arXiv subjects

Linfeng Xu

Publications and source records attributed to Linfeng Xu.

At least 19 recordsLinked to original sources

arXiv2026

Bistable fronts in periodic media: phase reduction and realization of circle flows

We establish a phase reduction and a converse realization theorem for front dynamics in one-dimensional periodic reaction-diffusion-advection equations. For sufficiently large periods under local bistability, and sufficiently small periods when the homogenized equation admits a stationary front, we construct strictly ordered invariant front families that are normally exponentially attracting and locally complete for entire orbits. Modulo spatial-period translations, the dynamics on each family reduces exactly to a circle flow: rotations correspond to propagating pulsating fronts, equilibria to stationary fronts, and connecting orbits to transition fronts between stationary fronts. Conversely, every smooth circle flow can be realized, up to time-preserving topological conjugacy, as the quotient dynamics of such a family for a periodic, locally bistable equation with constant diffusion and no advection. Realizations with a Cantor set of stationary phases and a connecting orbit in each complementary interval illustrate the richness of front dynamics in these media. We also obtain first-order phase-velocity expansions in both period limits, quantitative propagation laws near zero frozen speed, and global exponential orbital stability of propagating pulsating fronts.

math.DS↗

arXiv2026

Bistable pulsating waves with periodic advection: homogenization and sharp speed asymptotics

We study bistable pulsating waves for reaction-diffusion equations with general periodic advection in arbitrary space dimension, allowing the diffusion matrix to be nonsymmetric. Assuming that the homogenized equation admits a traveling wave with nonzero speed in a given direction, we construct moving pulsating waves for all sufficiently small spatial periods $L$ and prove their convergence to the homogenized wave as $L\to0^+$. The existence range and convergence are uniform in the propagation direction when the homogenized speeds never vanish. We also prove uniqueness of the wave speed for arbitrary periods, profile uniqueness for moving waves, and stationary-wave uniqueness in the standing case under continuity of the competing profile. For spatially homogeneous reactions, we derive the expansion $c_L=c_0+Lc_1+O(L^2)$ and an explicit formula for $c_1$. Examples with constant diffusion and zero-mean periodic advection show that $c_1$ can have either sign, demonstrating that the heterogeneity in advection may accelerate or decelerate propagation relative to the homogenized limit and that the general $O(L)$ speed estimate is sharp.

math.AP↗

arXiv2026

Dual-Mode Low-Rank Learner with Bridge-Prototype Ensemble for Vision-Language Class-Incremental Learning

Benefiting from transferable visual-textual alignment, CLIP has been widely adopted for class-incremental learning (CIL). However, existing learners either repeatedly update components shared across tasks, leading to knowledge overwriting, or overly isolate new-task updates, hindering the reuse of CLIP's transferable knowledge and limiting plasticity. Moreover, the text-based or bimodal classifier designs still fail to effectively integrate complementary information from the visual and textual modalities. To address these challenges, we introduce DuLBE, which couples dual-mode low-rank learning with a bridge-prototype ensemble classifier for exemplar-free CIL. DuLBE allocates two visual low-rank update modes according to the gradient demand and uses gradient routing to coordinate them: a compact and rewritable shared mode is selected from historically occupied visual directions to reuse transferable knowledge, while residual modes provide low-interference channels for task-specific variations. Building on the resulting stable inter-modal structure, we further construct geodesic bridges between visual prototypes and text embeddings on the unit hypersphere, and ensemble reliable bridge prototypes to compensate for the modality-gap limitations of textual decision boundaries. Extensive experiments under multiple settings show that DuLBE achieves state-of-the-art CIL performance while retaining the high parameter efficiency of low-rank tuning.

cs.CV↗

arXiv2026

An Upper Bound for the Mean Speed of Transition Fronts and Unbounded Front Widths for Fisher KPP Equations in Almost Periodic Media

