arXiv subjects

Xinyi Li

Publications and source records attributed to Xinyi Li.

At least 19 recordsLinked to original sources

arXiv2026

Fractal dimensions of paths on three-dimensional random-walk traces

We study four paths that join the starting site to the final position of a simple random walk of $N=L^2$ steps on the infinite cubic lattice. The paths are selected on the walk trace---the graph of visited sites and traversed bonds---by different rules: the undirected shortest path $S_1$, the directed shortest path $S_2$, the time-respecting shortest path $S_3$, and the depth $D_e$ of the final site in a depth-first-search tree. Monte Carlo simulations for $L$ up to 32768 give mean lengths scaling as $L^{d_O}$, with $d_{S_1}=1.48005(9)$, $d_{S_2}=1.49868(5)$, $d_{S_3}=1.51205(5)$, and $d_{D_e}=1.7099(7)$, so that $d_{S_1}<d_{S_2}<d_{S_3}<d_{\rm LE}<d_{D_e}$, where $d_{\rm LE}=1.62400(5)$ is the known loop-erased-random-walk exponent. Imposing traversal directions increases the shortest-path exponent, and imposing time order increases it further; these constraints therefore change the scaling exponent, not only the amplitude. For every path, the standard deviation scales with the same exponent as the mean, so it is scale-invariant, unlike the visited-site mass; the rescaled length distributions collapse onto a finite-width scaling function. No analytical theory currently predicts these exponents; our results provide precise numerical benchmarks for future studies of path geometry on random-walk traces.

cond-mat.stat-mech↗

arXiv2026

LLM-PowerTrace: A Dataset of Time-Resolved GPU Power Traces for AI Compute

AI compute is becoming large and fast-changing electrical loads. Its impacts on data center infrastructure and power grids depend not only on total energy consumption, but also on how their power draw moves over sub-second to minute timescales, including peaks, ramps, and synchronized fluctuations across accelerators. Existing energy benchmarks for large language models (LLMs) report aggregate quantities such as joules per token and rarely release the underlying time-series measurements, leaving these power dynamics poorly characterized and difficult to model. We introduce LLM-PowerTrace, an open dataset of time-resolved, per-GPU power traces for LLM fine-tuning and inference, sampled every 100\,ms on varying NVIDIA platforms paired with complete workload and system metadata. For fine-tuning, LLM-PowerTrace profiles open model families spanning a wide range of model sizes and fine-tuning methods, together with controlled sweeps over batch size, sequence length, precision, parallelism, and checkpointing. For inference, it covers variations in concurrency, GPU frequency, KV-cache and weight quantization, prompt and output lengths, and request-arrival patterns. LLM-PowerTrace profiles a set of open model families across a wide range of model sizes, and controlled sweeps over batch size, sequence length, precision, parallelism, and checkpointing for fine-tuning, and it sweeps concurrency, GPU frequency, KV cache and weight quantization, prompt and output lengths, and request arrival patterns for inference. Built upon power traces, we define power-grid-facing metrics as well as AI-compute power\&energy scaling law for extrapolating beyond the measured settings. Together, LLM-PowerTrace provides a dataset foundation for modeling, forecasting, and managing the fast-changing electrical behavior of AI compute.

eess.SY↗

arXiv2026

PinGER: Token-Efficient Generative Retrieval with Semantic IDs

Generative retrieval replaces nearest-neighbor search with token-by-token decoding of an item's semantic ID (SID). But existing SID-based methods primarily use L levels of tokens sequentially to represent each item in the input history. As a result, a fixed context window holds L times fewer items than it would with one embedding per item. We present PinGER, a generative retriever deployed at Pinterest that retains SID outputs while making input histories compact, built on three ideas. (1) An asymmetric attention mask over interleaved SID and dense tokens lets later items attend only to the dense ones, so the model is supervised at every SID position in training yet serves one token per item while computing the same function. (2) Generation is controllable through goal-conditioned outputs, reinforcement learning, and a prefix-diversity penalty, which together steer retrieval toward surface-specific goals and diverse candidates. (3) A serving stack built for efficient wide-beam generation is paired with decoding constrained to valid identifiers and candidate resolution from a host-local index. Deployed in Related Pins, PinGER lifts saves of fresh Pins by 3.60% and overall saves by 0.62%, while reducing the surface's end-to-end latency by 0.7% and eliminating the cost of the nearest-neighbor search it replaces.

