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Inhyeok Choi

Publications and source records attributed to Inhyeok Choi.

At least 19 recordsLinked to original sources
arXiv2026

Non-arithmeticity of length spectra of subgroups of mapping class groups

In this paper, we prove that every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichm\"uller length spectrum. Namely, Teichm\"uller translation lengths of its pseudo-Anosov elements generate a dense additive subgroup of $\mathbb{R}$. We prove this by introducing the notion of cross-ratios on $\mathcal{MF}$ and $\mathcal{PMF}$, and studying its geometric and dynamical properties, despite the lack of negatively curved features of the Teichm\"uller space nor the conformal geometry on $\mathcal{PMF}$.

math.GT↗
arXiv2026

SAGE: Training-Free Semantic Evidence Composition for Edge-Cloud Inference under Hard Uplink Budgets

Edge-cloud hybrid inference offloads difficult inputs to a powerful remote model, but the uplink channel imposes hard per-request constraints on the number of bits that can be transmitted. We show that selecting transmitted content based solely on attention-based importance, the standard approach in collaborative inference, is inherently limited under hard budgets. Two findings support this claim. First, replacing high-importance units with low-importance but complementary ones improves server accuracy. This shows that what matters is not individual importance but how well the transmitted set covers diverse aspects of the input. Second, spatially uniform selection without any content information achieves competitive accuracy at moderate budgets. This confirms that spatial coverage alone carries independent value. Based on this analysis, we propose SAGE (Semantic Attention-Guided Evidence), a principled, training-free method that combines importance filtering with embedding-diversity sampling. SAGE achieves 93% of the server ceiling in offloaded accuracy while transmitting fewer than half of the available evidence units on ImageNet-1K, substantially outperforming importance-only composition.

cs.LG↗
arXiv2026

Not Like Transformers: Drop the Beat Representation for Dance Generation with Mamba-Based Diffusion Model

Dance is a form of human motion characterized by emotional expression and communication, playing a role in various fields such as music, virtual reality, and content creation. Existing methods for dance generation often fail to adequately capture the inherently sequential, rhythmical, and music-synchronized characteristics of dance. In this paper, we propose \emph{MambaDance}, a new dance generation approach that leverages a Mamba-based diffusion model. Mamba, well-suited to handling long and autoregressive sequences, is integrated into our two-stage diffusion architecture, substituting off-the-shelf Transformer. Additionally, considering the critical role of musical beats in dance choreography, we propose a Gaussian-based beat representation to explicitly guide the decoding of dance sequences. Experiments on AIST++ and FineDance datasets for each sequence length show that our proposed method effectively generates plausible dance movements while reflecting essential characteristics, consistently from short to long dances, compared to the previous methods. Additional qualitative results and demo videos are available at \small{https://vision3d-lab.github.io/mambadance}.

cs.CV↗
arXiv2026

ASPEN: Spectral-Temporal Fusion for Cross-Subject Brain Decoding

Cross-subject generalization in EEG-based brain-computer interfaces (BCIs) remains challenging due to individual variability in neural signals. We investigate whether spectral representations offer more stable features for cross-subject transfer than temporal waveforms. Through correlation analyses across three EEG paradigms (SSVEP, P300, and Motor Imagery), we find that spectral features exhibit consistently higher cross-subject similarity than temporal signals. Motivated by this observation, we introduce ASPEN, a hybrid architecture that combines spectral and temporal feature streams via multiplicative fusion, requiring cross-modal agreement for features to propagate. Experiments across six benchmark datasets reveal that ASPEN is able to dynamically achieve the optimal spectral-temporal balance depending on the paradigm. ASPEN achieves the best unseen-subject accuracy on three of six datasets and competitive performance on others, demonstrating that multiplicative multimodal fusion enables effective cross-subject generalization.

cs.LG↗
arXiv2026

Classification of horospherical invariant measures in higher rank: The Full Story

In this paper, we classify horospherical invariant Radon measures for Anosov subgroups of arbitrary semisimple real algebraic groups. This generalizes the works of Burger and Roblin in rank one to higher ranks. At the same time, this extends the works of Furstenberg, Veech, and Dani, and a special case of Ratner's theorem for finite-volume homogeneous spaces to infinite-volume Anosov homogeneous spaces. Especially, this resolves the open problems proposed by Landesberg--Lee--Lindenstrauss--Oh and by Oh. Our measure classification is in fact for a more general class of discrete subgroups, including relatively Anosov subgroups with respect to any parabolic subgroups, not necessarily minimal. We also obtain results for their normal subgroups. Our method is rather geometric, not relying on continuous flows or ergodic theorems.

math.DS↗
arXiv2025

Divergence-type semigroups in Kleinian groups and Hausdorff dimension

Let $\Gamma$ be a non-elementary, non-convex-cocompact Kleinian group acting on $\mathbb{H}^{d}$. We show that the Hausdorff dimension of the sublinearly conical Myrberg limit set of $\Gamma$ is equal to the critical exponent of $\Gamma$. This gives a different proof of a theorem by M. Mj and W. Yang. Along the way, we construct subsemigroups of $\Gamma$ of divergence type and develop the Patterson--Sullivan theory.

math.DS↗
arXiv2025

Invariant measures on the space of measured laminations for subgroups of mapping class group