In this paper, we investigate transition fronts and spreading solutions of Fisher--KPP equations in one-dimensional almost periodic media, both on the real line and on the lattice. Let $λ_1$ be the supremum of the spectrum of the linearized operator acting on $L^2(\R)$ or $\ell^2(\Z)$, respectively, and let $L(λ_1)$ denote the spatial Lyapunov exponent at the spectral parameter $λ_1$. We prove that, if $L(λ_1)>0$, the global mean speed of any transition front is at most $λ_1/L(λ_1)$. Moreover, if a solution of the Cauchy problem spreads faster than this bound, its transition width is unbounded along a sequence of times. This occurs for a class of initial data with slowly decaying exponential tails. This contrasts with periodic media, where pulsating fronts exist at every speed above the minimal speed. As applications, we consider almost Mathieu coefficients and a continuous quasiperiodic coefficient with two frequencies. Together with the results of Nadin--Rossi and Liang--Wang--Zhou--Zhou \citep{LWZZ24}, our results provide an almost complete picture of the admissible speeds of generalized transition fronts, while leaving the critical cases open.

math.AP↗

arXiv2026

High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations

A discrete entropy inequality is the principal nonlinear stability estimate available for systems of conservation laws, and evaluating it presupposes a physically admissible state. So far, however, the two have been secured separately. Entropy-stable schemes are almost always semi-discrete, are built around one selected entropy pair, and take for granted the positivity of density and pressure that makes the entropy well defined in the first place, whereas bound-preserving limiters keep the solution admissible but deliver no entropy estimate. For the special relativistic Euler equations, the two cannot be separated at all, since the conservative-to-primitive map is implicit, and an inadmissible state therefore has no entropy to correct. Here we construct high-order discontinuous Galerkin and finite volume schemes that, to our knowledge, for the first time, are entropy stable in the fully discrete sense for an arbitrary prescribed finite family of convex entropy pairs, a property we call multi-entropy stability, and are provably admissible wherever an entropy is evaluated. All of this is achieved by a single cellwise projection, and neither conservation nor the design order is lost. The construction rests on relativistic causality, which bounds every characteristic speed by the speed of light. Consequently, the numerical viscosity can be fixed once for all states and all equations of state, and one two-point building block then serves the whole entropy family. Since only the convexity of the admissible set and this speed bound are used, the same route remains open for related systems. Finally, in computations with four equations of state, the schemes retain high-order accuracy close to vacuum, produce no inadmissible state in strong shocks, near-vacuum shock--vortex interaction or jets with Lorentz factor above $70$, and confirm the monotone decay of every enforced discrete entropy.

math.NA↗

arXiv2026

Design and Validation of a Portable EEG-tES Platform Supporting High-Rate EEG Recording and Temporal Interference Stimulation

Background: Closed-loop neuromodulation integrating electroencephalography (EEG) and transcranial electrical stimulation (tES) has strong potential for neuroscience research and clinical applications. However, existing platforms often rely on benchtop instrumentation or FPGA-centered architectures, limiting portability and increasing system complexity. Methods: We developed a compact wearable bidirectional platform integrating 8-channel EEG acquisition and 2-channel tES within a single microcontroller unit (MCU). An ADS1299-based front-end supports up to 8 kHz sampling per channel for simultaneous neural and stimulation signal recording. The stimulation module uses direct digital synthesis (DDS) technique to generate programmable tDCS, tACS, and tTIS waveforms, with optimized firmware design enabling real-time operation on the microcontroller. Results: Experimental evaluation demonstrated high signal fidelity, with EEG correlation coefficients reaching $99\%$ under controlled conditions and $93.5\%$ on a gelatine head phantom. Stimulation performance showed current errors below $1\%$ across tDCS, tACS, and tTIS modes. The platform also reliably recorded concurrent EEG--tES signals without saturation during high-amplitude and high-frequency stimulation. Conclusion: These findings demonstrate that an MCU-centered architecture can effectively support simultaneous EEG sensing and multimodal tES delivery in a compact wearable form factor, while maintaining accurate stimulation and robust signal acquisition. Significance: This work provides a practical foundation for portable closed-loop neuromodulation systems with integrated host software, expanding access to personalized stimulation paradigms, and future point-of-care neurotechnology applications.

