arXiv subjects

Donghyun Kim

Publications and source records attributed to Donghyun Kim.

At least 37 records · Page 2Linked to original sources

arXiv2026

An explicit formula for Koornwinder moments and Rains' positivity conjecture

The asymmetric simple exclusion process (ASEP) is an important particle model with deep connections to orthogonal polynomials. Motivated by this connection, Corteel and Williams introduced the Koornwinder moments $M^{Z}_λ$ at $ t=q $, which generalize the moments of Askey--Wilson polynomials. They showed that the partition function of the two-species ASEP is equal to $M^{Z}_λ$ for a one-row partition $ λ$. In this paper, we investigate a conjecture of Rains on the positivity of the minimal numerator of the Koornwinder moment $M^{Z}_λ$. We derive the first explicit formula for this moment, thereby obtaining a precise formulation of the conjecture by determining the minimal denominator of $M^{Z}_λ$. We also propose a generalization of the conjecture for the more general Koornwinder moments $M^{Z}_{λ,μ}$ indexed by two partitions at special parameter values. We prove the generalized Rains' conjecture in two special cases: $(ξ,q)=(1,0)$ and $(ξ,q)=(1,1)$. For $(ξ,q)=(1,0)$, we construct a lattice path model and obtain a combinatorial formula for $M^{Z}_{λ,μ}$ in terms of non-intersecting lattice paths. For $(ξ,q)=(1,1)$, we establish an explicit product formula for $M^{Z}_{λ,μ}$ and give a combinatorial interpretation using lecture hall tableaux.

math.CO↗

arXiv2026

Personal AI Agent for Camera Roll VQA

We study the personal camera roll visual question answering setting. In this setting, a conversational AI assistant can access a user's personal camera roll and retrieve relevant photos to answer queries, ranging from simple factual questions (e.g., ``Name of the food I tried yesterday?'') to more open-ended ones (e.g., ``Recommend some dishes I have never eaten before''). Given the vast nature of the personal camera roll (i.e., multiple years, hundreds to thousands of photos), a successful AI assistant needs to understand a long-horizon, highly personalized visual content stream in order to navigate and locate the correct and/or relevant information. To support this, we collect and manually annotate questions that mimic real-world usage. The final dataset, camroll, contains 50 users, 31,476 images, and 2,500 QA pairs. We further design camroll-agent, a conversational AI agent equipped with hierarchical memory and a minimal set of tools for efficient navigation over large, personalized visual memory. Experimental results show that camroll-agent outperforms numerous baselines and methods for long-context understanding AI agents system. Together, the camroll dataset and camroll-agent highlight the gap in AI agents' long-context reasoning: personalized visual memory requires different approaches from standard long-context textual memory, especially when consistency, visual details, and user-specific context are present.

cs.CV↗

arXiv2026

Diversity Over Frequency: Rethinking Tool Use in Visual Chain-of-Thought Agents

Visual agents employ external visual tools within visual chains of thought to incorporate fine-grained evidence. While prior work has mainly studied these tools in visual search tasks, their role in more complex visual reasoning remains underexplored. In this paper, we move beyond simple visual search tasks to investigate more challenging tasks, including 3D spatial reasoning and medical visual question answering, where agents must integrate tool-acquired local evidence with the global context. We identify a {tool-use collapse phenomenon: models progressively stop using tools while still achieving higher task accuracy. Moreover, we observe a clear asymmetry: (i) completely eliminating tool use degrades performance, whereas (ii) incentivizing tool use yields only marginal gains despite substantially increasing usage. We find that vanilla training and tool-use encouragement both reduce rollout diversity, explaining why higher tool use does not yield stronger reasoning performance. Motivated by these findings, we add an entropy regularization term to encourage diverse rollout exploration, achieving the best performance despite gradually declining tool usage. Overall, our findings suggest a training-time view of tools as scaffolding, where broader exploration over language generation and visual tool invocation improves reasoning despite tool-use collapse. Project page: https://scaffolded-exploration.github.io

