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Ting Huang

Publications and source records attributed to Ting Huang.

At least 19 recordsLinked to original sources
arXiv2026

Threshold Ramsey multiplicity and extremal colorings for odd cycles

The Ramsey number $r(H)$ of a graph $H$ is the minimum positive integer $n$ such that every red/blue edge-coloring of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $H$. The threshold Ramsey multiplicity $m(H)$ of $H$ is the minimum number of monochromatic copies of $H$ over all red/blue edge-colorings of $K_{r(H)}$. The only family for which $m(H)$ has been determined is stars, due to Harary and Prins (1974). Let $C_k$ be a cycle on $k$ vertices. Conlon, Fox, Sudakov, and Wei (2022) conjectured that $m(C_k)=(k-1)!/2$ for every sufficiently large odd integer $k$. In this paper, we confirm the conjecture and characterize all the extremal colorings of $K_{2k-1}$. This is also the second family for which $m(H)$ has been determined.

math.CO↗
arXiv2026

MobileVLA-R1 2.0: RL-Enhanced Reasoning for Mobile Robot Control

Grounding natural-language instructions into reliable and executable actions remains a fundamental challenge for vision-language-action (VLA) systems on mobile robots, due to the persistent gap between high-level semantic reasoning and low-level locomotion and manipulation control. Existing approaches often rely on implicit reasoning or monolithic action prediction, making it difficult to maintain coherent long-horizon decision making while producing precise and adaptable robot actions. To address this challenge, we propose MobileVLA-R1 2.0, an RL-enhanced VLA framework that explicitly couples structured embodied reasoning with executable mobile robot control. The framework learns multi-granularity reasoning over embodied trajectories through supervised Chain-of-Thought (CoT) alignment and reinforcement learning, improving reasoning-to-action consistency beyond purely behavioral supervision. To support both locomotion and manipulation, we further introduce a reasoning-conditioned action decoder that maps multimodal reasoning representations to task-level action targets, which are subsequently translated into embodiment-specific commands by robot controllers. This design provides a unified perception-reasoning-action interface while decoupling high-level action generation from robot-specific actuation. We conduct extensive evaluations on language-guided navigation, quadruped control, and humanoid mobile manipulation, covering VLN-CE, QUARD, and real-world deployments on Unitree Go2 and G1 robots. MobileVLA-R1 2.0 consistently outperforms strong VLA baselines, achieving an average 1.6 point improvement in SR on VLN-CE and a 10.0 point improvement in full-task success on real-world G1 mobile manipulation tasks over MobileVLA-R1, while demonstrating robust long-horizon instruction following and closed-loop execution across different robotic platforms.

cs.CV↗
arXiv2026

REER-PT: Reverse-Engineered Reasoning for Perplexity-Guided Pre-training Data Augmentation

As language-model compute continues to scale, high-quality training data is becoming an increasingly important bottleneck. Conventional next-token prediction supervises what follows a context but leaves the intermediate reasoning behind that continuation implicit. We introduce \textbf{REER-PT}, a scalable framework that extends Reverse-Engineered Reasoning (REER) to raw pre-training data. REER-PT identifies continuations that are difficult to predict but can still be inferred from the preceding context, and inserts concise reasoning annotations that reconstruct the missing connection between context and continuation. Candidate annotations are generated and refined offline, with perplexity serving as the optimization signal. Constraints on length and target leakage filter out unhelpful or trivial annotations. This sparse transformation preserves the source text and remains compatible with standard next-token prediction, avoiding online reasoning rollouts during pre-training. We apply REER-PT to transform a source pre-training corpus into an augmented one. Across augmented-data, original-token, and selected-continuation comparisons, perplexity reductions range from 0.42 to 7.29, and only about 0.05\% of annotation 13-grams appear verbatim in the source text. We then train two 680M-parameter models with the same architecture and training configuration on the source and augmented corpora, respectively. The augmented-data model gains up to 2.07 percentage points on several knowledge and reasoning benchmarks. Together, the perplexity analysis indicates improved continuation predictability, while the controlled pre-training experiments suggest that this augmentation can improve model performance without changing the standard pre-training objective.

