Reconstruction from multi-view images is a fundamental challenge in computer vision that has been extensively studied over the past decades. Recently, neural radiance fields have driven significant advancements, especially through methods using implicit functions and volume rendering, achieving high levels of accuracy. A core component of these methods is the mapping that transforms an implicit function's output into corresponding volume densities. Despite its critical role, this mapping has received limited attention in existing literature. In this paper, we provide a comprehensive and systematic study of mapping functions, examining their properties and representations. We first outline the necessary conditions for the mapping function and propose a family of functions that meet these criteria, to ensure first-order unbiasedness. We further demonstrate that the mappings employed by NeuS and VolSDF, two representative neural implicit surface techniques, are special cases within this broader family. Building on our theoretical framework, we introduce several new mapping functions and evaluate their effectiveness through numerical experiments. Our approach offers a fresh perspective on this well-established problem, opening avenues for the development of new techniques in the field.
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Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin
PDF ↗The emerging diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of the data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each noise level, with efforts concentrated on refining inter-level denoising strategies. While leveraging additional second-order Hessian geometry to enhance the sampling quality of Langevin is a common practice in Markov chain Monte Carlo (MCMC), the naive attempts to utilize Hessian geometry in high-dimensional DMs lead to quadratic-complexity computational costs, rendering them non-scalable. In this work, we introduce a novel Levenberg-Marquardt-Langevin (LML) method that approximates the diffusion Hessian geometry in a training-free manner, drawing inspiration from the celebrated Levenberg-Marquardt optimization algorithm. Our approach introduces two key innovations: (1) A low-rank approximation of the diffusion Hessian, leveraging the DMs' inherent structure and circumventing explicit quadratic-complexity computations; (2) A damping mechanism to stabilize the approximated Hessian. This LML approximated Hessian geometry enables the diffusion sampling to execute more accurate steps and improve the image generation quality. We further conduct a theoretical analysis to substantiate the approximation error bound of low-rank approximation and the convergence property of the damping mechanism. Extensive experiments across multiple pretrained DMs validate that the LML method significantly improves image generation quality, with negligible computational overhead.
Out-of-Distribution (OOD) detection is critical for safely deploying deep models in open-world environments, where inputs may lie outside the training distribution. During inference on a model trained exclusively with In-Distribution (ID) data, we observe a salient gradient phenomenon: around an ID sample, the local gradient directions for "enhancing" that sample's predicted class remain relatively consistent, whereas OOD samples--unseen in training--exhibit disorganized or conflicting gradient directions in the same neighborhood. Motivated by this observation, we propose an inference-stage technique to short-circuit those feature coordinates that spurious gradients exploit to inflate OOD confidence, while leaving ID classification largely intact. To circumvent the expense of recomputing the logits after this gradient short-circuit, we further introduce a local first-order approximation that accurately captures the post-modification outputs without a second forward pass. Experiments on standard OOD benchmarks show our approach yields substantial improvements. Moreover, the method is lightweight and requires minimal changes to the standard inference pipeline, offering a practical path toward robust OOD detection in real-world applications.
Structure and continuous motion estimation from point correspondences is a fundamental problem in computer vision that has been powered by well-known algorithms such as the familiar 5-point or 8-point algorithm. However, despite their acclaim, these algorithms are limited to processing point correspondences originating from a pair of views each one representing an instantaneous capture of the scene. Yet, in the case of rolling shutter cameras, or more recently, event cameras, this synchronization breaks down. In this work, we present a unified approach for structure and linear motion estimation from 2D point correspondences with arbitrary timestamps, from an arbitrary set of views. By formulating the problem in terms of first-order dynamics and leveraging a constant velocity motion model, we derive a novel, linear point incidence relation allowing for the efficient recovery of both linear velocity and 3D points with predictable degeneracies and solution multiplicities. Owing to its general formulation, it can handle correspondences from a wide range of sensing modalities such as global shutter, rolling shutter, and event cameras, and can even combine correspondences from different collocated sensors. We validate the effectiveness of our solver on both simulated and real-world data, where we show consistent improvement across all modalities when compared to recent approaches. We believe our work opens the door to efficient structure and motion estimation from asynchronous data.