cs.CV↗

arXiv2026

Your Embedding Model is SMARTer Than You Think

Multimodal retrieval relies heavily on single-vector retrievers, which compress rich, sequential token sequences into one single global representation. While efficient, they discard fine-grained, local evidence critical for dense retrieval tasks. Multi-vector approaches were introduced as a solution, but they strictly require training and many ignore the necessity of a globally summarizing representation. To address this, we introduce SMART, a framework that unlocks the latent multi-vector capabilities of standard single-vector models. We first demonstrate that standard contrastive training on the pooled embedding implicitly shapes the retrieval geometry of preceding hidden states via gradient flow. By applying direct late-interaction over these frozen hidden states during inference, SMART acts as a plug-and-play upgrade that consistently improves performance across diverse modalities, improving even the state-of-the-art models further on MMEB-V2. We also reveal SMART's superior performance, as simple lightweight post-training not only saves time and compute, but also brings forth further improvement on Visual Document retrieval, allowing a single-vector model to outperform SoTA multi-vector counterparts. Ultimately, SMART offers both a highly efficient inference enhancement and a powerful finetuning technique for multimodal retrieval. We open source our code and weights at https://github.com/HanSolo9682/SMART.

cs.IR↗

arXiv2026

How Noisy Poses Break Inverse Dynamics: Analysis and Mitigation for Video-Based Joint Torque Estimation

Recent advances in monocular 3D human pose estimation enable accurate body tracking from video. However, translating these kinematic estimates into physical quantities, such as joint torques, remains challenging due to noise amplification through inverse dynamics. In this work, we provide a systematic analysis of how pose estimation noise propagates through the inverse dynamics pipeline. We present three key findings: (1) pose noise is amplified by approximately 1,000x when computing joint torques via numerical differentiation, (2) proximal joints (spine, hips) are up to 10x more sensitive to noise than distal joints (wrists, hands), and (3) low-pass filtering before differentiation substantially reduces this amplification. To enable this analysis, we develop SMPL-Dynamics, a fully differentiable inverse dynamics module for the SMPL body model that requires no external physics simulators. Our module supports end-to-end gradient computation, and we demonstrate this through differentiable pose refinement, which reduces torque error by 93% with negligible change in pose.

cs.CV↗

arXiv2026

Mind the Motions: Benchmarking Theory-of-Mind in Everyday Body Language

Our ability to interpret others' mental states through nonverbal cues (NVCs) is fundamental to our survival and social cohesion. While existing Theory of Mind (ToM) benchmarks have primarily focused on false-belief tasks and reasoning with asymmetric information, they overlook other mental states beyond belief and the rich tapestry of human nonverbal communication. We present Motion2Mind, a framework for evaluating the ToM capabilities of machines in interpreting NVCs. Leveraging an expert-curated body-language reference as a proxy knowledge base, we build Motion2Mind, a carefully curated video dataset with fine-grained nonverbal cue annotations paired with manually verified psychological interpretations. It encompasses 222 types of nonverbal cues and 397 mind states. Our evaluation reveals that current AI systems struggle significantly with NVC interpretation, exhibiting not only a substantial performance gap in Detection, as well as patterns of over-interpretation in Explanation compared to human annotators.

cs.CL↗

arXiv2026

Diffusion Policy for Coordinated Control of a Nonholonomic Mobile Base and Dual Arms in Door Opening and Passing

Opening heavy, self closing doors, especially those that require pulling remains a long standing challenge in robotics. Humans naturally employ both arms in a dexterous manner, rotating the handle, widening the gap, holding the door, switching arms when needed, and moving through while maintaining clearance. To replicate such behaviors, a robot must perform a long sequence of motions spanning multiple stages and interactions with different parts of the door. Traditional approaches rely on state machines that transition between manually defined stages (e.g., pulling after the knob is rotated, passing after the gap is sufficiently wide). While intuitive, these methods lack robustness, as hand crafted trajectories fail to generalize to the diversity of real world conditions without extensive engineering effort. Recent advances in imitation learning offer a scalable alternative, yet no existing visual action model has demonstrated simultaneous coordination of a nonholonomic base and dual arms for the complete door opening and passing task. In this paper, we tackle this complex, highly constrained problem using a diffusion based visuomotor control policy. Our results demonstrate that a single end to end policy can be learned to execute long horizon tasks requiring tight coordination between manipulation and locomotion. The resulting policy not only achieves a high success rate in opening and traversing damped pull doors but also demonstrates strong robustness to external disturbances capabilities that are difficult to realize with traditional methods.