eess.SP↗

arXiv2026

SAFE-Merge: Data-Free Continual Model Merging with General Knowledge Preservation

Data-free continual model merging must incorporate a stream of specialized models while retaining both pretrained general knowledge and previously acquired tasks, without access to task data. Existing methods mainly merge task updates by suppressing interference among downstream tasks; while this protects previously acquired tasks, it overlooks the safety of the pretrained knowledge itself, whose erosion degrades generalization to held-out distributions and weakens the foundation for future task acquisition. We propose SAFE-Merge, a simple data-free continual-merging framework that first decides which parameter updates are safe to retain, and then recovers the task information lost through masking. Specifically, to ensure safety, risk-aware sparse masking selects parameter updates that carry task-specific information while posing low risk to general knowledge. Masked low-rank recovery then compensates for the lost task information using only the same retained parameter updates, while leaving all masked-out parameters strictly unchanged. Finally, the combined update is fused into the backbone, incurring no additional inference cost. Across vision and language benchmarks, SAFE-Merge consistently achieves the best H-score. On longer CLIP task sequences, it substantially improves H-score over NUFILT while also achieving the highest accuracy.

cs.LG↗

arXiv2026

Continual Learning with Vision-Language Models via Semantic-Geometry Preservation

Continual learning of pretrained vision-language models (VLMs) is prone to catastrophic forgetting, yet current approaches adapt to new tasks without explicitly preserving the cross-modal semantic geometry inherited from pretraining and previous stages, allowing new-task supervision to induce geometric distortion. We observe that the most pronounced drift tends to concentrate in vulnerable neighborhoods near the old-new semantic interface, where shared visual patterns are easily re-explained by new textual semantics. To address this under an exemplar-free constraint, we propose Semantic Geometry Preservation for Continual Learning (SeGP-CL). SeGP-CL first probes the drift-prone region by constructing a compact set of adversarial anchors with dual-targeted projected gradient descent (DPGD), which drives selected new-task seeds toward old-class semantics while remaining faithful in raw visual space. During training, we preserve cross-modal structure by anchor-guided cross-modal geometry distillation (ACGD), and stabilize the textual reference frame across tasks via a lightweight text semantic-geometry regularization (TSGR). After training, we estimate anchor-induced raw-space drift to transfer old visual prototypes and perform dual-path inference by fusing cross-modal and visual cues. Extensive experiments on five continual learning benchmarks demonstrate that SeGP-CL consistently improves stability and forward transfer, achieving state-of-the-art performance while better preserving semantic geometry of VLMs. Code is available at: https://github.com/chiyuan-IVIPLab/SeGP-CL.

cs.CV↗

arXiv2026

Spreading speeds for Fisher-KPP equations with slowly decaying initial data in an almost periodic setting

This paper investigates the long-times behavior of the Fisher-KPP equation with slowly decaying initial data in an almost periodic medium. We mainly focus on two classes of initial data: exponentially decaying initial data and inital data that decay more slowly than any exponential function. Employing the Hamilton-Jacobi approach, we provide a unified framwork for analyzing the Cauchy problem with initial data in both cases. We demonstrate that the level sets of the solution can be estimated by the generalized principal eigenvalue of the linearized operator and the decay rate of the initial data.

math.AP↗

arXiv2026

GQL-Based Physical-Constraint-Preserving High-Order Finite Difference Schemes for Special Relativistic Hydrodynamics in Arbitrary Dimensions

