecture was made to classify deep holes by Cheng and Murray in 2007. Since then a lot of effort has been made to prove the conjecture, or its various forms. In this paper, we classify deep holes completely for generalized Reed-Solomon codes $RS_p (D,k)$, where $p$ is a prime, $|D| > k \geqslant \frac{p-1}{2}$. Our techniques are built on the idea of deep hole trees, and several results concerning the Erd{ö}s-Heilbronn conjecture.

cs.IT↗

arXiv2013

Traps to the BGJT-Algorithm for Discrete Logarithms

In the recent breakthrough paper by Barbulescu, Gaudry, Joux and Thom{é}, a quasi-polynomial time algorithm (QPA) is proposed for the discrete logarithm problem over finite fields of small characteristic. The time complexity analysis of the algorithm is based on several heuristics presented in their paper. We show that some of the heuristics are problematic in their original forms, in particular, when the field is not a Kummer extension. We believe that the basic idea behind the new approach should still work, and propose a fix to the algorithm in non-Kummer cases, without altering the quasi-polynomial time complexity. The modified algorithm is also heuristic. Further study is required in order to fully understand the effectiveness of the new approach.

math.NT↗

arXiv2012

Sub-Linear Root Detection, and New Hardness Results, for Sparse Polynomials Over Finite Fields

We present a deterministic 2^O(t)q^{(t-2)(t-1)+o(1)} algorithm to decide whether a univariate polynomial f, with exactly t monomial terms and degree <q, has a root in F_q. A corollary of our method --- the first with complexity sub-linear in q when t is fixed --- is that the nonzero roots in F_q can be partitioned into at most 2 \sqrt{t-1} (q-1)^{(t-2)(t-1)} cosets of two subgroups S_1,S_2 of F^*_q, with S_1 in S_2. Another corollary is the first deterministic sub-linear algorithm for detecting common degree one factors of k-tuples of t-nomials in F_q[x] when k and t are fixed. When t is not fixed we show that each of the following problems is NP-hard with respect to BPP-reductions, even when p is prime: (1) detecting roots in F_p for f, (2) deciding whether the square of a degree one polynomial in F_p[x] divides f, (3) deciding whether the discriminant of f vanishes, (4) deciding whether the gcd of two t-nomials in F_p[x] has positive degree. Finally, we prove that if the complexity of root detection is sub-linear (in a refined sense), relative to the straight-line program encoding, then NEXP is not in P/Poly.

math.NT↗

arXiv2012

On Certain Computations of Pisot Numbers

This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number $α$ such that $\Q[α] = \F$ given a real Galois extension $\F$ of $\Q$ by its integral basis. This algorithm is based on the lattice reduction, and it runs in time polynomial in the size of the integral basis. Next, we show that for a fixed Pisot number $α$, one can compute $ [α^n] \pmod{m}$ in time polynomial in $(\log (m n))^{O(1)}$, where $m$ and $n$ are positive integers.

math.NT↗

arXiv2011

Counting Value Sets: Algorithm and Complexity

Let $p$ be a prime. Given a polynomial in $\F_{p^m}[x]$ of degree $d$ over the finite field $\F_{p^m}$, one can view it as a map from $\F_{p^m}$ to $\F_{p^m}$, and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on computing the cardinality of this value set. We show an elementary connection between this cardinality and the number of points on a family of varieties in affine space. We then apply Lauder and Wan's $p$-adic point-counting algorithm to count these points, resulting in a non-trivial algorithm for calculating the cardinality of the value set. The running time of our algorithm is $(pmd)^{O(d)}$. In particular, this is a polynomial time algorithm for fixed $d$ if $p$ is reasonably small. We also show that the problem is #P-hard when the polynomial is given in a sparse representation, $p=2$, and $m$ is allowed to vary, or when the polynomial is given as a straight-line program, $m=1$ and $p$ is allowed to vary. Additionally, we prove that it is NP-hard to decide whether a polynomial represented by a straight-line program has a root in a prime-order finite field, thus resolving an open problem proposed by Kaltofen and Koiran in \cite{Kaltofen03,KaltofenKo05}.

math.NT↗