arXiv subjects

Ziyuan Zhao

Publications and source records attributed to Ziyuan Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Longest cycles intersect linearly in highly connected graphs

A longstanding conjecture attributed to Smith (1984) asserts that for every $k\ge2$, any two longest cycles in a $k$-connected graph share at least $k$ vertices. In this paper, we prove the first linear lower bound, showing that any two longest cycles in a $k$-connected graph share at least $k/600$ vertices. Departing from previous Turán-type extremal arguments, we develop a novel structural approach that also yields applications to related problems on longest cycles and paths.

math.CO↗

arXiv2026

crossMoDA Challenge: Evolution of Cross-Modality Domain Adaptation Techniques for Vestibular Schwannoma and Cochlea Segmentation from 2021 to 2023

The cross-Modality Domain Adaptation (crossMoDA) challenge series, initiated in 2021 in conjunction with the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), focuses on unsupervised cross-modality segmentation, learning from contrast-enhanced T1 (ceT1) and transferring to T2 MRI. The task is an extreme example of domain shift chosen to serve as a meaningful and illustrative benchmark. From a clinical application perspective, it aims to automate Vestibular Schwannoma (VS) and cochlea segmentation on T2 scans for more cost-effective VS management. Over time, the challenge objectives have evolved to enhance its clinical relevance. The challenge evolved from using single-institutional data and basic segmentation in 2021 to incorporating multi-institutional data and Koos grading in 2022, and by 2023, it included heterogeneous routine data and sub-segmentation of intra- and extra-meatal tumour components. In this work, we report the findings of the 2022 and 2023 editions and perform a retrospective analysis of the challenge progression over the years. The observations from the successive challenge contributions indicate that the number of outliers decreases with an expanding dataset. This is notable since the diversity of scanning protocols of the datasets concurrently increased. The winning approach of the 2023 edition reduced the number of outliers on the 2021 and 2022 testing data, demonstrating how increased data heterogeneity can enhance segmentation performance even on homogeneous data. However, the cochlea Dice score declined in 2023, likely due to the added complexity from tumour sub-annotations affecting overall segmentation performance. While progress is still needed for clinically acceptable VS segmentation, the plateauing performance suggests that a more challenging cross-modal task may better serve future benchmarking.

eess.IV↗

arXiv2026

An exact formula for Erdős' problem 1005

In 1943, Erdős considered the minimum number $f(n)$ of terms between two fractions in the Farey sequence of order $n$ whose numerators and denominators are oppositely ordered. Determining the constant $c$ in $f(n)=(c+o(1))n$ is known as Erdős Problem 1005. Recently, Cipollini solved this asymptotic problem by proving that $f(n)=(1/4+o(1))n$. Following his framework, we give an analytic proof of an exact formula for $f(n)$ for all sufficiently large $n$. Combining this with a finite computer verification, we further determine $f(n)$ for every integer $n\geq 4$.

math.NT↗

arXiv2026

CoMoL: Efficient Mixture of LoRA Experts via Dynamic Core Space Merging

Large language models (LLMs) achieve remarkable performance on diverse downstream and domain-specific tasks via parameter-efficient fine-tuning (PEFT). However, existing PEFT methods, particularly MoE-LoRA architectures, suffer from limited parameter efficiency and coarse-grained adaptation due to the proliferation of LoRA experts and instance-level routing. To address these issues, we propose Core Space Mixture of LoRA (\textbf{CoMoL}), a novel MoE-LoRA framework that incorporates expert diversity, parameter efficiency, and fine-grained adaptation. Specifically, CoMoL introduces two key components: core space experts and core space routing. Core space experts store each expert in a compact core matrix, preserving diversity while controlling parameter growth. Core space routing dynamically selects and activates the appropriate core experts for each token, enabling fine-grained, input-adaptive routing. Activated core experts are then merged via a soft-merging strategy into a single core expert, which is combined with a shared LoRA to form a specialized LoRA module. Besides, the routing network is projected into the same low-rank space as the LoRA matrices, further reducing parameter overhead without compromising expressiveness. Extensive experiments demonstrate that CoMoL retains the adaptability of MoE-LoRA architectures while achieving parameter efficiency comparable to standard LoRA, consistently outperforming existing methods across multiple tasks.

