Search arXiv⌕ Search

arXiv subjects

Xi Li

Publications and source records attributed to Xi Li.

At least 19 recordsLinked to original sources
arXiv2026

Optimal Error Estimates With Polynomial Dependence on $ε^{-1}$ for Mixed Finite Element Methods of the Cahn-Hilliard-Navier-Stokes System

In this paper, we analyze a first-order convex-splitting mixed finite element scheme for the Cahn--Hilliard--Navier--Stokes system, tracking explicitly how the error constants depend on the interface width $ε$. Due to the strong nonlinear coupling inherent in the CHNS system and the singular dependence of the Cahn--Hilliard equation on $ε$, conventional energy-based analyzes often lead to severe dependence of the error constants on $ε^{-1}$, and may even result in exponential growth. Such dependence significantly limits the applicability of the resulting error estimates in the small-interfacial-thickness regime. To overcome this difficulty, we develop a robust parameter error analysis framework with respect to interfacial thickness $ε$. In particular, by introducing $H^{-1}$ approximation properties for the Ritz projection and the Ritz and Stokes quasi-projection operators, together with spectral-type estimates for the discrete perturbed Cahn--Hilliard operator, we effectively control the singular terms arising from the interfacial thickness parameter in the error analysis. Compared with the classical results, which address only the Allen-Cahn or Cahn-Hilliard equation, we adopt a three-term discrete Gagliardo-Nirenberg inequality analysis technique and achieve a substantial reduction in the degree of polynomial dependence for the coupled system. Numerical experiments are presented to verify the effectiveness of the theoretical results and to demonstrate the robustness of the method for different parameters of interfacial thickness.

math.NA↗
arXiv2026

Compact Attention: Exploiting Structured Spatio-Temporal Sparsity for Fast Video Generation

The quadratic computational complexity of self-attention mechanisms imposes a critical constraint on transformer-based video generation, particularly for synthesizing ultra-long and high-definition sequences. While most sparse attention techniques employ fixed or heuristic patterns, they often struggle to accommodate the heterogeneous and layer-specific redundancies inherent in video diffusion transformers (VDiTs). We find that different attention heads consistently concentrate most of their attention mass in different coarse query-key regions, a behavior we call functional specialization. Although individual attention values vary with the generated content, these regions remain similar across prompts and random seeds. Leveraging these insights, we introduce Compact Attention, a hardware-aware sparse attention framework for efficient long-video synthesis. We quantify this stability and use it to construct searchable, reusable, head-specific masks. Based on the observation, we propose a deformable dual-window sparse pattern mechanism that flexibly approximates local and axial attention regions within one tile-aligned mask family. To avoid manually choosing a mask for each head, we develop a recall-driven offline auto-search algorithm that identifies high-quality sparse masks while leveraging temporal stability for mask reuse. Extensive evaluations on Wan2.1 (14B) and Hunyuan-Video demonstrate that Compact Attention achieves 2.25x/3.03x attention speedups over FlashAttention-2 and 1.20x/1.74x over FlashAttention-3, respectively, while maintaining visual quality and temporal consistency comparable to full-attention baselines. Project Page: https://yo-ava.github.io/Compact-Attention.github.io/

cs.CV↗
arXiv2026

Leveraging Distributed Sensing and Hyperdimensional Computing for Non-Line-of-Sight Passive Object Sensing

In smart factory environments, passive entities such as humans and movable obstacles may interfere with autonomous robot operations, posing significant safety risks. Detecting potential conflicts between robots and entities outside their field-of-view (FoV) is therefore of paramount importance. However, conventional passive object detection systems rely on sensors such as LiDAR, radar, or cameras, which operate under direct line-of-sight (LoS) and are limited by obstacles and occlusions. To overcome these limitations, integrated sensing and communication (ISAC) enables environmental perception via the communication infrastructure thanks to cooperation among distributed wireless devices. In this paper, we propose a framework for passive entity sensing beyond the robot's FoV that relies solely on distributed channel measurements from the communication infrastructure to perform risk-aware classification. These measurements are embedded into high-dimensional representations using hyperdimensional computing (HDC), enabling robust and scalable learning without explicit channel reconstruction. Numerical simulations based on a commercial ray tracer and ROS-based validation in realistic smart factory scenarios demonstrate improved safety and enhanced path planning with up to 89% accuracy under severe occlusions, while maintaining low computational complexity.

