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Xiang Wang

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preprint2026arXiv

Bi-Mem: Bidirectional Construction of Hierarchical Memory for Personalized LLMs via Inductive-Reflective Agents

Constructing memory from users' long-term conversations overcomes LLMs' contextual limitations and enables personalized interactions. Recent studies focus on hierarchical memory to model users' multi-granular behavioral patterns via clustering and aggregating historical conversations. However, conversational noise and memory hallucinations can be amplified during clustering, causing locally aggregated memories to misalign with the user's global persona. To mitigate this issue, we propose Bi-Mem, an agentic framework ensuring hierarchical memory fidelity through bidirectional construction. Specifically, we deploy an inductive agent to form the hierarchical memory: it extracts factual information from raw conversations to form fact-level memory, aggregates them into thematic scenes (i.e., local scene-level memory) using graph clustering, and infers users' profiles as global persona-level memory. Simultaneously, a reflective agent is designed to calibrate local scene-level memories using global constraints derived from the persona-level memory, thereby enforcing global-local alignment. For coherent memory recall, we propose an associative retrieval mechanism: beyond initial hierarchical search, a spreading activation process allows facts to evoke contextual scenes, while scene-level matches retrieve salient supporting factual information. Empirical evaluations demonstrate that Bi-Mem achieves significant improvements in question answering performance on long-term personalized conversational tasks.

preprint2026arXiv

Differentially Private Subspace Fine-Tuning for Large Language Models

Fine-tuning large language models on downstream tasks is crucial for realizing their cross-domain potential but often relies on sensitive data, raising privacy concerns. Differential privacy (DP) offers rigorous privacy guarantees and has been widely adopted in fine-tuning; however, naively injecting noise across the high-dimensional parameter space creates perturbations with large norms, degrading performance and destabilizing training. To address this issue, we propose DP-SFT, a two-stage subspace fine-tuning method that substantially reduces noise magnitude while preserving formal DP guarantees. Our intuition is that, during fine-tuning, significant parameter updates lie within a low-dimensional, task-specific subspace, while other directions change minimally. Hence, we only inject DP noise into this subspace to protect privacy without perturbing irrelevant parameters. In phase one, we identify the subspace by analyzing principal gradient directions to capture task-specific update signals. In phase two, we project full gradients onto this subspace, add DP noise, and map the perturbed gradients back to the original parameter space for model updates, markedly lowering noise impact. Experiments on multiple datasets demonstrate that DP-SFT enhances accuracy and stability under rigorous DP constraints, accelerates convergence, and achieves substantial gains over DP fine-tuning baselines.

preprint2026arXiv

Diffusion Attention Expert Model for Predicting and Semi-automatic Localizing STAS in Lung Cancer Histopathological Images

Accurate intraoperative and postoperative diagnosis of spread through air spaces (STAS) is essential for guiding surgical decisions and postoperative management in lung cancer. However, histopathological assessment is labor-intensive and is prone to missed or incorrect diagnoses. We propose a Diffusion Attention Expert Model (DAEM) to detect STAS in frozen sections (FSs) and paraffin sections (PSs). Its diffusion attention expert module leverages full attention aggregation to learn multi-scale features from histopathological images, while a dual-branch architecture strengthens multi-scale feature representation. On an internal dataset, DAEM achieves AUCs of 0.8946 for FSs and 0.9112 for PSs. Validation on external multi-center datasets from eight institutions demonstrates strong generalizability and interpretability. Using tumor microenvironment (TME) features in PSs, we further enable semi-automatic measurement of STAS location and its distance from the primary tumor. Several quantitative TME metrics are identified as potential biomarkers for STAS, including micropapillary-type STAS. Overall, DAEM offers a clinically actionable framework for STAS assessment by enabling accurate and interpretable detection on FSs and PSs, supporting postoperative risk stratification through quantitative TME-based analysis.

preprint2026arXiv

DynamicPO: Dynamic Preference Optimization for Recommendation

In large language model (LLM)-based recommendation systems, direct preference optimization (DPO) effectively aligns recommendations with user preferences, requiring multi-negative objective functions to leverage abundant implicit-feedback negatives and sharpen preference boundaries. However, our empirical analyses reveal a counterintuitive phenomenon, preference optimization collapse, where increasing the number of negative samples can lead to performance degradation despite a continuously decreasing training loss. We further theoretically demonstrate that this collapse arises from gradient suppression, caused by the dominance of easily discriminable negatives over boundary-critical negatives that truly define user preference boundaries. As a result, boundary-relevant signals are under-optimized, weakening the model's decision boundary. Motivated by these observations, we propose DynamicPO (Dynamic Preference Optimization), a lightweight and plug-and-play framework comprising two adaptive mechanisms: Dynamic Boundary Negative Selection, which identifies and prioritizes informative negatives near the model's decision boundary, and Dual-Margin Dynamic beta Adjustment, which calibrates optimization strength per sample according to boundary ambiguity. Extensive experiments on three public datasets show that DynamicPO effectively prevents optimization collapse and improves recommendation accuracy on multi-negative preference optimization methods, with negligible computational overhead. Our code and datasets are available at https://github.com/xingyuHuxingyu/DynamicPO.

preprint2026arXiv

Internalizing Safety Understanding in Large Reasoning Models via Verification

While explicit Chain-of-Thought (CoT) empowers large reasoning models (LRMs), it enables the generation of riskier final answers. Current alignment paradigms primarily rely on externally enforced compliance, optimizing models to detect malicious prompts rather than evaluating the safety of their own outputs. We argue that this approach remains largely behavioral: our empirical analysis reveals that ostensibly aligned models lack intrinsic safety understanding, often failing to verify their own response safety and remaining vulnerable to adversarial jailbreaks. To address this fundamental limitation, we propose Safety Internal (SInternal), a framework that internalizes safety specifications by training LRMs exclusively on safety verification tasks to critique their own generated answers using expert reasoning trajectories. We demonstrate that learning to verify induces a strong generalization for response safety, significantly enhancing robustness against out-of-domain jailbreaks. Furthermore, when combined with reinforcement learning, SInternal serves as a superior initialization compared to standard supervised fine-tuning, suggesting that internalizing safety understanding creates a more robust foundation for alignment than merely mimicking safe behaviors. Our codes are available at https://github.com/AlphaLab-USTC/SInternal

preprint2026arXiv

MSAVBench: Towards Comprehensive and Reliable Evaluation of Multi-Shot Audio-Video Generation

Video generation is rapidly evolving from single-shot synthesis to complex multi-shot audio-video (MSAV) narratives to meet real-world demands. However, evaluating such frontier models remains a fundamental challenge. Existing benchmarks are limited in scope and data diversity, and rely on rigid evaluation pipelines, preventing systematic and reliable assessment of modern MSAV models. To bridge these gaps, we introduce MSAVBench, the first comprehensive benchmark and adaptive hybrid evaluation framework for multi-shot audio-video generation. Our benchmark spans four key dimensions, video, audio, shot, and reference, covering diverse task settings, varying shot counts of up to 15, and challenging non-realistic scenarios. Our evaluation framework improves robustness through an adaptive self-correction mechanism for shot segmentation, instance-wise rubrics for subjective metrics, and tool-grounded evidence extraction for complex judgments. Furthermore, MSAVBench achieves high alignment with human judgments, reaching a Spearman rank correlation of 91.5%. Our systematic evaluation of 19 state-of-the-art closed- and open-source models shows that current systems still struggle with director-level control and fine-grained audio-visual synchronization, while modular or agentic generation pipelines offer a promising path toward narrowing the gap between open- and closed-source models. We will release the benchmark data and evaluation code to facilitate future research.

preprint2026arXiv

R^2-Mem: Reflective Experience for Memory Search

Deep search has recently emerged as a promising paradigm for enabling agents to retrieve fine-grained historical information without heavy memory pre-managed. However, existing deep search agents for memory system repeat past error behaviors because they fail to learn from the prior high- and low-quality search trajectories. To address this limitation, we propose R^2-Mem, a reflective experience framework for memory search systems. In the offline stage, a Rubric-guided Evaluator scores low- and high-quality steps in historical trajectories, and a self-Reflection Learner distills the corresponding abstract experience. During the online inference, the retrieved experience will guide future search actions to avoid repeated mistakes and maintain high-quality behaviors. Extensive experiments demonstrate that R^2-Mem consistently improves both effectiveness and efficiency over strong baselines, improving F1 scores by up to 22.6%, while reducing token consumption by 12.9% and search iterations by 20.2%. These results verify that R^2-Mem provides a RL-free and low-cost solution for self-improving LLM agents.

preprint2026arXiv

Reasoning Can Be Restored by Correcting a Few Decision Tokens

Large reasoning models (LRMs) substantially outperform their base LLM counterparts on challenging reasoning benchmarks, yet it remains poorly understood where base models go wrong during token-by-token generation and how to narrow this gap efficiently. We study the base-reasoning gap through quantifying token-level distributional disagreement between a base model and a stronger reasoning model using likelihood-based divergences. Across benchmarks, we find that the reasoning advantage is highly sparse and concentrates on a small set of early, planning-related decision tokens. For instance, on Qwen3-0.6B, only ~8% of generated tokens account for the salient disagreement, and these tokens concentrate early in the response, are strongly enriched in planning-related decisions (17x), and coincide with high base-model uncertainty -- suggesting that base models fail mainly at early planning points that steer the subsequent reasoning trajectory. Building on these findings, we propose disagreement-guided token intervention, a simple inference-time delegation scheme that performs a one-token takeover by the reasoning model only at high-disagreement positions and immediately switches back to the base model. With a small intervention budget, this sparse delegation substantially recovers and can even surpass the performance of a same-size reasoning model on challenging reasoning tasks. Code is available at https://github.com/AlphaLab-USTC/RRTokenIntervention.

