arXiv subjects

Seongmin Ok

Publications and source records attributed to Seongmin Ok.

7 recordsLinked to original sources

arXiv2026

A.X K2 Technical Report

We introduce A.X K2, a 688B-parameter Mixture-of-Experts (MoE) language model trained from scratch as a high-performance foundation for \emph{agentic} applications. Trained on approximately 8.5T tokens---fewer than its predecessor, A.X K1---on a smaller but higher-quality mixture with substantially expanded agentic and software-engineering data, it nonetheless improves over A.X K1 across the board, by over 30 percentage points on some benchmarks, reflecting large gains in token efficiency. To support long contexts efficiently, we introduce Sparse Gated Attention (SGA), which combines sparse attention with gated attention, and adopt Gated Norm (GN) to stabilize large-scale training. SGA is trained natively at 128K through a \emph{sparse} indexer warmup that optimizes the indexer against its own sparse top-$k$ selection rather than the dense attention distribution, making adaptation markedly cheaper: each query reads only 2,048 positions, yet long-context quality is unchanged and A.X K2 scores 94.6 on RULER out to 256K. The outlier suppression of GN in turn keeps 4-bit NVFP4 serving within one point of FP8 accuracy. A simple yet effective Think-Fusion recipe further lets users switch between thinking and non-thinking modes within a single unified model. Extensive evaluations show that A.X K2 performs competitively against strong open-weight baselines, matching or exceeding them on math and Korean-language benchmarks.

cs.AI↗

arXiv2026

A.X K1 Technical Report

We introduce A.X K1, a 519B-parameter Mixture-of-Experts (MoE) language model trained from scratch. Our design leverages scaling laws to optimize training configurations and vocabulary size under fixed computational budgets. A.X K1 is pre-trained on a corpus of approximately 10T tokens, curated by a multi-stage data processing pipeline. Designed to bridge the gap between reasoning capability and inference efficiency, A.X K1 supports explicitly controllable reasoning to facilitate scalable deployment across diverse real-world scenarios. We propose a simple yet effective Think-Fusion training recipe, enabling user-controlled switching between thinking and non-thinking modes within a single unified model. Extensive evaluations demonstrate that A.X K1 achieves performance competitive with leading open-source models, while establishing a distinctive advantage in Korean-language benchmarks.

cs.CL↗

arXiv2018

Dynamic choosability of triangle-free graphs and sparse random graphs

The \textit{$r$-dynamic choosability} of a graph $G$, written ${\rm ch}_r(G)$, is the least $k$ such that whenever each vertex is assigned a list of at least $k$ colors a proper coloring can be chosen from the lists so that every vertex $v$ has at least $\min\{d_G(v),r\}$ neighbors of distinct colors. Let ${\rm ch}(G)$ denote the choice number of $G$. In this paper, we prove ${\rm ch}_r(G)\leq (1+o(1)){\rm ch}(G)$ when $\frac{Δ(G)}{δ(G)}$ is bounded. We also show that there exists a constant $C$ such that for the random graph $G=G(n,p)$ with $\frac{2}{n}<p\leq \frac{1}{2}$, it holds that ${\rm ch}_2(G)\leq {\rm ch}(G) + C$, asymptotically almost surely. Also if $G$ is triangle-free regualr graph, then ${\rm ch}_2(G)\leq {\rm ch}(G)+86$ holds.

math.CO↗

arXiv2017

The Bipartition Polynomial of a Graph: Reconstruction, Decomposition, and Applications

The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving graph properties. In addition, we can show that the bipartition polynomial is polynomially reconstructible, which means that we can recover it from the multiset of bipartition polynomials of one-edge-deleted subgraphs.

math.CO↗

arXiv2016

Density of Zeros of the Tutte Polynomial

The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This is the first density result for the zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.

math.CO↗

arXiv2016

Characterizing graphs of maximum matching width at most 2

The maximum matching width is a width-parameter that is defined on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the graphs of maximum matching width at most 2 using the minor obstruction set. Also, we compute the exact value of the maximum matching width of a grid.

math.CO↗

arXiv2014

Characterizing width two for variants of treewidth

In this paper, we consider the notion of \emph{special treewidth}, recently introduced by Courcelle\cite{Courcelle2012}. In a special tree decomposition, for each vertex $v$ in a given graph, the bags containing $v$ form a rooted path. We show that the class of graphs of special treewidth at most two is closed under taking minors, and give the complete list of the six minor obstructions. As an intermediate result, we prove that every connected graph of special treewidth at most two can be constructed by arranging blocks of special treewidth at most two in a specific tree-like fashion. Inspired from the notion of special treewidth, we introduce three natural variants of treewidth, namely \emph{spaghetti treewidth}, \emph{strongly chordal treewidth} and \emph{directed spaghetti treewidth}. All these parameters lie between pathwidth and treewidth, and we provide common structural properties on these parameters. For each parameter, we prove that the class of graphs having the parameter at most two is minor closed, and we characterize those classes in terms of a \emph{tree of cycles} with additional conditions. Finally, we show that for each $k\geq 3$, the class of graphs with special treewidth, spaghetti treewidth, directed spaghetti treewidth, or strongly chordal treewidth, respectively at most $k$, is not closed under taking minors.

math.CO↗