cs.IR↗

arXiv2026

FG-ConvNO: A Geometry-Aware Neural Operator for Propeller CFD Prediction

Computational Fluid Dynamics (CFD) is essential in contemporary engineering design, yet it remains expensive to compute and can take thousands of CPU/GPU hours or more for a single high-fidelity simulation. Recent developments in machine learning for scientific modeling have led to powerful surrogate frameworks that can approximate flow fields and physical quantities by using a fraction of the computational cost. However, most of these methods require largescale homogeneous datasets or simple geometries, exhibiting severe generalization gaps when applied to complex and data-scarce configurations. To address this, we propose the Factorized Geometry Convolutional Neural Operator (FG-ConvNO) for robust geometry-aware propeller pressure prediction under limited training data. We introduce geometryaware encoding, efficient interpolation-based decoding, and auxiliary global quantity supervision. In addition, we incorporate DISCO blocks that use discrete continuous convolutions to make the model discretization agnostic. In our experiments, FG-ConvNO achieves the highest accuracy for both surface pressure and global thrust prediction on a procedurally generated propeller CFD dataset. Geometry-aware encoding and architectural simplification improve stability, while random vertex subsampling enhances robustness. Overall, adding geometric priors to grid-based convolutional operators reduces overfitting on complex propeller geometries and improves generalization in low-data regimes.

cs.LG↗

arXiv2026

The boosted loop-erased random walk

We consider a near-critical version of loop-erased random walk (LERW) by boosting the weight of the underlying random walk according to its length before loop-erasure. We construct the scaling limit in natural parametrization in the two-dimensional unit disk and the three-dimensional unit ball. The boosted scaling limit undergoes a phase transition in mutual absolute continuity with the classical LERW scaling limit; in the disk the transition occurs at boost rate $m^2=π^2/4$. As the boost increases, the curve becomes macroscopically space-filling, in the sense that unvisited cubes have side length $O(m^{-1})$, while its Hausdorff dimension at each finite boost is unchanged. These results are motivated by Makarov--Smirnov's questions on near-critical lattice models. In the planar chordal setting, we also construct a continuum loop tilt below the spectral threshold of the domain and calculate its Loewner driving function.

math.PR↗

arXiv2026

Simultaneous Unimodularity of Positive Integer Matrices and Their Entrywise Cubes

We solve an open problem posed by Richard Guy in his book Unsolved Problems in Number Theory. We prove that, for every integer $n\geq10$, there exist infinitely many $n\times n$ integer matrices $A$ such that every entry is $\ge2$ and $\det A=\det A^{[3]}=1$, where $A^{[3]}$ denotes the entrywise cube of $A$. The matrices may be chosen compatibly, so they can form the leading principal blocks of a single infinite positive integer array. The order-ten case is reduced to an inhomogeneous system consisting of one linear and one diagonal cubic equation. The circle method then provides infinitely many positive integral solutions. To pass from order $n$ to order $n+1$, we introduce a bordering construction that preserves the signed cofactor vectors of both the matrix and its entrywise cube. Iterating this construction yields the result in every order $n\geq10$.

math.NT↗

arXiv2026

From Surface to Depth: Towards Cognitive Appraisal Reasoning in Multimodal Emotion Understanding

Recent multimodal large language models (MLLMs) increasingly incorporate explainable reasoning for emotion understanding. However, reasoning based mainly on observable affective cues can reduce emotion understanding to superficial cue-label associations, giving rise to the Clever Hans effect. Such shortcuts become unreliable when affective cues are implicit, conflicting across modalities, linguistically misleading, or obscured by redundant details. In contrast, human emotions are shaped by how individuals interpret and evaluate surrounding events beyond observable cues. Inspired by appraisal theories of emotion, we formulate multimodal emotion understanding as a progression from perception to cognitive appraisal, and introduce a dataset, a model, and a benchmark to support this novel paradigm. CogEmo-40K is a large-scale instruction-tuning dataset constructed through a perception-to-appraisal pipeline to elicit evidence-grounded reasoning across six cognitive appraisal dimensions underlying emotion. CogEmo-MoE is a compact sparse MLLM that introduces interleaved MoE blocks for appraisal-specific adaptation, enabling effective appraisal reasoning at a substantially smaller scale than typical emotion MLLMs. CogEmo-Bench introduces an Appraisal Evidence Quality Score (AEQS) to assess cognitive-affective understanding across six complementary appraisal dimensions, addressing the limitation of conventional emotion metrics that evaluate what emotion is predicted but not why it arises. Extensive experiments show that our paradigm not only leads CogEmo-Bench, but also exhibits strong cross-domain generalization. Our findings suggest that perception-to-appraisal reasoning can move beyond surface-level cue-label associations toward more reliable multimodal emotion understanding and closer cognitive alignment between MLLMs and humans.