High-order accurate simulations of special relativistic hydrodynamics (RHD) are prone to numerical breakdown if intrinsic physical constraints (positive rest-mass density/pressure and subluminal velocity) are violated near strong discontinuities. In this work, we develop a robust and efficient physical-constraint-preserving (PCP) flux-limiting framework for high-order schemes, using finite-difference WENO as a representative example. By leveraging the geometric quasilinearization (GQL) representation, which equivalently reformulates the nonlinear RHD constraints into a family of linear inequalities, we integrate a Zalesak-type Flux-Corrected Transport (FCT) update into a scalar-style limiter that acts directly on conservative variables. A critical innovation is the explicit, non-iterative determination of limiting parameters via a rational stereographic parameterization of the GQL normal vector. This technique transforms the required worst-case minimization over auxiliary variables into a generalized Rayleigh-quotient formulation, allowing the optimal parameters to be obtained by solving small symmetric eigenvalue problems ($2\times2$ in 1D; $(d+1)\times(d+1)$ in $d$ dimensions). Relaxed variants are further introduced to reduce computational costs in multidimensions while retaining the PCP guarantee. Extensive numerical benchmarks ranging from 1D to 3D, including ultra-relativistic Riemann problems and astrophysical jets, demonstrate that the proposed method robustly enforces physical admissibility, sharply resolves discontinuities, and maintains design-order accuracy for smooth solutions.

math.NA↗

arXiv2026

DesCLIP: Robust Continual Learning via General Attribute Descriptions for VLM-Based Visual Recognition

Continual learning of vision-language models (VLMs) focuses on leveraging cross-modal pretrained knowledge to incrementally adapt to expanding downstream tasks and datasets, while tackling the challenge of knowledge forgetting. Existing research often focuses on connecting visual features with specific class text in downstream tasks, overlooking the latent relationships between general and specialized knowledge. Our findings reveal that forcing models to optimize inappropriate visual-text matches exacerbates forgetting of VLM's recognition ability. To tackle this issue, we propose DesCLIP, which leverages general attribute (GA) descriptions to guide the understanding of specific class objects, enabling VLMs to establish robust vision-GA-class trilateral associations rather than relying solely on vision-class connections. Specifically, we introduce a language assistant to generate concrete GA description candidates via proper request prompts. Then, an anchor-based embedding filter is designed to obtain highly relevant GA description embeddings, which are leveraged as the paired text embeddings for visual-textual instance matching, thereby tuning the visual encoder. Correspondingly, the class text embeddings are gradually calibrated to align with these shared GA description embeddings. Extensive experiments demonstrate the advancements and efficacy of our proposed method, with comprehensive empirical evaluations highlighting its superior performance in VLM-based recognition compared to existing continual learning methods.

cs.CV↗

arXiv2026

Null-Space Filtering for Data-Free Continual Model Merging: Preserving Stability, Promoting Plasticity

Data-free continual model merging (DFCMM) aims to fuse independently fine-tuned models into a single backbone that evolves with incoming tasks without accessing task data. This paper revisits two fundamental desiderata for DFCMM: stability, avoiding interference with earlier tasks, and plasticity, adapting faithfully to each new task. This poses a challenge that existing approaches fail to address: how to bridge data-level desiderata with parameter-space optimization to ensure stability and plasticity in the absence of task data. To this end, we propose NUFILT (NUll-space FILTering), a data-free framework that directly links these desiderata into parameter-space optimization. Our key observation is that task vectors approximately align with representation subspaces, providing structural surrogates for enforcing stability and plasticity. Accordingly, we design a null-space projector that preserves prior responses by filtering overlapping components of new task vectors, ensuring stability. We further introduce a lightweight LoRA adapter that injects complementary task-specific signals to enable plasticity. The adapter is trained with a projection-based surrogate loss that preserves consistency with prior knowledge while introducing novel directions. This joint filtering-adaptation process enables the backbone to absorb new knowledge while retaining existing behaviors, with updates fused back in a layer-wise linear fashion without extra parameters or inference cost. Theoretically, we establish approximate subspace alignment guarantees that justify null-space filtering. Empirically, NUFILT achieves state-of-the-art performance with minimal forgetting on both vision and NLP benchmarks, improving average accuracy by 4-7% over OPCM and WUDI-Merging, while narrowing the gap to fine-tuning and reducing computation overhead. The code is available at: https://github.com/zihuanqiu/NUFILT

cs.LG↗

arXiv2026

SAVA-X: Ego-to-Exo Imitation Error Detection via Scene-Adaptive View Alignment and Bidirectional Cross View Fusion