cs.RO↗
arXiv2026

Quantum tomography of bright squeezed vacuum via strong-field ionization

Strong-field physics uses intense optical fields to probe and control electron motion on ultrafast timescales. Recent advances in bright squeezed vacuum have brought macroscopic quantum states of light into the ultrafast strong-field regime, opening prospects for high-harmonic generation and photoionization. Yet linking its phase-space structure to subcycle electron dynamics remains challenging. Here, we demonstrate strong-field tunneling ionization of xenon using a phase-referenced combination of coherent and squeezed fields, with the coherent field defining the ionization clock and quadrature fluctuations of the zero-mean squeezed field providing control. The squeezed field selectively modulates atomic tunneling barriers and electron wave packets, imprinting signatures on photoelectron momentum distributions, number statistics, and energy spectra. Using coincidence measurements of photon number and phase-sensitive photoelectron momentum distributions, we perform quantum state tomography of the driving field by reconstructing its Wigner function. These results establish a bidirectional interface between quantum optics and nonperturbative strong-field electron dynamics, in which the driving quantum field shapes subcycle electron motion while photoionization provides a phase-sensitive probe of the field's quantum state. This work opens new routes toward controlling electron dynamics with quantum light and phase-sensitive quantum state metrology through ultrafast strong-field electron dynamics.

physics.atom-ph↗
arXiv2026

Hiding in Plain Sight: A Diffusion-based Mitigation of Geolocation Privacy Leakage in Vision-Language Models

Multimodal large reasoning models (MLRMs) have demonstrated remarkable capabilities in complex visual understanding. However, this very power introduces a critical yet underexplored privacy threat: adversaries can exploit MLRMs to precisely infer users' geographic locations from casually shared photographs, by performing structured reasoning over subtle visual cues such as architectural styles, vegetation, and lighting conditions. In this work, we present a systematic study of MLRM-driven geolocation privacy leakage. We first reveal that refusal-based safeguards are critically insufficient, as carefully crafted jailbreak prompts can raise model response rates to 100%. We further identify that existing defenses, which inject imperceptible perturbations into shared images, suffer from structural limitations intrinsic to their pixel-space optimization, resulting in degraded black-box transferability and pronounced visual artifacts. Motivated by these findings, we propose a diffusion-based framework that provides targeted, proactive defense against geolocation privacy leakage. By injecting perturbations into the latent space of a diffusion model during reverse sampling, our method operates directly on high-level semantic representations, thereby resolving the effectiveness-utility bottlenecks by construction. We further ground our optimization with GeoCLIP, a model explicitly aligned with GPS coordinates, as a surrogate to pinpoint and disrupt the geographic signals that MLRMs exploit for location inference. This targeted semantic disruption yields significantly stronger black-box transferability while preserving perceptual image quality, offering a seamless integration on social media platforms. Code is available at https://github.com/RachelWolowitz/Hiding_in_plain_sight.