cs.CL↗

arXiv2026

Longest cycles and Dirac-type results in highly connected graphs

A classical theorem of Nash-Williams states that if $G$ is a $2$-connected graph on $n$ vertices with minimum degree at least $(n+2)/3$, then for every longest cycle $C$ of $G$, the graph $G-V(C)$ is edgeless. Motivated by a higher-connectivity analogue, Bondy conjectured in 1980 that if $G$ is a $k$-connected graph on $n$ vertices with minimum degree at least $(n+k(k-1))/(k+1)$, then for every longest cycle $C$ of $G$, every path in $G-V(C)$ has at most $k-1$ vertices. This conjecture is known for $k\le 3$ and remains open for all $k\ge 4$. In this paper, we prove Bondy's conjecture for all sufficiently large graphs. The key ingredient is a new Dirac-type theorem that gives a lower bound on the length of a longest cycle in a $k$-connected graph, which also yields a partial solution to a conjecture of Jung from 1990. Along the way, we develop several new tools, including a DFS lemma and an average-degree analogue of the Bondy--Jackson theorem. We conclude with a discussion of related problems and a counterexample to a conjecture of Voss from 1991.

math.CO↗

arXiv2026

Leaf-to-leaf paths and cycles in degree-critical graphs

An $n$-vertex graph is degree 3-critical if it has $2n - 2$ edges and no proper induced subgraph with minimum degree at least 3. In 1988, Erdős, Faudree, Gyárfás, and Schelp asked whether one can always find cycles of all short lengths in these graphs, which was disproven by Narins, Pokrovskiy, and Szabó through a construction based on leaf-to-leaf paths in trees whose vertices have degree either 1 or 3. They went on to suggest several weaker conjectures about cycle lengths in degree 3-critical graphs and leaf-to-leaf path lengths in these so-called 1-3 trees. We resolve three of their questions either fully or up to a constant factor. Our main results are the following: - every $n$-vertex degree 3-critical graph has $Ω(\log n)$ distinct cycle lengths; -every tree with maximum degree $Δ\ge 3$ and $\ell$ leaves has at least $\log_{Δ-1}\, ((Δ-2)\ell)$ distinct leaf-to-leaf path lengths; - for every integer $N\geq 1$, there exist arbitrarily large 1-3 trees which have $O(N^{0.91})$ distinct leaf-to-leaf path lengths smaller than $N$, and, conversely, every 1-3 tree on at least $2^N$ vertices has $Ω(N^{2/3})$ distinct leaf-to-leaf path lengths smaller than $N$. Several of our proofs rely on purely combinatorial means, while others exploit a connection to an additive problem that might be of independent interest.

math.CO↗

arXiv2026

Multi-Agent Debate with Memory Masking

Large language models (LLMs) have recently demonstrated impressive capabilities in reasoning tasks. Currently, mainstream LLM reasoning frameworks predominantly focus on scaling up inference-time sampling to enhance performance. In particular, among all LLM reasoning frameworks, *multi-agent debate* (MAD), which employs multiple LLMs as agents to perform reasoning in the way of multi-round debate, has emerged as a powerful reasoning paradigm since it allows agents to access previous memories to alleviate fallacious content and refine their reasoning iteratively in each debate round. However, although MAD significantly improves the reasoning capabilities of LLMs, in this paper, we observe that there remain erroneous memories, and LLM agents are vulnerable to these erroneous memories. To explore this phenomenon, we provide a theoretical insight that the performance of MAD is highly dependent on the quality of memories derived from the previous debate, indicating that the existence of erroneous memories poses a threat to the performance of MAD. To address this problem, we introduce a simple yet effective multi-agent debate framework, *multi-agent debate with memory masking* (MAD-M$^2$), to improve the robustness of MAD by allowing LLM agents to mask erroneous memories from the previous debate round at the beginning of each debate round. In this way, MAD-M$^2$ can polish the contextual information before each debate round by preserving informative and meaningful memories while discarding the erroneous memories. Extensive experiments and analyses on mainstream mathematical and logical reasoning benchmarks demonstrate that MAD-M$^2$ can identify the erroneous memories and achieve better performance in reasoning than MAD.