cs.RO↗

arXiv2026

Rethinking Graph Convolution for 2D-to-3D Hand Pose Lifting

Graph convolutional networks (GCNs) are widely used for 3D hand pose estimation, where the hand skeleton is encoded as a fixed adjacency graph. We revisit whether this is the most effective way to incorporate hand topology in 2D-to-3D lifting. In this paper, we perform controlled, parameter-matched ablations on the FPHA benchmark and show that standard multi-head self-attention consistently outperforms GCN baselines. Even when the GCN is strengthened with multi-hop adjacency and matched parameter count, self-attention reduces MPJPE from 12.36 mm to 10.09 mm. A skeleton-constrained graph attention network recovers most of this gap, indicating that input-dependent aggregation is a major source of improvement, while fully connected attention yields additional gains. We further show that hand topology is most effective when introduced as a soft structural prior through graph-distance positional encoding, rather than as a hard adjacency constraint. These results suggest that, for hand pose lifting, adaptive spatial attention is a more effective inductive bias than fixed graph convolution.

cs.CV↗

arXiv2026

Think as Needed: Geometry-Driven Adaptive Perception for Autonomous Driving

Autonomous driving scenes range from empty highways to dense intersections with dozens of interacting road users, yet current 3D detection models apply a fixed computation budget to every frame, wasting resources on simple scenes while lacking capacity for complex ones. Existing approaches compound this problem: Transformer-based interaction models scale quadratically with the number of detected objects, and frame-by-frame processing causes the system to immediately forget objects the moment they become occluded. We propose Enhanced HOPE, an adaptive perception architecture that measures the geometric complexity of each incoming LiDAR frame using an unsupervised statistical estimator and routes it through a shallow or deep processing path accordingly, requiring no manual scene labels. To keep interaction modeling efficient, we replace quadratic pairwise attention with a linear-time subspace-based network that groups nearby objects into clusters and processes them jointly. The computational savings from these two mechanisms free up resources for a persistent temporal memory module that retains previously detected objects and traffic rules across frames, enabling the system to recall occluded objects seconds after they disappear from view. On the nuScenes and CARLA benchmarks, Enhanced HOPE reduces latency by 38% on simple scenes with no accuracy loss, improves mean Average Precision by 2.7 points on rare long-tail scenarios, and tracks objects through occlusions lasting over 5 seconds, where all tested baselines fail.

cs.CV↗

arXiv2026

Signatures of Massive Neutrinos in the Cosmic Web via Persistent Homology

We present the second paper in our program characterizing the impact of massive neutrinos on the multiscale cosmic web using global topology and persistent homology. Building on the methodology established in Paper I, based on discrete Morse theory, we analyze a subset of the Quijote simulations to compute persistent diagrams, Betti curves, and additional topological statistics for both dark matter and halo density fields, across redshifts z=0,1,2. A central result of our study is the first clear demonstration that apex points in persistent diagrams are especially sensitive to neutrino mass, with enhanced sensitivity for specific pairs of saddle points at high redshift. In addition, Betti curves from dark matter density fields broaden and flatten with increasing neutrino masses, exhibiting two characteristic density thresholds where Betti numbers remain invariant. These mass-dependent signatures are detectable at the few-percent level, even for $M_ν \sim 0.1$ eV, providing a robust, physically grounded probe of massive neutrinos in the cosmic web. While traditional two-point statistics encode only pairwise correlations and cannot fully break parameter degeneracies, persistent homology captures higher-order, multiscale information that can lift these degeneracies. Moreover, its high sensitivity to the sum of neutrino masses makes it a promising complement to conventional analyses. Our results thus establish a solid foundation for forward-modeling or emulator-based approaches using persistent homology and environment-based statistics to constrain neutrino mass - potentially enabling direct detection - and additional cosmological parameters, with immediate relevance for ongoing and upcoming galaxy surveys, including DESI, Euclid, and Rubin-LSST.

