arXiv subjects

Tanbir Ahmed

Publications and source records attributed to Tanbir Ahmed.

4 recordsLinked to original sources

arXiv2026

Unified Multi-Dialectal Neural Machine Translation for Bangla Using the Dwadash Benchmark Corpus

Neural Machine Translation (NMT) and Large Language Models (LLMs) excel at cross-lingual tasks but often fail to capture intra-lingual morphological variation, marginalizing dialectal speakers. In Bangla, existing translation frameworks commonly rely on Standard Colloquial Bangla (SCB) as an intermediate pivot, which can compound errors and reduce cross-dialectal nuance. To address this gap, we introduce a unified, multi-directional NMT system for direct translation between SCB and eleven regional variants. We first review prior dialectal NLP resources to identify existing technological gaps. As a foundational contribution, we construct and release a large multi-dialect parallel corpus for Bangla, comprising 14,562 aligned rows and 51,541 non-null sentence pairs through the integration of seven prior datasets and native-speaker-verified manual augmentation. Using this corpus, we benchmark state-of-the-art sequence-to-sequence architectures with parameter-efficient Weight-Decomposed Low-Rank Adaptation (DoRA). Results show that deep monolingual pre-training is more effective than large multilingual capacity for this task. The compact BanglaT5 model outperforms NLLB-200 and mBART-50 by up to 13.96 BLEU, achieving 29.26 BLEU, 57.26 chrF++, and 49.68 METEOR. A dataset scaling study shows diminishing returns beyond 3,000 parallel pairs and indicates that linguistic proximity to Standard Bangla is more important than raw data volume for translation quality. Finally, we deploy the optimized model as an INT8-quantized web application, providing a scalable, open-source framework for inclusive language technology and equitable digital access.

cs.CL↗

arXiv2025

Symbolic Sets for Proving Bounds on Rado Numbers

Given a linear equation $\cal E$ of the form $ax + by = cz$ where $a$, $b$, $c$ are positive integers, the $k$-colour Rado number $R_k({\cal E})$ is the smallest positive integer $n$, if it exists, such that every $k$-colouring of the positive integers $\{1, 2, \dotsc, n\}$ contains a monochromatic solution to $\cal E$. In this paper, we consider $k = 3$ and the linear equations $ax + by = bz$ and $ax + ay = bz$. Using SAT solvers, we compute a number of previously unknown Rado numbers corresponding to these equations. We prove new general bounds on Rado numbers inspired by the satisfying assignments discovered by the SAT solver. Our proofs require extensive case-based analyses that are difficult to check for correctness by hand, so we automate checking the correctness of our proofs via an approach which makes use of a new tool we developed with support for operations on symbolically-defined sets -- e.g., unions or intersections of sets of the form $\{f(1), f(2), \dotsc, f(a)\}$ where $a$ is a symbolic variable and $f$ is a function possibly dependent on $a$. No computer algebra system that we are aware of currently has sufficiently capable support for symbolic sets, leading us to develop a tool supporting symbolic sets using the Python symbolic computation library SymPy coupled with the Satisfiability Modulo Theories solver Z3.

math.CO↗

arXiv2023

Self-Similar Algebras with connections to Run-length Encoding and Rational Languages

A self-similar algebra $\left(\mathfrak{A}, ψ\right)$ is an associative algebra $\mathfrak{A}$ with a morphism of algebras $ψ: \mathfrak{A} \longrightarrow M_d \left( \mathfrak{A}\right)$, where $M_d \left( \mathfrak{A}\right)$ is the set of $d\times d$ matrices with coefficients from $\mathfrak{A}$. We study the connection between self-similar algebras with run-length encoding and rational languages. In particular, we provide a curious relationship between the eigenvalues of a sequence of matrices related to a specific self-similar algebra and the smooth words over a 2-letter alphabet. We also consider the language $L(s)$ of words $u$ in $(Σ\times Σ)^*$ where $Σ=\{0,1\}$ such that $s\cdot u$ is a unit in $\mathfrak{A}$. We prove that $L(s)$ is rational and provide an asymptotic formula for the number of words of a given length in $L(s)$.

math.CO↗

arXiv2014

On the van der Waerden numbers w(2;3,t)

We present results and conjectures on the van der Waerden numbers w(2;3,t) and on the new palindromic van der Waerden numbers pdw(2;3,t). We have computed the new number w(2;3,19) = 349, and we provide lower bounds for 20 <= t <= 39, where for t <= 30 we conjecture these lower bounds to be exact. The lower bounds for 24 <= t <= 30 refute the conjecture that w(2;3,t) <= t^2, and we present an improved conjecture. We also investigate regularities in the good partitions (certificates) to better understand the lower bounds. Motivated by such reglarities, we introduce *palindromic van der Waerden numbers* pdw(k; t_0,...,t_{k-1}), defined as ordinary van der Waerden numbers w(k; t_0,...,t_{k-1}), however only allowing palindromic solutions (good partitions), defined as reading the same from both ends. Different from the situation for ordinary van der Waerden numbers, these "numbers" need actually to be pairs of numbers. We compute pdw(2;3,t) for 3 <= t <= 27, and we provide lower bounds, which we conjecture to be exact, for t <= 35. All computations are based on SAT solving, and we discuss the various relations between SAT solving and Ramsey theory. Especially we introduce a novel (open-source) SAT solver, the tawSolver, which performs best on the SAT instances studied here, and which is actually the original DLL-solver, but with an efficient implementation and a modern heuristic typical for look-ahead solvers (applying the theory developed in the SAT handbook article of the second author).

math.CO↗