preprint2026arXiv

Rubric-based On-policy Distillation

On-policy distillation (OPD) is a powerful paradigm for model alignment, yet its reliance on teacher logits restricts its application to white-box scenarios. We contend that structured semantic rubrics can serve as a scalable alternative to teacher logits, enabling OPD using only teacher-generated responses. To prove it, we introduce ROPD, a simple yet foundational framework for rubric-based OPD. Specifically, ROPD induces prompt-specific rubrics from teacher-student contrasts, and then utilizes these rubrics to score the student rollouts for on-policy optimization. Empirically, ROPD outperforms the advanced logit-based OPD methods across most scenarios, and achieving up to a 10x gain in sample efficiency. These results position rubric-based OPD as a flexible, black-box-compatible alternative to the prevailing logit-based OPD, offering a simple yet strong baseline for scalable distillation across proprietary and open-source LLMs. Code is available at https://github.com/Peregrine123/ROPD_official.

preprint2026arXiv

Scaling Retrieval-Augmented Reasoning with Parallel Search and Explicit Merging

Deep search agents have proven effective in enhancing LLMs by retrieving external knowledge during multi-step reasoning. However, existing methods often generate a single query for retrieval at each reasoning step, limiting information coverage and introducing high noise. This may result in low signal-to-noise ratios (SNR) during search, degrading reasoning accuracy and leading to unnecessary reasoning steps. In this paper, we introduce MultiSearch, an RL-based framework that addresses these limitations through multi-query retrieval and explicit merging of retrieved information. At each reasoning step, MultiSearch generates queries from multiple perspectives and retrieves external information in parallel, expanding the scope of relevant information and mitigating the reliance on any single retrieval result. Then, the agent consolidates and refines retrieved information at the merging process, improving the SNR and ensuring more accurate reasoning. Additionally, we propose a reinforcement learning framework with a multi-process reward design to optimize agents for both multi-query retrieval and information consolidation. Extensive experiments on seven benchmarks demonstrate that MultiSearch outperforms baseline methods, enhancing the SNR of retrieval and improving reasoning performance in question-answering tasks.

preprint2026arXiv

Self-ReSET: Learning to Self-Recover from Unsafe Reasoning Trajectories

Large Reasoning Models possess remarkable capabilities for self-correction in general domain; however, they frequently struggle to recover from unsafe reasoning trajectories under adversarial attacks. Existing alignment methods attempt to mitigate this vulnerability by fine-tuning the model on expert data including reflection traces or adversarial prefixes. Crucially, these approaches are often hindered by static training data which inevitably deviate from model's dynamic, on-policy reasoning traces, resulting in model hardly covering its vast generation space and learning to recover from its own failures. To bridge this gap, we propose Self-ReSET, a pure reinforcement learning framework designed to equip LRMs with the intrinsic capacity to recover from their own safety error trajectories, which are subsequently reused as an initial state for reinforcement learning. Extensive experiments across various LRMs and benchmarks demonstrate that Self-ReSET significantly enhances robustness against adversarial attacks especially out-of-distribution (OOD) jailbreak prompts while maintaining general utility, along with efficient data utilization. Further analysis reveals that our method effectively fosters self-recovery patterns, enabling models to better identify and recover from unsafe intermediate error states back to benign paths. Our codes and data are available at https://github.com/Ing1024/Self-ReSET.

preprint2026arXiv

SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation

On-policy distillation (OPD) is a standard tool for transferring teacher behavior to a smaller student, but it implicitly assumes that teacher and student predictions are comparable token by token, an assumption that fails whenever the two models tokenize the same text differently. Under heterogeneous tokenizers, exact shared-token matching silently discards a large fraction of the teacher signal at precisely the positions where vocabularies disagree. We propose \textbf{\underline{Sim}ple \underline{C}ross-\underline{T}okenizer OPD (SimCT)}, which restores this signal by enlarging the supervision space: alongside shared tokens, SimCT compares teacher and student over short multi-token continuations that both tokenizers can realize, leaving the OPD loss form itself unchanged. We show that these units are the finest jointly tokenizable supervision interface, and that coarser alternatives remove teacher-student distinctions that are useful for on-policy learning. Across three heterogeneous teacher-student pairs on mathematical reasoning and code-generation benchmarks, SimCT shows consistent gains over shared-vocabulary OPD and representative cross-tokenizer baselines, with ablations confirming that the improvements come from recovering supervision discarded by exact shared-token matching. Code is available at \href{https://github.com/sunjie279/SimCT-}{https://github.com/sunjie279/SimCT-}.

preprint2026arXiv

Skill1: Unified Evolution of Skill-Augmented Agents via Reinforcement Learning

A persistent skill library allows language model agents to reuse successful strategies across tasks. Maintaining such a library requires three coupled capabilities. The agent selects a relevant skill, utilizes it during execution, and distills new skills from experience. Existing methods optimize these capabilities in isolation or with separate reward sources, resulting in partial and conflicting evolution. We propose Skill1, a framework that trains a single policy to co-evolve skill selection, utilization, and distillation toward a shared task-outcome objective. The policy generates a query to search the skill library, re-ranks candidates to select one, solves the task conditioned on it, and distills a new skill from the trajectory. All learning derives from a single task-outcome signal. Its low-frequency trend credits selection and its high-frequency variation credits distillation. Experiments on ALFWorld and WebShop show that Skill1 outperforms prior skill-based and reinforcement learning baselines. Training dynamics confirm the co-evolution of the three capabilities, and ablations show that removing any credit signal degrades the evolution.

preprint2026arXiv

SOD: Step-wise On-policy Distillation for Small Language Model Agents

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

preprint2026arXiv

Teaching Large Language Models When Not to Know: Learning Temporal Critique for Ex-Ante Reasoning

Large language models (LLMs) often fail to reason under temporal cutoffs: when prompted to answer from the standpoint of an earlier time, they exploit knowledge that became available only later. We study this failure through the lens of ex-ante reasoning, where a model must rely exclusively on information knowable before a cutoff. Through a systematic analysis of prompt-level interventions, we find that temporal leakage is highly sensitive to cutoff formulation and instruction placement: explicit cutoff statements outperform implicit historical framings, and prefix constraints reduce leakage more effectively than suffix constraints. These findings indicate that prompting can steer models into a temporal frame, but does not endow them with the ability to verify whether a response is temporally admissible. We further argue that supervised fine-tuning is insufficient, since ex-ante correctness is not an intrinsic property of an answer, but a relation between the answer and the cutoff. To address this gap, we propose TCFT, a Temporal Critique Fine-Tuning framework that trains models to acquire cutoff-aware temporal verification. Given a query, a cutoff, and a candidate response, TCFT teaches the model to identify post-cutoff leakage, explain temporal boundary violations, and judge temporal admissibility. Experiments with Qwen2.5-7B-Instruct and Qwen2.5-14B-Instruct show that TCFT consistently outperforms prompting and SFT baselines, reducing average leakage by 41.89 and 37.79 percentage points, respectively.

preprint2026arXiv

Think, then Score: Decoupled Reasoning and Scoring for Video Reward Modeling

Recent advances in generative video models are increasingly driven by post-training and test-time scaling, both of which critically depend on the quality of video reward models (RMs). An ideal reward model should predict accurate rewards that align with human preferences across diverse scenarios. However, existing paradigms face a fundamental dilemma: \textit{Discriminative RMs} regress rewards directly on features extracted by multimodal large language models (MLLMs) without explicit reasoning, making them prone to shortcut learning and heavily reliant on massive data scaling for generalization. In contrast, \textit{Generative RMs} with Chain-of-Thought (CoT) reasoning exhibit superior interpretability and generalization potential, as they leverage fine-grained semantic supervision to internalize the rationales behind human preferences. However, they suffer from inherent optimization bottlenecks due to the coupling of reasoning and scoring within a single autoregressive inference chain. To harness the generalization benefits of CoT reasoning while mitigating the training instability of coupled reasoning and scoring, we introduce DeScore, a training-efficient and generalizable video reward model. DeScore employs a decoupled ``think-then-score'' paradigm: an MLLM first generates an explicit CoT, followed by a dedicated discriminative scoring module consisting of a learnable query token and a regression head that predicts the final reward. DeScore is optimized via a two-stage framework: (1) a discriminative cold start incorporating a random mask mechanism to ensure robust scoring capabilities, and (2) a dual-objective reinforcement learning stage that independently refines CoT reasoning quality and calibrates the final reward, ensuring that higher-quality reasoning directly translates to superior model performance.