Industrial quality inspection plays a critical role in modern manufacturing by identifying defective products during production. While single-modality approaches using either 3D point clouds or 2D RGB images suffer from information incompleteness, multimodal anomaly detection offers promise through the complementary fusion of crossmodal data. However, existing methods face challenges in effectively integrating unimodal results and improving discriminative power. To address these limitations, we first reinterpret memory bank-based anomaly scores in single modalities as isotropic Euclidean distances in local feature spaces. Dynamically evolving from Euclidean metrics, we propose a novel \underline G eometry-\underline G uided \underline S core \underline F usion (G^ 2 SF) framework that progressively learns an anisotropic local distance metric as a unified score for the fusion task. Through a geometric encoding operator, a novel Local Scale Prediction Network (LSPN) is proposed to predict direction-aware scaling factors that characterize first-order local feature distributions, thereby enhancing discrimination between normal and anomalous patterns. Additionally, we develop specialized loss functions and score aggregation strategy from geometric priors to ensure both metric generalization and efficacy. Comprehensive evaluations on the MVTec-3D AD and Eyecandies datasets demonstrate the state-of-the-art detection performance of our method, and detailed ablation analysis validates each component's contribution. Our code is available at https://github.com/ctaoaa/G2SF.
Preconditioned stochastic optimization algorithms, exemplified by Shampoo, outperform first-order optimizers by offering theoretical convergence benefits and practical gains in large-scale neural network training. However, they incur substantial memory overhead due to the storage demands of non-diagonal preconditioning matrices. To address this, we introduce 4-bit quantization for Shampoo's preconditioners. We introduce two key methods: First, we apply Cholesky decomposition followed by quantization of the Cholesky factors, reducing memory usage by leveraging their lower triangular structure while better preserving spectral properties to minimize information loss. To our knowledge, this is the first quantization approach applied to Cholesky factors of preconditioners. Second, we incorporate error feedback in the quantization process, efficiently storing Cholesky factor and error state in the lower and upper triangular parts of the same matrix. Through extensive experiments, we demonstrate that combining Cholesky quantization with error feedback enhances memory efficiency and algorithm performance in large-scale deep-learning tasks. Theoretically, we also provide convergence proofs for quantized Shampoo under both smooth and non-smooth stochastic optimization settings.
Zero-shot compositional action recognition (ZS-CAR) aims to identify unseen verb-object compositions in the videos by exploiting the learned knowledge of verb and object primitives during training. Despite compositional learning's progress in ZS-CAR, two critical challenges persist: 1) Missing compositional structure constraint, leading to spurious correlations between primitives; 2) Neglecting semantic hierarchy constraint, leading to semantic ambiguity and impairing the training process. In this paper, we argue that human-like symbolic reasoning offers a principled solution to these challenges by explicitly modeling compositional and hierarchical structured abstraction. To this end, we propose a logic-driven ZS-CAR framework LogicCAR that integrates dual symbolic constraints: Explicit Compositional Logic and Hierarchical Primitive Logic. Specifically, the former models the restrictions within the compositions, enhancing the compositional reasoning ability of our model. The latter investigates the semantical dependencies among different primitives, empowering the models with fine-to-coarse reasoning capacity. By formalizing these constraints in first-order logic and embedding them into neural network architectures, LogicCAR systematically bridges the gap between symbolic abstraction and existing models. Extensive experiments on the Sth-com dataset demonstrate that our LogicCAR outperforms existing baseline methods, proving the effectiveness of our logic-driven constraints.
Towards Measuring and Modeling Geometric Structures in Time Series Forecasting via Image Modality
PDF ↗Time Series forecasting is critical in diverse domains such as weather forecasting, financial investment, and traffic management. While traditional numerical metrics like mean squared error (MSE) can quantify point-wise accuracy, they fail to evaluate the geometric structure of time series data, which is essential to understand temporal dynamics. To address this issue, we propose the time series Geometric Structure Index (TGSI), a novel evaluation metric that transforms time series into images to leverage their inherent two-dimensional geometric representations. However, since the image transformation process is non-differentiable, TGSI cannot be directly integrated as a training loss. We further introduce the Shape-Aware Temporal Loss (SATL), a multi-component loss function operating in the time series modality to bridge this gap and enhance structure modeling during training. SATL combines three components: a first-order difference loss that measures structural consistency through the MSE between first-order differences, a frequency domain loss that captures essential periodic patterns using the Fast Fourier Transform while minimizing noise, and a perceptual feature loss that measures geometric structure difference in time-series by aligning temporal features with geometric structure features through a pre-trained temporal feature extractor and time-series image autoencoder. Experiments across multiple datasets demonstrate that models trained with SATL achieve superior performance in both MSE and the proposed TGSI metrics compared to baseline methods, without additional computational cost during inference.
