Van Khu Vu

Dat Thanh Tran, Van Khu Vu, Yining Ma

Neural-guided Ant Colony Optimization (ACO) suffers from a fundamental training-inference misalignment: policies are typically trained to generate static priors (e.g., heatmaps), yet deployed to guide iterative, long-horizon search processes. In this paper, we present DyNACO, a novel framework that achieves dynamic neural guidance by periodically observing the pheromone distribution and the incumbent solution. To make DyNACO tractable at scale, we pair the policy with a perturbation-based ACO backend and a scope-restricted refinement mechanism that jointly ensure efficacy and stable credit assignment. On TSP, DyNACO scales to 100,000-node instances and outperforms neural baselines while often reducing total runtime compared to the unguided solver. We extend DyNACO to CVRP via a capacity-aware backend, consistently improving the unguided baseline with less than 1% neural overhead. We further provide in-depth analysis validating the model's generalization capabilities and elucidating why dynamic guidance outperforms static priors. Our work underscores the necessity of aligning neural training with iterative search dynamics in learning-guided optimization. The code is available at https://github.com/shoraaa/DyNACO.

Van Long Phuoc Pham, Yeow Meng Chee, Kui Cai et al.

The sequence reconstruction problem for insertion/deletion channels has attracted significant attention owing to their applications recently in some emerging data storage systems, such as racetrack memories, DNA-based data storage. Our goal is to investigate the reconstruction problem for sticky-insdel channels where both sticky-insertions and sticky-deletions occur. If there are only sticky-insertion errors, the reconstruction problem for sticky-insertion channel is a special case of the reconstruction problem for tandem-duplication channel which has been well-studied. In this work, we consider the $(t, s)$-sticky-insdel channel where there are at most $t$ sticky-insertion errors and $s$ sticky-deletion errors when we transmit a message through the channel. For the reconstruction problem, we are interested in the minimum number of distinct outputs from these channels that are needed to uniquely recover the transmitted vector. We first provide a recursive formula to determine the minimum number of distinct outputs required. Next, we provide an efficient algorithm to reconstruct the transmitted vector from erroneous sequences.

Yeow Meng Chee, Hoang Ta, Van Khu Vu

Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programming hierarchy of outer bounds for this quantity. However, the size of the semidefinite programs (SDPs) grows exponentially with respect to the level of the hierarchy, thus making their computation unscalable. In this work, by exploiting the symmetries in the SDP, we show that, for a fixed output dimension of the quantum channel, we can compute the SDP in time polynomial with respect to the level of the hierarchy and input dimension. As a direct consequence of our result, the optimal fidelity can be approximated with an accuracy of $ε$ in $\mathrm{poly}(1/ε, \text{input dimension})$ time.

Hoang Viet Nguyen, Manh Hung Nguyen, Hoang Ta et al.

Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to their geometric locality and practical relevance. In these codes, stabilizer measurements yield a syndrome that must be decoded into a recovery operation, making decoding a central bottleneck for scalable real time operation. Existing decoders are commonly classified into two categories. Classical algorithmic decoders provide strong and well established baselines, but may incur substantial computational overhead at large code distances or under stringent latency constraints. Machine learning based decoders offer fast GPU inference and flexible function approximation, yet many approaches do not explicitly exploit the lattice geometry and local structure of topological codes, which can limit performance. In this work, we propose QuantumSMoE, a quantum vision transformer based decoder that incorporates code structure through plus shaped embeddings and adaptive masking to capture local interactions and lattice connectivity, and improves scalability via a mixture of experts layer with a novel auxiliary loss. Experiments on the toric code demonstrate that QuantumSMoE outperforms state-of-the-art machine learning decoders as well as widely used classical baselines.