cs.CL↗
arXiv2026

New upper bound for the Ramsey number of odd cycles

The \emph{$k$-color Ramsey number} $R_k(C_{2\ell+1})$ is the least integer $n$ such that any $k$-edge-coloring of a complete graph $K_n$ has a monochromatic odd cycle $C_{2\ell+1}$. Axenovich, Cames van Batenburg, Janzer, Michel, and Rundstr\"om~(JCT-B, 2026) recently proved \[ R_k(C_{2\ell+1})\le (4\ell-2)^k k^{k/\ell}+1, \] and Miyazaki, Mulrenin, Pohoata, and Zheng further improved the factor $k^{k/\ell}$ to $(k!)^{1/\ell}$. As Jenssen and Skokan (AM, 2021) determined $R_k(C_{2\ell+1})$ for fixed $k$ and sufficiently large $\ell$, it becomes even more interesting to seek better bound for fixed $\ell$ and sufficiently large $k$. In this paper, we show \[ R_k(C_{2\ell+1}) \le \frac{2\ell}{2\ell-1}(2\ell-1)^k(k!)^{1/\ell} \exp\!\left(k^{1-1/\ell}+O_\ell\!\left(k^{1-2/\ell}+\log k\right)\right)+1 \] for every fixed $\ell\ge 2$ and sufficiently large $k$, which improves the bound of Miyazaki et al. by a factor $2^{k-o(k)}$, and the bound of Axenovich et al. by a factor $(2\e^{1/\ell})^{k-o(k)}$.

math.CO↗
arXiv2026

ConsiSpace: Learning Geometric Consistency Matters for Video Spatial Reasoning

Video spatial reasoning is essential for navigation-oriented perception and long-video question answering, where models must infer spatial relations across long horizons under changing viewpoints. However, existing multimodal large language models (MLLMs) remain largely semantic-centric, and often fail to reliably aggregate consistent spatial evidence from redundant video observations, leading to inefficient or unstable reasoning. To address these issues, we propose ConsiSpace, a geometry-consistency-aware framework for geometry-sensitive video spatial reasoning that turns spatial consistency into both an evidence organization principle and an explicit post-SFT learning signal. We build a geometry-consistent memory (GCM) including implicit evidence tokens and explicit geometric cues, and leverage efficient organization strategies to compactly preserve task-related spatial evidence. Furthermore, we utilize unified consistency self-supervised reinforcement learning (UC-SSRL) after supervised fine-tuning to improve cross-view stability, with answer-, metric-, and topology-consistency rewards. Extensive experiments on three spatial-reasoning benchmarks, VSI-Bench, OSI-Bench, and MMSI-Video-Bench, show consistent gains, improving the average score by 12.6 points over the strongest baselines.

cs.CV↗
arXiv2026

A note on tree-cycle Ramsey numbers

Let $R(T_n,C_m)$ denote the Ramsey number of a tree $T_n$ on $n$ vertices versus a cycle $C_m$ of length $m$. Burr, Erd\H{o}s, Faudree, Rousseau, and Schelp (1982) asked for the least function $f(m)$ such that $R(T_n,C_m)=2n-1$ for every odd $m\ge 3$ whenever $n\ge f(m)$. They proved that $f(m)\le 756m^{10}$. This bound was later improved to $25m$ by Brennan (2016) and to $4m-8$ by Fan and Lin (2025). In this note, we show that $f(m)\le 2m-4$ by using a different method and conjecture that $f(m)=\lceil (2m-1)/3\rceil$.

math.CO↗
arXiv2026

Odd covers for complete graphs and complete 3-graphs

The Graham-Pollak theorem says that one needs at least $n - 1$ complete bipartite graphs to cover each edge of a complete graph $K_{n}$ on $n$ vertices exactly once. The odd cover problem is a parity analogue which seeks the minimum number of complete bipartite graphs, denoted by $b_2(n)$, such that each edge of $ K_n $ is covered an odd number of times. An odd cover of a complte 3-graph $K_n^{(3)}$ on $n$ vertices is a family of complete $3$-partite $3$-graphs such that every triple is covered an odd number of times. Let $b_3(n)$ be the minimum size of such a family. The values of $b_2(n)$ and $b_3(n)$ are determined for some $n$ in several previous works. In this paper, we first determine the value of $b_2(n)$ for all $n$, which confirms a conjecture due to Buchanan et al. (JGT, 2026), and then show $b_3(n+1)=b_2(n)$ by which the value of $b_3(n)$ is determined for all $n$, that resolves a question posed by Leader and Tan (EJC, 2026).

