Zhengchun Zhou

Yu-Xuan Zhang, Hua Meng, Xue-Mei Cao et al.

Multi-Instance Learning (MIL) is a recent machine learning paradigm which is immensely useful in various real-life applications, like image analysis, video anomaly detection, text classification, etc. It is well known that most of the existing machine learning classifiers are highly vulnerable to adversarial perturbations. Since MIL is a weakly supervised learning, where information is available for a set of instances, called bag and not for every instances, adversarial perturbations can be fatal. In this paper, we have proposed two adversarial perturbation methods to analyze the effect of adversarial perturbations to interpret the vulnerability of MIL methods. Out of the two algorithms, one can be customized for every bag, and the other is a universal one, which can affect all bags in a given data set and thus has some generalizability. Through simulations, we have also shown the effectiveness of the proposed algorithms to fool the state-of-the-art (SOTA) MIL methods. Finally, we have discussed through experiments, about taking care of these kind of adversarial perturbations through a simple strategy. Source codes are available at https://github.com/InkiInki/MI-UAP.

Yu-Xuan Zhang, Zhengchun Zhou, Xingxing He et al.

Multi-instance learning (MIL) is a widely-applied technique in practical applications that involve complex data structures. MIL can be broadly categorized into two types: traditional methods and those based on deep learning. These approaches have yielded significant results, especially with regards to their problem-solving strategies and experimental validation, providing valuable insights for researchers in the MIL field. However, a considerable amount of knowledge is often trapped within the algorithm, leading to subsequent MIL algorithms that solely rely on the model's data fitting to predict unlabeled samples. This results in a significant loss of knowledge and impedes the development of more intelligent models. In this paper, we propose a novel data-driven knowledge fusion for deep multi-instance learning (DKMIL) algorithm. DKMIL adopts a completely different idea from existing deep MIL methods by analyzing the decision-making of key samples in the data set (referred to as the data-driven) and using the knowledge fusion module designed to extract valuable information from these samples to assist the model's training. In other words, this module serves as a new interface between data and the model, providing strong scalability and enabling the use of prior knowledge from existing algorithms to enhance the learning ability of the model. Furthermore, to adapt the downstream modules of the model to more knowledge-enriched features extracted from the data-driven knowledge fusion module, we propose a two-level attention module that gradually learns shallow- and deep-level features of the samples to achieve more effective classification. We will prove the scalability of the knowledge fusion module while also verifying the efficacy of the proposed architecture by conducting experiments on 38 data sets across 6 categories.

Zhonghao Liang, Dongmei Huang, Qunying Liao et al.

In recent years, the construction of non-GRS type linear codes has attracted considerable attention due to that they can effectively resist both the Sidelnikov-Shestakov attack and the Wieschebrink attack. Constructing linear complementary dual (LCD) codes and determining the hull of linear codes have long been important topics in coding theory, as they play the crucial role in constructing entanglement-assisted quantum error-correcting codes (EAQECCs), certain communication systems and cryptography. In this paper, by utilizing a class of non-GRS type linear codes, namely, generalized Roth-Lempel (in short, GRL) codes, we firstly construct several classes of Euclidean LCD codes, Hermitian LCD codes, and linear codes with small-dimensional hulls, generalized the main results given by Wu et al. in 2021. We also present an upper bound for the number of a class of Euclidean GRL codes with 1-dimensional hull, and then for several classes of Hermitian GRL codes, we firstly derive an upper bound for the dimension of the hull, and prove that the bound is attainable. Secondly, as an application, we obtain several families of EAQECCs. Thirdly, we prove that the GRL code is non-GRS for $k >\ell$. Finally, some corresponding examples for LCD MDS codes and LCD NMDS codes are presented.

Hengfeng Liu, Chunming Tang, Zhengchun Zhou et al.

A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes supporting combinatorial $t$-designs have attracted growing interest, yet constructing such codes remains highly challenging. In 2020, Ding and Tang initiated the study of NMDS codes supporting 2-designs by constructing the first infinite family, followed by several other constructions for $t > 2$, all with length at most $q + 1$. Although NMDS codes can, in principle, exceed this length, known examples supporting 2-designs and having length greater than $q + 1$ are extremely rare and limited to a few sporadic binary and ternary cases. In this paper, we present the first \emph{generic construction} of $q$-ary NMDS codes supporting 2-designs with lengths \emph{exceeding $q + 1$}. Our method leverages new connections between elliptic curve codes, finite abelian groups, subset sums, and combinatorial designs, resulting in an infinite family of such codes along with their weight distributions.

