论文检索

Computer Vision · Image and Video Generation

Haoyu Wu, Diankun Wu, Tianyu He, Junliang Guo, Yang Ye, Yueqi Duan, Jiang Bian

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model’s intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view–conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods.

Computer Vision · Image and Video Generation

Yuandong Pu, Le Zhuo, Songhao Han, Jinbo Xing, Kaiwen Zhu, Shuo Cao, Bin Fu, Si Liu, Hongsheng Li, Yu Qiao 等

Image editing has achieved remarkable progress recently. Modern editing models could already follow complex instructions to manipulate the original content. However, beyond completing the editing instructions, the accompanying physical effects are the key to the generation realism. For example, removing an object should also remove its shadow, reflections, and interactions with nearby objects. Unfortunately, existing models and benchmarks mainly focus on instruction completion but overlook these physical effects. So, at this moment, how far are we from physically realistic image editing? To answer this, we introduce PICABench, which systematically evaluates physical realism across eight sub-dimension(spanning optics, mechanics, and state transitions) for most of the common editing operations(add, remove, attribute change, etc). We further propose the PICAEval, a reliable evaluation protocol that uses VLM-as-a-judge with per-case, region-level human annotations and questions. Beyond benchmarking, we also explore effective solutions by learning physics from videos and construct a training dataset PICA-100K.After evaluating most of the mainstream models, we observe that physical realism remains a challenging problem with large rooms to explore. We hope that our benchmark and proposed solutions can serve as a foundation for future work moving from naive content editing toward physically consistent realism.

Applications · Neuroscience, Cognitive Science

Rabia Gondur, Patricia Stan, Matthew A Smith, Benjamin Cowley

An ongoing quest in neuroscience is to find the preferred stimulus of a sensory neuron. This search lays the foundation for understanding how selectivity emerges in the primate visual stream---from simple edge-detecting neurons to highly-selective face neurons---as well as for the architectures and activation functions of deep neural networks. The prevailing notion is that a visual neuron primarily responds to a single preferred visual feature, like an oriented edge or the shape of an object, resulting in a 'one-tailed' distribution of responses to natural images. However, surprisingly, we instead find 'two-tailed' response distributions of primate visual cortical neurons, suggesting that these neurons have both preferred and anti-preferred stimuli. We experimentally validated anti-preferred stimuli by recording responses from macaque V4 to model-optimized stimuli. We find that these anti-preferred stimuli are important for describing a neuron's tuning, as both preferred and anti-preferred images are needed to predict a neuron's responses to natural images. Moreover, in a psychophysics task, humans rely on anti-preferred images to interpret and predict V4 stimulus tuning; this was not the case for internal units from a deep neural network. Interestingly, we find no discernible differences in image statistics between preferred and anti-preferred images. This suggests that by encoding anti-preferred features, a V4 population seemingly doubles its capacity for feature selectivity, allowing for a more flexible downstream readout. Overall, we establish anti-preferred stimuli as an important encoding property of V4 neurons. Our work embarks on a new quest in neuroscience to search for anti-preferred stimuli along the visual stream and offers a new perspective on how feature selectivity arises in the visual cortex and deep neural networks.

Applications · Language, Speech and Dialog

Xiao Liu, Da Yin, Zirui Wu, Yansong Feng

Large Language Models (LLMs) can enhance their reasoning capabilities by using external tools. However, many tasks lack predefined tools. Prior works have explored instructing LLMs to generate tools on their own, but such approaches depend heavily on internal knowledge and struggle when tasks fall outside the model’s knowledge scope. To address this limitation, we propose RefTool, a reference-guided framework for automatic tool creation that leverages external materials, such as textbooks and knowledge snippets. RefTool consists of two modules: (1) tool creation, where LLMs generate executable tools from reference content, validate them using illustrative examples, and organize them hierarchically into a toolbox; and (2) tool utilization, where LLMs navigate the toolbox structure to select and apply the appropriate tools to solve problems. Experiments on causality, physics, and chemistry benchmarks demonstrate that RefTool outperforms existing tool-creation and domain-specific reasoning methods by 12.3% on average accuracy, while being cost-efficient and broadly generalizable to non-scientific tasks, e.g., extremely low-resource language translation. Analyses reveal that grounding tool creation in references produces accurate and faithful tools, and that the hierarchical structure facilitates effective tool selection. RefTool enables LLMs to overcome internal knowledge limitations, advancing generalizable reasoning in knowledge-intensive domains.