math.CO↗
arXiv2026

On the threshold Ramsey multiplicity conjectures for paths and even cycles

The Ramsey number $r(H)$ of a graph $H$ is the minimum positive integer $n$ such that every red/blue edge-coloring of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $H$. The threshold Ramsey multiplicity $m(H)$ of $H$ is the minimum number of monochromatic copies of $H$ over all red/blue edge-colorings of $K_{r(H)}$. Let $P_t$ and $C_t$ be a path and a cycle on $t$ vertices, respectively. In this paper, by using combinatorial and local random construction, we show that $$m(C_{2t})\le t^{-\gamma+o(1)}\frac{(2t-1)!}{2}, \qquad m(P_{2t+1})\le t^{-\gamma+o(1)}\frac{t}{2}(2t)!,$$ and $$m(P_{2t})\leq \left(\frac{7}{8}+o(1)\right)\frac{(2t)!}{2},$$ for sufficiently large $t$, where $\gamma=1/(1+\sqrt{2})$. These results disprove two conjectures on the threshold Ramsey multiplicity for even cycles and paths, due to Conlon, Fox, Sudakov, and Wei.

math.CO↗
arXiv2026

Let Geometry GUIDE: Layer-wise Unrolling of Geometric Priors in Multimodal LLMs

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in 2D visual tasks but still struggle to understand physical space in real-world visual streams. Recently, feed-forward geometric foundation models that implicitly extract geometric priors from visual inputs have offered a promising direction. However, many existing geometry-aware MLLMs extract features from a single deep encoder layer and perform one-shot fusion at the language-model input, potentially overlooking complementary information across geometric encoder layers, limiting access to fine-grained geometric cues, and hindering progressive cross-modal adaptation. To address these limitations, we propose GUIDE (Geometric Unrolling Inside MLLM Early-layers), a progressive framework for integrating geometric priors. GUIDE samples and aligns multi-level features from the geometric encoder and sequentially injects them into the early layers of the MLLM. This design enables the MLLM to continuously access multi-granularity geometric cues and progressively integrate them with visual representations during layer-wise semantic abstraction. GUIDE further introduces a dual context-aware gating mechanism at both the token and layer levels, selectively regulating geometric information to reduce redundant injection and interference with pretrained representations. Extensive experiments on spatial reasoning and 3D scene understanding benchmarks, including VSI-Bench, ScanRefer, and Scan2Cap, validate the effectiveness and cross-task applicability of GUIDE. Our 5B and 9B models achieve average scores of 71.5 and 72.1 on VSI-Bench, respectively.

cs.CV↗
arXiv2026

When to Memorize and When to Stop: Gated Recurrent Memory for Long-Context Reasoning

While reasoning over long context is crucial for various real-world applications, it remains challenging for large language models (LLMs) as they suffer from performance degradation as the context length grows. Recent work MemAgent has tried to tackle this by processing context chunk-by-chunk in an RNN-like loop and updating a textual memory for final answering. However, this naive recurrent memory update faces two crucial drawbacks: (i) memory can quickly explode because it can update indiscriminately, even on evidence-free chunks; and (ii) the loop lacks an exit mechanism, leading to unnecessary computation after even sufficient evidence is collected. To address these issues, we propose GRU-Mem, which incorporates two text-controlled gates for more stable and efficient long-context reasoning. Specifically, in GRU-Mem, the memory only updates when the update gate is open and the recurrent loop will exit immediately once the exit gate is open. To endow the model with such capabilities, we introduce two reward signals $r^{\text{update}}$ and $r^{\text{exit}}$ within end-to-end RL, rewarding the correct updating and exiting behaviors respectively. Experiments on various long-context reasoning tasks demonstrate the effectiveness and efficiency of GRU-Mem, which generally outperforms the vanilla MemAgent with up to 400\% times inference speed acceleration.

cs.CL↗
arXiv2026

Surrogate Ensemble in Expensive Multi-Objective Optimization via Deep Q-Learning

Surrogate-assisted Evolutionary Algorithms~(SAEAs) have shown promising robustness in solving expensive optimization problems. A key aspect that impacts SAEAs' effectiveness is surrogate model selection, which in existing works is predominantly decided by human developer. Such human-made design choice introduces strong bias into SAEAs and may hurt their expected performance on out-of-scope tasks. In this paper, we propose a reinforcement learning-assisted ensemble framework, termed as SEEMOO, which is capable of scheduling different surrogate models within a single optimization process, hence boosting the overall optimization performance in a cooperative paradigm. Specifically, we focus on expensive multi-objective optimization problems, where multiple objective functions shape a compositional landscape and hence challenge surrogate selection. SEEMOO comprises following core designs: 1) A pre-collected model pool that maintains different surrogate models; 2) An attention-based state-extractor supports universal optimization state representation of problems with varied objective numbers; 3) a deep Q-network serves as dynamic surrogate selector: Given the optimization state, it selects desired surrogate model for current-step evaluation. SEEMOO is trained to maximize the overall optimization performance under a training problem distribution. Extensive benchmark results demonstrate SEEMOO's surrogate ensemble paradigm boosts the optimization performance of single-surrogate baselines. Further ablation studies underscore the importance of SEEMOO's design components.