preprint2026arXiv

To Call or Not to Call: Diagnosing Intrinsic Over-Calling Bias in LLM Agents

LLM agents exhibit a consistent tendency to over-call, invoking tools even in situations where none is needed. On the When2Call benchmark, six models from three families show high call accuracy but much lower no-call accuracy, leaving overall accuracy in the 55%-70% range. We trace this to an Intrinsic Bias Hypothesis (IBH): the call/no-call decision mapping carries an activation-independent call offset, so the model favors call even at activation parity. Using Sparse Autoencoders (SAEs), we recover behavior-aligned feature bases for the call/no_call decision, reduce them to a signed activation margin, and estimate the offset directly. Across all six models, the model is decision-neutral only when no_call activation outweighs call activation, consistent with IBH. We then causally test IBH with Adaptive Margin-Calibrated Steering (AMCS), a closed-form counter-bias shift along SAE decoder directions. Cancelling the diagnosed offset mitigates over-calling and improves overall accuracy with a negligible drop in call accuracy. Our work recasts over-calling from an empirical phenomenon into a mechanistic object amenable to causal correction. Code is available at https://github.com/SKURA502/agent-sae/.

preprint2026arXiv

UniVLR: Unifying Text and Vision in Visual Latent Reasoning for Multimodal LLMs

Multimodal large language models are increasingly expected to perform thinking with images, yet existing visual latent reasoning methods still rely on explicit textual chain-of-thought interleaved with visual latent tokens. This interleaved design limits efficiency and keeps reasoning fragmented across separate text and vision channels. We propose UniVLR, a unified visual latent reasoning framework that treats textual reasoning and auxiliary visual evidence as a shared visual workspace. Instead of preserving text CoT as an independent inference-time path, UniVLR renders reasoning traces together with auxiliary images and learns to compress this unified representation into compact visual latent tokens. At inference time, the model reasons only through visual latents and directly decodes the final answer, avoiding both external tool calls and verbose text reasoning. Experiments on real-world perception and visual reasoning tasks show that UniVLR outperforms prior visual latent reasoning methods while using substantially fewer generated reasoning tokens, suggesting a more unified and efficient paradigm for visual thinking in MLLMs.

preprint2023arXiv

CrossCBR: Cross-view Contrastive Learning for Bundle Recommendation

Bundle recommendation aims to recommend a bundle of related items to users, which can satisfy the users' various needs with one-stop convenience. Recent methods usually take advantage of both user-bundle and user-item interactions information to obtain informative representations for users and bundles, corresponding to bundle view and item view, respectively. However, they either use a unified view without differentiation or loosely combine the predictions of two separate views, while the crucial cooperative association between the two views' representations is overlooked. In this work, we propose to model the cooperative association between the two different views through cross-view contrastive learning. By encouraging the alignment of the two separately learned views, each view can distill complementary information from the other view, achieving mutual enhancement. Moreover, by enlarging the dispersion of different users/bundles, the self-discrimination of representations is enhanced. Extensive experiments on three public datasets demonstrate that our method outperforms SOTA baselines by a large margin. Meanwhile, our method requires minimal parameters of three set of embeddings (user, bundle, and item) and the computational costs are largely reduced due to more concise graph structure and graph learning module. In addition, various ablation and model studies demystify the working mechanism and justify our hypothesis. Codes and datasets are available at https://github.com/mysbupt/CrossCBR.

preprint2023arXiv

HyRSM++: Hybrid Relation Guided Temporal Set Matching for Few-shot Action Recognition

Recent attempts mainly focus on learning deep representations for each video individually under the episodic meta-learning regime and then performing temporal alignment to match query and support videos. However, they still suffer from two drawbacks: (i) learning individual features without considering the entire task may result in limited representation capability, and (ii) existing alignment strategies are sensitive to noises and misaligned instances. To handle the two limitations, we propose a novel Hybrid Relation guided temporal Set Matching (HyRSM++) approach for few-shot action recognition. The core idea of HyRSM++ is to integrate all videos within the task to learn discriminative representations and involve a robust matching technique. To be specific, HyRSM++ consists of two key components, a hybrid relation module and a temporal set matching metric. Given the basic representations from the feature extractor, the hybrid relation module is introduced to fully exploit associated relations within and cross videos in an episodic task and thus can learn task-specific embeddings. Subsequently, in the temporal set matching metric, we carry out the distance measure between query and support videos from a set matching perspective and design a Bi-MHM to improve the resilience to misaligned instances. In addition, we explicitly exploit the temporal coherence in videos to regularize the matching process. Furthermore, we extend the proposed HyRSM++ to deal with the more challenging semi-supervised few-shot action recognition and unsupervised few-shot action recognition tasks. Experimental results on multiple benchmarks demonstrate that our method achieves state-of-the-art performance under various few-shot settings. The source code is available at https://github.com/alibaba-mmai-research/HyRSMPlusPlus.

preprint2023arXiv

Real-World Image Super Resolution via Unsupervised Bi-directional Cycle Domain Transfer Learning based Generative Adversarial Network

Deep Convolutional Neural Networks (DCNNs) have exhibited impressive performance on image super-resolution tasks. However, these deep learning-based super-resolution methods perform poorly in real-world super-resolution tasks, where the paired high-resolution and low-resolution images are unavailable and the low-resolution images are degraded by complicated and unknown kernels. To break these limitations, we propose the Unsupervised Bi-directional Cycle Domain Transfer Learning-based Generative Adversarial Network (UBCDTL-GAN), which consists of an Unsupervised Bi-directional Cycle Domain Transfer Network (UBCDTN) and the Semantic Encoder guided Super Resolution Network (SESRN). First, the UBCDTN is able to produce an approximated real-like LR image through transferring the LR image from an artificially degraded domain to the real-world LR image domain. Second, the SESRN has the ability to super-resolve the approximated real-like LR image to a photo-realistic HR image. Extensive experiments on unpaired real-world image benchmark datasets demonstrate that the proposed method achieves superior performance compared to state-of-the-art methods.

preprint2023arXiv

Semantic Encoder Guided Generative Adversarial Face Ultra-Resolution Network

Face super-resolution is a domain-specific image super-resolution, which aims to generate High-Resolution (HR) face images from their Low-Resolution (LR) counterparts. In this paper, we propose a novel face super-resolution method, namely Semantic Encoder guided Generative Adversarial Face Ultra-Resolution Network (SEGA-FURN) to ultra-resolve an unaligned tiny LR face image to its HR counterpart with multiple ultra-upscaling factors (e.g., 4x and 8x). The proposed network is composed of a novel semantic encoder that has the ability to capture the embedded semantics to guide adversarial learning and a novel generator that uses a hierarchical architecture named Residual in Internal Dense Block (RIDB). Moreover, we propose a joint discriminator which discriminates both image data and embedded semantics. The joint discriminator learns the joint probability distribution of the image space and latent space. We also use a Relativistic average Least Squares loss (RaLS) as the adversarial loss to alleviate the gradient vanishing problem and enhance the stability of the training procedure. Extensive experiments on large face datasets have proved that the proposed method can achieve superior super-resolution results and significantly outperform other state-of-the-art methods in both qualitative and quantitative comparisons.

preprint2022arXiv

Benchmarking Unsupervised Anomaly Detection and Localization

Unsupervised anomaly detection and localization, as of one the most practical and challenging problems in computer vision, has received great attention in recent years. From the time the MVTec AD dataset was proposed to the present, new research methods that are constantly being proposed push its precision to saturation. It is the time to conduct a comprehensive comparison of existing methods to inspire further research. This paper extensively compares 13 papers in terms of the performance in unsupervised anomaly detection and localization tasks, and adds a comparison of inference efficiency previously ignored by the community. Meanwhile, analysis of the MVTec AD dataset are also given, especially the label ambiguity that affects the model fails to achieve full marks. Moreover, considering the proposal of the new MVTec 3D-AD dataset, this paper also conducts experiments using the existing state-of-the-art 2D methods on this new dataset, and reports the corresponding results with analysis.

preprint2022arXiv

Causal Attention for Interpretable and Generalizable Graph Classification

In graph classification, attention and pooling-based graph neural networks (GNNs) prevail to extract the critical features from the input graph and support the prediction. They mostly follow the paradigm of learning to attend, which maximizes the mutual information between the attended graph and the ground-truth label. However, this paradigm makes GNN classifiers recklessly absorb all the statistical correlations between input features and labels in the training data, without distinguishing the causal and noncausal effects of features. Instead of underscoring the causal features, the attended graphs are prone to visit the noncausal features as the shortcut to predictions. Such shortcut features might easily change outside the training distribution, thereby making the GNN classifiers suffer from poor generalization. In this work, we take a causal look at the GNN modeling for graph classification. With our causal assumption, the shortcut feature serves as a confounder between the causal feature and prediction. It tricks the classifier to learn spurious correlations that facilitate the prediction in in-distribution (ID) test evaluation, while causing the performance drop in out-of-distribution (OOD) test data. To endow the classifier with better interpretation and generalization, we propose the Causal Attention Learning (CAL) strategy, which discovers the causal patterns and mitigates the confounding effect of shortcuts. Specifically, we employ attention modules to estimate the causal and shortcut features of the input graph. We then parameterize the backdoor adjustment of causal theory -- combine each causal feature with various shortcut features. It encourages the stable relationships between the causal estimation and prediction, regardless of the changes in shortcut parts and distributions. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of CAL.

preprint2022arXiv

Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

A family of quadratic finite volume method (FVM) schemes are constructed and analyzed over tetrahedral meshes. In order to prove stability and error estimate, we propose the minimum V-angle condition on tetrahedral meshes, and the surface and volume orthogonal conditions on dual meshes. Through the element analysis technique, the local stability is equivalent to a positive definiteness of a $9\times9$ element matrix, which is difficult to analyze directly or even numerically. With the help of the surface orthogonal condition and congruent transformation, this element matrix is reduced into a block diagonal matrix, then we carry out the stability result under the minimum V-angle condition. It is worth mentioning that the minimum V-angle condition of the tetrahedral case is very different from a simple extension of the minimum angle condition for triangular meshes, while it is also convenient to use in practice. Based on the stability, we prove the optimal $ H^{1} $ and $L^2$ error estimates respectively, where the orthogonal conditions play an important role in ensuring optimal $L^2$ convergence rate. Numerical experiments are presented to illustrate our theoretical results.