Applications · Time Series

Yan Ge, Zhengyang Zhou, Qihe Huang, Yuxuan Liang, Yang Wang

Modern spatio-temporal learning techniques usually exploit sampled discrete observations to foresee the future. Actually, spatio-temporal dynamics are continuous and evolve continuously across time and space, thus modeling spatio-temporal dynamics in a continuous space can be a long-standing challenge. Existing deep learning architectures often fail to generalize to unseen regions and new graph topologies, while many physics-driven approaches are confined to Euclidean grids and poorly scale to complex graph structures. To address this gap, we propose PhySTA, a physics-inspired spatio-temporal learning framework designed for efficient and scalable arbitrary inference over graph-structured data. PhySTA integrates two key modules: (1) Continuous Operator-based Spectrum-Temporal Learning (CoSTL), which leverages a Graph-Time Fourier Neural Operator combined with Time-Gated Spectral Segmentation Perception to model continuous dynamics in operator space, and (2) Adaptive Multi-scale Interaction (AMI) that constructs multi-scale subgraphs and introduces node-edge coupled convolution to capture discrete interaction patterns and refine continuous predictions. By bridging operator learning with node-edge-graph interaction, PhySTA achieves both continuity-aware dynamic modeling and hierarchical interactive refinement. Extensive experiments across large-scale benchmarks demonstrate that PhySTA attains state-of-the-art accuracy while reducing computation cost and lowering parameter overhead.

Applications · Robotics

Zhiqian Lan, Yuxuan Jiang, Ruiqi Wang, Xuanbing Xie, Rongkui Zhang, Yicheng Zhu, LI PEIHANG, Tianshuo Yang, Tianxing Chen, Haoyu Gao 等

Vision-language-action (VLA) models have shown promise as generalist robotic policies by jointly leveraging visual, linguistic, and proprioceptive modalities to generate action trajectories. While recent benchmarks have advanced VLA research in domestic tasks, professional science-oriented domains remain underexplored. We introduce AutoBio, a simulation framework and benchmark designed to evaluate robotic automation in biology laboratory environments—an application domain that combines structured protocols with demanding precision and multimodal interaction. AutoBio extends existing simulation capabilities through a pipeline for digitizing real-world laboratory instruments, specialized physics plugins for mechanisms ubiquitous in laboratory workflows, and a rendering stack that support dynamic instrument interfaces and transparent materials through physically based rendering. Our benchmark comprises biologically grounded tasks spanning three difficulty levels, enabling standardized evaluation of language-guided robotic manipulation in experimental protocols. We provide infrastructure for demonstration generation and seamless integration with VLA models. Baseline evaluations with SOTA VLA models reveal significant gaps in precision manipulation, visual reasoning, and instruction following in scientific workflows. By releasing AutoBio, we aim to catalyze research on generalist robotic systems for complex, high-precision, and multimodal professional environments.

Applications · Robotics

Luke Strgar, Sam Kriegman

The co-design of robot morphology and neural control typically requires using reinforcement learning to approximate a unique control policy gradient for each body plan, demanding massive amounts of training data to measure the performance of each design. Here we show that a universal, morphology-agnostic controller can be rapidly and directly obtained by gradient-based optimization through differentiable simulation. This process of morphological pretraining allows the designer to explore non-differentiable changes to a robot's physical layout (e.g. adding, removing and recombining discrete body parts) and immediately determine which revisions are beneficial and which are deleterious using the pretrained model. We term this process "zero-shot evolution" and compare it with the simultaneous co-optimization of a universal controller alongside an evolving design population. We find the latter results in _diversity collapse_, a previously unknown pathology whereby the population—and thus the controller's training data—converges to similar designs that are easier to steer with a shared universal controller. We show that zero-shot evolution with a pretrained controller quickly yields a diversity of highly performant designs, and by fine-tuning the pretrained controller on the current population throughout evolution, diversity is not only preserved but significantly increased as superior performance is achieved. Videos and code can be found at: https://lukestrgar.com/codesign-mpt-project-page/