cs.CL↗

arXiv2026

Draft-Thinking: Learning Efficient Reasoning in Long Chain-of-Thought LLMs

Long chain-of-thought~(CoT) has become a dominant paradigm for enhancing the reasoning capability of large reasoning models~(LRMs); however, the performance gains often come with a substantial increase in reasoning budget. Recent studies show that existing CoT paradigms tend to induce systematic overthinking, unnecessarily coupling reasoning capability with reasoning cost. Most prior approaches reduce token usage through post hoc techniques such as token compression, truncation, or length penalties, without explicitly addressing the core mechanisms of reasoning. We propose \textbf{Draft-Thinking}, which guides models to first learn a concise \textit{draft-style} reasoning structure that retains only the critical reasoning steps. Through a \textit{progressive curriculum learning}, the model stably internalizes this efficient reasoning pattern as its capability scales. Moreover, Draft-Thinking introduces adaptive prompting, which elevates reasoning depth to a flexible, model-selectable behavior. Extensive experiments demonstrate that Draft-Thinking substantially reduces reasoning budget while largely preserving reasoning performance; for example, on MATH500, it achieves an 82.6\% reduction in reasoning budget at the cost of only a 2.6\% performance drop.

cs.AI↗

arXiv2026

Dean's conjecture and cycles modulo k

Dean conjectured three decades ago that every graph with minimum degree at least $k\ge 3$ contains a cycle whose length is divisible by $k$. While the conjecture has been verified for $k\in \{3,4\}$, it remains open for $k\ge 5$. A weaker version, also proposed by Dean, asserting that every $k$-connected graph contains a cycle of length divisible by $k$, was resolved by Gao, Huo, Liu, and Ma using the notion of admissible cycles. In this paper, we resolve Dean's conjecture for all $k\ge 6$. In fact, we prove a stronger result by showing that every graph with minimum degree at least $k$ contains cycles of length $r \pmod k$ for every even integer $r$, unless every end-block belongs to a specific family of exceptional graphs, which fail only to contain cycles of length $2 \pmod k$. We also establish a strengthened result on the existence of admissible cycles. Our proof introduces two sparse graph families, called trigonal graphs and tetragonal graphs, which provide a flexible framework for studying path and cycle lengths and may be of independent interest.

math.CO↗

arXiv2025

UI-TARS-2 Technical Report: Advancing GUI Agent with Multi-Turn Reinforcement Learning

The development of autonomous agents for graphical user interfaces (GUIs) presents major challenges in artificial intelligence. While recent advances in native agent models have shown promise by unifying perception, reasoning, action, and memory through end-to-end learning, open problems remain in data scalability, multi-turn reinforcement learning (RL), the limitations of GUI-only operation, and environment stability. In this technical report, we present UI-TARS-2, a native GUI-centered agent model that addresses these challenges through a systematic training methodology: a data flywheel for scalable data generation, a stabilized multi-turn RL framework, a hybrid GUI environment that integrates file systems and terminals, and a unified sandbox platform for large-scale rollouts. Empirical evaluation demonstrates that UI-TARS-2 achieves significant improvements over its predecessor UI-TARS-1.5. On GUI benchmarks, it reaches 88.2 on Online-Mind2Web, 47.5 on OSWorld, 50.6 on WindowsAgentArena, and 73.3 on AndroidWorld, outperforming strong baselines such as Claude and OpenAI agents. In game environments, it attains a mean normalized score of 59.8 across a 15-game suite-roughly 60% of human-level performance-and remains competitive with frontier proprietary models (e.g., OpenAI o3) on LMGame-Bench. Additionally, the model can generalize to long-horizon information-seeking tasks and software engineering benchmarks, highlighting its robustness across diverse agent tasks. Detailed analyses of training dynamics further provide insights into achieving stability and efficiency in large-scale agent RL. These results underscore UI-TARS-2's potential to advance the state of GUI agents and exhibit strong generalization to real-world interactive scenarios.