cs.CV↗
arXiv2026

OPTS-TTPO: Enhancing Finite-Sample Policy-Gradient Learning with Tree Search

The policy-gradient theorem gives the exact gradient under the current policy, but finite on-policy samples may miss rare high-return trajectories. We study whether tree search improves their coverage within a fixed budget while controlling gradient bias. We introduce On-Policy Parallel Tree Search (OPTS) and Tree Trajectory Policy Optimization (TTPO) using on-policy tree trajectories, which sample new suffixes from the current policy at visited states. This needs no action-distribution correction, although branching changes state visitation. Our Branch Aggregation Lemma shows that branch-weighted tree statistics recover chain expectations when branch choices and weights are fixed before outgoing transitions are sampled. OPTS selects expansion states using estimated performance differences. Under deterministic dynamics, exact values, and max-backup advantages, the induced search policy's expected return improves monotonically with the budget. We bound the gradient bias from adaptive expansion and show that max backup assigns prefix credit to actions leading to better discovered suffixes. Against a finite chain reference, TTPG's measured bias stays near its no-branching level, while NaivePG's bias grows from 0.1251 to 0.4884. At matched budgets, reward- and value-guided OPTS improve correct-answer coverage and majority-vote accuracy over independent sampling. At matched branch counts, OPTS + TTPG gains coverage with a modest bias increase relative to Fixed-branch + TTPG. Under matched interaction or rollout budgets, OPTS-TTPO improves MuJoCo tail returns over PPO by up to 28.6%, achieves a 34-22-1 win-loss-tie record against PPO on Atari-57 under the last-100-log mean-return metric, and improves micro-averaged avg@32 and pass@32 over PPO across all four Qwen3 models.

cs.CL↗
arXiv2026

ExceptionDrive: A Planning-Oriented Counterfactual Corner-Case Benchmark for Autonomous Driving

Average performance on routine driving benchmarks does not establish planner reliability under rare, safety-critical hazards. We proposed ExceptionDrive, a counterfactual planning benchmark that uses VLM-assisted screening, localized multi-view editing, and quality auditing to insert hazards into real nuScenes scenes while preserving their context. Its 21 tasks span six safety families and define hazard or conflict regions, local safety constraints, and acceptable responses. Because hazard insertion can invalidate the recorded human trajectory, our reference-free protocol evaluates edited predictions using Unsafe Rate (UR), Hazard Clearance Compliance (HCC), Hazard Proximity Response (HPR), and Counterfactual Trajectory Shift (CTS), which measure core-region intrusion, clearance compliance, clearance relative to a prescribed margin, and counterfactual trajectory change. Seven representative planners frequently intrude into hazard regions or provide insufficient clearance. We also develop a Reminder Agent that, without sample-specific task labels, converts visual evidence and the shared taxonomy into structured records of hazard presence, type, and a recommended high-level strategy. The agent neither predicts trajectories nor controls the vehicle; its records guide a VLM-based decision agent. In zero-shot experiments, the reminders improve strategy accuracy and reduce under-warning.

cs.RO↗
arXiv2026

UniRect-CoT: Enhancing Generation in Unified Multimodal Models via Reflective Rectification with Inherent Understanding

Unified Multimodal Models (UMMs) aim to integrate visual understanding and generation within a single structure. However, these models exhibit a notable capability mismatch, where their understanding capability often outperforms their generation capability. This mismatch suggests that the model's rich internal knowledge, while effective for understanding tasks, is not fully utilized during generation. To address this, we draw inspiration from the human ``Thinking-While-Drawing'' paradigm, where humans continuously reflect on intermediate results and revise them according to their understanding of the intended target. In this paper, we propose UniRect-CoT, a training-free unified rectification chain-of-thought framework. We regard the multi-step denoising process in UMMs as an intrinsic visual reasoning process, whose intermediate states provide opportunities for continuous reflection and rectification. By leveraging the UMM's inherent understanding to reflect on intermediate results in light of the target instruction and rectify them accordingly, our framework forms a reflective chain of thought within a single denoising trajectory, enabling the model's internal knowledge to guide generation throughout the process. Specifically, the UMM generates a state-conditioned reflection, whose autoregressive negative log-likelihood under the same model defines a model-native differentiable semantic loss that translates textual reflection into gradients for latent rectification. Extensive experiments demonstrate that UniRect-CoT generalizes across existing flow-based UMMs, consistently enhancing overall text-to-image generation performance.

