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Jie Ji

Publications and source records attributed to Jie Ji.

At least 19 recordsLinked to original sources
arXiv2026

Uniqueness for the spatially homogeneous Boltzmann equation in critical Sobolev spaces

We study the spatially homogeneous Boltzmann equation without angular cutoff for very soft potentials satisfying the inverse power law relation $\gamma+4s=1$. Our main results establish the existence, uniqueness, stability and regularization estimates of solutions in the critical Sobolev space $ H^{-(\gamma + 2s + \frac{3}{2})} $ with a logarithmic correction. Combined with the recently established monotonicity of the Fisher information, the solutions extend globally in time. Our primary tools are energy estimates based on a simultaneous dyadic localization in the phase and frequency variables, together with sharp commutator estimates between the collision operator and the localization operators.

math.AP↗
arXiv2026

Equilibria and linear stability for the Boltzmann equation with radial anharmonic confining potentials

We study the Boltzmann equation in the whole space under the radial anharmonic confining potentials $\Phi(x)=|x|^p/p$ for $p>2$ and $\Phi(x)=\langle x\rangle^p/p$ for $1 2$, the nonlinear equilibrium manifold is parametrized by mass, temperature, and the three components of angular momentum; for $1<p<2$, integrability excludes rotating equilibria and only mass and energy remain as equilibrium parameters. We then identify the five-dimensional stationary space of the equation linearized about an arbitrary equilibrium and construct an explicit projection determined by the conserved moments. After normalization, the collision term takes the form $C_Me^{-\widetilde\Phi(x)}\mathsf L$, so its microscopic coercivity degenerates at spatial infinity. A far-field weight-transfer estimate compensates for this degeneracy. After subtracting the stationary projection, the corresponding semigroup solution converges algebraically in exponentially weighted $L^2$ spaces. The rate is governed by the growth exponent $p$ and the gap between the two weights, up to an arbitrarily small loss. For $1<p<2$, the mismatch between the two-dimensional nonlinear equilibrium manifold and the five-dimensional linear stationary space yields a conditional obstruction to nonlinear asymptotic attraction for perturbations carrying nonzero angular momentum.

math.AP↗
arXiv2026

SinD 2.0: A Multi-City UAV Dataset with Semantic Risk Annotations for SOTIF-Oriented Safety Validation at Signalized Intersections

Safety validation at signalized intersections remains a critical bottleneck for the deployment of autonomous driving systems (ADS), as these scenarios involve dense heterogeneous traffic, contested right of way, and long-tail safety-critical interactions, posing significant challenges to the Safety of the Intended Functionality (SOTIF). Existing naturalistic driving datasets often suffer from geographical homogeneity, sparsity of safety-critical events, and lack of semantic risk annotations, which limit the evaluation of algorithmic generalizability and targeted SOTIF verification. To address these gaps, this paper introduces SinD 2.0, a large-scale drone-based intersection dataset dedicated to cross-domain ADS safety analysis. The main contributions of SinD 2.0 are: (1) Cross-domain diversity: It covers six signalized intersections across four Chinese cities, capturing distinct intersection topologies and regional driving behavior characteristics; (2) High-density risk interactions: A total of 32,682 safety-critical events are extracted via surrogate safety measures, significantly enriching the density of boundary test scenarios; (3) Hierarchical semantic annotations: Besides integration with high-definition (HD) maps and Signal Phase and Timing (SPaT) data, it provides multi-dimensional semantic labels including traffic violations, high-risk interactions, visual shielding, and narrow feasible areas; (4) Full-stack testing toolchain: It supports automated scenario extraction, prediction-only evaluation, open-loop replay, reactive closed-loop testing, and photorealistic rendering. Benchmark experiments demonstrate that SinD 2.0 exhibits significant domain shifts across cities, and the semantic risk subsets can effectively expose the performance limitations of ADS algorithms. The dataset, annotations, and testing toolchain are available at https://github.com/SOTIF-AVLab/SinD/tree/main.

cs.RO↗
arXiv2026

Runaway avalanches in plasmas with external electric fields: spatially inhomogeneous case in a perturbation framework

We consider the Landau-Coulomb equation for a (hydrogen) plasma heated by an external electric field. In this setting, theoretical and experimental results in plasma physics show the emergence of so-called \emph{runaway electrons} which are linearly accelerating but only lead to a minimal increase of the plasma temperature. Runaway electrons are a major obstacle in nuclear fusion since they can overcome the confinement and damage the structure of the reactor. We rigorously prove the well-posedness of the underlying nonlinear \emph{open} Landau-Coulomb system in a perturbative setting and the conjectured growth bounds for the mean velocity and plasma temperature. We show that the mean velocity is linearly increasing in time, and capture the sharp logarithmic growth of the temperature. Furthermore, we prove that the electron distribution can be asymptotically described by a scattering-type Maxwellian. Due to the different nature of the electron-electron and electron-ion interactions, we recast the equation as a novel coupled system that allows us to isolate the dissipation structures of the two operators. For the coupled system, we perform a micro-macro decomposition to show convergence to the scattering-type Maxwellian.