Binh Vu, Shuche Wang, Van Khu Vu

The problem of computing the cardinality of the intersection of multiple balls in the Hamming space has attracted a lot of attention recently due to their applications in the list reconstruction problem and information retrieval in Associative Memories. In previous work, most of the results are for the cases where the radii of each ball, $r$ and the distance between the centers of these balls, $k$ are fixed when the length $n$ of each codeword tend to infinity. In this work, we focus on the case where $r = αn$ and $k=βn$ for some constants $α$ and $β$ and compute the maximum asymptotic rate of the cardinality of the intersection of three balls. We provide the maximum asymptotic rate as a function of two parameters $α$ and $β$. We also provide numerical results and compare these results with the intersection of two balls.

Phuc Tran, Van Vu

Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r σ_i u_i v_i^\top,$ where $σ_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right singular vectors. For a parameter $1 \le p \le r$, $A_p := \sum_{i=1}^p σ_i u_i v_i^\top$ is the best rank $p$ approximation of $A$. In practice, one often chooses $p$ to be small, leading to the commonly used phrase "low-rank approximation". Low-rank approximation plays a central role in data science because it can substantially reduce the dimensionality of the original data, the matrix $A$. For a large data matrix $A$, one typically computes a rank-$p$ approximation $A_p$ for a suitably chosen small $p$, stores $A_p$, and uses it as input for further computations. The reduced dimension of $A_p$ enables faster computations and significant data compression. In practice, noise is inevitable. We often have access only to noisy data $\tilde A = A + E$, where $E$ represents the noise. Consequently, the low-rank approximation used as input in many downstream tasks is $\tilde A_p$, the best rank $p$ approximation of $\tilde A$, rather than $A_p$. Therefore, it is natural and important to estimate the error $ \| \tilde A_p - A_p \|$. This error plays a critical role in estimating the accuracy of the output of any process involving a low-rank approximation of noisy input. In this paper, we develop a new method (based on contour analysis) to bound $\| \tilde A_p - A_p \|$. With this method, we can exploit new parameters that measure the skewness between the noise matrix $E$ and the singular vectors of $A$, avoiding the worst-case analysis used in traditional approaches. In many settings, we obtain notable quantitative improvements compared to classical approaches (using the Eckart-Young-Mirsky theorem or the Davis-Kahan theorem).

Huimin Lao, Huy Pham, Hoang Ta et al.

Sum-rank codes provide a generalized framework for Hamming and rank-metric codes, with codewords represented as tuples of matrices and weight given by the sum of the block ranks. In this paper, we introduce and study a block-tensor-rank invariant for sum-rank metric codes. To each code, we associate its \emph{block tensor rank}: the smallest number of block-simple tensors, namely rank-one matrices supported inside single blocks, whose linear span contains the code. In general, determining the block tensor rank of a sum-rank code is challenging. Our main structural result shows that the block tensor rank decomposes additively across the blocks of the code, thereby reducing its computation to a tensor-rank problem on each block projection. Consequently, we derive two complementary lower bounds on the block tensor rank, referred to as the \emph{projection-wise bound} and the \emph{coordinate-code bound}. Moreover, by combining the coordinate-code bound with the classical Singleton and Griesmer bounds for codes in the Hamming metric, we obtain explicit lower bounds, called the \emph{Singleton coordinate-code bound} and the \emph{Griesmer coordinate-code bound}, respectively. We further construct families of sum-rank codes whose block tensor ranks attain the Singleton or Griesmer coordinate-code bounds. These constructions are based on Hamming-metric codes achieving the corresponding classical bounds. Finally, we show that, in certain cases, the block tensor ranks of two known families of sum-rank codes in the literature do not attain the Singleton coordinate-code bound.

Dat Thanh Tran, Khai Quang Tran, Khoi Anh Pham et al.

This study presents Neural Focused Ant Colony Optimization (NeuFACO), a non-autoregressive framework for the Traveling Salesman Problem (TSP) that combines advanced reinforcement learning with enhanced Ant Colony Optimization (ACO). NeuFACO employs Proximal Policy Optimization (PPO) with entropy regularization to train a graph neural network for instance-specific heuristic guidance, which is integrated into an optimized ACO framework featuring candidate lists, restricted tour refinement, and scalable local search. By leveraging amortized inference alongside ACO stochastic exploration, NeuFACO efficiently produces high-quality solutions across diverse TSP instances.