cs.MM↗

arXiv2026

Characterization and scaling limit of three-dimensional loop-erased random walk and random-walk loop-catchers

Random-walk loop-catchers (RWLC) are a one-parameter family of random subsets of the trace of a random walk, recently introduced in [Cai 2026, arXiv:2607.18070], which interpolates between loop-erased random walk (LERW) and the full walk trace, satisfying a recovery property. We prove that the continuous version of this recovery property uniquely characterizes the scaling limit of LERW and RWLC in three dimensions, using a Green-function test via entangled multipath LERW, as outlined in [Cai 2026, arXiv:2607.18070]. For LERW, this resolves the 3D case of the conjecture of Sapozhnikov--Shiraishi [Sapozhnikov--Shiraishi 2018, Probab. Theory Related Fields 172, 615--662] and gives a new and axiomatic proof of the existence of the scaling limit, which was first proved in [Kozma 2007, Acta Math. 199, 29--152]. For RWLC, this gives the construction of 3D Brownian loop-catchers. The characterization also yields inversion invariance of the 3D LERW scaling limit.

math.PR↗

arXiv2026

A zero-one law for swap-invariant events in uniform spanning forests

We prove that every event invariant under swaps has probability zero or one for either the free or the wired spanning forest on any connected, locally finite, infinite network. Applications include the constancy of the number of components and of the total number of excessive ends. For the free forest, these results resolve longstanding questions of Benjamini, Lyons, Peres, and Schramm [Ann. Probab. (2001), Question 15.7] on constancy of the component count and of Lyons, Morris, and Schramm [Electron. J. Probab. (2008), Question 7.7] on the zero-one law for one-endedness. In the latter case, we obtain the stronger conclusion that the total number of excessive ends is deterministic.

math.PR↗

arXiv2026

In-Context Learning for Robots: Methods and Applications

General-purpose robots must infer what a new task requires and translate that understanding into appropriate physical action. In-context learning (ICL) for robots supports this process by using demonstrations and interaction to direct existing competence with neural parameters held fixed during deployment. We organize this literature review around the interfaces connecting contextual evidence to execution, distinguishing four families: context-conditioned policies, geometric demonstration transfer, world-model-based control, and skill- and agent-based execution. Comparing these interfaces clarifies their transfer assumptions and the roles of training, correspondence, and memory in making context useful. Across manipulation and navigation, we examine how these mechanisms preserve taught requirements as objects, environments, and execution conditions change. This analysis links method design to evaluation practices that distinguish responsiveness to teaching, physical transfer, and benefits from retained experience. The resulting agenda connects compositional task acquisition and faithful transfer with physical recursive self-improvement, in which experience improves the ability to learn subsequent tasks.

cs.RO↗

arXiv2026

Studying Detection Rule Generation as a Unified Task

Security systems use detection rules to identify suspicious activity. Existing studies often investigate rule generation for specific security systems, devoting substantial effort to developing dedicated methods and evaluation setups. Such customization contributes to fragmented research, limiting method reuse and result comparability across systems. We therefore study detection rule generation as a unified task across diverse natural language inputs and rule languages. To support method reuse, we propose UniRule, which abstracts diverse rules into shared natural language representations for retrieval. To enable consistent evaluation, we introduce a protocol that compares rules under shared criteria and aggregates the results into method scores. Experiments demonstrate the effectiveness of UniRule and the reliability of the evaluation protocol. They also show that method performance in one setting can be predicted from results in others, with average error close to that obtained using that setting's own data. These findings support studying detection rule generation as a unified task.

cs.CR↗

arXiv2026

Intersection Exponents of Simple Random Walks in Two and Three Dimensions

The probability that several independent random walks avoid one another decays algebraically with the number of steps $N\to\infty$ in two and three dimensions, $P_N\sim N^{-ξ/2}$, where the intersection exponent $ξ$ depends on the number of random walks. More generally, one may consider several groups of independent random walks, with intersections allowed within each group and forbidden between different groups. We first study intersection exponents in two dimensions, where our results agree with the known exact formulas and test the numerical approach. In three dimensions, where no general exact expression is known, we determine $ξ$ for a range of cases. For two groups containing $k$ and $m$ random walks, respectively, we obtain the exponents $ξ(k,m)$ for $k=1,2$ and $m=1,2,\ldots,7$. We further extend $m$ to a continuous parameter $λ$, allowing us to obtain numerical values for $ξ(k,λ)$ for $k=1,2,3$ and $0.25\leqλ\leq3$. Away from the smallest moment orders, these functions increase with $λ$ with decreasing slopes, as expected from the strict concavity of Brownian intersection exponents. We also investigate three-group configurations for several representative cases. The resulting integer and continuous exponents supply numerical values for analytical studies of non-intersecting random paths.

