Two-Point Resolution in Spectral Super-Resolution

Two-point super-resolution is an important problem in many signal processing applications. In this paper, we aim to establish a resolution theory for two-point super-resolution from a single snapshot. We consider a complex two-point model with unequal amplitudes and a nontrivial relative phase, and derive super-resolution upper bounds (SRUs) guaranteeing resolvability as well as super-resolution lower bounds (SRLs) below which stable reconstruction is impossible. The resulting bounds provide an explicit characterization of how the amplitude ratio and, more importantly, the relative phase affect the resolution limit for both source-number detection and location estimation. In the in-phase regime, the classical resolution exponents are retained: \((σ/m)^{1/2}\) for source-number detection and \((σ/m)^{1/3}\) for location estimation. In the out-of-phase regimes, the phase term significantly changes the resolution limit: it acts as a direct subtractive term in the near-endpoint regime, and improves the scaling orders in the large-phase regime to \(σ/m\) for source-number detection and \((σ/m)^{1/2}\) for location estimation. Extensive numerical experiments across different phase regimes and reconstruction algorithms validate the predicted scaling laws and theoretical resolution boundaries. Moreover, comparison with our resolution limit in all phase regimes reveals the optimality of \(\ell_0\), ML, and ESPRIT algorithms, and the non-optimality of SVT, MUSIC, and the convex method, a finding that, to the best of our knowledge, has not been reported before. Collectively, our results show that the phase of amplitudes is not merely a nuisance in super-resolution, but a key factor that can be exploited to improve stable resolvability.

Closed-Form Concept Erasure via Double Projections

While modern generative models such as diffusion-based architectures have enabled impressive creative capabilities, they also raise important safety and ethical risks. These concerns have led to growing interest in concept erasure, the process of removing unwanted concepts from model representations. Existing approaches often achieve strong erasure performance but rely on iterative optimization and may inadvertently distort unrelated concepts. In this work, we present a simple yet principled alternative: a linear transformation framework that achieves concept erasure analytically, without any training. Our method adapts a pretrained model through two sequential, closed-form steps: first, computing a proxy projection of the target concept, and second, applying a constrained transformation within the left null space of known concept directions. This design yields a deterministic and geometrically interpretable procedure for safe, efficient, and theory-grounded concept removal. Across a wide range of experiments, including object and style erasure on multiple Stable Diffusion variants and the flow-matching model (FLUX), our approach matches or surpasses the performance of state-of-the-art methods while preserving non-target concepts more faithfully. Requiring only a few seconds to apply, it offers a lightweight and drop-in tool for controlled model editing, advancing the goal of safer and more responsible generative models.

Machine Unlearning under Retain-Forget Entanglement

Forgetting a subset in machine unlearning is rarely an isolated task. Often, retained samples that are closely related to the forget set can be unintentionally affected, particularly when they share correlated features from pretraining or exhibit strong semantic similarities. To address this challenge, we propose a novel two-phase optimization framework specifically designed to handle such retai-forget entanglements. In the first phase, an augmented Lagrangian method increases the loss on the forget set while preserving accuracy on less-related retained samples. The second phase applies a gradient projection step, regularized by the Wasserstein-2 distance, to mitigate performance degradation on semantically related retained samples without compromising the unlearning objective. We validate our approach through comprehensive experiments on multiple unlearning tasks, standard benchmark datasets, and diverse neural architectures, demonstrating that it achieves effective and reliable unlearning while outperforming existing baselines in both accuracy retention and removal fidelity.

PROBE: Diagnosing Residual Concept Capacity in Erased Text-to-Video Diffusion Models

Concept erasure techniques for text-to-video (T2V) diffusion models report substantial suppression of sensitive content, yet current evaluation is limited to checking whether the target concept is absent from generated frames, treating output-level suppression as evidence of representational removal. We introduce PROBE, a diagnostic protocol that quantifies the \textit{reactivation potential} of erased concepts in T2V models. With all model parameters frozen, PROBE optimizes a lightweight pseudo-token embedding through a denoising reconstruction objective combined with a novel latent alignment constraint that anchors recovery to the spatiotemporal structure of the original concept. We make three contributions: (1) a multi-level evaluation framework spanning classifier-based detection, semantic similarity, temporal reactivation analysis, and human validation; (2) systematic experiments across three T2V architectures, three concept categories, and three erasure strategies revealing that all tested methods leave measurable residual capacity whose robustness correlates with intervention depth; and (3) the identification of temporal re-emergence, a video-specific failure mode where suppressed concepts progressively resurface across frames, invisible to frame-level metrics. These findings suggest that current erasure methods achieve output-level suppression rather than representational removal. We release our protocol to support reproducible safety auditing. Our code is available at https://github.com/YiweiXie/PRObingBasedEvaluation.