preprint2022arXiv

Context-aware Proposal Network for Temporal Action Detection

This technical report presents our first place winning solution for temporal action detection task in CVPR-2022 AcitivityNet Challenge. The task aims to localize temporal boundaries of action instances with specific classes in long untrimmed videos. Recent mainstream attempts are based on dense boundary matchings and enumerate all possible combinations to produce proposals. We argue that the generated proposals contain rich contextual information, which may benefits detection confidence prediction. To this end, our method mainly consists of the following three steps: 1) action classification and feature extraction by Slowfast, CSN, TimeSformer, TSP, I3D-flow, VGGish-audio, TPN and ViViT; 2) proposal generation. Our proposed Context-aware Proposal Network (CPN) builds on top of BMN, GTAD and PRN to aggregate contextual information by randomly masking some proposal features. 3) action detection. The final detection prediction is calculated by assigning the proposals with corresponding video-level classifcation results. Finally, we ensemble the results under different feature combination settings and achieve 45.8% performance on the test set, which improves the champion result in CVPR-2021 ActivityNet Challenge by 1.1% in terms of average mAP.

preprint2022arXiv

Cross Pairwise Ranking for Unbiased Item Recommendation

Most recommender systems optimize the model on observed interaction data, which is affected by the previous exposure mechanism and exhibits many biases like popularity bias. The loss functions, such as the mostly used pointwise Binary Cross-Entropy and pairwise Bayesian Personalized Ranking, are not designed to consider the biases in observed data. As a result, the model optimized on the loss would inherit the data biases, or even worse, amplify the biases. For example, a few popular items take up more and more exposure opportunities, severely hurting the recommendation quality on niche items -- known as the notorious Mathew effect. In this work, we develop a new learning paradigm named Cross Pairwise Ranking (CPR) that achieves unbiased recommendation without knowing the exposure mechanism. Distinct from inverse propensity scoring (IPS), we change the loss term of a sample -- we innovatively sample multiple observed interactions once and form the loss as the combination of their predictions. We prove in theory that this way offsets the influence of user/item propensity on the learning, removing the influence of data biases caused by the exposure mechanism. Advantageous to IPS, our proposed CPR ensures unbiased learning for each training instance without the need of setting the propensity scores. Experimental results demonstrate the superiority of CPR over state-of-the-art debiasing solutions in both model generalization and training efficiency. The codes are available at https://github.com/Qcactus/CPR.

preprint2022arXiv

Deconfounding to Explanation Evaluation in Graph Neural Networks

Explainability of graph neural networks (GNNs) aims to answer "Why the GNN made a certain prediction?", which is crucial to interpret the model prediction. The feature attribution framework distributes a GNN's prediction to its input features (e.g., edges), identifying an influential subgraph as the explanation. When evaluating the explanation (i.e., subgraph importance), a standard way is to audit the model prediction based on the subgraph solely. However, we argue that a distribution shift exists between the full graph and the subgraph, causing the out-of-distribution problem. Furthermore, with an in-depth causal analysis, we find the OOD effect acts as the confounder, which brings spurious associations between the subgraph importance and model prediction, making the evaluation less reliable. In this work, we propose Deconfounded Subgraph Evaluation (DSE) which assesses the causal effect of an explanatory subgraph on the model prediction. While the distribution shift is generally intractable, we employ the front-door adjustment and introduce a surrogate variable of the subgraphs. Specifically, we devise a generative model to generate the plausible surrogates that conform to the data distribution, thus approaching the unbiased estimation of subgraph importance. Empirical results demonstrate the effectiveness of DSE in terms of explanation fidelity.

preprint2022arXiv

Discovering Invariant Rationales for Graph Neural Networks

Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data biases, especially shortcut features, to compose rationales and make predictions without probing the critical and causal patterns. Moreover, such data biases easily change outside the training distribution. As a result, these models suffer from a huge drop in interpretability and predictive performance on out-of-distribution data. In this work, we propose a new strategy of discovering invariant rationale (DIR) to construct intrinsically interpretable GNNs. It conducts interventions on the training distribution to create multiple interventional distributions. Then it approaches the causal rationales that are invariant across different distributions while filtering out the spurious patterns that are unstable. Experiments on both synthetic and real-world datasets validate the superiority of our DIR in terms of interpretability and generalization ability on graph classification over the leading baselines. Code and datasets are available at https://github.com/Wuyxin/DIR-GNN.

preprint2022arXiv

Equivariant and Invariant Grounding for Video Question Answering

Video Question Answering (VideoQA) is the task of answering the natural language questions about a video. Producing an answer requires understanding the interplay across visual scenes in video and linguistic semantics in question. However, most leading VideoQA models work as black boxes, which make the visual-linguistic alignment behind the answering process obscure. Such black-box nature calls for visual explainability that reveals ``What part of the video should the model look at to answer the question?''. Only a few works present the visual explanations in a post-hoc fashion, which emulates the target model's answering process via an additional method. Nonetheless, the emulation struggles to faithfully exhibit the visual-linguistic alignment during answering. Instead of post-hoc explainability, we focus on intrinsic interpretability to make the answering process transparent. At its core is grounding the question-critical cues as the causal scene to yield answers, while rolling out the question-irrelevant information as the environment scene. Taking a causal look at VideoQA, we devise a self-interpretable framework, Equivariant and Invariant Grounding for Interpretable VideoQA (EIGV). Specifically, the equivariant grounding encourages the answering to be sensitive to the semantic changes in the causal scene and question; in contrast, the invariant grounding enforces the answering to be insensitive to the changes in the environment scene. By imposing them on the answering process, EIGV is able to distinguish the causal scene from the environment information, and explicitly present the visual-linguistic alignment. Extensive experiments on three benchmark datasets justify the superiority of EIGV in terms of accuracy and visual interpretability over the leading baselines.

preprint2022arXiv

Exploring Lottery Ticket Hypothesis in Media Recommender Systems

Media recommender systems aim to capture users' preferences and provide precise personalized recommendation of media content. There are two critical components in the common paradigm of modern recommender models: (1) representation learning, which generates an embedding for each user and item; and (2) interaction modeling, which fits user preferences towards items based on their representations. In spite of great success, when a great amount of users and items exist, it usually needs to create, store, and optimize a huge embedding table, where the scale of model parameters easily reach millions or even larger. Hence, it naturally raises questions about the heavy recommender models: Do we really need such large-scale parameters? We get inspirations from the recently proposed lottery ticket hypothesis (LTH), which argues that the dense and over-parameterized model contains a much smaller and sparser sub-model that can reach comparable performance to the full model. In this paper, we extend LTH to media recommender systems, aiming to find the winning tickets in deep recommender models. To the best of our knowledge, this is the first work to study LTH in media recommender systems. With MF and LightGCN as the backbone models, we found that there widely exist winning tickets in recommender models. On three media convergence datasets -- Yelp2018, TikTok and Kwai, the winning tickets can achieve comparable recommendation performance with only 29%~48%, 7%~10% and 3%~17% of parameters, respectively.

preprint2022arXiv

Focus Your Distribution: Coarse-to-Fine Non-Contrastive Learning for Anomaly Detection and Localization

The essence of unsupervised anomaly detection is to learn the compact distribution of normal samples and detect outliers as anomalies in testing. Meanwhile, the anomalies in real-world are usually subtle and fine-grained in a high-resolution image especially for industrial applications. Towards this end, we propose a novel framework for unsupervised anomaly detection and localization. Our method aims at learning dense and compact distribution from normal images with a coarse-to-fine alignment process. The coarse alignment stage standardizes the pixel-wise position of objects in both image and feature levels. The fine alignment stage then densely maximizes the similarity of features among all corresponding locations in a batch. To facilitate the learning with only normal images, we propose a new pretext task called non-contrastive learning for the fine alignment stage. Non-contrastive learning extracts robust and discriminating normal image representations without making assumptions on abnormal samples, and it thus empowers our model to generalize to various anomalous scenarios. Extensive experiments on two typical industrial datasets of MVTec AD and BenTech AD demonstrate that our framework is effective in detecting various real-world defects and achieves a new state-of-the-art in industrial unsupervised anomaly detection.

preprint2022arXiv

Hybrid Relation Guided Set Matching for Few-shot Action Recognition

Current few-shot action recognition methods reach impressive performance by learning discriminative features for each video via episodic training and designing various temporal alignment strategies. Nevertheless, they are limited in that (a) learning individual features without considering the entire task may lose the most relevant information in the current episode, and (b) these alignment strategies may fail in misaligned instances. To overcome the two limitations, we propose a novel Hybrid Relation guided Set Matching (HyRSM) approach that incorporates two key components: hybrid relation module and set matching metric. The purpose of the hybrid relation module is to learn task-specific embeddings by fully exploiting associated relations within and cross videos in an episode. Built upon the task-specific features, we reformulate distance measure between query and support videos as a set matching problem and further design a bidirectional Mean Hausdorff Metric to improve the resilience to misaligned instances. By this means, the proposed HyRSM can be highly informative and flexible to predict query categories under the few-shot settings. We evaluate HyRSM on six challenging benchmarks, and the experimental results show its superiority over the state-of-the-art methods by a convincing margin. Project page: https://hyrsm-cvpr2022.github.io/.