cond-mat.stat-mech↗

arXiv2026

Industrial Dexterity Benchmark: A Hardware-Software Benchmarking Platform for Industrial Dexterous Manipulation

Dexterous manipulation remains a critical bottleneck in industrial automation; tasks such as cable routing, connector insertion, and precision assembly still rely heavily on manual labor despite decades of robotics research. This work presents a progression from classical, modular robotics pipelines toward an end-to-end multimodal imitation-learning framework for industrial dexterous manipulation. As a part of this work, we introduce three key contributions: a set of Industrial Dexterity Benchmark (IDB) boards aimed to mimic datacenter cable management, automotive cable harnesses, and gearbox assembly tasks; a scalable imitation learning framework (DAG-ROS); and a multimodal diffusion-based policy framework (AG-iDP3) that creates models fusing RGB images, point clouds, joint positions, and wrist-frame wrench data. Focusing on the datacenter cable manipulation board, we evaluate the performance of a task involving cleaning a single cable over variations of an end-to-end AI policy using 48 trials per configuration. The best performing configuration, a multimodal expansion Diffusion Policy (DP), includes a multi-view RGB image source passed through an R3M encoder and reaches a 78% grasp and insert combined task success rate. This performance marks a significant improvement over the 36% observed from the single-camera RGB DP baseline. Each of the tested configurations requires only approximately 100 teleoperated demonstrations per task phase. These results indicate that the correct learned policy can outperform classical vision and control robotic methods in robustness, generalization, and deployment efficiency, justifying a shift toward scalable robotic automation for high up-time industrial environments.

cs.RO↗

arXiv2026

UAVs Meet Embodied Intelligence: Bridging Human Intents and Flying Dynamics Via Harnessing Physical-Digital AI Agents

Unmanned aerial vehicles (UAVs) extend embodied intelligence into continuous three-dimensional space, where perception, reasoning, physical embodiment, and action are tightly coupled through flight and environmental interaction. Recent advances in foundation models, world models, and AI agents are shifting UAV autonomy from task-specific perception and control toward systems that can interpret human intent, understand open environments, reason about physical consequences, and organize complex behaviors under embodiment and flight-dynamic constraints. We characterize this emerging paradigm as UAV embodied intelligence (UAV EI) and distinguish it from its system realization, the embodied-intelligent UAV (EI UAV). To provide a unified view of the field, we introduce a 5+5 framework that describes UAV EI through five capability dimensions and EI UAVs through five architectural layers spanning physical embodiment, general cognition, embodied skills, external interaction, and system harnessing. Based on this framework, we systematically review recent progress in embodied morphology, embodied perception, world models, embodied planning, vision-language navigation, embodied manipulation, and embodied collaboration. We further identify long-horizon autonomy, predictive physical reasoning, test-time skill acquisition, and autonomous capability evolution as key challenges toward more general aerial embodied intelligence. Finally, we argue that harnessing physical-digital AI agents, through persistent coupling of digital intelligence with physical sensing, dynamics, action, and feedback, provides a system-level pathway toward adaptive and continuously evolving UAV autonomy. Project resources are available at our project website and GitHub repository.

cs.RO↗

arXiv2026

SlipSense: Multimodal Tactile Learning for Low-Latency and Generalized Slip Detection

Slip detection is fundamental to dexterous manipulation, yet existing systems often lack precise characterization of detection latency and cross-platform generalization. We present SlipSense, a multimodal tactile slip-detection framework built on TacV5, a compact sensor integrating a $32 \times 32$ piezoresistive array operating at 240 Hz and a 3-axis MEMS accelerometer operating at 8 kHz. The piezoresistive array captures spatial pressure distributions, while the accelerometer captures friction-induced vibrations, providing complementary slip cues. The framework performs modality-specific encoding, intra-sensor fusion, and cross-modal attention with causal temporal prediction at 240 Hz. Experiments on a dataset of 1.4 million frames spanning 37 objects demonstrate the complementarity of the two modalities. SlipSense achieves 96.7% Macro F1 with a false-positive rate below 1.6%, detecting 76% of slip events within 23.1 ms. When trained solely on UMI data, SlipSense generalizes zero-shot to a Tesollo dexterous hand, transferring across unseen objects, distinct sensor units, and robotic platforms without retraining.