Error detection is crucial in industrial training, healthcare, and assembly quality control. Most existing work assumes a single-view setting and cannot handle the practical case where a third-person (exo) demonstration is used to assess a first-person (ego) imitation. We formalize Ego$\rightarrow$Exo Imitation Error Detection: given asynchronous, length-mismatched ego and exo videos, the model must localize procedural steps on the ego timeline and decide whether each is erroneous. This setting introduces cross-view domain shift, temporal misalignment, and heavy redundancy. Under a unified protocol, we adapt strong baselines from dense video captioning and temporal action detection and show that they struggle in this cross-view regime. We then propose SAVA-X, an Align-Fuse-Detect framework with (i) view-conditioned adaptive sampling, (ii) scene-adaptive view embeddings, and (iii) bidirectional cross-attention fusion. On the EgoMe benchmark, SAVA-X consistently improves AUPRC and mean tIoU over all baselines, and ablations confirm the complementary benefits of its components. Code is available at https://github.com/jack1ee/SAVAX.

cs.CV↗

arXiv2025

Generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media

This paper is concerned with the asymptotic behavior of the generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media where one scale is fixed and another one approaches zero or infinity. We transform the problem into the homogenization of certain effective Hamiltonian and then establish the asymptotic limits and the convergence rates. Based on the analysis of the asymptotic behavior of effective Hamiltonians, we investigate how the heterogeneity of the advection and growth rates affect on the propagation in the case where the media has very rapid or slow spatial oscillation: We show a normal scale perturbation of the growth rate with mean zero can accelerate the propagation in the media with rapid or slow oscillation; and an advection with slow oscillation and mean zero can decelerate the propagation in 1-D case.

math.AP↗

arXiv2025

MINGLE: Mixture of Null-Space Gated Low-Rank Experts for Test-Time Continual Model Merging

Continual model merging integrates independently fine-tuned models sequentially without access to the original training data, offering a scalable and efficient solution for continual learning. However, existing methods face two critical challenges: parameter interference among tasks, which leads to catastrophic forgetting, and limited adaptability to evolving test distributions. To address these issues, we introduce the task of Test-Time Continual Model Merging (TTCMM), which leverages a small set of unlabeled test samples during inference to alleviate parameter conflicts and handle distribution shifts. We propose MINGLE, a novel framework for TTCMM. MINGLE employs a mixture-of-experts architecture with parameter-efficient, low-rank experts, which enhances adaptability to evolving test distributions while dynamically merging models to mitigate conflicts. To further reduce forgetting, we propose Null-Space Constrained Gating, which restricts gating updates to subspaces orthogonal to prior task representations, thereby suppressing activations on old tasks and preserving past knowledge. We further introduce an Adaptive Relaxation Strategy that adjusts constraint strength dynamically based on interference signals observed during test-time adaptation, striking a balance between stability and adaptability. Extensive experiments on standard continual merging benchmarks demonstrate that MINGLE achieves robust generalization, significantly reduces forgetting, and consistently surpasses previous state-of-the-art methods by 7-9% on average across diverse task orders. Our code is available at: https://github.com/zihuanqiu/MINGLE