Knowledge Graph Query Embedding (KGQE) aims to embed First-Order Logic (FOL) queries in a low-dimensional KG space for complex reasoning over incomplete KGs. To enhance the generalization of KGQE models, recent studies integrate various external information (such as entity types and relation context) to better capture the logical semantics of FOL queries. The whole process is commonly referred to as Query Pattern Learning (QPL). However, current QPL methods typically suffer from the pattern-entity alignment bias problem, leading to the learned defective query patterns limiting KGQE models' performance. To address this problem, we propose an effective Query Instruction Parsing Plugin (QIPP) that leverages the context awareness of Pre-trained Language Models (PLMs) to capture latent query patterns from code-like query instructions. Unlike the external information introduced by previous QPL methods, we first propose code-like instructions to express FOL queries in an alternative format. This format utilizes textual variables and nested tuples to convey the logical semantics within FOL queries, serving as raw materials for a PLM-based instruction encoder to obtain complete query patterns. Building on this, we design a query-guided instruction decoder to adapt query patterns to KGQE models. To further enhance QIPP's effectiveness across various KGQE models, we propose a query pattern injection mechanism based on compressed optimization boundaries and an adaptive normalization component, allowing KGQE models to utilize query patterns more efficiently. Extensive experiments demonstrate that our plug-and-play method improves the performance of eight basic KGQE models and outperforms two state-of-the-art QPL methods.
Logic-Aware Knowledge Graph Reasoning for Structural Sparsity under Large Language Model Supervision
PDF ↗Knowledge Graph (KG) reasoning aims to predict missing entities in incomplete triples, which requires adequate structural information to derive accurate embeddings. However, KGs in the real world are not as dense as the idealized benchmarks, where sparse graph structures restrict the comprehensive structural information for superior performance. Although the logical semantics in KGs shows its potential in alleviating the impact of structural sparsity, there still exist some challenges. The deficient supervision and the semantic gap of logic make it difficult to introduce logical semantics in sparse KG reasoning. To this end, we propose a novel KG reasoning approach LoLLM injecting logic with the supervised information supplied by the Large Language Model (LLM), which is proved to be effective in evaluating and scoring. Firstly, LoLLM derives structural embeddings employing a graph convolutional network (GCN) with relation-aware and triple-aware attention. LoLLM secondly constructs reasoning paths instantiated from the first-order logic rules extracted from sparse KGs, and injects the logical semantics by a designed LLM-enhanced tuning strategy. We propose a textual loss (TL) and a logical loss (LL) in the optimization and obtain logical tuning embeddings of KG in this process. Finally, LoLLM fuses structural embeddings from the GCN and logical tuning embeddings from the LLM-enhanced tuning for scoring and incomplete triple prediction. Extensive experiments on two sparse KGs and a benchmark show that LoLLM outperforms state-of-the-art structure-based and Language Model (LM)-augmented baselines. Moreover, the logic rules with corresponding confidences provide explicit explanations as an interpretable paradigm.
The rapid growth of decentralized applications, while revolutionizing financial transactions, has created an attractive target for malicious attacks. Existing approaches to detecting attacks often rely on predefined rules or simplistic and overly-specialized models, which lack the flexibility to handle the wide spectrum of diverse and dynamically changing attack types. To address this challenge, we present a general and extensible framework, MoE (Monitoring Ethereum), that leverages runtime verification to detect a wide range of attacks on Ethereum. MoE features an expressive attack modeling language, based on Metric First-order Temporal Logic (MFOTL), that can formalize a wide range of attacks. We integrate a novel semantic lifting approach that extracts system behaviors relevant for various attacks, which can be analyzed using the monitoring tool MonPoly. Furthermore, we also equip MoE with quantitative capabilities to evaluate the similarity between a transaction and an attack formula to enhance its performance in identifying attacks, including near-miss attacks. We carry out extensive experiments with MoE on a labeled benchmark and a large-scale dataset containing over one million transactions. On the labeled benchmark, MoE successfully detects 92.0% attacks and achieves a 45.0% higher recall rate than competing state-of-the-art tool. MoE finds 3,319 attacks with 95.4% precision on the large dataset. Furthermore, MoE uses quantitative analysis to uncover 8% additional attacks. Finally, the average time for monitoring a transaction is less than 23 ms, positioning MoE as a promising practical solution for real-time attack detection for Ethereum.