math.AP↗
arXiv2026

ZO-SAM: Zero-Order Sharpness-Aware Minimization for Efficient Sparse Training

Deep learning models, despite their impressive achievements, suffer from high computational costs and memory requirements, limiting their usability in resource-constrained environments. Sparse neural networks significantly alleviate these constraints by dramatically reducing parameter count and computational overhead. However, existing sparse training methods often experience chaotic and noisy gradient signals, severely hindering convergence and generalization performance, particularly at high sparsity levels. To tackle this critical challenge, we propose Zero-Order Sharpness-Aware Minimization (ZO-SAM), a novel optimization framework that strategically integrates zero-order optimization within the SAM approach. Unlike traditional SAM, ZO-SAM requires only a single backpropagation step during perturbation, selectively utilizing zero-order gradient estimations. This innovative approach reduces the backpropagation computational cost by half compared to conventional SAM, significantly lowering gradient variance and effectively eliminating associated computational overhead. By harnessing SAM's capacity for identifying flat minima, ZO-SAM stabilizes the training process and accelerates convergence. These efficiency gains are particularly important in sparse training scenarios, where computational cost is the primary bottleneck that limits the practicality of SAM. Moreover, models trained with ZO-SAM exhibit improved robustness under distribution shift, further broadening its practicality in real-world deployments.

cs.LG↗
arXiv2026

Forget-It-All: Multi-Concept Machine Unlearning via Concept-Aware Neuron Masking

The widespread adoption of text-to-image (T2I) diffusion models has raised concerns about their potential to generate copyrighted, inappropriate, or sensitive imagery. As a practical solution, machine unlearning aims to erase unwanted concepts without retraining from scratch. While most existing methods are effective for single-concept unlearning, they often struggle when removing multiple concepts, causing significant challenges in unlearning effectiveness, generation quality, and sensitivity to hyperparameters and datasets. We take a unique perspective on multi-concept unlearning by leveraging model sparsity and propose the Forget It All (FIA) framework. FIA first introduces Contrastive Concept Saliency to quantify each weight connection's contribution to a target concept. It then identifies Concept Sensitive Neurons by combining temporal and spatial information, ensuring that only neurons consistently responsive to the target concept are selected. Finally, FIA constructs masks from the identified neurons and fuses them into a unified multi-concept mask, where Concept Agnostic Neurons that broadly support general content generation are preserved while concept-specific neurons are pruned to remove the targets. FIA is training-free and requires minimal hyperparameter tuning for new tasks, enabling plug-and-play use. Extensive experiments across three distinct unlearning tasks demonstrate that FIA achieves more reliable multi-concept unlearning, improving forgetting effectiveness while maintaining generation fidelity and quality. Code is available at https://github.com/kaiyuan02415/Forget-It-All

cs.CV↗
arXiv2025

Mie-tronics supermodes and symmetry breaking in nonlocal metasurfaces

It is usually believed that symmetry breaking in photonic systems leads to weaker optical confinement, such as in the case of metasurfaces when bound states in the continuum are replaced by quasi-bound states with lower quality factors (Q factors). Here we show that symmetry breaking can instead enhance light trapping by strengthening in-plane nonlocal coupling pathways. We consider finite-size arrays of optical resonators supporting Mie resonances (a Mie-tronics platform) and employ diffraction and multiple-scattering analyses. We demonstrate that diffractive bands and Mie-tronics supermodes originate from the same underlying Mie resonances but differ fundamentally in their physical nature. Finite arrays exhibit Q-factor enhancement driven by redistributed radiation channels, and reversing the trends predicted by infinite-lattice theories. We reveal that controlled symmetry breaking opens new electromagnetic coupling channels, enabling polarization conversion in nonlocal metasurfaces. These novel findings establish a unified wave-physics platform linking both scattering and diffraction theories. Also, they outline the design principles for multi-functional metasurfaces that exploit nonlocality for advanced light manipulation, computation, and emission control.

physics.optics↗
arXiv2025

Modality-Aware SAM: Sharpness-Aware-Minimization Driven Gradient Modulation for Harmonized Multimodal Learning