preprint2022arXiv

Invariant Grounding for Video Question Answering

Video Question Answering (VideoQA) is the task of answering questions about a video. At its core is understanding the alignments between visual scenes in video and linguistic semantics in question to yield the answer. In leading VideoQA models, the typical learning objective, empirical risk minimization (ERM), latches on superficial correlations between video-question pairs and answers as the alignments. However, ERM can be problematic, because it tends to over-exploit the spurious correlations between question-irrelevant scenes and answers, instead of inspecting the causal effect of question-critical scenes. As a result, the VideoQA models suffer from unreliable reasoning. In this work, we first take a causal look at VideoQA and argue that invariant grounding is the key to ruling out the spurious correlations. Towards this end, we propose a new learning framework, Invariant Grounding for VideoQA (IGV), to ground the question-critical scene, whose causal relations with answers are invariant across different interventions on the complement. With IGV, the VideoQA models are forced to shield the answering process from the negative influence of spurious correlations, which significantly improves the reasoning ability. Experiments on three benchmark datasets validate the superiority of IGV in terms of accuracy, visual explainability, and generalization ability over the leading baselines.

preprint2022arXiv

Learning from Untrimmed Videos: Self-Supervised Video Representation Learning with Hierarchical Consistency

Natural videos provide rich visual contents for self-supervised learning. Yet most existing approaches for learning spatio-temporal representations rely on manually trimmed videos, leading to limited diversity in visual patterns and limited performance gain. In this work, we aim to learn representations by leveraging more abundant information in untrimmed videos. To this end, we propose to learn a hierarchy of consistencies in videos, i.e., visual consistency and topical consistency, corresponding respectively to clip pairs that tend to be visually similar when separated by a short time span and share similar topics when separated by a long time span. Specifically, a hierarchical consistency learning framework HiCo is presented, where the visually consistent pairs are encouraged to have the same representation through contrastive learning, while the topically consistent pairs are coupled through a topical classifier that distinguishes whether they are topic related. Further, we impose a gradual sampling algorithm for proposed hierarchical consistency learning, and demonstrate its theoretical superiority. Empirically, we show that not only HiCo can generate stronger representations on untrimmed videos, it also improves the representation quality when applied to trimmed videos. This is in contrast to standard contrastive learning that fails to learn appropriate representations from untrimmed videos.

preprint2022arXiv

Let Invariant Rationale Discovery Inspire Graph Contrastive Learning

Leading graph contrastive learning (GCL) methods perform graph augmentations in two fashions: (1) randomly corrupting the anchor graph, which could cause the loss of semantic information, or (2) using domain knowledge to maintain salient features, which undermines the generalization to other domains. Taking an invariance look at GCL, we argue that a high-performing augmentation should preserve the salient semantics of anchor graphs regarding instance-discrimination. To this end, we relate GCL with invariant rationale discovery, and propose a new framework, Rationale-aware Graph Contrastive Learning (RGCL). Specifically, without supervision signals, RGCL uses a rationale generator to reveal salient features about graph instance-discrimination as the rationale, and then creates rationale-aware views for contrastive learning. This rationale-aware pre-training scheme endows the backbone model with the powerful representation ability, further facilitating the fine-tuning on downstream tasks. On MNIST-Superpixel and MUTAG datasets, visual inspections on the discovered rationales showcase that the rationale generator successfully captures the salient features (i.e. distinguishing semantic nodes in graphs). On biochemical molecule and social network benchmark datasets, the state-of-the-art performance of RGCL demonstrates the effectiveness of rationale-aware views for contrastive learning. Our codes are available at https://github.com/lsh0520/RGCL.

preprint2022arXiv

MLGOPerf: An ML Guided Inliner to Optimize Performance

For the past 25 years, we have witnessed an extensive application of Machine Learning to the Compiler space; the selection and the phase-ordering problem. However, limited works have been upstreamed into the state-of-the-art compilers, i.e., LLVM, to seamlessly integrate the former into the optimization pipeline of a compiler to be readily deployed by the user. MLGO was among the first of such projects and it only strives to reduce the code size of a binary with an ML-based Inliner using Reinforcement Learning. This paper presents MLGOPerf; the first end-to-end framework capable of optimizing performance using LLVM's ML-Inliner. It employs a secondary ML model to generate rewards used for training a retargeted Reinforcement learning agent, previously used as the primary model by MLGO. It does so by predicting the post-inlining speedup of a function under analysis and it enables a fast training framework for the primary model which otherwise wouldn't be practical. The experimental results show MLGOPerf is able to gain up to 1.8% and 2.2% with respect to LLVM's optimization at O3 when trained for performance on SPEC CPU2006 and Cbench benchmarks, respectively. Furthermore, the proposed approach provides up to 26% increased opportunities to autotune code regions for our benchmarks which can be translated into an additional 3.7% speedup value.

preprint2022arXiv

Reinforced Causal Explainer for Graph Neural Networks

Explainability is crucial for probing graph neural networks (GNNs), answering questions like "Why the GNN model makes a certain prediction?". Feature attribution is a prevalent technique of highlighting the explanatory subgraph in the input graph, which plausibly leads the GNN model to make its prediction. Various attribution methods exploit gradient-like or attention scores as the attributions of edges, then select the salient edges with top attribution scores as the explanation. However, most of these works make an untenable assumption - the selected edges are linearly independent - thus leaving the dependencies among edges largely unexplored, especially their coalition effect. We demonstrate unambiguous drawbacks of this assumption - making the explanatory subgraph unfaithful and verbose. To address this challenge, we propose a reinforcement learning agent, Reinforced Causal Explainer (RC-Explainer). It frames the explanation task as a sequential decision process - an explanatory subgraph is successively constructed by adding a salient edge to connect the previously selected subgraph. Technically, its policy network predicts the action of edge addition, and gets a reward that quantifies the action's causal effect on the prediction. Such reward accounts for the dependency of the newly-added edge and the previously-added edges, thus reflecting whether they collaborate together and form a coalition to pursue better explanations. As such, RC-Explainer is able to generate faithful and concise explanations, and has a better generalization power to unseen graphs. When explaining different GNNs on three graph classification datasets, RC-Explainer achieves better or comparable performance to SOTA approaches w.r.t. predictive accuracy and contrastivity, and safely passes sanity checks and visual inspections. Codes are available at https://github.com/xiangwang1223/reinforced_causal_explainer.

preprint2022arXiv

Revisiting Domain Generalized Stereo Matching Networks from a Feature Consistency Perspective

Despite recent stereo matching networks achieving impressive performance given sufficient training data, they suffer from domain shifts and generalize poorly to unseen domains. We argue that maintaining feature consistency between matching pixels is a vital factor for promoting the generalization capability of stereo matching networks, which has not been adequately considered. Here we address this issue by proposing a simple pixel-wise contrastive learning across the viewpoints. The stereo contrastive feature loss function explicitly constrains the consistency between learned features of matching pixel pairs which are observations of the same 3D points. A stereo selective whitening loss is further introduced to better preserve the stereo feature consistency across domains, which decorrelates stereo features from stereo viewpoint-specific style information. Counter-intuitively, the generalization of feature consistency between two viewpoints in the same scene translates to the generalization of stereo matching performance to unseen domains. Our method is generic in nature as it can be easily embedded into existing stereo networks and does not require access to the samples in the target domain. When trained on synthetic data and generalized to four real-world testing sets, our method achieves superior performance over several state-of-the-art networks.

preprint2022arXiv

Rumor Detection with Self-supervised Learning on Texts and Social Graph

Rumor detection has become an emerging and active research field in recent years. At the core is to model the rumor characteristics inherent in rich information, such as propagation patterns in social network and semantic patterns in post content, and differentiate them from the truth. However, existing works on rumor detection fall short in modeling heterogeneous information, either using one single information source only (e.g. social network, or post content) or ignoring the relations among multiple sources (e.g. fusing social and content features via simple concatenation). Therefore, they possibly have drawbacks in comprehensively understanding the rumors, and detecting them accurately. In this work, we explore contrastive self-supervised learning on heterogeneous information sources, so as to reveal their relations and characterize rumors better. Technically, we supplement the main supervised task of detection with an auxiliary self-supervised task, which enriches post representations via post self-discrimination. Specifically, given two heterogeneous views of a post (i.e. representations encoding social patterns and semantic patterns), the discrimination is done by maximizing the mutual information between different views of the same post compared to that of other posts. We devise cluster-wise and instance-wise approaches to generate the views and conduct the discrimination, considering different relations of information sources. We term this framework as Self-supervised Rumor Detection (SRD). Extensive experiments on three real-world datasets validate the effectiveness of SRD for automatic rumor detection on social media.

preprint2022arXiv

Temporal Feature Alignment and Mutual Information Maximization for Video-Based Human Pose Estimation