With the increasing prevalence of Web-based platforms handling vast amounts of user data, machine unlearning has emerged as a crucial mechanism to uphold users' right to be forgotten, enabling individuals to request the removal of their specified data from trained models. However, the auditing of machine unlearning processes remains significantly underexplored. Although some existing methods offer unlearning auditing by leveraging backdoors, these backdoor-based approaches are inefficient and impractical, as they necessitate involvement in the initial model training process to embed the backdoors. In this paper, we propose a TAilored Posterior diffErence (TAPE) method to provide unlearning auditing independently of original model training. We observe that the process of machine unlearning inherently introduces changes in the model, which contains information related to the erased data. TAPE leverages unlearning model differences to assess how much information has been removed through the unlearning operation. Firstly, TAPE mimics the unlearned posterior differences by quickly building unlearned shadow models based on first-order influence estimation. Secondly, we train a Reconstructor model to extract and evaluate the private information of the unlearned posterior differences to audit unlearning. Existing privacy reconstructing methods based on posterior differences are only feasible for model updates of a single sample. To enable the reconstruction effective for multi-sample unlearning requests, we propose two strategies, unlearned data perturbation and unlearned influence-based division, to augment the posterior difference. Extensive experimental results indicate the significant superiority of TAPE over the state-of-the-art unlearning verification methods, at least 4.5x efficiency speedup and supporting the auditing for broader unlearning scenarios.
Graph Contrastive Learning (GCL) is a widely adopted approach in self-supervised graph representation learning, applying contrastive objectives to produce effective representations. However, current GCL methods primarily focus on capturing implicit semantic relationships, often overlooking the structural commonsense embedded within the graph's structure and attributes, which contains underlying knowledge crucial for effective representation learning. Due to the lack of explicit information and clear guidance in general graph, identifying and integrating such structural commonsense in GCL poses a significant challenge. To address this gap, we propose a novel framework called Structural Commonsense Unveiling in Graph Contrastive Learning (Str-GCL). Str-GCL leverages first-order logic rules to represent structural commonsense and explicitly integrates them into the GCL framework. It introduces topological and attribute-based rules without altering the original graph and employs a representation alignment mechanism to guide the encoder in effectively capturing this commonsense. To the best of our knowledge, this is the first attempt to directly incorporate structural commonsense into GCL. Extensive experiments demonstrate that Str-GCL outperforms existing GCL methods, providing a new perspective on leveraging structural commonsense in graph representation learning.
Projecting knowledge graph queries into an embedding space using geometric models (points, boxes and spheres) can help to answer queries for large incomplete knowledge graphs. In this work, we propose a symbolic learning-free approach using fuzzy logic to address the shape-closure problem that restricted geometric-based embedding models to only a few shapes (e.g. ConE) for answering complex logical queries. The use of symbolic approach facilitates non-closure geometric models (e.g. point, box) to handle logical operators (including negation). This enabled our newly proposed spherical embeddings (SpherE) in this work to use a polar coordinate system to effectively represent hierarchical relation. Results show that the SpherE model can answer existential positive first-order logic and negation queries. We show that SpherE significantly outperforms the point and box embeddings approaches while generating semantically meaningful hierarchy-aware embeddings.
To answer complex queries on knowledge graphs, logical reasoning over incomplete knowledge needs learning-based methods because they are capable of generalizing over unobserved knowledge. Therefore, an appropriate dataset is fundamental to both obtaining and evaluating such methods under this paradigm. In this paper, we propose a comprehensive framework for data generation, model training, and method evaluation that covers the combinatorial space of Existential First-order Queries with multiple variables (EFOk). The combinatorial query space in our framework significantly extends those defined by set operations in the existing literature. Additionally, we construct a dataset, EFOk-CQA, with 741 query types for empirical evaluation, and our benchmark results provide new insights into how query hardness affects the results. Furthermore, we demonstrate that the existing dataset construction process is systematically biased and hinders the appropriate development of query-answering methods, highlighting the importance of our work. Our code and data are provided in https://github.com/HKUST-KnowComp/EFOK-CQA.
In federated learning (FL), the assumption that datasets from different devices are independent and identically distributed (i.i.d.) often does not hold due to user differences, and the presence of various data modalities across clients makes using a single model impractical. Personalizing certain parts of the model can effectively address these issues by allowing those parts to differ across clients, while the remaining parts serve as a shared model. However, we found that partial model personalization may exacerbate client drift (each client's local model diverges from the shared model), thereby reducing the effectiveness and efficiency of FL algorithms. We propose an FL framework based on the alternating direction method of multipliers (ADMM), referred to as FedAPM, to mitigate client drift. We construct the augmented Lagrangian function by incorporating first-order and second-order proximal terms into the objective, with the second-order term providing fixed correction and the first-order term offering compensatory correction between the local and shared models. Our analysis demonstrates that FedAPM, by using explicit estimates of the Lagrange multiplier, is more stable and efficient in terms of convergence compared to other FL frameworks. We establish the global convergence of FedAPM training from arbitrary initial points to a stationary point, achieving three types of rates: constant, linear, and sublinear, under mild assumptions. We conduct experiments using four heterogeneous and multimodal datasets with different metrics to validate the performance of FedAPM. Specifically, FedAPM achieves faster and more accurate convergence, outperforming the SOTA methods with average improvements of 12.3% in test accuracy, 16.4% in F1 score, and 18.0% in AUC while requiring fewer communication rounds.