In multimodal learning, dominant modalities often overshadow others, limiting generalization. We propose Modality-Aware Sharpness-Aware Minimization (M-SAM), a model-agnostic framework that applies to many modalities and supports early and late fusion scenarios. In every iteration, M-SAM in three steps optimizes learning. \textbf{First, it identifies the dominant modality} based on modalities' contribution in the accuracy using Shapley. \textbf{Second, it decomposes the loss landscape}, or in another language, it modulates the loss to prioritize the robustness of the model in favor of the dominant modality, and \textbf{third, M-SAM updates the weights} by backpropagation of modulated gradients. This ensures robust learning for the dominant modality while enhancing contributions from others, allowing the model to explore and exploit complementary features that strengthen overall performance. Extensive experiments on four diverse datasets show that M-SAM outperforms the latest state-of-the-art optimization and gradient manipulation methods and significantly balances and improves multimodal learning.

cs.CV↗
arXiv2025

The Right to be Forgotten in Pruning: Unveil Machine Unlearning on Sparse Models

Machine unlearning aims to efficiently eliminate the memory about deleted data from trained models and address the right to be forgotten. Despite the success of existing unlearning algorithms, unlearning in sparse models has not yet been well studied. In this paper, we empirically find that the deleted data has an impact on the pruned topology in a sparse model. Motivated by the observation and the right to be forgotten, we define a new terminology ``un-pruning" to eliminate the impact of deleted data on model pruning. Then we propose an un-pruning algorithm to approximate the pruned topology driven by retained data. We remark that any existing unlearning algorithm can be integrated with the proposed un-pruning workflow and the error of un-pruning is upper-bounded in theory. Also, our un-pruning algorithm can be applied to both structured sparse models and unstructured sparse models. In the experiment, we further find that Membership Inference Attack (MIA) accuracy is unreliable for assessing whether a model has forgotten deleted data, as a small change in the amount of deleted data can produce arbitrary MIA results. Accordingly, we devise new performance metrics for sparse models to evaluate the success of un-pruning. Lastly, we conduct extensive experiments to verify the efficacy of un-pruning with various pruning methods and unlearning algorithms. Our code is released at https://github.com/NKUShaw/SparseModels .

cs.LG↗
arXiv2025

Unconventional localization of light with Mie-tronics

Localization of light requires high-Q cavities or spatial disorder, yet the wave nature of light may open novel opportunities. Here we suggest to employ Mie-tronics as a powerful approach to achieve the hybridization of different resonances for the enhanced confinement of light via interference effects. Contrary to a conventional approach, we employ the symmetry breaking in finite arrays of resonators to boost the Q factors by in-plane multiple scattering. Being applied to photonic moire structures, our approach yields a giant enhancement of the Purcell factor via twist-induced coupling between degenerate collective modes. Our findings reveal how finely tuned cooperative scattering can surpass conventional limits, advancing the control of wave localization in many subwavelength systems.

physics.optics↗
arXiv2025

Label-free super-resolution color flow imaging using ultrasound phase microscopy

Ultrasound vascular imaging is limited by acoustic diffraction, restricting visualization of microvessels essential for understanding organ function and disease. Label-free super-resolution methods exploiting endogenous red blood cells have faced challenges in acquisition time and complexity. Here we introduce ultrasound phase microscopy (UPM), a label-free technique that achieves sub-wavelength resolution flow imaging by exploiting phase differences between consecutively beamformed frames with mismatched apodizations, without requiring localization or tracking. Validated in vivo across multiple species, organs, and ultrasound platforms, UPM attains spatial resolutions better than 5 um up to tenfold improvement over conventional color flow imaging while accelerating data acquisition by nearly two orders of magnitude compared to ultrasound localization microscopy. UPM enables rapid, high resolution vascular imaging and offers a practical approach for label-free super-resolution vascular imaging.

eess.SP↗
arXiv2025

Sculpting Memory: Multi-Concept Forgetting in Diffusion Models via Dynamic Mask and Concept-Aware Optimization

Text-to-image (T2I) diffusion models have achieved remarkable success in generating high-quality images from textual prompts. However, their ability to store vast amounts of knowledge raises concerns in scenarios where selective forgetting is necessary, such as removing copyrighted content, reducing biases, or eliminating harmful concepts. While existing unlearning methods can remove certain concepts, they struggle with multi-concept forgetting due to instability, residual knowledge persistence, and generation quality degradation. To address these challenges, we propose \textbf{Dynamic Mask coupled with Concept-Aware Loss}, a novel unlearning framework designed for multi-concept forgetting in diffusion models. Our \textbf{Dynamic Mask} mechanism adaptively updates gradient masks based on current optimization states, allowing selective weight modifications that prevent interference with unrelated knowledge. Additionally, our \textbf{Concept-Aware Loss} explicitly guides the unlearning process by enforcing semantic consistency through superclass alignment, while a regularization loss based on knowledge distillation ensures that previously unlearned concepts remain forgotten during sequential unlearning. We conduct extensive experiments to evaluate our approach. Results demonstrate that our method outperforms existing unlearning techniques in forgetting effectiveness, output fidelity, and semantic coherence, particularly in multi-concept scenarios. Our work provides a principled and flexible framework for stable and high-fidelity unlearning in generative models. The code will be released publicly.