Multi-frame human pose estimation has long been a compelling and fundamental problem in computer vision. This task is challenging due to fast motion and pose occlusion that frequently occur in videos. State-of-the-art methods strive to incorporate additional visual evidences from neighboring frames (supporting frames) to facilitate the pose estimation of the current frame (key frame). One aspect that has been obviated so far, is the fact that current methods directly aggregate unaligned contexts across frames. The spatial-misalignment between pose features of the current frame and neighboring frames might lead to unsatisfactory results. More importantly, existing approaches build upon the straightforward pose estimation loss, which unfortunately cannot constrain the network to fully leverage useful information from neighboring frames. To tackle these problems, we present a novel hierarchical alignment framework, which leverages coarse-to-fine deformations to progressively update a neighboring frame to align with the current frame at the feature level. We further propose to explicitly supervise the knowledge extraction from neighboring frames, guaranteeing that useful complementary cues are extracted. To achieve this goal, we theoretically analyzed the mutual information between the frames and arrived at a loss that maximizes the task-relevant mutual information. These allow us to rank No.1 in the Multi-frame Person Pose Estimation Challenge on benchmark dataset PoseTrack2017, and obtain state-of-the-art performance on benchmarks Sub-JHMDB and Pose-Track2018. Our code is released at https://github. com/Pose-Group/FAMI-Pose, hoping that it will be useful to the community.

preprint2022arXiv

Time-aware Path Reasoning on Knowledge Graph for Recommendation

Reasoning on knowledge graph (KG) has been studied for explainable recommendation due to it's ability of providing explicit explanations. However, current KG-based explainable recommendation methods unfortunately ignore the temporal information (such as purchase time, recommend time, etc.), which may result in unsuitable explanations. In this work, we propose a novel Time-aware Path reasoning for Recommendation (TPRec for short) method, which leverages the potential of temporal information to offer better recommendation with plausible explanations. First, we present an efficient time-aware interaction relation extraction component to construct collaborative knowledge graph with time-aware interactions (TCKG for short), and then introduce a novel time-aware path reasoning method for recommendation. We conduct extensive experiments on three real-world datasets. The results demonstrate that the proposed TPRec could successfully employ TCKG to achieve substantial gains and improve the quality of explainable recommendation.

preprint2022arXiv

Training Free Graph Neural Networks for Graph Matching

We present a framework of Training Free Graph Matching (TFGM) to boost the performance of Graph Neural Networks (GNNs) based graph matching, providing a fast promising solution without training (training-free). TFGM provides four widely applicable principles for designing training-free GNNs and is generalizable to supervised, semi-supervised, and unsupervised graph matching. The keys are to handcraft the matching priors, which used to be learned by training, into GNN's architecture and discard the components inessential under the training-free setting. Further analysis shows that TFGM is a linear relaxation to the quadratic assignment formulation of graph matching and generalizes TFGM to a broad set of GNNs. Extensive experiments show that GNNs with TFGM achieve comparable (if not better) performances to their fully trained counterparts, and demonstrate TFGM's superiority in the unsupervised setting. Our code is available at https://github.com/acharkq/Training-Free-Graph-Matching.

preprint2021arXiv

A Survey on Accuracy-oriented Neural Recommendation: From Collaborative Filtering to Information-rich Recommendation

Influenced by the great success of deep learning in computer vision and language understanding, research in recommendation has shifted to inventing new recommender models based on neural networks. In recent years, we have witnessed significant progress in developing neural recommender models, which generalize and surpass traditional recommender models owing to the strong representation power of neural networks. In this survey paper, we conduct a systematic review on neural recommender models from the perspective of recommendation modeling with the accuracy goal, aiming to summarize this field to facilitate researchers and practitioners working on recommender systems. Specifically, based on the data usage during recommendation modeling, we divide the work into collaborative filtering and information-rich recommendation: 1) collaborative filtering, which leverages the key source of user-item interaction data; 2) content enriched recommendation, which additionally utilizes the side information associated with users and items, like user profile and item knowledge graph; and 3) temporal/sequential recommendation, which accounts for the contextual information associated with an interaction, such as time, location, and the past interactions. After reviewing representative work for each type, we finally discuss some promising directions in this field.

preprint2021arXiv

Graph Convolution Machine for Context-aware Recommender System

The latest advance in recommendation shows that better user and item representations can be learned via performing graph convolutions on the user-item interaction graph. However, such finding is mostly restricted to the collaborative filtering (CF) scenario, where the interaction contexts are not available. In this work, we extend the advantages of graph convolutions to context-aware recommender system (CARS, which represents a generic type of models that can handle various side information). We propose \textit{Graph Convolution Machine} (GCM), an end-to-end framework that consists of three components: an encoder, graph convolution (GC) layers, and a decoder. The encoder projects users, items, and contexts into embedding vectors, which are passed to the GC layers that refine user and item embeddings with context-aware graph convolutions on user-item graph. The decoder digests the refined embeddings to output the prediction score by considering the interactions among user, item, and context embeddings. We conduct experiments on three real-world datasets from Yelp and Amazon, validating the effectiveness of GCM and the benefits of performing graph convolutions for CARS. Our implementations are available at \url{https://github.com/wujcan/GCM}.

preprint2021arXiv

Learning Intents behind Interactions with Knowledge Graph for Recommendation

Knowledge graph (KG) plays an increasingly important role in recommender systems. A recent technical trend is to develop end-to-end models founded on graph neural networks (GNNs). However, existing GNN-based models are coarse-grained in relational modeling, failing to (1) identify user-item relation at a fine-grained level of intents, and (2) exploit relation dependencies to preserve the semantics of long-range connectivity. In this study, we explore intents behind a user-item interaction by using auxiliary item knowledge, and propose a new model, Knowledge Graph-based Intent Network (KGIN). Technically, we model each intent as an attentive combination of KG relations, encouraging the independence of different intents for better model capability and interpretability. Furthermore, we devise a new information aggregation scheme for GNN, which recursively integrates the relation sequences of long-range connectivity (i.e., relational paths). This scheme allows us to distill useful information about user intents and encode them into the representations of users and items. Experimental results on three benchmark datasets show that, KGIN achieves significant improvements over the state-of-the-art methods like KGAT, KGNN-LS, and CKAN. Further analyses show that KGIN offers interpretable explanations for predictions by identifying influential intents and relational paths. The implementations are available at https://github.com/huangtinglin/Knowledge_Graph_based_Intent_Network.

preprint2021arXiv

Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two dimensional Hubbard model

Understanding electronic properties that violate the Landau Fermi liquid paradigm in cuprate superconductors remains a major challenge in condensed matter physics. The strange metal state in overdoped cuprates that exhibits linear-in-temperature scattering rate and dc resistivity is a particularly puzzling example. Here, we compute the electronic scattering rate in the two-dimensional Hubbard model using cluster generalization of dynamical mean-field theory. We present a global phase diagram documenting an apparent non-Fermi liquid phase, in between the pseudogap and Fermi liquid phase in the doped Mott insulator regime. We discover that in this non-Fermi liquid phase, the electronic scattering rate $γ_k(T)$ can display linear temperature dependence as temperature $T$ goes to zero. In the temperature range that we can access, the $T-$ dependent scattering rate is isotropic on the Fermi surface, in agreement with recent experiments. Using fluctuation diagnostic techniques, we identify antiferromagnetic fluctuations as the physical origin of the $T-$ linear electronic scattering rate.

preprint2020arXiv

A Multi-View Approach Based on Naming Behavioral Modeling for Aligning Chinese User Accounts across Multiple Networks

Hundreds of millions of Chinese people have become social network users in recent years, and aligning the accounts of common Chinese users across multiple social networks is valuable to many inter-network applications, e.g., cross-network recommendation, cross-network link prediction. Many methods have explored the proper ways of utilizing account name information into aligning the common English users' accounts. However, how to properly utilize the account name information when aligning the Chinese user accounts remains to be detailedly studied. In this paper, we firstly discuss the available naming behavioral models as well as the related features for different types of Chinese account name matchings. Secondly, we propose the framework of Multi-View Cross-Network User Alignment (MCUA) method, which uses a multi-view framework to creatively integrate different models to deal with different types of Chinese account name matchings, and can consider all of the studied features when aligning the Chinese user accounts. Finally, we conduct experiments to prove that MCUA can outperform many existing methods on aligning Chinese user accounts between Sina Weibo and Twitter. Besides, we also study the best learning models and the top-k valuable features of different types of name matchings for MCUA over our experimental data sets.

preprint2020arXiv

Bilinear Graph Neural Network with Neighbor Interactions

Graph Neural Network (GNN) is a powerful model to learn representations and make predictions on graph data. Existing efforts on GNN have largely defined the graph convolution as a weighted sum of the features of the connected nodes to form the representation of the target node. Nevertheless, the operation of weighted sum assumes the neighbor nodes are independent of each other, and ignores the possible interactions between them. When such interactions exist, such as the co-occurrence of two neighbor nodes is a strong signal of the target node's characteristics, existing GNN models may fail to capture the signal. In this work, we argue the importance of modeling the interactions between neighbor nodes in GNN. We propose a new graph convolution operator, which augments the weighted sum with pairwise interactions of the representations of neighbor nodes. We term this framework as Bilinear Graph Neural Network (BGNN), which improves GNN representation ability with bilinear interactions between neighbor nodes. In particular, we specify two BGNN models named BGCN and BGAT, based on the well-known GCN and GAT, respectively. Empirical results on three public benchmarks of semi-supervised node classification verify the effectiveness of BGNN -- BGCN (BGAT) outperforms GCN (GAT) by 1.6% (1.5%) in classification accuracy.Codes are available at: https://github.com/zhuhm1996/bgnn.