cs.CV↗
arXiv2026

RefineDrive: Reliable Failure-Guided Learning for Vision-Language-Action Driving

Vision-Language-Action (VLA) models for autonomous driving rely heavily on successful expert demonstrations, leaving model-specific failures underexploited. Learning from these failures is hindered by unreliable diagnoses, poorly matched correction targets, and coarse rewards. We propose RefineDrive, a failure-guided post-training framework that learns from self-generated failures through targeted supervision and safety-aware reinforcement learning. Reliable Diagnosis derives structured, verifiable feedback on collisions and drivable-area violations directly from simulator states. Minimum-Correction Target Retrieval searches a clustered human trajectory bank for nearby corrections that satisfy hard-safety constraints in the current scene, prioritizing preservation of the failed prediction's motion pattern. Conditioned on the driving context and failed trajectory, Correction SFT learns to generate the diagnosis followed by the retrieved correction as a training-only auxiliary task. We then apply GRPO with a Safety-Layered Reward that strictly prioritizes hard-safe trajectories, retains continuous safety feedback for both unsafe and hard-safe trajectories, and rewards driving progress only after hard safety is satisfied. At inference, the policy directly predicts trajectories from the driving context without an explicit diagnosis or repair stage. On NAVSIM v1, RefineDrive improves the 4B base SFT policy from 87.7 to 91.7 PDMS. Using the same checkpoint without additional training, RefineDrive achieves 89.4 EPDMS on the original NAVTEST scenes evaluated with NAVSIM v2 extended metrics. Controlled ablations support the benefits of structured diagnosis supervision, retrieved corrections, and safety-layered optimization for direct planning.

cs.CV↗
arXiv2026

One Perception, All Maneuvers: Directional Traffic Signal Understanding for Maneuver-Level Signal Intent Prediction

Traffic lights are a key regulatory signal for autonomous driving at urban intersections, yet existing traffic signal perception is still predominantly formulated as instance-level detection or color recognition. Such formulations identify where traffic lights are and what colors they display, but leave a critical semantic gap before downstream planning: which ego maneuver is controlled by each visible signal and what dynamic permission the signal expresses for that maneuver. In this paper, we formulate Directional Traffic Signal Understanding, a decision-oriented task that predicts structured signal states for straight, left-turn, right-turn, and U-turn maneuvers from a front-view image. Each state contains the associated signal color and signal-implied passability. Based on OpenLane-V2, we provide a direction-level benchmark with maneuver-level supervision and metrics for color recognition, passability, full-frame consistency, and safety-critical errors. A direction-aware baseline combines global context, localized traffic-light evidence, and maneuver-specific representations. Experiments show that direction-level modeling improves passability prediction over image-level classifiers and detection-oriented pipelines, particularly at complex multi-signal intersections. The resulting representation provides a direct and interpretable traffic-signal interface for downstream planning together with topology, route, and surrounding-agent information.

cs.CV↗
arXiv2026

Topological Necessities: Mechanism-Invariant Strategic Subgoals for Cross-Embodiment Goal-Conditioned Control

Long-horizon goal-conditioned reinforcement learning delegates control to a high-level module that proposes subgoals, but existing subgoals are implicit byproducts of value functions or latent actions, tied to the executor that produced them. We study a different object: a route-conditioned order of unavoidable stages that every successful executor must traverse, recoverable from offline trajectories and belonging to none of them. Its defining properties are topological: an unskippable stage is a separating set that every admissible path must cross, and a loop in free space forces a route choice. We read the two by homology in dimensions 0 and 1 over a transport-weighted carrier built from successful trajectories, yielding an enumerable gate set with shell-level certificates; the certified gates are what we call topological necessities. Certified gates enter the decision loop as a recursive topological gate hierarchy. Under a fixed, isomorphic free space, the object survives executor replacement: gates frozen on PointMaze data transfer without retraining to Ant and Humanoid, attaining the highest Humanoid aggregate under a unified interface (96.1), with +36.0 over a map-privileged reference on the multi-route task (p=1.4e-5); the planner saturates PointMaze (100+/-0) and matches or exceeds the strongest baselines on AntMaze (giant +22.9) and Kitchen (+15.8/+12.6).