Applications · Robotics

Feiyu Wu, Xu Zheng, Yue Qu, Zhuocheng Wang, Zicheng Feng, HUI LI

While Large Language Models (LLMs) show immense promise as planners for embodied AI, their stochastic nature and lack of formal reasoning capabilities prevent the strict safety guarantees required for physical deployment. Current approaches fall short: they either rely on other unreliable LLMs for safety checks or simply reject unsafe plans without offering a path to success. This work bridges this critical gap by introducing the Verifiable Iterative Refinement Framework (VIRF), a neuro-symbolic architecture that shifts the paradigm from a passive safety gatekeeper to an active safety collaborator. Where prior verifiers simply reject failures, our framework provides causal, pedagogical feedback that teaches the LLM why its plan was unsafe, enabling intelligent repairs rather than mere avoidance.Our core contribution is a novel tutor-apprentice dialogue, where a deterministic Logic Tutor, grounded in a formal safety ontology, provides causal and explanatory feedback to an LLM Apprentice planner. This pedagogical interaction allows the apprentice to perform intelligent, creative plan repairs, resolving safety conflicts rather than merely avoiding them. To ground this dialogue in verifiable truth, we introduce a scalable knowledge acquisition pipeline that synthesizes a comprehensive safety knowledge base from real-world documents, a process that simultaneously reveals and corrects significant blind spots in existing benchmarks. On a new suite of challenging home safety tasks, VIRF achieves a perfect 0\% Hazardous Action Rate (HAR), completely eliminating unsafe actions while attaining a 77.3\% Goal-Condition Rate (GCR)—the highest among all baselines. It does so with remarkable efficiency, requiring only 1.1 correction iterations on average. By acting as a verifiable safety scaffold, VIRF demonstrates a principled and robust pathway toward building embodied agents that are not just capable, but fundamentally trustworthy.

Applications · Physics

Xianglong Hou, Xinquan Huang, Paris Perdikaris

Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive (AR) prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce the Continuous Flow Operator (CFO), a framework that learns continuous-time PDE dynamics without the computational burden of standard continuous approaches, e.g., neural ODE. The key insight is repurposing flow matching to directly learn the right-hand side of PDEs without backpropagating through ODE solvers. CFO fits temporal splines to trajectory data, using finite-difference estimates of time derivatives at knots to construct probability paths whose velocities closely approximate the true PDE dynamics. A neural operator is then trained via flow matching to predict these analytic velocity fields. This approach is inherently time-resolution invariant: training accepts trajectories sampled on trajectory-specific, non-uniform time grids while inference queries solutions at any temporal resolution through ODE integration. Across four benchmarks (Lorenz, 1D Burgers, 2D diffusion-reaction, 2D shallow water), CFO demonstrates superior long-horizon stability and remarkable data efficiency. CFO trained on only 25% of irregularly subsampled time points outperforms autoregressive baselines trained on complete data, with relative error reductions up to 87%. Despite requiring numerical integration at inference, CFO achieves competitive efficiency, exceeding AR accuracy using only half the AR rollout step budget, while uniquely enabling reverse-time inference and arbitrary temporal querying. Code is available at https://github.com/shannon-hou/CFO_official

Deep Learning · Theory

Jingzhe Shi, Qinwei (Martin) Ma, Hongyi Liu, Hang Zhao, Jenq-Neng Hwang, Lei Li

Long Context Language Models have drawn great attention in the past few years. There has been work discussing the impact of long context on Language Model performance: some find that long irrelevant context could harm performance, while some experimentally summarize loss reduction by relevant long context as Scaling Laws. This calls for a more thorough understanding of how long context impacts Language Modeling. In this work, we (1) propose to use `Intrinsic Entropy' for explaining the impact of context length on language modeling; and (2) conduct experiments on natural language and synthetic data, validating our proposed theoretical assumptions and deductions. Our theoretical framework can provide practical insights such as establishing that training dataset size dictates an optimal context length and bounds context length scaling for certain cases. We hope our work may inspire new long context Language Models, as well as future work studying the physics of Language Models.