cs.NE↗
arXiv2026

3D CoCa v2: Contrastive Learners with Test-Time Search for Generalizable Spatial Intelligence

Spatial intelligence refers to the ability to perceive, reason about, and describe objects and their relationships within three-dimensional environments, forming a foundation for embodied perception and scene understanding. 3D captioning aims to describe 3D scenes in natural language; however, it remains challenging due to the sparsity and irregularity of point clouds and, more critically, the weak grounding and limited out-of-distribution (OOD) generalization of existing captioners across drastically different environments, including indoor and outdoor 3D scenes. To address this challenge, we propose 3D CoCa v2, a generalizable 3D captioning framework that unifies contrastive vision-language learning with 3D caption generation and further improves robustness via test-time search (TTS) without updating the captioner parameters. 3D CoCa v2 builds on a frozen CLIP-based semantic prior, a spatially-aware 3D scene encoder for geometry, and a multimodal decoder jointly optimized with contrastive and captioning objectives, avoiding external detectors or handcrafted proposals. At inference, TTS produces diverse caption candidates and performs reward-guided selection using a compact scene summary. Experiments show improvements over 3D CoCa of +1.50 CIDEr@0.5IoU on ScanRefer and +1.61 CIDEr@0.5IoU on Nr3D, and +3.8 CIDEr@0.25 in zero-shot OOD evaluation on TOD3Cap. Code will be released at https://github.com/AIGeeksGroup/3DCoCav2.

cs.CV↗
arXiv2025

OpenGround: Planning-based Online Perception for Open-World 3D Visual Grounding

3D visual grounding aims to locate objects based on natural language descriptions in 3D scenes. Existing supervised methods are limited by generalization and recent zero-shot methods typically rely on a predefined Object Lookup Table (OLT) to query Visual Language Models (VLMs) for reasoning about object locations via a single step grounding, which limits the applications in scenarios with undefined targets and complex queries. To address these problems, we present OpenGround, a novel zero-shot framework for open-world 3D visual grounding that remains compatible with recent zero-shot methods. OpenGround integrates Task-Chain Planning to decompose a query into a plan of context-to-target sub-goals for progressive grounding, and Context-Guided Perception to perceive novel objects online under context guidance from the task chain. We also propose a new dataset named OpenTarget, which contains over 7000 object-description pairs to mimic open-world evaluation. Extensive experiments demonstrate that OpenGround achieves competitive performance on Nr3D, state-of-the-art on ScanRefer, and delivers a substantial 17.6\% improvement on OpenTarget. Project Page at https://why-102.github.io/openground.io/.

cs.CV↗
arXiv2025

TRACE: A Generalizable Drift Detector for Streaming Data-Driven Optimization

Many optimization tasks involve streaming data with unknown concept drifts, posing a significant challenge as Streaming Data-Driven Optimization (SDDO). Existing methods, while leveraging surrogate model approximation and historical knowledge transfer, are often under restrictive assumptions such as fixed drift intervals and fully environmental observability, limiting their adaptability to diverse dynamic environments. We propose TRACE, a TRAnsferable C}oncept-drift Estimator that effectively detects distributional changes in streaming data with varying time scales. TRACE leverages a principled tokenization strategy to extract statistical features from data streams and models drift patterns using attention-based sequence learning, enabling accurate detection on unseen datasets and highlighting the transferability of learned drift patterns. Further, we showcase TRACE's plug-and-play nature by integrating it into a streaming optimizer, facilitating adaptive optimization under unknown drifts. Comprehensive experimental results on diverse benchmarks demonstrate the superior generalization, robustness, and effectiveness of our approach in SDDO scenarios.