cs.CV↗
arXiv2025

FairSAM: Fair Classification on Corrupted Image Data Through Sharpness-Aware Minimization

Image classification models trained on clean data often degrade sharply when exposed to corrupted test or deployment data, such as images with impulse noise, Gaussian noise, or environmental noise. This degradation reduces overall performance and disproportionately affects demographic subgroups, raising algorithmic bias concerns. Although robust learning algorithms such as Sharpness-Aware Minimization improve overall robustness and generalization, they do not address biased performance degradation across demographic subgroups. Existing fairness-aware machine learning methods reduce performance disparities but struggle to maintain robust and equitable accuracy across demographic subgroups under data corruption. This limitation reveals an inherent tension between robustness and fairness under corrupted data. To address these challenges, we introduce a metric to assess performance degradation across subgroups under data corruption. We propose FairSAM, a framework that integrates Fairness-oriented strategies into SAM to equalize performance across demographic groups under corrupted conditions. Experiments on multiple real-world datasets and prediction tasks show that FairSAM balances robustness and fairness in corrupted image classification. The framework yields a structured solution for fair and robust image classification in the presence of data corruption.

cs.LG↗
arXiv2025

Optimal Transport for Brain-Image Alignment: Unveiling Redundancy and Synergy in Neural Information Processing

The design of artificial neural networks (ANNs) is inspired by the structure of the human brain, and in turn, ANNs offer a potential means to interpret and understand brain signals. Existing methods primarily align brain signals with stimulus signals using Mean Squared Error (MSE), which focuses only on local point-wise alignment and ignores global matching, leading to coarse interpretations and inaccuracies in brain signal decoding. In this paper, we address these issues through optimal transport (OT) and theoretically demonstrate why OT provides a more effective alignment strategy than MSE. Specifically, we construct a transport plan between brain voxel embeddings and image embeddings, enabling more precise matching. By controlling the amount of transport, we mitigate the influence of redundant information. We apply our alignment model directly to the Brain Captioning task by feeding brain signals into a large language model (LLM) instead of images. Our approach achieves state-of-the-art performance across ten evaluation metrics, surpassing the previous best method by an average of 6.11\% in single-subject training and 3.81\% in cross-subject training. Additionally, we have uncovered several insightful conclusions that align with existing brain research. We unveil the redundancy and synergy of brain information processing through region masking and data dimensionality reduction visualization experiments. We believe our approach paves the way for a more precise understanding of brain signals in the future. The code is available at https://github.com/NKUShaw/OT-Alignment4brain-to-image.

q-bio.NC↗
arXiv2024

Heat Flows with Prescribed Singularities from 3-dimensional Manifold

In this paper, we study singular heat flows from a 3-dimensional complete bounded Riemannian manifold without boundary into the hyperbolic space with prescribe singularity along a closed curve. We prove the existence and regularity of the singular heat flows. Furthermore, we prove that the singular heat flows converge to a singular harmonic map at an exponential rate.

math.AP↗
arXiv2024

Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail

We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global existence and uniqueness around the space $H^{-\frac12}_3\cap L^1_{7}\cap L\log L$. Additionally, we furnish several quantitative assessments regarding the smoothing estimates in weighted Sobolev spaces. The new ingredients of the proof lie in the localized techniques in both phase space and frequency space.

math.AP↗
arXiv2024

Condense, Don't Just Prune: Enhancing Efficiency and Performance in MoE Layer Pruning

Mixture-of-Experts (MoE) has garnered significant attention for its ability to scale up neural networks while utilizing the same or even fewer active parameters. However, MoE does not alleviate the massive memory requirements of networks, which limits their practicality in real-world applications, especially in the era of large language models (LLMs). While recent work explores the possibility of removing entire layers of MoE to reduce memory, the performance degradation is still notable. In this paper, we propose ConDense-MoE (CD-MoE), which, instead of dropping the entire MoE layer, condenses the large, sparse MoE layer into a smaller, denser layer with only a few experts activated for all tokens, while maintaining hardware friendliness. Our approach is specifically designed for fine-grained MoE with shared experts, where Feed-Forward Networks are split into many small experts, with certain experts isolated to serve as shared experts that are always activated, such as DeepSeekMoE and QwenMoE. We demonstrate the effectiveness of our method. Specifically, for the DeepSeekMoE-16B model, our approach maintains 90% of the average accuracy while reducing memory usage by 27.5% and increasing inference speed by 1.26 times. Moreover, we show that by applying lightweight expert fine-tuning -- only to the condensed layers -- and using 5 hours on a single 80G A100 GPU, we can successfully recover 98% of the original performance. Our code is available at: https://github.com/duterscmy/CD-MoE/tree/main.

cs.LG↗