cs.RO↗

arXiv2026

HalifaxDT: A Wireless Digital Twin from Open Geospatial Data

Wireless digital twins can support site-specific analysis, planning, and experimentation for future wireless networks. However, constructing them at city scale remains challenging when accurate 3D city models are unavailable. This paper presents HalifaxDT, a wireless digital twin of the Halifax Peninsula in Nova Scotia, Canada, constructed from heterogeneous open geospatial and spectrum data. HalifaxDT combines building footprints, LiDAR elevation products, building metadata, and spectrum licensing records through a workflow that reconciles multiple sources of building-height information while preserving the provenance of geometry decisions. The resulting terrain, buildings, and gateway metadata are integrated into Sionna RT for wireless simulation. We evaluate HalifaxDT through two use cases. The first compares its coverage predictions with a reference derived from field measurements and with an analytical baseline. The second uses the digital twin to predict the received signal under normal operating conditions and detect interference. The coverage results show that HalifaxDT better preserves the spatial structure of the measured radio map than the analytical baseline. The interference study shows that deviations from the predicted reference can reveal interference that is difficult to detect from received power alone. We also identify current fidelity limitations, including simplified material representation, missing vegetation, and the need for broader RF calibration and synchronization with live measurements.

cs.NI↗

arXiv2026

Efficient and Robust Absolute Pose Estimation via Gravity-Prior-Driven Transformation Decoupling and Pose Refinement

Estimation of the absolute pose of an object is an essential task for various robotic applications. Recently, incorporating gravity direction as prior information has emerged as a popular approach to simplify absolute pose estimation. However, developing a robust and efficient algorithm to solve this challenging problem remains a difficult question due to large amounts of mismatches. In addition, obtaining an accurate pose solution from selected inlier correspondences with gravity prior is still a research gap. In this paper, we propose a novel transformation strategy that exploits geometric relations derived from the gravity prior. Through transformation decoupling, the original 6 degrees of freedom (DoF) absolute pose estimation problem is simplified into a 4-DoFs problem: 1-DoF for the rotation angle and 3-DoFs for translation, significantly improving the efficiency. For the 1-DoF rotation angle, we apply a one-dimensional global voting algorithm for optimal estimation. Once the optimal rotation is obtained, the mismatched correspondences are preliminarily filtered, and translation estimation, a linear problem, can be easily solved. Furthermore, to obtain accurate pose results, we introduce a novel pose refinement algorithm to enhance the accuracy of both rotation and translation. Extensive experiments on synthetic data and three publicly available real-world datasets (TUM RGB-D, ETH3D, and RobotCar) demonstrate that the proposed method achieves stronger performance compared to existing state-of-the-art (SOTA) approaches. To further validate our method, we integrated it into ORB-SLAM2. The results on the KITTI dataset show it effectively reduces drift and improves trajectory alignment during relocalization. The source code will be released upon acceptance.

cs.CV↗

arXiv2026

Integrating LLM and Diffusion-Based Agents for Social Simulation

Large language models (LLMs) offer strong semantic reasoning capabilities for user modeling, but applying LLM-based simulation to an entire social network is computationally expensive and often unreliable for users with sparse behavioral histories. Meanwhile, conventional information diffusion models efficiently exploit historical propagation patterns and social structures, but provide limited understanding of item content and user-item semantic compatibility. We propose HySID, a hybrid framework for individual-level information adoption prediction that combines semantic reasoning with structural diffusion. HySID first analyzes the historical user-relation graph to adaptively select a small set of structurally informative core users. It then applies LLM-based simulation to estimate the engagement of these users and converts the judgments into a diffusion-compatible seed. Finally, a plug-in diffusion backbone propagates this seed through historical interaction structures to rank potential adopters across the full user population. This design enables LLMs to focus on users for whom semantic reasoning is most informative while allowing neural diffusion models to generalize the evidence to users that are not explicitly simulated. Experiments on three real-world datasets from Weibo, Zhihu, and KuaiRand show that HySID consistently improves four diffusion backbones in Recall and NDCG, while outperforming full-population LLM simulation baselines. At the same time, selective simulation reduces LLM inference cost by approximately 83\% to 99.9\%, demonstrating that HySID provides an effective and computationally practical approach to scalable information adoption prediction.

cs.CY↗