arXiv subjects

Hoang Ta

Publications and source records attributed to Hoang Ta.

18 recordsLinked to original sources

arXiv2026

A Sum-of-Squares Hierarchy with Quadratic Convergence for Quantum Channel Coding

Computing the optimal success probability for transmitting classical messages through a single use of a quantum channel is NP-hard, even for two messages. An existing semidefinite programming hierarchy based on symmetric extensions provides convergent upper bounds with an a priori error estimate that decays as the inverse square root of the extension level. In this work, we construct a Hermitian sum-of-squares hierarchy for an arbitrary number of messages and prove quadratic convergence in its level. The error bound is proportional to the advantage over random guessing. Our approach combines state-discrimination duality with positive polynomial kernels on products of spheres to construct feasible polynomial dual certificates. For binary messages, the resulting bounds give a multiplicative approximation from above of the trace-norm contraction coefficient.

quant-ph↗

arXiv2026

Variance Driven Exploration: A Provable and Efficient Methodology for Pure Exploration in Highly Stochastic Environments

We propose Variance Driven Exploration (VarDE), a principled approach for pure exploration in highly stochastic environments, where the exploration process is dominated by stochastic variance. VarDE is built on a fundamental principle: sampling effort should be allocated to minimize the uncertainty of the final decision. We formalize the uncertainty of the final decision through a smooth decision function and derive allocation rules that explicitly capture how stochastic noise in individual components affects the reliability of the final output. We apply this methodology to three core problems of pure exploration -- Best Arm Identification (BAI), Monte Carlo Tree Search (MCTS), and Best-Policy Identification (BPI) -- with theoretical guarantees on variance decay and simple regret. Empirically, we demonstrate consistent and significant improvements of VarDE over existing methods, with especially strong gains in highly stochastic environments.

cs.LG↗

arXiv2026

Near-Optimal Covering Sequences

An $(n,R)$-covering sequence over a finite alphabet $\Sigma_q = \{0,1,\dots, q-1\}$ is a cyclic sequence whose consecutive length-$n$ windows form a covering code of radius $R$. Equivalently, every word in $\Sigma_q^n$ is within Hamming distance $R$ of at least one window. We give a deterministic and explicit construction of such sequences whose length, for every fixed alphabet size $q$, every fixed radius $R$, and every sufficiently large $n$, attains the sphere-covering lower bound up to a constant factor depending only on $q$ and $R$. Thus, in the fixed-radius regime, the construction removes the logarithmic factor in the general probabilistic upper bounds of [Chung and Cooper, \emph{Random Structures \& Algorithms}, 2004] and [Vu, \emph{Advances in Applied Mathematics}, 2005]. It also complements the earlier explicit constructions of [Chee, Etzion, Ta, and Vu, \emph{Designs, Codes and Cryptography}, 2025], which include constant factor bounds for the special binary radius-one families $n=2^a-1$ and $n=2^a$, where $a\ge1$.

math.CO↗

arXiv2026

Block Tensor Rank of Sum-Rank Metric Codes

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.

cs.IT↗

arXiv2026

Implementation and Optimization of HQC Decoding on NPU-Integrated Devices

Hamming Quasi-Cyclic (HQC) has been selected by NIST for standardization as an additional code-based key-encapsulation mechanism, providing algorithmic diversity alongside lattice-based post-quantum cryptography. Efficient deployment of HQC on mobile and embedded platforms, however, requires careful optimization of its decoding procedure, whose Reed-Muller and Reed-Solomon components dominate the computational cost. This paper studies HQC decoding on Qualcomm Hexagon processors in NPU-integrated devices, focusing on the Hexagon Vector eXtensions (HVX) backend rather than a tensor-inference engine. We observe that HQC decoding naturally exposes vector-structured computation, including Reed-Muller reliability vectors, Hadamard-transform coefficients, Reed-Solomon syndrome vectors, finite-field products, and packed support-point evaluations. Based on this observation, we redesign the dominant decoding kernels around HVX-friendly data layouts and execution patterns, including a vectorized Reed-Muller Hadamard transform, scalar-equivalent peak selection, HVX-oriented finite-field arithmetic, vectorized syndrome computation, and shortened-support locator-root evaluation. We implement and evaluate the optimized decoder using both Hexagon simulator measurements and real-device experiments on a Snapdragon~8 Gen~2 hardware development kit. The results show that Hexagon/HVX-assisted decoding substantially reduces latency and energy consumption, improving energy efficiency by up to $18.13\times$ while significantly offloading host CPU work. These results indicate that NPU-integrated mobile platforms can serve as effective backends for structured post-quantum cryptographic decoding when the underlying kernels are reformulated around vector execution.