Neuro-symbolic computing aims to integrate neural learning with symbolic reasoning to address the fundamental challenge of symbol grounding. While neural networks excel at pattern recognition, they struggle to maintain logical consistency. Conversely, symbolic systems provide formal reasoning capabilities but lack mechanisms for handling perceptual uncertainty. This paper introduces EmALC , a novel neuro-symbolic framework that bridges neural perception with symbolic logic through differentiable fuzzy semantics. Our approach addresses a key limitation of existing methods: while previous neuro-symbolic approaches like Logic Tensor Networks employ first-order fuzzy logic, where key reasoning problems are undecidable, EmALC ensures decidable reasoning by leveraging a fuzzy variant of ALC -- a decidable fragment of first-order logic. Unlike previous approaches that often compromise logical soundness for learning capability, EmALC maintains provable semantic consistency through a hierarchical loss function while mitigating reasoning shortcuts via rule-based revision strategies. Experimental evaluation demonstrates EmALC's effectiveness: on ontology revision tasks, it achieves 100% success rate in correcting masked groundings while preserving semantic integrity; on semantic image interpretation tasks, it improves object classification F1-scores by up to 5.56% through ontology-guided knowledge revision.
TIDFormer: Exploiting Temporal and Interactive Dynamics Makes A Great Dynamic Graph Transformer
PDF ↗Due to the proficiency of self-attention mechanisms (SAMs) in capturing dependencies in sequence modeling, several existing dynamic graph neural networks (DGNNs) utilize Transformer architectures with various encoding designs to capture sequential evolutions of dynamic graphs. However, the effectiveness and efficiency of these Transformer-based DGNNs vary significantly, highlighting the importance of properly defining the SAM on dynamic graphs and comprehensively encoding temporal and interactive dynamics without extra complex modules. In this work, we propose TIDFormer, a dynamic graph TransFormer that fully exploits Temporal and Interactive Dynamics in an efficient manner. We clarify and verify the interpretability of our proposed SAM, addressing the open problem of its uninterpretable definitions on dynamic graphs in previous works. To model the temporal and interactive dynamics, respectively, we utilize the calendar-based time partitioning information and extract informative interaction embeddings for both bipartite and non-bipartite graphs using merely the sampled first-order neighbors. In addition, we jointly model temporal and interactive features by capturing potential changes in historical interaction patterns through a simple decomposition. We conduct extensive experiments on several dynamic graph datasets to verify the effectiveness and efficiency of TIDFormer. The experimental results demonstrate that TIDFormer excels, outperforming state-of-the-art models across most datasets and experimental settings. Furthermore, TIDFormer exhibits significant efficiency advantages compared to previous Transformer-based methods.
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational problem posed by reasoning. Inspired by human reasoning, we introduce a method of first-order relational probabilistic inference that satisfies both criteria, and can handle hybrid (discrete and continuous) variables. Specifically, we extend sum-of-squares logic of expectation to relational settings, demonstrating that lifted reasoning in the bounded-degree fragment for knowledge bases of bounded quantifier rank can be performed in polynomial time, even with an a priori unknown and/or countably infinite set of objects. Crucially, our notion of tractability is framed in proof-theoretic terms, which extends beyond the syntactic properties of the language or queries. We are able to derive the tightest bounds provable by proofs of a given degree and size and establish completeness in our sum-of-squares refutations for fixed degrees.
Multiple agents operating in a shared environment can interfere with each other’s ability to reach their goals. One of the approaches to address this issue is enacting a social law – a set of rules that restricts some possible behaviors of the agents. A social law is considered robust if it guarantees that each agent can achieve its goal independently of the actions of other agents. Recent work has shown how to verify that a given social law, encoded in an MA-STRIPS formalism, is robust by compilation to classical planning. Follow-up work presented an extended compilation which can handle numeric multi-agent planning. In this paper, we present a new compilation, which can handle both classical and numeric multi-agent planning formalisms, as well as any other multi-agent planning formalism with instantaneous actions, in which action preconditions can be negated using first-order logic with equality. This opens the door to using social laws in even richer planning formalisms. Our empirical evaluation shows that the added expressivity of the new compilation does not hurt its performance, and it achieves comparable performance to the previous state-of-the-art compilations.