astro-ph.CO↗

arXiv2026

PAC-BENCH: Evaluating Multi-Agent Collaboration under Privacy Constraints

We are entering an era in which individuals and organizations increasingly deploy dedicated AI agents that interact and collaborate with other agents. However, the dynamics of multi-agent collaboration under privacy constraints remain poorly understood. In this work, we present $PAC\text{-}Bench$, a benchmark for systematic evaluation of multi-agent collaboration under privacy constraints. Experiments on $PAC\text{-}Bench$ show that privacy constraints substantially degrade collaboration performance and make outcomes depend more on the initiating agent than the partner. Further analysis reveals that this degradation is driven by recurring coordination breakdowns, including early-stage privacy violations, overly conservative abstraction, and privacy-induced hallucinations. Together, our findings identify privacy-aware multi-agent collaboration as a distinct and unresolved challenge that requires new coordination mechanisms beyond existing agent capabilities.

cs.AI↗

arXiv2026

Delaunay Canopy: Building Wireframe Reconstruction from Airborne LiDAR Point Clouds via Delaunay Graph

Reconstructing building wireframe from airborne LiDAR point clouds yields a compact, topology-centric representation that enables structural understanding beyond dense meshes. Yet a key limitation persists: conventional methods have failed to achieve accurate wireframe reconstruction in regions afflicted by significant noise, sparsity, or internal corners. This failure stems from the inability to establish an adaptive search space to effectively leverage the rich 3D geometry of large, sparse building point clouds. In this work, we address this challenge with Delaunay Canopy, which utilizes the Delaunay graph as a geometric prior to define a geometrically adaptive search space. Central to our approach is Delaunay Graph Scoring, which not only reconstructs the underlying geometric manifold but also yields region-wise curvature signatures to robustly guide the reconstruction. Built on this foundation, our corner and wire selection modules leverage the Delaunay-induced prior to focus on highly probable elements, thereby shaping the search space and enabling accurate prediction even in previously intractable regions. Extensive experiments on the Building3D Tallinn city and entry-level datasets demonstrate state-of-the-art wireframe reconstruction, delivering accurate predictions across diverse and complex building geometries.

cs.CV↗

arXiv2026

Fourier Decomposition for Explicit Representation of 3D Point Cloud Attributes

While 3D point clouds are widely used in vision applications, their irregular and sparse nature make them challenging to handle. In response, numerous encoding approaches have been proposed to capture the rich semantic information of point clouds. Yet, a critical limitation persists: a lack of consideration for colored point clouds, which serve as more expressive 3D representations encompassing both color and geometry. While existing methods handle color and geometry separately on a per-point basis, this leads to a limited receptive field and restricted ability to capture relationships across multiple points. To address this, we pioneer a colored point cloud encoding methodology that leverages 3D Fourier decomposition to disentangle color and geometric features while extending the receptive field through spectral-domain operations. Our analysis confirms that our approach effectively separates feature components, where the amplitude uniquely captures color attributes and the phase encodes geometric structure, thereby enabling independent learning and utilization of both attributes. We validate our colored point cloud encoding approach on classification, segmentation, and style transfer tasks, achieving state-of-the-art results on the DensePoint dataset.

cs.CV↗

arXiv2026

Spatially Grounded Long-Horizon Task Planning in the Wild

Recent advances in robot manipulation increasingly leverage Vision-Language Models (VLMs) for high-level reasoning, such as decomposing task instructions into sequential action plans expressed in natural language that guide downstream low-level motor execution. However, current benchmarks do not assess whether these plans are spatially executable, particularly in specifying the exact spatial locations where the robot should interact to execute the plan, limiting evaluation of real-world manipulation capability. To bridge this gap, we define a novel task of grounded planning and introduce GroundedPlanBench, a newly curated benchmark for spatially grounded long-horizon action planning in the wild. GroundedPlanBench jointly evaluates hierarchical sub-action planning and spatial action grounding (where to act), enabling systematic assessment of whether generated sub-actions are spatially executable for robot manipulation. We further introduce Video-to-Spatially Grounded Planning (V2GP), an automated data generation framework that leverages real-world robot video demonstrations to improve spatially grounded long-horizon planning. Our evaluations reveal that spatially grounded long-horizon planning remains a major bottleneck for current VLMs. Our results demonstrate that V2GP provides a promising approach for improving both action planning and spatial grounding performance, validated on our benchmark as well as through real-world robot manipulation experiments, advancing progress toward spatially actionable planning.

cs.RO↗

arXiv2026

GuideTWSI: A Diverse Tactile Walking Surface Indicator Dataset from Synthetic and Real-World Images for Blind and Low-Vision Navigation