cs.CR↗

arXiv2026

A Fast Hierarchical Splitting Approach for Non-Adaptive Learning of Random Hypergraphs

This work focuses on the problem of learning an unknown $3$-uniform hypergraph using edge-detecting queries. Our goal is to design a querying strategy that recovers the hyperedge set using as few queries as possible. We restrict our attention to random hypergraphs under the Erd\H{o}s--R\'enyi (ER) model, in which each potential hyperedge appears independently with probability $q = \Theta(n^{-3(1-\theta)})$ for $\theta \in (0;1)$. Prior work [Austhof-Reyzin-Tani, ISIT 2025] presents a testing-decoding scheme that uses $O(\bar{m}\log n)$ tests but requires a decoding time of $\Omega(n^3)$, where $\bar{m} = q\binom{n}{3}$ denotes the expected number of hyperedges. In this work, we extend the binary splitting framework and adapt it to the $3$-uniform hypergraph setting. We obtain a testing-decoding scheme that recovers the hyperedge set with high probability using $O(\bar{m} \log n)$ tests and achieves decoding time $O(\bar{m}^{5/3}\log n)$ for the case $\theta > \dfrac{2}{3}$ and $O(\bar{m}^{5/3}\log^2{\bar{m}}\log n)$ for the case $\theta \leq \dfrac{2}{3}$. In particular, the decoding runtime is subcubic in $n$ whenever $\theta<\frac{3}{5}$, providing a new test-decoding tradeoff compared with existing schemes.

cs.IT↗

arXiv2026

Nearly Optimal Bounds for Computing Decision Tree Splits in Data Streams

We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that outputs a split within additive $\epsilon$ error of the optimal split, improving upon the two-pass algorithm of Pham et al. (ISIT 2025). Furthermore, we provide a matching one-pass lower bound showing that $\Omega(M^2/\epsilon)$ space is indeed necessary. For classification, we also obtain a one-pass algorithm using $\tilde{O}(1/\epsilon)$ space for approximating the optimal Gini split, improving upon the previous $\tilde{O}(1/\epsilon^2)$-space algorithm. We complement these results with matching space lower bounds: $\Omega(1/\epsilon)$ for Gini impurity and $\Omega(1/\epsilon)$ for misclassification (which matches the upper bound obtained by sampling). Our algorithms exploit the Lipschitz property of the loss functions and use reservoir sampling along with Count--Min sketches with range queries. Our lower bounds follow from careful reductions from the INDEX problem.

cs.DS↗

arXiv2026

A Mixture of Experts Vision Transformer for High-Fidelity Surface Code Decoding

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.

quant-ph↗

arXiv2025

A Fast Binary Splitting Approach for Non-Adaptive Learning of Erd\H{o}s--R\'enyi Graphs

We study the problem of learning an unknown graph via group queries on node subsets, where each query reports whether at least one edge is present among the queried nodes. In general, learning arbitrary graphs with $n$ nodes and $k$ edges is hard in the non-adaptive setting, requiring $\Omega\big(\min\{k^2\log n,\,n^2\}\big)$ tests even when a small error probability is allowed. We focus on learning Erd\H{o}s--R\'enyi (ER) graphs $G\sim\mathrm{ER}(n,q)$ in the non-adaptive setting, where the expected number of edges is $\bar{k}=q\binom{n}{2}$, and we aim to design an efficient testing--decoding scheme, namely, a non-adaptive test design together with a decoding algorithm, achieving asymptotically vanishing error probability. Prior work (Li--Fresacher--Scarlett, NeurIPS 2019) presents a testing--decoding scheme that attains an order-optimal number of tests $O(\bar{k}\log n)$ but incurs $\Omega(n^2)$ decoding time, whereas their proposed sublinear-time algorithm incurs an extra $(\log \bar{k})(\log n)$ factor in the number of tests. We extend the binary splitting approach, recently developed for non-adaptive group testing, to the ER graph learning setting, and prove that the edge set can be recovered with high probability using $O(\bar{k}\log n)$ tests while attaining decoding time $O(\bar{k}^{1+\delta}\log n)$ for any fixed $\delta>0$.