cs.AI↗

arXiv2025

Addressing Personalized Bias for Unbiased Learning to Rank

Unbiased learning to rank (ULTR), which aims to learn unbiased ranking models from biased user behavior logs, plays an important role in Web search. Previous research on ULTR has studied a variety of biases in users' clicks, such as position bias, presentation bias, and outlier bias. However, existing work often assumes that the behavior logs are collected from an ``average'' user, neglecting the differences between different users in their search and browsing behaviors. In this paper, we introduce personalized factors into the ULTR framework, which we term the user-aware ULTR problem. Through a formal causal analysis of this problem, we demonstrate that existing user-oblivious methods are biased when different users have different preferences over queries and personalized propensities of examining documents. To address such a personalized bias, we propose a novel user-aware inverse-propensity-score estimator for learning-to-rank objectives. Specifically, our approach models the distribution of user browsing behaviors for each query and aggregates user-weighted examination probabilities to determine propensities. We theoretically prove that the user-aware estimator is unbiased under some mild assumptions and shows lower variance compared to the straightforward way of calculating a user-dependent propensity for each impression. Finally, we empirically verify the effectiveness of our user-aware estimator by conducting extensive experiments on two semi-synthetic datasets and a real-world dataset.

cs.IR↗

arXiv2025

Intersections of longest cycles in vertex-transitive and highly connected graphs

Motivated by the classical conjectures of Lovász, Thomassen, and Smith, recent work has renewed interest in the study of longest cycles in important graph families, such as vertex-transitive and highly connected graphs. In particular, Groenland et al.\ proved that if two longest cycles and in a graph share $m$ vertices, then there exists a vertex cut of size $O(m^{8/5})$ separating them, yielding improved bounds toward these conjectures. Their proof combines Turán-type arguments with computer-assisted search. We prove two results addressing problems of Babai (1979) and Smith (1984) on intersections of longest cycles in vertex-transitive and highly connected graphs. First, we strengthen the bound of Groenland et al.\ by showing that if two longest cycles and in a graph share $m$ vertices, then there exists a vertex cut of size $O(m^{3/2})$ separating them. As a consequence, we show that in every $k$-connected graph, any two longest cycles intersect in at least $Ω(k^{2/3})$ vertices, improving the best known bound toward Smith's conjecture. Our proof is purely combinatorial, employing supersaturation-type estimates beyond the existing Turán-type approach. Second, we prove that in every connected vertex-transitive graph on $n$ vertices, any two longest cycles intersect in at least $f(n)$ vertices for some function $f(n)\to\infty$ as $n\to\infty$, thereby resolving a problem of Babai (1979) for the class of vertex-transitive graphs central to his original motivation. In doing so, we introduce a new method for constructing longer cycles in vertex-transitive graphs based on a given cycle, which may be of independent interest.

math.CO↗

arXiv2024

Energy-efficient Hybrid Model Predictive Trajectory Planning for Autonomous Electric Vehicles

To tackle the twin challenges of limited battery life and lengthy charging durations in electric vehicles (EVs), this paper introduces an Energy-efficient Hybrid Model Predictive Planner (EHMPP), which employs an energy-saving optimization strategy. EHMPP focuses on refining the design of the motion planner to be seamlessly integrated with the existing automatic driving algorithms, without additional hardware. It has been validated through simulation experiments on the Prescan, CarSim, and Matlab platforms, demonstrating that it can increase passive recovery energy by 11.74\% and effectively track motor speed and acceleration at optimal power. To sum up, EHMPP not only aids in trajectory planning but also significantly boosts energy efficiency in autonomous EVs.

cs.RO↗

arXiv2024

Graph Neural Networks for Protein-Protein Interactions -- A Short Survey

Protein-protein interactions (PPIs) play key roles in a broad range of biological processes. Numerous strategies have been proposed for predicting PPIs, and among them, graph-based methods have demonstrated promising outcomes owing to the inherent graph structure of PPI networks. This paper reviews various graph-based methodologies, and discusses their applications in PPI prediction. We classify these approaches into two primary groups based on their model structures. The first category employs Graph Neural Networks (GNN) or Graph Convolutional Networks (GCN), while the second category utilizes Graph Attention Networks (GAT), Graph Auto-Encoders and Graph-BERT. We highlight the distinctive methodologies of each approach in managing the graph-structured data inherent in PPI networks and anticipate future research directions in this domain.