For a non-elementary subgroup of the mapping class group of a surface, we study its invariant Radon measures on the space of measured laminations, by classifying them on the recurrent measured laminations. In particular, given a divergence-type subgroup, we show the uniquely ergodic by explicitly constructing the ergodic measure. This generalizes Lindenstrauss--Mirzakhani's result and Hamenst\"adt's result for the full mapping class group, in which case the ergodic measure is the Thurston measure. As a special case, we deduce that for a convex cocompact subgroup, every invariant ergodic Radon measure on the space of all measured laminations is either the unique measure on recurrent measured laminations, or a counting measure on the orbit of a non-recurrent measured lamination. Our method is geometric and does not rely on continuous or homogeneous flows on the ambient space or a dynamical system associated with a finite measure space. This leads to a unifying approach for various metric spaces, including Teichm\"uller spaces and partially $\operatorname{CAT}(-1)$ spaces.

math.DS↗
arXiv2025

Percolation in acylindrically hyperbolic groups

Let $G$ be an acylindrically hyperbolic group. We prove that Bernoulli bond percolation on every Cayley graph of $G$ has a nonuniqueness phase, in which there are infinitely many infinite clusters. This generalizes Hutchcroft's result for Gromov hyperbolic graphs to relatively hyperbolic groups, mapping class groups and rank-1 CAT(0) groups for example.

math.GR↗
arXiv2025

Metric weak proper discontinuity for pseudo-Anosov maps

We present a metric version of weak proper discontinuity (WPD) for pseudo-Anosov maps on surfaces. As an application, we show that there are plenty of quasi-morphisms on the homeomorphism group of a torus or a hyperbolic surface that are unbounded on certain homeomorphisms with large fixed set.

math.GT↗
arXiv2025

Acylindrically hyperbolic groups and counting problems

We show that Morse elements are generic in acylindrically hyperbolic groups. As an application, we observe that fully irreducible outer automorphisms are generic in the outer automorphism group of a finite-rank free group.

math.GR↗
arXiv2025

Pivoting technique for the circle homeomorphism group

We adapt Gou{\"e}zel's pivoting technique to the circle homeomorphism group. As an application, we give different proofs of Gilabert Vio's probabilistic Tits alternative and Malicet's exponential synchronization.

math.DS↗
arXiv2024

Smoothing countable group actions on metrizable spaces

We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenst\"{a}dt regarding finitely generated groups, and our proof is based upon her idea. This also gives a simple proof of a theorem due to Deroin, Kleptsyn and Navas regarding one-manifolds. We also establish an analogous result for closed subgroups of locally compact groups.

math.GR↗
arXiv2024

Counting pseudo-Anosovs as weakly contracting isometries

We show that pseudo-Anosov mapping classes are generic in every Cayley graph of the mapping class group of a finite-type hyperbolic surface. Our method also yields an analogous result for rank-one CAT(0) groups and hierarchically hyperbolic groups with Morse elements. Finally, we prove that Morse elements are generic in every Cayley graph of groups that are quasi-isometric to (well-behaved) hierarchically hyperbolic groups. This gives a quasi-isometry invariant theory of counting group elements in groups beyond relatively hyperbolic groups.

math.GT↗
arXiv2024

Confined subgroups in groups with contracting elements

In this paper, we study the growth of confined subgroups through boundary actions of groups with contracting elements. We establish that the growth rate of a confined subgroup is strictly greater than half of the ambient growth rate in groups with purely exponential growth. Along the way, several results are obtained on the Hopf decomposition for boundary actions of subgroups with respect to conformal measures. In particular, we prove that confined subgroups are conservative, and examples of subgroups with nontrivial Hopf decomposition are constructed. We show a connection between Hopf decomposition and quotient growth and provide a dichotomy on quotient growth of Schreier graphs for subgroups in hyperbolic groups.

math.GR↗
arXiv2024

Contracting isometries and differentiability of the escape rate

Let $G$ be a countable group whose action on a metric space $X$ involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm{\"u}ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on $G$. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of $G$ on $X$ is weakly properly discontinuous (WPD), we discuss continuity of the asymptotic entropy of random walks on $G$.

math.GR↗
arXiv2023

Random walks on groups and superlinear divergent geodesics

In this paper, we study random walks on groups that contain superlinear divergent geodesics, in the line of thoughts of Goldsborough-Sisto. The existence of a superlinear divergent geodesic is a quasi-isometry invariant which allows us to execute Gou\"ezel's pivoting technique. We develop the theory of superlinear divergence and establish a central limit theorem for random walks on these groups.

math.GT↗
arXiv2023

Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces

We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition, we prove that non-elementary random walks exhibit at least linear growth of translation lengths. As a corollary, almost every random walk on mapping class groups eventually becomes pseudo-Anosov and almost every random walk on $\mathrm{Out}(F_n)$ eventually becomes fully irreducible. If the underlying measure further has finite first moment, then the growth rate of translation lengths is equal to the drift, the escape rate of the random walk. We then apply our technique to investigate the random walks induced by the action of mapping class groups on Teichm{ü}ller spaces. In particular, we prove the spectral theorem under finite first moment condition, generalizing a result of Dahmani and Horbez.

math.GT↗