preprint2020arXiv

CBR-Net: Cascade Boundary Refinement Network for Action Detection: Submission to ActivityNet Challenge 2020 (Task 1)

In this report, we present our solution for the task of temporal action localization (detection) (task 1) in ActivityNet Challenge 2020. The purpose of this task is to temporally localize intervals where actions of interest occur and predict the action categories in a long untrimmed video. Our solution mainly includes three components: 1) feature encoding: we apply three kinds of backbones, including TSN [7], Slowfast[3] and I3d[1], which are both pretrained on Kinetics dataset[2]. Applying these models, we can extract snippet-level video representations; 2) proposal generation: we choose BMN [5] as our baseline, base on which we design a Cascade Boundary Refinement Network (CBR-Net) to conduct proposal detection. The CBR-Net mainly contains two modules: temporal feature encoding, which applies BiLSTM to encode long-term temporal information; CBR module, which targets to refine the proposal precision under different parameter settings; 3) action localization: In this stage, we combine the video-level classification results obtained by the fine tuning networks to predict the category of each proposal. Moreover, we also apply to different ensemble strategies to improve the performance of the designed solution, by which we achieve 42.788% on the testing set of ActivityNet v1.3 dataset in terms of mean Average Precision metrics.

preprint2020arXiv

Disentangled Graph Collaborative Filtering

Learning informative representations of users and items from the interaction data is of crucial importance to collaborative filtering (CF). Present embedding functions exploit user-item relationships to enrich the representations, evolving from a single user-item instance to the holistic interaction graph. Nevertheless, they largely model the relationships in a uniform manner, while neglecting the diversity of user intents on adopting the items, which could be to pass time, for interest, or shopping for others like families. Such uniform approach to model user interests easily results in suboptimal representations, failing to model diverse relationships and disentangle user intents in representations. In this work, we pay special attention to user-item relationships at the finer granularity of user intents. We hence devise a new model, Disentangled Graph Collaborative Filtering (DGCF), to disentangle these factors and yield disentangled representations. Specifically, by modeling a distribution over intents for each user-item interaction, we iteratively refine the intent-aware interaction graphs and representations. Meanwhile, we encourage independence of different intents. This leads to disentangled representations, effectively distilling information pertinent to each intent. We conduct extensive experiments on three benchmark datasets, and DGCF achieves significant improvements over several state-of-the-art models like NGCF, DisenGCN, and MacridVAE. Further analyses offer insights into the advantages of DGCF on the disentanglement of user intents and interpretability of representations. Our codes are available in https://github.com/xiangwang1223/disentangled_graph_collaborative_filtering.

preprint2020arXiv

Dynamics for droplet-based electricity generators

The finding of droplet-based electricity generator (DEG), based on the moving boundary of electrical double layer, has triggered great research enthusiasm, and a breakthrough in instantaneous electric power density was achieved recently. However, the dynamic mechanism for such droplet-based electricity generators remains elusive, impeding optimization of the DEG for practical applications. Through comprehensive experiments, we developed a dynamic model of surface charge density that can explain the underlying mechanism for the DEGs. The spreading droplet in touch with the top electrode can be equivalently regarded as an additional part of the top plate of the DEG capacitor, and the change of droplet area causes the change of surface charge density of the plates, driving electrons to migrate between the two plates. The insight of the dynamic mechanism paves a way for optimal design and practical applications of DEGs

preprint2020arXiv

Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets

Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima -- at least those discovered by gradient-based optimization -- turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with as few as two segments. We give mathematical explanations for this phenomenon, assuming generic properties (such as dropout stability and noise stability) of well-trained deep nets, which have previously been identified as part of understanding the generalization properties of deep nets. Our explanation holds for realistic multilayer nets, and experiments are presented to verify the theory.

preprint2020arXiv

Hierarchical Fashion Graph Network for Personalized Outfit Recommendation

Fashion outfit recommendation has attracted increasing attentions from online shopping services and fashion communities.Distinct from other scenarios (e.g., social networking or content sharing) which recommend a single item (e.g., a friend or picture) to a user, outfit recommendation predicts user preference on a set of well-matched fashion items.Hence, performing high-quality personalized outfit recommendation should satisfy two requirements -- 1) the nice compatibility of fashion items and 2) the consistence with user preference. However, present works focus mainly on one of the requirements and only consider either user-outfit or outfit-item relationships, thereby easily leading to suboptimal representations and limiting the performance. In this work, we unify two tasks, fashion compatibility modeling and personalized outfit recommendation. Towards this end, we develop a new framework, Hierarchical Fashion Graph Network(HFGN), to model relationships among users, items, and outfits simultaneously. In particular, we construct a hierarchical structure upon user-outfit interactions and outfit-item mappings. We then get inspirations from recent graph neural networks, and employ the embedding propagation on such hierarchical graph, so as to aggregate item information into an outfit representation, and then refine a user's representation via his/her historical outfits. Furthermore, we jointly train these two tasks to optimize these representations. To demonstrate the effectiveness of HFGN, we conduct extensive experiments on a benchmark dataset, and HFGN achieves significant improvements over the state-of-the-art compatibility matching models like NGNN and outfit recommenders like FHN.

preprint2020arXiv

Interactive Path Reasoning on Graph for Conversational Recommendation

Traditional recommendation systems estimate user preference on items from past interaction history, thus suffering from the limitations of obtaining fine-grained and dynamic user preference. Conversational recommendation system (CRS) brings revolutions to those limitations by enabling the system to directly ask users about their preferred attributes on items. However, existing CRS methods do not make full use of such advantage -- they only use the attribute feedback in rather implicit ways such as updating the latent user representation. In this paper, we propose Conversational Path Reasoning (CPR), a generic framework that models conversational recommendation as an interactive path reasoning problem on a graph. It walks through the attribute vertices by following user feedback, utilizing the user preferred attributes in an explicit way. By leveraging on the graph structure, CPR is able to prune off many irrelevant candidate attributes, leading to better chance of hitting user preferred attributes. To demonstrate how CPR works, we propose a simple yet effective instantiation named SCPR (Simple CPR). We perform empirical studies on the multi-round conversational recommendation scenario, the most realistic CRS setting so far that considers multiple rounds of asking attributes and recommending items. Through extensive experiments on two datasets Yelp and LastFM, we validate the effectiveness of our SCPR, which significantly outperforms the state-of-the-art CRS methods EAR (arXiv:2002.09102) and CRM (arXiv:1806.03277). In particular, we find that the more attributes there are, the more advantages our method can achieve.

preprint2020arXiv

LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation

Graph Convolution Network (GCN) has become new state-of-the-art for collaborative filtering. Nevertheless, the reasons of its effectiveness for recommendation are not well understood. Existing work that adapts GCN to recommendation lacks thorough ablation analyses on GCN, which is originally designed for graph classification tasks and equipped with many neural network operations. However, we empirically find that the two most common designs in GCNs -- feature transformation and nonlinear activation -- contribute little to the performance of collaborative filtering. Even worse, including them adds to the difficulty of training and degrades recommendation performance. In this work, we aim to simplify the design of GCN to make it more concise and appropriate for recommendation. We propose a new model named LightGCN, including only the most essential component in GCN -- neighborhood aggregation -- for collaborative filtering. Specifically, LightGCN learns user and item embeddings by linearly propagating them on the user-item interaction graph, and uses the weighted sum of the embeddings learned at all layers as the final embedding. Such simple, linear, and neat model is much easier to implement and train, exhibiting substantial improvements (about 16.0\% relative improvement on average) over Neural Graph Collaborative Filtering (NGCF) -- a state-of-the-art GCN-based recommender model -- under exactly the same experimental setting. Further analyses are provided towards the rationality of the simple LightGCN from both analytical and empirical perspectives.

preprint2020arXiv

Multi-Level Temporal Pyramid Network for Action Detection

Currently, one-stage frameworks have been widely applied for temporal action detection, but they still suffer from the challenge that the action instances span a wide range of time. The reason is that these one-stage detectors, e.g., Single Shot Multi-Box Detector (SSD), extract temporal features only applying a single-level layer for each head, which is not discriminative enough to perform classification and regression. In this paper, we propose a Multi-Level Temporal Pyramid Network (MLTPN) to improve the discrimination of the features. Specially, we first fuse the features from multiple layers with different temporal resolutions, to encode multi-layer temporal information. We then apply a multi-level feature pyramid architecture on the features to enhance their discriminative abilities. Finally, we design a simple yet effective feature fusion module to fuse the multi-level multi-scale features. By this means, the proposed MLTPN can learn rich and discriminative features for different action instances with different durations. We evaluate MLTPN on two challenging datasets: THUMOS'14 and Activitynet v1.3, and the experimental results show that MLTPN obtains competitive performance on Activitynet v1.3 and outperforms the state-of-the-art approaches on THUMOS'14 significantly.