cs.LG↗
arXiv2026

The optimal search on graph by continuous-time quantum walks

Chakraborty and Leonardo have shown that a spatial search by quantum walk is optimal for almost all graphs. However, we observed that on some graphs, certain states cannot be searched optimally. We present a method for constructing an optimal graph that searches an arbitrary state and provides the optimal condition. We also analyze the monotonicity of the search performance and conclude that the search performance can be improved by adding edges.

quant-ph↗
arXiv2026

The quantum algorithm for graph isomorphism problem

The graph isomorphism (GI) problem is the computational problem of finding a permutation of vertices of a given graph $G_1$ that transforms $G_1$ to another given graph $G_2$ and preserves the adjacency. In this work, we propose a quantum algorithm to determine whether there exists such a permutation. To find such a permutation, we introduce isomorphic equivalent graphs of the given graphs to be tested. We proof that the GI problem of the equivalent graphs is equivalent to the GI problem of the given graphs. The idea of the algorithm is to determine whether there exists a permutation can transform the eigenvectors of the adjacency matrix of the equivalent graphs each other. The cost time of the algorithm is polynomial.

quant-ph↗
arXiv2026

On reducible partition of graphs and its application to Hadwiger conjecture

An undirected graph $H$ is called a minor of the graph $G$ if $H$ can be formed from $G$ by deleting edges and vertices and by contracting edges. If $G$ does not have a graph $H$ as a minor, then we say that $G$ is $H$-free. Hadwiger conjecture claim that the chromatic number of $G$ may be closely related to whether it contains $K_{n+1}$ minors. To study the coloring of a $K_{n+1}$-free $G$, we propose a new concept of reducible partition of vertex set $V_G$ of $G$. A reducible partition(RP) of a graph $G$ with $K_n$ minors and without $K_{n+1}$ minors is defined as a two-tuples $\{S_1 \subseteq V_G,S_2\subseteq V_G\}$ which satisfy the following condisions:\\ (1) $S_1 \cup S_2 = V_G, S_1 \cap S_2 = \emptyset $\\ (2) $S_2$ is dominated by $S_1$, \\ (3) the induced subgraph $G\left[S_1\right]$ is a forest,\\ (4) the induced subgraph $G\left[S_2\right]$ is $K_{n}$-free.\\ Further, one can obtain a special reducible partition(SRP) $\{S_1,S_2\}$ of $V_G$, which satisf the following condisions:\\ (1) $S_1 \cup S_2 = V_G, S_1 \cap S_2 = \emptyset $ \\ (2) $S_1$ is an independent set,\\ (4) the induced subgraph $G\left[S_2\right]$ is $K_{n}$-free.\\ We will show that both SRP and RP are always exist for any graph. With the SRP of a $K_{n+1}$-free graph $G$, one can obtain some usefull conclusion on the coloring of $G$.

math.GM↗
arXiv2026

Cipher-Structure-Aware Variational Quantum Cryptanalysis: A Reversible Public-Diagnostic Framework

We introduce a cipher-structure-aware variational framework for key recovery from public data in reduced block ciphers. Public S-box differential constraints and candidate-key-dependent inverse-round residuals are converted into phase separators through reversible compute-phase-uncompute circuits. The principal separator is a hybrid DDT construction that combines pairwise and synchronized multi-pair differential constraints before residual refinement. The construction is specified by public functions and does not require a key-indexed phase table in the physical circuit. We formalize the public-instance model, prove one-sided completeness of the structural diagnostics, and derive a conditional lower-tail bound for false-key diagnostic gaps under an explicitly stated sub-Gaussian moment condition. This statistical statement concerns the diagnostic landscape, not convergence of a finite-depth QAOA optimizer. On ten independent random three-pair instances of 16-bit simplified AES, an 18-layer Hybrid-DDT schedule reaches a mean public-consistent-key probability of 0.529785, with values from 0.388892 to 0.770937, ranks the correct key first in every run, and has largest observed false-key probability 0.008723. The result is a reduced-cipher mechanism study, not an attack on full AES.

