arXiv subjects

Jiaqi Gu

Publications and source records attributed to Jiaqi Gu.

At least 19 recordsLinked to original sources

arXiv2026

Lone-Pair Stereoactivity Overrides Mass Scaling of Thermal Expansion and Heat Conduction in Non-vander Waals Layered Bismuth Oxychalcogenides

Heavier chalcogens are generally expected to soften isostructural semiconductor lattices, raising thermal expansion and lowering thermal conductivity. Layered bismuth oxychalcogenides, Bi2O2X (X = S, Se, Te), are mixed-anion crystals whose covalent slabs and ionic sheets are bound electrostatically rather than by van der Waals forces and whose Bi3+ 6s^2 lone pairs can become stereochemically active. Despite the rapid development of Bi2O2Se for fin and gate-all-around transistors, its fundamental thermal expansion and heat transport mechanisms remain poorly understood. Here, we show that lone-pair stereoactivity, not chalcogen mass, governs both properties. Path-integral molecular dynamics shows that the volumetric thermal expansion coefficient at 300 K decreases from 8.14 x 10^-5 K^-1 in Bi2O2S to 6.72 x 10^-5 and 6.61 x 10^-5 K^-1 in Bi2O2Se and Bi2O2Te, respectively, despite a 13% larger unit cell in the telluride, whereas substituting the S mass into Bi2O2Se changes its value by only 0.6%. Lone-pair-driven Bi off-centering in orthorhombic Bi2O2S makes b-axis expansion 1.63 times a-axis expansion yet leaves in-plane thermal conduction isotropic within 3%. Phonon transport calculations including four-phonon scattering and Wigner coherence predict a thermal conductivity maximum in Bi2O2Se (1.83 and 0.95 W m^-1 K^-1 in the in-plane and cross-plane directions, respectively, at 300 K) because Bi2O2S is limited by anharmonic scattering and Bi2O2Te by slow cross-plane phonons. Thermoreflectance measurements from 300 to 500 K and in situ X-ray diffraction on Bi2O2Se single crystals agree with these predictions within 6.4%. Phonon Boltzmann transport simulations of 12-nm-wide fins, which run hotter than Fourier diffusion predicts, show that Bi2O2Se minimizes the hotspot temperature and the thermal-mismatch strain at the gate dielectric.

cond-mat.mtrl-sci↗

arXiv2026

Delaunay Weighted Two-sample Test for High-dimensional Data by Incorporating Geometric Information

Two-sample hypothesis testing is a fundamental problem with various applications, which faces new challenges in the high-dimensional context. To mitigate the issue of the curse of dimensionality, high-dimensional data are typically assumed to lie on a low-dimensional manifold. To incorporate geometric information in the data, we propose to apply the Delaunay triangulation and develop the Delaunay weight to measure the geometric proximity among data points. In contrast to existing similarity measures that only utilize pairwise distances, the Delaunay weight can take both the distance and direction information into account. A detailed computation procedure is developed to learn the unknown manifold and approximate the Delaunay weight. We further propose a novel nonparametric test statistic using the Delaunay weight matrix. Asymptotic normality under the null and consistency under the alternative of the test statistic are developed. Applied to simulated data, the new test shows robustness to the learning of the unknown manifold and exhibits substantial power gain if the distributions differ in the principal directions of covariance matrices. The proposed test also detects significant differences on a real dataset of mice protein expression levels.

stat.ME↗

arXiv2026

MM-OPD: Towards One More Bottleneck Between Perception and Reasoning

Recent multimodal large language models (MLLMs) advance visual reasoning by strengthening both perception and reasoning, implicitly assuming a process that transitions seamlessly from perception to reasoning. However, we observe a counterintuitive phenomenon that challenges this assumption: holding the model, question, and decoding fixed, we replace images with their caption or code representations (symbolic views), which seems to be redundant given the clear image structures, but the performance surprisingly improves by 10.2% to 23.6% across model scales and datasets. We term this performance gap as the Symbolic Visual Gap and then take a closer look at it. Through experiments, we find that although the visual evidence can already appear in the reasoning trace for the image-input model, the symbolic-view-input model shows much higher attention to the correct evidence than the image-input model. This suggests that despite good capabilities from current works in perception and reasoning themselves, another bottleneck exists between perception and reasoning in selecting perceived visual information as appropriate evidence for subsequent reasoning. To handle this bottleneck, since the symbolic view steers attention toward correct evidence and is readily obtained at scale, it provides supervision for evidence selection without manually labeled evidence. Building on this, we introduce MM-OPD, a multimodal on-policy self-distillation framework for symbolic-to-visual correction that transfers guidance from symbolic-conditioned behavior to the image-conditioned policy through residual token-level targets, steering the model toward correct visual evidence. Experiments across benchmarks and model scales show that MM-OPD improves a broad range of multimodal abilities, with gains in visual perception, chart and document understanding, mathematical reasoning, and general VQA.