preprint2020arXiv

Neural Graph Collaborative Filtering

Learning vector representations (aka. embeddings) of users and items lies at the core of modern recommender systems. Ranging from early matrix factorization to recently emerged deep learning based methods, existing efforts typically obtain a user's (or an item's) embedding by mapping from pre-existing features that describe the user (or the item), such as ID and attributes. We argue that an inherent drawback of such methods is that, the collaborative signal, which is latent in user-item interactions, is not encoded in the embedding process. As such, the resultant embeddings may not be sufficient to capture the collaborative filtering effect. In this work, we propose to integrate the user-item interactions -- more specifically the bipartite graph structure -- into the embedding process. We develop a new recommendation framework Neural Graph Collaborative Filtering (NGCF), which exploits the user-item graph structure by propagating embeddings on it. This leads to the expressive modeling of high-order connectivity in user-item graph, effectively injecting the collaborative signal into the embedding process in an explicit manner. We conduct extensive experiments on three public benchmarks, demonstrating significant improvements over several state-of-the-art models like HOP-Rec and Collaborative Memory Network. Further analysis verifies the importance of embedding propagation for learning better user and item representations, justifying the rationality and effectiveness of NGCF. Codes are available at https://github.com/xiangwang1223/neural_graph_collaborative_filtering.

preprint2020arXiv

New superconvergent structures developed from the finite volume element method in 1D

New superconvergent structures are introduced by the finite volume element method (FVEM), which allow us to choose the superconvergent points freely. The general orthogonal condition and the modified M-decomposition (MMD) technique are established to prove the superconvergence properties of the new structures. In addition, the relationships between the orthogonal condition and the convergence properties for the FVE schemes are carried out in Table 1. Numerical results are given to illustrate the theoretical results.

preprint2020arXiv

Reinforced Negative Sampling over Knowledge Graph for Recommendation

Properly handling missing data is a fundamental challenge in recommendation. Most present works perform negative sampling from unobserved data to supply the training of recommender models with negative signals. Nevertheless, existing negative sampling strategies, either static or adaptive ones, are insufficient to yield high-quality negative samples --- both informative to model training and reflective of user real needs. In this work, we hypothesize that item knowledge graph (KG), which provides rich relations among items and KG entities, could be useful to infer informative and factual negative samples. Towards this end, we develop a new negative sampling model, Knowledge Graph Policy Network (KGPolicy), which works as a reinforcement learning agent to explore high-quality negatives. Specifically, by conducting our designed exploration operations, it navigates from the target positive interaction, adaptively receives knowledge-aware negative signals, and ultimately yields a potential negative item to train the recommender. We tested on a matrix factorization (MF) model equipped with KGPolicy, and it achieves significant improvements over both state-of-the-art sampling methods like DNS and IRGAN, and KG-enhanced recommender models like KGAT. Further analyses from different angles provide insights of knowledge-aware sampling. We release the codes and datasets at https://github.com/xiangwang1223/kgpolicy.

preprint2020arXiv

Temporal Fusion Network for Temporal Action Localization:Submission to ActivityNet Challenge 2020 (Task E)

This technical report analyzes a temporal action localization method we used in the HACS competition which is hosted in Activitynet Challenge 2020.The goal of our task is to locate the start time and end time of the action in the untrimmed video, and predict action category.Firstly, we utilize the video-level feature information to train multiple video-level action classification models. In this way, we can get the category of action in the video.Secondly, we focus on generating high quality temporal proposals.For this purpose, we apply BMN to generate a large number of proposals to obtain high recall rates. We then refine these proposals by employing a cascade structure network called Refine Network, which can predict position offset and new IOU under the supervision of ground truth.To make the proposals more accurate, we use bidirectional LSTM, Nonlocal and Transformer to capture temporal relationships between local features of each proposal and global features of the video data.Finally, by fusing the results of multiple models, our method obtains 40.55% on the validation set and 40.53% on the test set in terms of mAP, and achieves Rank 1 in this challenge.

preprint2020arXiv

Visual Perception Model for Rapid and Adaptive Low-light Image Enhancement

Low-light image enhancement is a promising solution to tackle the problem of insufficient sensitivity of human vision system (HVS) to perceive information in low light environments. Previous Retinex-based works always accomplish enhancement task by estimating light intensity. Unfortunately, single light intensity modelling is hard to accurately simulate visual perception information, leading to the problems of imbalanced visual photosensitivity and weak adaptivity. To solve these problems, we explore the precise relationship between light source and visual perception and then propose the visual perception (VP) model to acquire a precise mathematical description of visual perception. The core of VP model is to decompose the light source into light intensity and light spatial distribution to describe the perception process of HVS, offering refinement estimation of illumination and reflectance. To reduce complexity of the estimation process, we introduce the rapid and adaptive $\mathbfβ$ and $\mathbfγ$ functions to build an illumination and reflectance estimation scheme. Finally, we present a optimal determination strategy, consisting of a \emph{cycle operation} and a \emph{comparator}. Specifically, the \emph{comparator} is responsible for determining the optimal enhancement results from multiple enhanced results through implementing the \emph{cycle operation}. By coordinating the proposed VP model, illumination and reflectance estimation scheme, and the optimal determination strategy, we propose a rapid and adaptive framework for low-light image enhancement. Extensive experiment results demenstrate that the proposed method achieves better performance in terms of visual comparison, quantitative assessment, and computational efficiency, compared with the currently state-of-the-arts.

preprint2020arXiv

Weakly-Supervised Semantic Segmentation by Iterative Affinity Learning

Weakly-supervised semantic segmentation is a challenging task as no pixel-wise label information is provided for training. Recent methods have exploited classification networks to localize objects by selecting regions with strong response. While such response map provides sparse information, however, there exist strong pairwise relations between pixels in natural images, which can be utilized to propagate the sparse map to a much denser one. In this paper, we propose an iterative algorithm to learn such pairwise relations, which consists of two branches, a unary segmentation network which learns the label probabilities for each pixel, and a pairwise affinity network which learns affinity matrix and refines the probability map generated from the unary network. The refined results by the pairwise network are then used as supervision to train the unary network, and the procedures are conducted iteratively to obtain better segmentation progressively. To learn reliable pixel affinity without accurate annotation, we also propose to mine confident regions. We show that iteratively training this framework is equivalent to optimizing an energy function with convergence to a local minimum. Experimental results on the PASCAL VOC 2012 and COCO datasets demonstrate that the proposed algorithm performs favorably against the state-of-the-art methods.

preprint2020arXiv

XTDrone: A Customizable Multi-Rotor UAVs Simulation Platform

A customizable multi-rotor UAVs simulation platform based on ROS, Gazebo and PX4 is presented. The platform, which is called XTDrone, integrates dynamic models, sensor models, control algorithm, state estimation algorithm, and 3D scenes. The platform supports multi UAVs and other robots. The platform is modular and each module can be modified, which means that users can test its own algorithm, such as SLAM, object detection, motion planning, attitude control, multi-UAV cooperation, and cooperation with other robots on the platform. The platform runs in lockstep, so the simulation speed can be adjusted according to the computer performance. In this paper, two cases, evaluating different visual SLAM algorithm and realizing UAV formation, are shown to demonstrate how the platform works.

preprint2019arXiv

A Survey on Face Data Augmentation

The quality and size of training set have great impact on the results of deep learning-based face related tasks. However, collecting and labeling adequate samples with high quality and balanced distributions still remains a laborious and expensive work, and various data augmentation techniques have thus been widely used to enrich the training dataset. In this paper, we systematically review the existing works of face data augmentation from the perspectives of the transformation types and methods, with the state-of-the-art approaches involved. Among all these approaches, we put the emphasis on the deep learning-based works, especially the generative adversarial networks which have been recognized as more powerful and effective tools in recent years. We present their principles, discuss the results and show their applications as well as limitations. Different evaluation metrics for evaluating these approaches are also introduced. We point out the challenges and opportunities in the field of face data augmentation, and provide brief yet insightful discussions.

preprint2019arXiv

Quantum-enhanced least-square support vector machine: simplified quantum algorithm and sparse solutions

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining exponential speed-up. Secondly, we propose a hybrid quantum-classical version for sparse solutions of LS-SVM. By encoding a large dataset into a quantum state, a much smaller transformed dataset can be extracted using quantum matrix toolbox, which is further processed in classical SVM. We also incorporate kernel methods into the above quantum algorithms, which uses both exponential growth Hilbert space of qubits and infinite dimensionality of continuous variable for quantum feature maps. The quantum LS-SVM exploits quantum properties to explore important themes for SVM such as sparsity and kernel methods, and stresses its quantum advantages ranging from speed-up to the potential capacity to solve classically difficult machine learning tasks.

preprint2018arXiv

Conditioning of Finite Volume Element Method for Diffusion Problems with General Simplicial Meshes

The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness matrix to the minimal eigenvalue of its symmetric part. This definition is motivated by the fact that the convergence rate of the generalized minimal residual method for the corresponding linear systems is determined by the ratio. An upper bound for the ratio is established by developing an upper bound for the maximal singular value and a lower bound for the minimal eigenvalue of the symmetric part. It is shown that the bound depends on three factors, the number of the elements in the mesh, the mesh nonuniformity measured in the Euclidean metric, and the mesh nonuniformity measured in the metric specified by the inverse diffusion matrix. It is also shown that the diagonal scaling can effectively eliminates the effects from the mesh nonuniformity measured in the Euclidean metric. Numerical results for a selection of examples in one, two, and three dimensions are presented.

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arxivconfidence 95%

external id: arxiv:2605.08936:author:5:xiang-wang

Imported May 20, 2026Synced May 21, 2026

arxivconfidence 95%

external id: arxiv:2605.07396:author:9:xiang-wang

Imported May 20, 2026Synced May 21, 2026

arxivconfidence 95%

external id: arxiv:2605.18882:author:5:xiang-wang

Imported May 20, 2026Synced May 21, 2026

arxivconfidence 95%

external id: arxiv:2605.00327:author:10:xiang-wang