quant-ph↗
arXiv2026

Beacon: LLM Multi-Agent Driven Hardware Design Space Exploration for Heterogeneous Multi-Chiplet Deep Learning Accelerators

Heterogeneous multi-chiplet accelerators allow chiplets to be configured independently to better match different operator characteristics and improve inference efficiency. However, heterogeneity makes simulator evaluation expensive, limiting the number of iterations affordable for hardware design space exploration (HW-DSE). Mainstream data-driven methods rely mainly on final metrics and a few predefined states, and require many search iterations to implicitly learn the relationships between input parameters and optimization objectives, making them less effective in this setting. In practice, evaluators also generate detailed reports on execution timelines, resource utilization, memory accesses, and communication behavior. Large language models (LLMs) can combine domain knowledge with these reports to explicitly identify bottleneck locations, degradation causes, and parameter adjustment directions, thereby improving each design decision under limited iteration budgets. Based on this observation, we propose Beacon, a report-driven LLM multi-agent framework for heterogeneous multi-chiplet HW-DSE. Beacon employs hierarchical agents for bottleneck localization, root-cause diagnosis, and hardware candidate generation, together with an Analysis Toolbox and RAG memory for closed-loop search. Under the same limited iteration budget, Beacon reduces the composite latency-energy-monetary-cost objective by 25.1\%--93.5\% compared with random search, Bayesian optimization, and reinforcement learning.

cs.AR↗
arXiv2026

Structured Variational Key Concentration for a Reduced AES Cipher

Grover search provides the generic quantum baseline for symmetric-key recovery by amplifying a reversible public-verification oracle. We investigate whether public round structure can instead shape a variational key register before exact verification. For simplified AES (S-AES), we construct phase separators from S-box differential-distribution constraints, candidate-key-dependent inverse diagnostics, and a global residual Hamming-shell term. Each component has a reversible compute-phase-uncompute realization. We prove a one-sided completeness statement for these diagnostics and derive a conditional lower-tail bound for false keys under a weakly correlated diagnostic model. On ten random three-pair 16-bit S-AES instances, an 18-layer schedule optimized with Adam achieves a mean public-consistent-key probability of 46.78 percent, ranks the correct key first in every run, and limits the largest observed false-key probability to 1.11 percent. The 16-bit study evaluates the induced key-register dynamics without shot sampling, while a separate gate-level S-DES experiment validates the reversible oracle pattern without a key-space phase table. The results establish a controlled reduced-cipher benchmark; they do not claim an attack on full AES or an asymptotic advantage over Grover. Within these limits, the construction provides a useful framework for analyzing how AES structure can be incorporated into quantum algorithms.

quant-ph↗
arXiv2026

Toward all-optical unsupervised Hebbian learning in deep photonic neuromorphic networks

We propose a deep photonic neuromorphic network (PNN) architecture based on phase-change material (PCM) synapses and local optical feedback for online, unsupervised Hebbian learning. The proposed architecture combines optical vector-matrix multiplication, non-volatile PCM synaptic weighting, and local coincidence-driven synaptic adaptation within a multilayer photonic crossbar framework compatible with photonic integrated circuits. Unlike conventional PNNs that rely on externally computed gradients, repeated optical-electrical-optical conversions, or global backpropagation, the proposed framework employs local Hebbian learning governed directly by correlated pre- and post-synaptic optical activity. To investigate the feasibility of the proposed learning mechanism, we implemented the PNN design using fiber-optic components, programmable variable optical attenuators, and real-time software control that incorporates PCM thermal dynamics. Supervised and unsupervised learning behaviors were experimentally evaluated under both offline and online learning conditions using representative image-recognition tasks. The experimental results demonstrate adaptive synaptic evolution, successful optical inference, and autonomous pattern encoding through local Hebbian learning under realistic fiber-optic hardware conditions. These results establish a pathway toward future integrated photonic neuromorphic systems capable of scalable and energy-efficient online Hebbian learning.

physics.optics↗