Tactile Walking Surface Indicators (TWSIs) are safety-critical landmarks that blind and low-vision (BLV) pedestrians use to locate crossings and hazard zones. From our observation sessions with BLV guide dog handlers, trainers, and an O&M specialist, we confirmed the critical importance of reliable and accurate TWSI segmentation for navigation assistance of BLV individuals. Achieving such reliability requires large-scale annotated data. However, TWSIs are severely underrepresented in existing urban perception datasets, and even existing dedicated paving datasets are limited: they lack robot-relevant viewpoints (e.g., egocentric or top-down) and are geographically biased toward East Asian directional bars - raised parallel strips used for continuous guidance along sidewalks. This narrow focus overlooks truncated domes - rows of round bumps used primarily in North America and Europe as detectable warnings at curbs, crossings, and platform edges. As a result, models trained only on bar-centric data struggle to generalize to dome-based warnings, leading to missed detections and false stops in safety-critical environments.

cs.RO↗

arXiv2026

Collaborative Planning with Concurrent Synchronization for Operationally Constrained UAV-UGV Teams

Collaborative planning under operational constraints is an essential capability for heterogeneous robot teams tackling complex large-scale real-world tasks. Unmanned Aerial Vehicles (UAVs) offer rapid environmental coverage, but flight time is often limited by energy constraints, whereas Unmanned Ground Vehicles (UGVs) have greater energy capacity to support long-duration missions, but movement is constrained by traversable terrain. Individually, neither can complete tasks such as environmental monitoring. Effective UAV-UGV collaboration therefore requires energy-constrained multi-UAV task planning, traversability-constrained multi-UGV path planning, and crucially, synchronized concurrent co-planning to ensure timely in-mission recharging. To enable these capabilities, we propose Collaborative Planning with Concurrent Synchronization (CoPCS), a learning-based approach that integrates a heterogeneous graph transformer for operationally constrained task encoding with a transformer decoder for joint, synchronized co-planning that enables UAVs and UGVs to act concurrently in a coordinated manner. CoPCS is trained end-to-end under a unified imitation learning paradigm. We conducted extensive experiments to evaluate CoPCS in both robotic simulations and physical robot teams. Experimental results demonstrate that our method provides the novel multi-robot capability of synchronized concurrent co-planning and substantially improves team performance. More details of this work are available on the project website: https://hcrlab.gitlab.io/project/CoPCS.

cs.RO↗

arXiv2026

Erase at the Core: Representation Unlearning for Machine Unlearning

Many approximate machine unlearning methods demonstrate strong logit-level forgetting -- such as near-zero accuracy on the forget set -- yet continue to preserve substantial information within their internal feature representations. We refer to this discrepancy as superficial forgetting. Recent studies indicate that most existing unlearning approaches primarily alter the final classifier, leaving intermediate representations largely unchanged and highly similar to those of the original model. To address this limitation, we introduce the Erase at the Core (EC), a framework designed to enforce forgetting throughout the entire network hierarchy. EC integrates multi-layer contrastive unlearning on the forget set with retain set preservation through deeply supervised learning. Concretely, EC attaches auxiliary modules to intermediate layers and applies both contrastive unlearning and cross-entropy losses at each supervision point, with layer-wise weighted losses. Experimental results show that EC not only achieves effective logit-level forgetting, but also substantially reduces representational similarity to the original model across intermediate layers. Furthermore, EC is model-agnostic and can be incorporated as a plug-in module into existing unlearning methods, improving representation-level forgetting while maintaining performance on the retain set.

cs.LG↗

arXiv2026

Toward Butler's conjecture

For a partition $ν$, let $λ,μ\subseteq ν$ be two distinct partitions such that $|ν/λ|=|ν/μ|=1$. Butler conjectured that the divided difference $\operatorname{I}_{λ,μ}[X;q,t]=(T_λ\widetilde{H}_μ[X;q,t]-T_μ\widetilde{H}_λ[X;q,t])/(T_λ-T_μ)$ of modified Macdonald polynomials of two partitions $λ$ and $μ$ is Schur positive. By introducing a new LLT equivalence called column exchange rule, we give a combinatorial formula for $\operatorname{I}_{λ,μ}[X;q,t]$, which is a positive monomial expansion. We also prove Butler's conjecture for some special cases.

math.CO↗