cs.LG↗
arXiv2025

MobileVLA-R1: Reinforcing Vision-Language-Action for Mobile Robots

Grounding natural-language instructions into continuous control for quadruped robots remains a fundamental challenge in vision language action. Existing methods struggle to bridge high-level semantic reasoning and low-level actuation, leading to unstable grounding and weak generalization in the real world. To address these issues, we present MobileVLA-R1, a unified vision-language-action framework that enables explicit reasoning and continuous control for quadruped robots. We construct MobileVLA-CoT, a large-scale dataset of multi-granularity chain-of-thought (CoT) for embodied trajectories, providing structured reasoning supervision for alignment. Built upon this foundation, we introduce a two-stage training paradigm that combines supervised CoT alignment with GRPO reinforcement learning to enhance reasoning consistency, control stability, and long-horizon execution. Extensive evaluations on VLN and VLA tasks demonstrate superior performance over strong baselines, with approximately a 5% improvement. Real-world deployment on a quadruped robot validates robust performance in complex environments. Code: https://github.com/AIGeeksGroup/MobileVLA-R1. Website: https://aigeeksgroup.github.io/MobileVLA-R1.

cs.RO↗
arXiv2025

Virtual Width Networks

We introduce Virtual Width Networks (VWN), a framework that delivers the benefits of wider representations without incurring the quadratic cost of increasing the hidden size. VWN decouples representational width from backbone width, expanding the embedding space while keeping backbone compute nearly constant. In our large-scale experiment, an 8-times expansion accelerates optimization by over 2 times for next-token and 3 times for next-2-token prediction. The advantage amplifies over training as both the loss gap grows and the convergence-speedup ratio increases, showing that VWN is not only token-efficient but also increasingly effective with scale. Moreover, we identify an approximately log-linear scaling relation between virtual width and loss reduction, offering an initial empirical basis and motivation for exploring virtual-width scaling as a new dimension of large-model efficiency.

cs.LG↗
arXiv2025

Nav-R1: Reasoning and Navigation in Embodied Scenes

Embodied navigation requires agents to integrate perception, reasoning, and action for robust interaction in complex 3D environments. Existing approaches often suffer from incoherent and unstable reasoning traces that hinder generalization across diverse environments, and difficulty balancing long-horizon semantic reasoning with low-latency control for real-time navigation. To address these challenges, we propose Nav-R1, an embodied foundation model that unifies reasoning in embodied environments. We first construct Nav-CoT-110K, a large-scale dataset of step-by-step Chains-of-Thought (CoT) for embodied tasks, which enables cold-start initialization with structured reasoning. Building on this foundation, we design a GRPO-based reinforcement learning framework with three complementary rewards: format, understanding, and navigation, to improve structural adherence, semantic grounding, and path fidelity. Furthermore, we introduce a Fast-in-Slow reasoning paradigm, decoupling deliberate semantic reasoning from low-latency reactive control for efficient yet coherent navigation. Extensive evaluations on embodied AI benchmarks demonstrate that Nav-R1 consistently outperforms strong baselines, with over 8% average improvement in reasoning and navigation performance. Real-world deployment on a mobile robot further validates its robustness under limited onboard resources. Code: https://github.com/AIGeeksGroup/Nav-R1. Website: https://aigeeksgroup.github.io/Nav-R1.

cs.RO↗
arXiv2025

3D-R1: Enhancing Reasoning in 3D VLMs for Unified Scene Understanding

Large vision-language models (VLMs) have made significant strides in 2D visual understanding tasks, sparking interest in extending these capabilities to 3D scene understanding. However, current 3D VLMs often struggle with robust reasoning and generalization due to limitations in high-quality spatial data and the static nature of viewpoint assumptions. To address these challenges, we propose 3D-R1, a foundation model that enhances the reasoning capabilities of 3D VLMs. Specifically, we first construct a high-quality synthetic dataset with CoT, named Scene-30K, leveraging existing 3D-VL datasets and a data engine based on Gemini 2.5 Pro. It serves as cold-start initialization data for 3D-R1. Moreover, we leverage RLHF policy such as GRPO in the reinforcement learning training process to enhance reasoning capabilities and introduce three reward functions: a perception reward, a semantic similarity reward and a format reward to maintain detection accuracy and answer semantic precision. Furthermore, we introduce a dynamic view selection strategy that adaptively chooses the most informative perspectives for 3D scene understanding. Extensive experiments demonstrate that 3D-R1 delivers an average improvement of 10% across various 3D scene benchmarks, highlighting its effectiveness in enhancing reasoning and generalization in 3D scene understanding. Code: https://github.com/AIGeeksGroup/3D-R1. Website: https://aigeeksgroup.github.io/3D-R1.

cs.CV↗