General Machine Learning · Probabilistic Methods

Mara Daniels, Liam Hodgkinson, Michael W Mahoney

Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting ML models to physical data. Popular PIML approaches, including neural operators, physics-informed neural networks, and neural ordinary differential equations, are typically fit to objectives that simultaneously include both data and physical constraints. However, the multi-objective nature of this approach creates ambiguity in the measurement of model quality. This is related to a poor understanding of epistemic uncertainty, and it can lead to surprising failure modes, even when existing metrics suggest strong fits. Working within a Gaussian process regression framework, we introduce the Physics-Informed Log Evidence (PILE) score. Bypassing the ambiguities of test losses, the PILE score is a single, uncertainty-aware metric that provides a selection principle for hyperparameters of a physics-informed model. We show that PILE minimization yields excellent choices for a wide variety of model parameters, including kernel bandwidth, least squares regularization weights, and even kernel function selection. We also show that, prior to data acquisition, a special data-free case of the PILE score identifies a-priori kernel choices that are "well adapted" to a given PDE. Beyond the kernel setting, we anticipate that the PILE score can be extended to PIML at large, and we outline approaches to do so.

General Machine Learning · Transfer, Multitask and Meta-learning

Pei Yang, Yuhang Zhuang, Qi Tan

The classical optimal transport such as Kantorovich's optimal transport and partial optimal transport could be too restrictive in applications due to the full-mass or fixed-mass preservation constraints. To remedy this limitation, we propose elastic optimal transport (ELOT) which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It aims to answer the problem of how to transport the probability mass adaptively between probability distributions, which is a fundamental topic in various areas of artificial intelligence. The strength of elastic optimal transport is its capability to transport adaptive-mass in the light of the geometry structure of the problem itself. As an application example in machine learning, we apply elastic optimal transport to both unsupervised domain adaptation and partial domain adaptation tasks. It adaptively transports masses from source domain to target domain by taking domain shift into consideration and respecting the ubiquity of noises or outliers in the data, in order to improve the generalization performance. The experiment results on the benchmarks show that ELOT significantly outperforms the state-of-the-art methods. As a powerful distribution matching tool, elastic optimal transport might be of interests to the broad areas such as artificial intelligence, healthcare, physics, operations research, urban science, etc. The source code is available in the supplementary material.

General Machine Learning · Representation Learning

Nanxi Li, Xiang Wang, Yuanjie Chen, Haode Zhang, HONG LI, Yong-Lu Li

While Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities in image and video understanding, their ability to comprehend the physical world has become an increasingly important research focus. Despite their improvements, current MLLMs struggle significantly with high-level physics reasoning. In this work, we investigate the first step of physical reasoning, i.e., **intuitive physics understanding**, revealing substantial limitations in understanding the dynamics of continuum objects. To isolate and evaluate this specific capability, we introduce two fundamental benchmark tasks: Next Frame Selection (NFS) and Temporal Coherence Verification (TCV). Our experiments demonstrate that even state-of-the-art MLLMs perform poorly on these foundational tasks. To address this limitation, we propose Scene Dynamic Field (SDF), a concise approach that leverages physics simulators within a multi-task fine-tuning framework. SDF substantially improves performance, achieving up to $20.7\%$ gains on fluid tasks while showing strong generalization to unseen physical domains. This work not only highlights a critical gap in current MLLMs but also presents a promising cost-efficient approach for developing more physically grounded MLLMs. Our code and data are available at https://github.com/andylinx/Scene-Dynamic-Field.

Zicheng Liu, Ben Fei, Di Huang

Generating physically stable and novel metal-organic frameworks (MOFs) for inverse design that meet specific performance targets is a significant challenge. Existing generative models often struggle to explore the vast chemical and structural space effectively, leading to suboptimal solutions or mode collapse. To address this, we propose PRO-MOF, a hierarchical reinforcement learning (HRL) framework for controllable MOF generation. Our approach decouples the MOF design process into two policies: a high-level policy for proposing chemical building blocks and a low-level policy for assembling their 3D structures. By converting the deterministic Flow Matching model into a Stochastic Differential Equation (SDE), we enable the low-level policy to perform compelling exploration. The framework is optimized in a closed loop with high-fidelity physical reward signals provided by a pre-trained universal atomistic model (UMA). Furthermore, we introduce a Pass@K Group Relative Policy Optimization (GRPO) scheme that effectively balances exploration and exploitation by rewarding in-group diversity. Experiments on multiple inverse design tasks, such as maximizing CO2 working capacity and targeting specific pore diameters, show that PRO-MOF significantly outperforms existing baselines, including diffusion-based methods and genetic algorithms, in both success rate and the discovery of top-performing materials. Our work demonstrates that hierarchical reinforcement learning combined with a high-fidelity physical environment is a powerful paradigm for solving complex material discovery problems.