Hengfeng Liu, Chunming Tang, Cuiling Fan et al.

The Gram matrix is a classical object formed from the pairwise inner products of a collection of vectors, with fundamental roles in functional analysis, statistics, combinatorics, and coding theory. In the realm of sequence design, maximum-length sequences (m-sequences) are among the most fundamental classes of sequences, traditionally characterized by their span, decimation, shift-and-add, balance, run, and ideal autocorrelation properties. In this paper, we bridge the two foundational concepts by uncovering novel structural features of m-sequences through the lens of a family of Gram matrices. Specifically, for each $1 \le t \le 2^n - 1$, we extract $n$ consecutive subsequences of length $t$ from an m-sequence of period $2^n - 1$, construct their corresponding $n \times n$ Gram matrix, and investigate its rank, denoted by $r_n(t)$. Utilizing semilinear representation of Galois groups and Bézoutian of polynomials, we derive an explicit formula for $r_n(t)$ for all $t$, thereby establishing the complete rank distribution of these Gram matrices. Notably, we prove that full rank is attained for approximately half of the admissible values of $t$. We further uncover the intricate dynamics of $r_n(t)$: rank-deficient states are strictly unstable (i.e., $r_n(t) < n$ implies $r_n(t+1) \ne r_n(t)$), whereas the full-rank state exhibits strong persistence, remaining at $n$ over a nontrivial interval of consecutive values of $t$. Altogether, our results fully characterize both the global rank distribution and the local dynamics of rank function, as invariant of m-sequences. As an application, our findings completely determine the hull distribution of the family of punctured cyclic simplex codes.

Shukai Wang, Cuiling Fan, Chunming Tang et al.

The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions $0\rightarrow 1$ and $1\rightarrow0$ differ substantially. In this paper, we introduce the notion of asymmetric Hamming bidistance (AHB) and its two-dimensional distribution, which separately captures directional discrepancies between codewords. This finer characterization enables a more discriminative analysis of decoding the error probabilities for maximum-likelihood decoding (MLD), particularly when conventional measures, such as weight distributions and existing discrepancy-based bounds, fail to distinguish code performance. Building on this concept, we derive a new upper bound on the average error probability for binary codes under MLD and show that, in general, it is incomparable with the two existing bounds derived by Cotardo and Ravagnani (IEEE Trans. Inf. Theory, 68 (5), 2022). To demonstrate its applicability, we compute the complete AHB distributions for several families of codes, including two-weight and three-weight projective codes (with the zero codeword removed) via strongly regular graphs and 3-class association schemes, as well as nonlinear codes constructed from symmetric balanced incomplete block designs (SBIBDs).

Hua Meng, Zhiguo Long, Michael Sioutis et al.

Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to multiple revision operators that all satisfy the rules under the same belief condition. In many practical applications, such as safety critical ones, it is important to specify a definite revision operator to enable agents to iteratively revise their beliefs in a deterministic way. In this paper, we propose a novel framework for iterated belief revision by characterizing belief information through preference relations. Semantically, both beliefs and new evidence are represented as belief algebras, which provide a rich and expressive foundation for belief revision. Building on traditional revision rules, we introduce additional postulates for revision with belief algebra, including an upper-bound constraint on the outcomes of revision. We prove that the revision result is uniquely determined given the current belief state and new evidence. Furthermore, to make the framework more useful in practice, we develop a particular algorithm for performing the proposed revision process. We argue that this approach may offer a more predictable and principled method for belief revision, making it suitable for real-world applications.

Mingxing Zhang, Zhengchun Zhou, Lanping Li et al.

Sequences play an important role in many engineering applications and systems. Searching sequences with desired properties has long been an interesting but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GAN). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for intractable problems with complex objectives which prevent mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary code sets (MOCCS) and optimal odd-length Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications. 2) HpGAN found new sequences which achieve four-times increase of signal-to-interference ratio--benchmarked against the well-known Legendre sequence--of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.