Semantic Search At LinkedIn

Semantic search with large language models (LLMs) enables retrieval by meaning rather than keyword overlap, but scaling it requires major inference efficiency advances. We present LinkedIn's LLM-based semantic search framework for AI Job Search and AI People Search, combining an LLM relevance judge, embedding-based retrieval, and a compact Small Language Model trained via multi-teacher distillation to jointly optimize relevance and engagement. A prefill-oriented inference architecture co-designed with model pruning, context compression, and text-embedding hybrid interactions boosts ranking throughput by over 75x under a fixed latency constraint while preserving near-teacher-level NDCG, enabling one of the first production LLM-based ranking systems with efficiency comparable to traditional approaches and delivering significant gains in quality and user engagement.

High Fidelity Textual User Representation over Heterogeneous Sources via Reinforcement Learning

Effective personalization on large-scale job platforms requires modeling members based on heterogeneous textual sources, including profiles, professional data, and search activity logs. As recommender systems increasingly adopt Large Language Models (LLMs), creating unified, interpretable, and concise representations from heterogeneous sources becomes critical, especially for latency-sensitive online environments. In this work, we propose a novel Reinforcement Learning (RL) framework to synthesize a unified textual representation for each member. Our approach leverages implicit user engagement signals (e.g., clicks, applies) as the primary reward to distill salient information. Additionally, the framework is complemented by rule-based rewards that enforce formatting and length constraints. Extensive offline experiments across multiple LinkedIn products, one of the world's largest job platforms, demonstrate significant improvements in key downstream business metrics. This work provides a practical, labeling-free, and scalable solution for constructing interpretable user representations that are directly compatible with LLM-based systems.

Automated anatomy-based post-processing reduces false positives and improved interpretability of deep learning intracranial aneurysm detection

Introduction: Deep learning (DL) models can help detect intracranial aneurysms on CTA, but high false positive (FP) rates remain a barrier to clinical translation, despite improvement in model architectures and strategies like detection threshold tuning. We employed an automated, anatomy-based, heuristic-learning hybrid artery-vein segmentation post-processing method to further reduce FPs. Methods: Two DL models, CPM-Net and a deformable 3D convolutional neural network-transformer hybrid (3D-CNN-TR), were trained with 1,186 open-source CTAs (1,373 annotated aneurysms), and evaluated with 143 held-out private CTAs (218 annotated aneurysms). Brain, artery, vein, and cavernous venous sinus (CVS) segmentation masks were applied to remove possible FPs in the DL outputs that overlapped with: (1) brain mask; (2) vein mask; (3) vein more than artery masks; (4) brain plus vein mask; (5) brain plus vein more than artery masks. Results: CPM-Net yielded 139 true-positives (TP); 79 false-negative (FN); 126 FP. 3D-CNN-TR yielded 179 TP; 39 FN; 182 FP. FPs were commonly extracranial (CPM-Net 27.3%; 3D-CNN-TR 42.3%), venous (CPM-Net 56.3%; 3D-CNN-TR 29.1%), arterial (CPM-Net 11.9%; 3D-CNN-TR 53.3%), and non-vascular (CPM-Net 25.4%; 3D-CNN-TR 9.3%) structures. Method 5 performed best, reducing CPM-Net FP by 70.6% (89/126) and 3D-CNN-TR FP by 51.6% (94/182), without reducing TP, lowering the FP/case rate from 0.88 to 0.26 for CPM-NET, and from 1.27 to 0.62 for the 3D-CNN-TR. Conclusion: Anatomy-based, interpretable post-processing can improve DL-based aneurysm detection model performance. More broadly, automated, domain-informed, hybrid heuristic-learning processing holds promise for improving the performance and clinical acceptance of aneurysm detection models.