cs.LG↗

arXiv2023

MetaGrad: Adaptive Gradient Quantization with Hypernetworks

A popular track of network compression approach is Quantization aware Training (QAT), which accelerates the forward pass during the neural network training and inference. However, not much prior efforts have been made to quantize and accelerate the backward pass during training, even though that contributes around half of the training time. This can be partly attributed to the fact that errors of low-precision gradients during backward cannot be amortized by the training objective as in the QAT setting. In this work, we propose to solve this problem by incorporating the gradients into the computation graph of the next training iteration via a hypernetwork. Various experiments on CIFAR-10 dataset with different CNN network architectures demonstrate that our hypernetwork-based approach can effectively reduce the negative effect of gradient quantization noise and successfully quantizes the gradients to INT4 with only 0.64 accuracy drop for VGG-16 on CIFAR-10.

cs.CV↗

arXiv2023

SemiGNN-PPI: Self-Ensembling Multi-Graph Neural Network for Efficient and Generalizable Protein-Protein Interaction Prediction

Protein-protein interactions (PPIs) are crucial in various biological processes and their study has significant implications for drug development and disease diagnosis. Existing deep learning methods suffer from significant performance degradation under complex real-world scenarios due to various factors, e.g., label scarcity and domain shift. In this paper, we propose a self-ensembling multigraph neural network (SemiGNN-PPI) that can effectively predict PPIs while being both efficient and generalizable. In SemiGNN-PPI, we not only model the protein correlations but explore the label dependencies by constructing and processing multiple graphs from the perspectives of both features and labels in the graph learning process. We further marry GNN with Mean Teacher to effectively leverage unlabeled graph-structured PPI data for self-ensemble graph learning. We also design multiple graph consistency constraints to align the student and teacher graphs in the feature embedding space, enabling the student model to better learn from the teacher model by incorporating more relationships. Extensive experiments on PPI datasets of different scales with different evaluation settings demonstrate that SemiGNN-PPI outperforms state-of-the-art PPI prediction methods, particularly in challenging scenarios such as training with limited annotations and testing on unseen data.

q-bio.MN↗

arXiv2023

Meta-hallucinator: Towards Few-Shot Cross-Modality Cardiac Image Segmentation

Domain shift and label scarcity heavily limit deep learning applications to various medical image analysis tasks. Unsupervised domain adaptation (UDA) techniques have recently achieved promising cross-modality medical image segmentation by transferring knowledge from a label-rich source domain to an unlabeled target domain. However, it is also difficult to collect annotations from the source domain in many clinical applications, rendering most prior works suboptimal with the label-scarce source domain, particularly for few-shot scenarios, where only a few source labels are accessible. To achieve efficient few-shot cross-modality segmentation, we propose a novel transformation-consistent meta-hallucination framework, meta-hallucinator, with the goal of learning to diversify data distributions and generate useful examples for enhancing cross-modality performance. In our framework, hallucination and segmentation models are jointly trained with the gradient-based meta-learning strategy to synthesize examples that lead to good segmentation performance on the target domain. To further facilitate data hallucination and cross-domain knowledge transfer, we develop a self-ensembling model with a hallucination-consistent property. Our meta-hallucinator can seamlessly collaborate with the meta-segmenter for learning to hallucinate with mutual benefits from a combined view of meta-learning and self-ensembling learning. Extensive studies on MM-WHS 2017 dataset for cross-modality cardiac segmentation demonstrate that our method performs favorably against various approaches by a lot in the few-shot UDA scenario.

cs.CV↗

arXiv2023

Multimodal Continuous Emotion Recognition: A Technical Report for ABAW5

We used two multimodal models for continuous valence-arousal recognition using visual, audio, and linguistic information. The first model is the same as we used in ABAW2 and ABAW3, which employs the leader-follower attention. The second model has the same architecture for spatial and temporal encoding. As for the fusion block, it employs a compact and straightforward channel attention, borrowed from the End2You toolkit. Unlike our previous attempts that use Vggish feature directly as the audio feature, this time we feed the pre-trained VGG model using logmel-spectrogram and finetune it during the training. To make full use of the data and alleviate over-fitting, cross-validation is carried out. The code is available at https://github.com/sucv/ABAW3.

cs.MM↗