arXiv subjects

Minkyu Jung

Publications and source records attributed to Minkyu Jung.

4 recordsLinked to original sources

arXiv2026

The Middle Stair for Complete Bipartite Parallel Chip-Firing

We prove the middle-stair conjecture for every complete bipartite graph. If a parallel chip-firing game on $K_{a,b}$ has configuration $\sigma$ with $2ab-a-b<|\sigma|<2ab$, then its eventual period is $2$. The balanced case $K_{a,a}$ was proved by Ji, Li, and Wang using one-parameter conjugate configurations. We introduce two-parameter conjugates $c^{k,\ell}$, in which the rank shift on one side supplies the additive offset on the other. These conjugates preserve both the total number of chips and the activity. An exact Ferrers-diagram count then produces a nonnegative conjugate with two-round firing coverage on one side. The coverage propagates in alternating two-round waves, giving activity $1/2$; non-clumpiness then forces period $2$.

math.CO↗

arXiv2026

A Local Classification of Four-Element Multiple Sumsets

For a finite set $A\subset\mathbb{Z}$, write $hA$ for its $h$-fold sumset, and let \[ R(h,k)=\{|hA|:A\subset\mathbb{Z},\ |A|=k\}. \] We determine the part of $R(h,4)$ lying between $4h+2$ and $6h-4$: for $h=4$ the only value is $5h-1$, while for $h\geq 5$ the only values are $5h-1$ and $5h+1$. This proves Rajagopal's conjectured gap $5h\notin R(h,4)$ for every $h\geq 4$. For $h\geq 6$, it also yields the new missing interval $[5h+2,6h-4]$, which lies outside Rajagopal's general excluded set. Lev's lower bound for the successive growth of multiple sumsets reduces the problem to normalized sets of affine diameter five, of which there are only six. Reflection and four elementary exact sumset computations finish the classification.

math.CO↗

arXiv2025

RoToR: Towards More Reliable Responses for Order-Invariant Inputs

Mitigating positional bias of language models (LMs) for listwise inputs is a well-known and important problem (e.g., lost-in-the-middle). While zero-shot order-invariant LMs have been proposed to solve this issue, their success on practical listwise problems has been limited. In this work, as a first contribution, we identify and overcome two limitations to make zero-shot invariant LMs more practical: (1) training and inference distribution mismatch arising from modifying positional ID assignments to enforce invariance, and (2) failure to adapt to mixture of order-invariant and sensitive inputs in practical listwise problems. Then, to overcome these issues we propose (1) RoToR, a zero-shot invariant LM for genuinely order-invariant inputs with minimal modifications of positional IDs, and (2) Selective Routing, an adaptive framework that handles both order-invariant and order-sensitive inputs in listwise tasks. On the Lost in the middle (LitM), Knowledge Graph QA (KGQA), and MMLU benchmarks, we show that RoToR with Selective Routing can effectively handle practical listwise input tasks in a zero-shot manner (https://github.com/soyoung97/RoToR)

cs.CL↗

arXiv2023

Blank Collapse: Compressing CTC emission for the faster decoding

Connectionist Temporal Classification (CTC) model is a very efficient method for modeling sequences, especially for speech data. In order to use CTC model as an Automatic Speech Recognition (ASR) task, the beam search decoding with an external language model like n-gram LM is necessary to obtain reasonable results. In this paper we analyze the blank label in CTC beam search deeply and propose a very simple method to reduce the amount of calculation resulting in faster beam search decoding speed. With this method, we can get up to 78% faster decoding speed than ordinary beam search decoding with a very small loss of accuracy in LibriSpeech datasets. We prove this method is effective not only practically by experiments but also theoretically by mathematical reasoning. We also observe that this reduction is more obvious if the accuracy of the model is higher.

cs.CL↗