cs.IT↗

arXiv2025

Constructions of Covering Sequences and Arrays

An $(n,R)$-covering sequence is a cyclic sequence whose consecutive $n$-tuples form a code of length $n$ and covering radius $R$. Using several construction methods improvements of the upper bounds on the length of such sequences for $n \leq 20$ and $1 \leq R \leq 3$, are obtained. The definition is generalized in two directions. An $(n,m,R)$-covering sequence code is a set of cyclic sequences of length $m$ whose consecutive $n$-tuples form a code of length~$n$ and covering radius $R$. The definition is also generalized to arrays in which the $m \times n$ sub-matrices form a covering code with covering radius $R$. We prove that asymptotically there are covering sequences that attain the sphere-covering bound up to a constant factor.

math.CO↗

arXiv2024

On de Bruijn Covering Sequences and Arrays

An $(m,n,R)$-de Bruijn covering array (dBCA) is a doubly periodic $M \times N$ array over an alphabet of size $q$ such that the set of all its $m \times n$ windows form a covering code with radius $R$. An upper bound of the smallest array area of an $(m,n,R)$-dBCA is provided using a probabilistic technique which is similar to the one that was used for an upper bound on the length of a de Bruijn covering sequence. A folding technique to construct a dBCA from a de Bruijn covering sequence or de Bruijn covering sequences code is presented. Several new constructions that yield shorter de Bruijn covering sequences and $(m,n,R)$-dBCAs with smaller areas are also provided. These constructions are mainly based on sequences derived from cyclic codes, self-dual sequences, primitive polynomials, an interleaving technique, folding, and mutual shifts of sequences with the same covering radius. Finally, constructions of de Bruijn covering sequences codes are also discussed.

cs.IT↗

arXiv2024

Constructing Decision Trees from Data Streams

In this work, we present data stream algorithms to compute optimal splits for decision tree learning. In particular, given a data stream of observations $x_i$ and their corresponding labels $y_i$, without the i.i.d. assumption, the objective is to identify the optimal split $j$ that partitions the data into two sets, minimizing the mean squared error (for regression) or the misclassification rate and Gini impurity (for classification). We propose several efficient streaming algorithms that require sublinear space and use a small number of passes to solve these problems. These algorithms can also be extended to the MapReduce model. Our results, while not directly comparable, complements the seminal work of Domingos-Hulten (KDD 2000) and Hulten-Spencer-Domingos (KDD 2001).

cs.DS↗

arXiv2024

Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach

Graph Neural Networks (GNNs), known as spectral graph filters, find a wide range of applications in web networks. To bypass eigendecomposition, polynomial graph filters are proposed to approximate graph filters by leveraging various polynomial bases for filter training. However, no existing studies have explored the diverse polynomial graph filters from a unified perspective for optimization. In this paper, we first unify polynomial graph filters, as well as the optimal filters of identical degrees into the Krylov subspace of the same order, thus providing equivalent expressive power theoretically. Next, we investigate the asymptotic convergence property of polynomials from the unified Krylov subspace perspective, revealing their limited adaptability in graphs with varying heterophily degrees. Inspired by those facts, we design a novel adaptive Krylov subspace approach to optimize polynomial bases with provable controllability over the graph spectrum so as to adapt various heterophily graphs. Subsequently, we propose AdaptKry, an optimized polynomial graph filter utilizing bases from the adaptive Krylov subspaces. Meanwhile, in light of the diverse spectral properties of complex graphs, we extend AdaptKry by leveraging multiple adaptive Krylov bases without incurring extra training costs. As a consequence, extended AdaptKry is able to capture the intricate characteristics of graphs and provide insights into their inherent complexity. We conduct extensive experiments across a series of real-world datasets. The experimental results demonstrate the superior filtering capability of AdaptKry, as well as the optimized efficacy of the adaptive Krylov basis.

cs.LG↗

arXiv2023

Efficient Approximation of Quantum Channel Fidelity Exploiting Symmetry

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 $\epsilon$ in $\mathrm{poly}(1/\epsilon, \text{input dimension})$ time.