Fangqi Zhu, Zhengyang Yan, Zicong Hong, Quanxin Shou, Xiao Ma, Song Guo

Vision-Language-Action (VLA) models have shown strong potential for general-purpose robotic manipulation, but their reliance on expert demonstrations limits their ability to learn from failures and perform self-corrections. Reinforcement learning (RL) addresses these through self-improving interactions with the physical environment, but suffers from high sample complexity on real robots. We introduce World-Model-based Policy Optimization (WMPO), a principled framework for on-policy VLA RL without interacting with the real environment. In contrast to widely used latent world models, WMPO focuses on pixel-based predictions that align the "imagined" trajectories with the VLA features pretrained with web-scale images. Crucially, WMPO enables the policy to perform on-policy GRPO that provides stronger performance than the often-used off-policy methods. Extensive experiments in both simulation and real-robot settings demonstrate that WMPO (i) substantially improves sample efficiency, (ii) achieves stronger overall performance, (iii) exhibits emergent behaviors such as self-correction, and (iv) demonstrates robust generalization and lifelong learning capabilities.

Ning Liu, Lu Zhang, Tian Gao, Yue Yu

Neural operators (NOs) excel at learning mappings between function spaces, serving as efficient forward solution approximators for PDE-governed systems. However, as black-box solvers, they offer limited insight into the underlying physical mechanism, due to the lack of interpretable representations of the physical parameters that drive the system. To tackle this challenge, we propose a new paradigm for learning disentangled representations from NO parameters, thereby effectively solving an inverse problem. Specifically, we introduce DisentangO, a novel hyper-neural operator architecture designed to unveil and disentangle latent physical factors of variation embedded within the black-box neural operator parameters. At the core of DisentangO is a multi-task NO architecture that distills the varying parameters of the governing PDE through a task-wise adaptive layer, alongside a variational autoencoder that disentangles these variations into identifiable latent factors. By learning these disentangled representations, DisentangO not only enhances physical interpretability but also enables more robust generalization across diverse systems. Empirical evaluations across supervised, semi-supervised, and unsupervised learning contexts show that DisentangO effectively extracts meaningful and interpretable latent features, bridging the gap between predictive performance and physical understanding in neural operator frameworks. Our code and data accompanying this paper are available at \url{https://github.com/ningliu-iga/DisentangO}.

Reinforcement Learning · Multi-agent

Xuefeng Wang, Lei Zhang, Henglin Pu, Ahmed Hussain Qureshi, Husheng Li

Existing reinforcement learning (RL) methods struggle with complex dynamical systems that demand interactions at high frequencies or irregular time intervals. Continuous-time RL (CTRL) has emerged as a promising alternative by replacing discrete-time Bellman recursion with differentiable value functions defined as viscosity solutions of the Hamilton–Jacobi–Bellman (HJB) equation. While CTRL has shown promise, its applications have been largely limited to the single-agent domain. This limitation stems from two key challenges: (i) conventional methods for solving HJB equations suffer from the curse of dimensionality (CoD), making them intractable in high-dimensional systems; and (ii) even with learning-based approaches to alleviate the CoD, accurately approximating centralized value functions in multi-agent settings remains difficult, which in turn destabilizes policy training. In this paper, we propose a CT-MARL framework that uses physics-informed neural networks (PINNs) to approximate HJB-based value functions at scale. To ensure the value is consistent with its differential structure, we align value learning with value-gradient learning by introducing a Value Gradient Iteration (VGI) module that iteratively refines value gradients along trajectories. This improves gradient accuracy, in turn yielding more precise value approximations and stronger policy learning. We evaluate our method using continuous‑time variants of standard benchmarks, including multi‑agent particle environment (MPE) and multi‑agent MuJoCo. Our results demonstrate that our approach consistently outperforms existing continuous‑time RL baselines and scales to complex cooperative multi-agent dynamics. Code is available at https://github.com/Wangxuefeng1024/Continuous-Time-Value-Iteration-for-Multi-Agent-Reinforcement-Learning.git.