cs.LG↗

arXiv2025

CMaP-SAM: Contraction Mapping Prior for SAM-driven Few-shot Segmentation

Few-shot segmentation (FSS) aims to segment new classes using few annotated images. While recent FSS methods have shown considerable improvements by leveraging Segment Anything Model (SAM), they face two critical limitations: insufficient utilization of structural correlations in query images, and significant information loss when converting continuous position priors to discrete point prompts. To address these challenges, we propose CMaP-SAM, a novel framework that introduces contraction mapping theory to optimize position priors for SAM-driven few-shot segmentation. CMaP-SAM consists of three key components: (1) a contraction mapping module that formulates position prior optimization as a Banach contraction mapping with convergence guarantees. This module iteratively refines position priors through pixel-wise structural similarity, generating a converged prior that preserves both semantic guidance from reference images and structural correlations in query images; (2) an adaptive distribution alignment module bridging continuous priors with SAM's binary mask prompt encoder; and (3) a foreground-background decoupled refinement architecture producing accurate final segmentation masks. Extensive experiments demonstrate CMaP-SAM's effectiveness, achieving state-of-the-art performance with 71.1 mIoU on PASCAL-$5^i$ and 56.1 on COCO-$20^i$ datasets. Code is available at https://github.com/Chenfan0206/CMaP-SAM.

cs.CV↗

arXiv2025

Closing the Oracle Gap: Increment Vector Transformation for Class Incremental Learning

Class Incremental Learning (CIL) aims to sequentially acquire knowledge of new classes without forgetting previously learned ones. Despite recent progress, current CIL methods still exhibit significant performance gaps compared to their oracle counterparts-models trained with full access to historical data. Inspired by recent insights on Linear Mode Connectivity (LMC), we revisit the geometric properties of oracle solutions in CIL and uncover a fundamental observation: these oracle solutions typically maintain low-loss linear connections to the optimum of previous tasks. Motivated by this finding, we propose Increment Vector Transformation (IVT), a novel plug-and-play framework designed to mitigate catastrophic forgetting during training. Rather than directly following CIL updates, IVT periodically teleports the model parameters to transformed solutions that preserve linear connectivity to previous task optimum. By maintaining low-loss along these connecting paths, IVT effectively ensures stable performance on previously learned tasks. The transformation is efficiently approximated using diagonal Fisher Information Matrices, making IVT suitable for both exemplar-free and exemplar-based scenarios, and compatible with various initialization strategies. Extensive experiments on CIFAR-100, FGVCAircraft, ImageNet-Subset, and ImageNet-Full demonstrate that IVT consistently enhances the performance of strong CIL baselines. Specifically, on CIFAR-100, IVT improves the last accuracy of the PASS baseline by +5.12% and reduces forgetting by 2.54%. For the CLIP-pre-trained SLCA baseline on FGVCAircraft, IVT yields gains of +14.93% in average accuracy and +21.95% in last accuracy. The code will be released.

cs.LG↗

arXiv2025

No Re-Train, More Gain: Upgrading Backbones with Diffusion model for Pixel-Wise and Weakly-Supervised Few-Shot Segmentation

Few-Shot Segmentation (FSS) aims to segment novel classes using only a few annotated images. Despite considerable progress under pixel-wise support annotation, current FSS methods still face three issues: the inflexibility of backbone upgrade without re-training, the inability to uniformly handle various types of annotations (e.g., scribble, bounding box, mask, and text), and the difficulty in accommodating different annotation quantity. To address these issues simultaneously, we propose DiffUp, a novel framework that conceptualizes the FSS task as a conditional generative problem using a diffusion process. For the first issue, we introduce a backbone-agnostic feature transformation module that converts different segmentation cues into unified coarse priors, facilitating seamless backbone upgrade without re-training. For the second issue, due to the varying granularity of transformed priors from diverse annotation types (scribble, bounding box, mask, and text), we conceptualize these multi-granular transformed priors as analogous to noisy intermediates at different steps of a diffusion model. This is implemented via a self-conditioned modulation block coupled with a dual-level quality modulation branch. For the third issue, we incorporate an uncertainty-aware information fusion module to harmonize the variability across zero-shot, one-shot, and many-shot scenarios. Evaluated through rigorous benchmarks, DiffUp significantly outperforms existing FSS models in terms of flexibility and accuracy.

cs.CV↗