quant-ph↗

arXiv2023

On the Asymptotic Nonnegative Rank of Matrices and its Applications in Information Theory

In this paper, we study the asymptotic nonnegative rank of matrices, which characterizes the asymptotic growth of the nonnegative rank of fixed nonnegative matrices under the Kronecker product. This quantity is important since it governs several notions in information theory such as the so-called exact R\'enyi common information and the amortized communication complexity. By using the theory of asymptotic spectra of V. Strassen (J. Reine Angew. Math. 1988), we define formally the asymptotic spectrum of nonnegative matrices and give a dual characterization of the asymptotic nonnegative rank. As a complementary of the nonnegative rank, we introduce the notion of the subrank of a nonnegative matrix and show that it is exactly equal to the size of the maximum induced matching of the bipartite graph defined on the support of the matrix (therefore, independent of the value of entries). Finally, we show that two matrix parameters, namely rank and fractional cover number, belong to the asymptotic spectrum of nonnegative matrices.

cs.IT↗

arXiv2022

A hierarchy of efficient bounds on quantum capacities exploiting symmetry

Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries in the recently introduced $D^{\#}$ in order to obtain a hierarchy of semidefinite programming bounds on various regularized quantities. As applications, we give a general procedure to give efficient bounds on the regularized Umegaki channel divergence as well as the classical capacity and two-way assisted quantum capacity of quantum channels. In particular, we obtain slight improvements for the capacity of the amplitude damping channel. We also prove that for fixed input and output dimensions, the regularized sandwiched R\'enyi divergence between any two quantum channels can be approximated up to an $\epsilon$ accuracy in time that is polynomial in $1/\epsilon$.

quant-ph↗

arXiv2021

Larger Corner-Free Sets from Combinatorial Degenerations

There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets in powers of a fixed small (directed or undirected) hypergraph, also called the Shannon capacity. An important instance of this is the corner problem studied in the context of multiparty communication complexity in the Number On the Forehead (NOF) model. Versions of this problem and the NOF connection have seen much interest (and progress) in recent works of Linial, Pitassi and Shraibman (ITCS 2019) and Linial and Shraibman (CCC 2021). We introduce and study a general algebraic method for lower bounding the Shannon capacity of directed hypergraphs via combinatorial degenerations, a combinatorial kind of "approximation" of subgraphs that originates from the study of matrix multiplication in algebraic complexity theory (and which play an important role there) but which we use in a novel way. Using the combinatorial degeneration method, we make progress on the corner problem by explicitly constructing a corner-free subset in $F_2^n \times F_2^n$ of size $Ω(3.39^n/poly(n))$, which improves the previous lower bound $Ω(2.82^n)$ of Linial, Pitassi and Shraibman (ITCS 2019) and which gets us closer to the best upper bound $4^{n - o(n)}$. Our new construction of corner-free sets implies an improved NOF protocol for the Eval problem. In the Eval problem over a group $G$, three players need to determine whether their inputs $x_1, x_2, x_3 \in G$ sum to zero. We find that the NOF communication complexity of the Eval problem over $F_2^n$ is at most $0.24n + O(\log n)$, which improves the previous upper bound $0.5n + O(\log n)$.

cs.CC↗

arXiv2021

Symmetric Subrank of Tensors and Applications

Strassen (Strassen, J. Reine Angew. Math., 375/376, 1987) introduced the subrank of a tensor as a natural extension of matrix rank to tensors. Subrank measures the largest diagonal tensor that can be obtained by applying linear operations to the different indices (legs) of the tensor (just like the matrix rank measures the largest diagonal matrix that can be obtained using row and column operations). Motivated by problems in combinatorics and complexity theory we introduce the new notion of symmetric subrank of tensors by restricting these linear operations to be the same for each index. We prove precise relations and separations between subrank and symmetric subrank. We prove that for symmetric tensors the subrank and the symmetric subrank are asymptotically equal. This proves the asymptotic subrank analogon of a conjecture known as Comon's conjecture in the theory of tensors. This result allows us to prove a strong connection between the general and symmetric version of an asymptotic duality theorem of Strassen. We introduce a representation-theoretic method to asymptotically bound the symmetric subrank called the symmetric quantum functional in analogy with the quantum functionals (Christandl, Vrana, Zuiddam, J. Amer. Math. Soc., 2021), and we study the relations between these functionals.

cs.CC↗