Fed-HeLLo: Efficient Federated Foundation Model Fine-Tuning with Heterogeneous LoRA Allocation

Federated Learning has recently been utilized to collaboratively fine-tune foundation models across multiple clients. Notably, federated low-rank adaptation LoRA-based fine-tuning methods have recently gained attention, which allows clients to fine-tune FMs with a small portion of trainable parameters locally. However, most existing methods do not account for the heterogeneous resources of clients or lack an effective local training strategy to maximize global fine-tuning performance under limited resources. In this work, we propose Fed-HeLLo, a novel federated LoRA-based fine-tuning framework that enables clients to collaboratively fine-tune an FM with different local trainable LoRA layers. To ensure its effectiveness, we develop several heterogeneous LoRA allocation (HLA) strategies that adaptively allocate local trainable LoRA layers based on clients' resource capabilities and the layer importance. Specifically, based on the dynamic layer importance, we design a Fisher Information Matrix score-based HLA that leverages dynamic gradient norm information. To better stabilize the training process, we consider the intrinsic importance of LoRA layers and design a Geometrically-Defined HLA strategy. It shapes the collective distribution of trainable LoRA layers into specific geometric patterns, such as Triangle, Inverted Triangle, Bottleneck, and Uniform. Moreover, we extend GD-HLA into a randomized version, named Randomized Geometrically-Defined HLA, for enhanced model accuracy with randomness. By co-designing the proposed HLA strategies, we incorporate both the dynamic and intrinsic layer importance into the design of our HLA strategy. We evaluate our approach on five datasets under diverse federated LoRA fine-tuning settings, covering three levels of data distribution from IID to extreme Non-IID. Results show that Fed-HeLLo with HLA strategies is both effective and efficient.

Erasing Concepts, Steering Generations: A Comprehensive Survey of Concept Suppression

Text-to-Image (T2I) models have demonstrated impressive capabilities in generating high-quality and diverse visual content from natural language prompts. However, uncontrolled reproduction of sensitive, copyrighted, or harmful imagery poses serious ethical, legal, and safety challenges. To address these concerns, the concept erasure paradigm has emerged as a promising direction, enabling the selective removal of specific semantic concepts from generative models while preserving their overall utility. This survey provides a comprehensive overview and in-depth synthesis of concept erasure techniques in T2I diffusion models. We systematically categorize existing approaches along three key dimensions: intervention level, which identifies specific model components targeted for concept removal; optimization structure, referring to the algorithmic strategies employed to achieve suppression; and semantic scope, concerning the complexity and nature of the concepts addressed. This multi-dimensional taxonomy enables clear, structured comparisons across diverse methodologies, highlighting fundamental trade-offs between erasure specificity, generalization, and computational complexity. We further discuss current evaluation benchmarks, standardized metrics, and practical datasets, emphasizing gaps that limit comprehensive assessment, particularly regarding robustness and practical effectiveness. Finally, we outline major challenges and promising future directions, including disentanglement of concept representations, adaptive and incremental erasure strategies, adversarial robustness, and new generative architectures. This survey aims to guide researchers toward safer, more ethically aligned generative models, providing foundational knowledge and actionable recommendations to advance responsible development in generative AI.

Erased or Dormant? Rethinking Concept Erasure Through Reversibility

To what extent does concept erasure eliminate generative capacity in diffusion models? While prior evaluations have primarily focused on measuring concept suppression under specific textual prompts, we explore a complementary and fundamental question: do current concept erasure techniques genuinely remove the ability to generate targeted concepts, or do they merely achieve superficial, prompt-specific suppression? We systematically evaluate the robustness and reversibility of two representative concept erasure methods, Unified Concept Editing and Erased Stable Diffusion, by probing their ability to eliminate targeted generative behaviors in text-to-image models. These methods attempt to suppress undesired semantic concepts by modifying internal model parameters, either through targeted attention edits or model-level fine-tuning strategies. To rigorously assess whether these techniques truly erase generative capacity, we propose an instance-level evaluation strategy that employs lightweight fine-tuning to explicitly test the reactivation potential of erased concepts. Through quantitative metrics and qualitative analyses, we show that erased concepts often reemerge with substantial visual fidelity after minimal adaptation, indicating that current methods suppress latent generative representations without fully eliminating them. Our findings reveal critical limitations in existing concept erasure approaches and highlight the need for deeper, representation-level interventions and more rigorous evaluation standards to ensure genuine, irreversible removal of concepts from generative models.