Computer Vision · Classification and Understanding

Chuangchuang Tan, Xiang Ming, Jinglu Wang, Renshuai Tao, Bin Li, Yunchao Wei, Yao Zhao, Yan Lu

The rapid advancement of AI-generated content (AIGC) has enabled the synthesis of visually convincing images; however, many such outputs exhibit subtle \textbf{semantic anomalies}, including unrealistic object configurations, violations of physical laws, or commonsense inconsistencies, which compromise the overall plausibility of the generated scenes. Detecting these semantic-level anomalies is essential for assessing the trustworthiness of AIGC media, especially in AIGC image analysis, explainable deepfake detection and semantic authenticity assessment.In this paper, we formalize \textbf{semantic anomaly detection and reasoning} for AIGC images and introduce \textbf{AnomReason}, a large-scale benchmark with structured annotations as quadruples \emph{(Name, Phenomenon, Reasoning, Severity)}. Annotations are produced by a modular multi-agent pipeline (\textbf{AnomAgent}) with lightweight human-in-the-loop verification, enabling scale while preserving quality. At construction time, AnomAgent processed approximately 4.17\,B GPT-4o tokens, providing scale evidence for the resulting structured annotations. We further show that models fine-tuned on AnomReason achieve consistent gains over strong vision-language baselines under our proposed semantic matching metric (\textit{SemAP} and \textit{SemF1}). Applications to {explainable deepfake detection} and {semantic reasonableness assessment of image generators} demonstrate practical utility. In summary, AnomReason and AnomAgent serve as a foundation for measuring and improving the semantic plausibility of AI-generated images. The code is available at \url{https://github.com/chuangchuangtan/Semantic-Visual-Anomaly-Detection-and-Reasoning}.

Computer Vision · Classification and Understanding

Hongyan Fei, Zexi Jia, Chuanwei Huang, Jinchao Zhang, Jie Zhou

Detecting deepfakes has become increasingly challenging as forgery faces synthesized by AI-generated methods, particularly diffusion models, achieve unprecedented quality and resolution. Existing forgery detection approaches relying on spatial and frequency features demonstrate limited efficacy against high-quality, entirely synthesized forgeries. In this paper, we propose a novel detection method grounded in the observation that facial attributes governed by complex physical laws and multiple parameters are inherently difficult to replicate. Specifically, we focus on illumination, particularly the specular reflection component in the Phong illumination model, which poses the greatest replication challenge due to its parametric complexity and nonlinear formulation. We introduce a fast and accurate face texture estimation method based on Retinex theory to enable precise specular reflection separation. Furthermore, drawing from the mathematical formulation of specular reflection, we posit that forgery evidence manifests not only in the specular reflection itself but also in its relationship with corresponding face texture and direct light. To address this issue, we design the Specular-Reflection-Inconsistency-Network (SRI-Net), incorporating a two-stage cross-attention mechanism to capture these correlations and integrate specular reflection related features with image features for robust forgery detection. Experimental results demonstrate that our method achieves superior performance on both traditional deepfake datasets and generative deepfake datasets, particularly those containing diffusion-generated forgery faces.

General Machine Learning · Representation Learning

Zhao-Rong Lai, Zheng-Sen Zhou, Liangda Fang, Yongsen Zheng, Ziliang Chen

Continuous-time graph representation (CTGR) is a widely-used methodology in machine learning, physics, bioinformatics, and social networks. The sequential survival process in a latent space with the squared $\ell_2$ distance is an important ultra-low-dimensional embedding for CTGR. However, the squared $\ell_2$ distance violates the triangle inequality, which may cause distortion of the relative node positions in the latent space and thus deteriorates in social, contact, and collaboration networks. Reverting to the $\ell_2$ distance is infeasible because the corresponding integral computation is intractable. To solve these problems, we propose a theoretically-sound $\ell_1$ latent distance based continuous-time graph representation ($\ell_1$LD-CTGR). It facilitates a true latent metric space for the sequential survival process. Moreover, the integral of the hazard function is found to be a closed-form piece-wise exponential integral, which well fits the ultra-low-dimensional embedding. To handle the non-differentiable $\ell_1$ norm, we successfully find a descent direction of the hazard function to replace the gradient, enabling mainstream learning architectures to learn the parameters. Extensive experiments using both synthetic and real-world data show the competitive performance of $\ell_1$LD-CTGR.