cs.CV↗

arXiv2026

DICS: Exploring Data Intrinsic Consistency for Visual Instruction Selection

Visual instruction tuning is crucial for advancing the vision-language alignment and instruction-following capabilities of Vision-Language Models (VLMs). However, identifying optimal subsets under a fixed ratio constraint from rapidly expanding datasets remains a significant bottleneck. While existing methods largely depend on distribution diversity or heuristic filtering, they often overlook the internal coherence within individual samples. To bridge this gap, we propose Data Intrinsic Consistency (DIC), a self-scoring metric designed to quantify the sample-level inter-component consistency. DIC consists of two modules: Visual Information Consistency (VIC), evaluating the alignment between visual content and instructions, and Response Information Consistency (RIC), assessing response coherence relative to the instruction. Building upon DIC, we introduce Data Intrinsic Consistency Selection (DICS), an adaptive data selection method that optimizes the trade-off between high intra-sample consistency and global distributional diversity under varying data budgets. Extensive experiments demonstrate that DICS consistently outperforms state-of-the-art methods across diverse dataset scales and model architectures, surpassing full-dataset fine-tuning while using only 25% of the LLaVA-1.5-665K data. We further curate DICS-6M, a 6M-sample multi-modal instruction corpus that enables the largest-scale visual instruction selection study to date; remarkably, DICS reaches 94.52\% of the official InternVL3-8B-Instruct performance using less than 25\% of its reported training data. Code can be seen at https://github.com/cqu-student/DICS

cs.CV↗

arXiv2026

OptiClear: Differentiable Curvilinear Design Rule Legalization for Inverse-Designed Photonic Devices

Photonic inverse design enables ultra-compact, high-performance devices with highly curvilinear and non-intuitive geometries, but the resulting layouts often violate fabrication design rules and hinder foundry manufacturing. Legalization methods designed for rectilinear Manhattan electrical layouts are not directly applicable to curvilinear inverse-designed photonic devices. Meanwhile, existing fabrication-aware inverse-design methods apply soft penalties on small features and sharp curvatures, but still cannot guarantee design-rule-compliant final layouts. In this work, we present OptiClear, a curvilinear design rule legalization framework for inverse-designed photonic devices. OptiClear provides two complementary legalization engines: OptiClear-R, a rule-based morphological legalizer that efficiently resolves violation regions through iterative morphology-guided mask processing, and OptiClear-D, a differentiable legalizer that formulates legalization as a minimum-distortion mask optimization problem under morphological stationary-point constraints, explicitly seeking a rule-compliant layout with minimal geometric deviation from the original design. We further develop customized differentiable morphological GPU operators that significantly improve the scalability of high-resolution mask legalization. Comprehensive evaluation across diverse inverse-designed photonic devices and a wide range of design-rule settings shows that OptiClear reduces design-rule violations from thousands to zero. The rule-based legalizer offers high runtime efficiency, while the differentiable legalizer more faithfully preserves the original optical functionality. This work establishes curvilinear design rule legalization as a practical post-design electronic-photonic design automation (EPDA) stage for translating high-performance inverse-designed photonic layouts into manufacturable tape-out-ready devices.

physics.optics↗

arXiv2026

PRISM: Photonics-Informed Inverse Lithography for Manufacturable Inverse-Designed Photonic Integrated Circuits

Recent advances in photonic inverse design have demonstrated the ability to automatically synthesize compact, high-performance photonic components that surpass conventional, hand-designed structures, offering a promising path toward scalable and functionality-rich photonic hardware. However, the practical deployment of inverse-designed PICs is bottlenecked by manufacturability: their irregular, subwavelength geometries are highly sensitive to fabrication variations, leading to large performance degradation, low yield, and a persistent gap between simulated optimality and fabricated performance. Unlike electronics, photonics lacks a systematic, flexible mask optimization flow. Fabrication deviations in photonic components cause large optical response drift and compounding error in cascaded circuits, while calibrating fabrication models remains costly and expertise-heavy, often requiring repeated fabrication cycles that are inaccessible to most designers. To bridge this gap, we introduce PRISM, a photonics-informed inverse lithography workflow that makes photonic mask optimization data-efficient, reliable, and optics-informed. PRISM (i) synthesizes compact, informative calibration patterns to minimize required fabrication data, (ii) trains a physics-grounded differentiable fabrication model, enabling gradient-based optimization, and (iii) performs photonics-informed inverse mask optimization that prioritizes performance-critical features beyond geometry matching. Across multiple inverse-designed components with both electron-beam lithography and deep ultra-violet photolithography processes, PRISM significantly boosts post-fabrication performance and yield while reducing calibration area and turnaround time, enabling and democratizing manufacturable and high-yield inverse-designed photonic hardware at scale.

physics.optics↗

arXiv2026

General-Purpose Photonic Computing Primitive for Contemporary Artificial Intelligence

Photonic computing offers a promising route to accelerating artificial intelligence (AI) by providing high analog bandwidth, low latency, and low energy consumption. However, existing optical neural networks (ONNs) struggle with substantial hardware overhead and limited support for the dynamic, arbitrary matrix operations essential for modern AI architectures. Here we present the dynamic universal encoding tensorcore (DUET), a general-purpose photonic computing paradigm based on vectorized operand differential interferometric cells (VODICs). By exploiting inherent structural symmetry, this design provides a full-range linear encoding interface that directly accommodates signed operands. This approach eliminates the sign-based path splitting, nonlinear remapping, and auxiliary preprocessing typically required in conventional ONNs, thereby reducing latency and minimizing hardware and memory overhead. We further implement a hardware-aware training (HAT) strategy to alleviate the impact of on-chip non-idealities and ensure stable inference. DUET is experimentally validated across diverse architectures and application domains, ranging from image classification and medical segmentation to Transformer-based content generation, demonstrating competitive performance. By extending optical computing to universal, full-range operators across diverse model architectures, DUET provides a viable pathway toward general-purpose optical acceleration for contemporary AI workloads.

physics.optics↗

arXiv2026

End-to-End Physical Design Automation Flow for Yield-Optimized Inverse-Designed Large-Scale Electronic-Photonic Integrated Circuits

As AI systems scale to multi-chiplet and wafer-level architectures, the demand for ultra-high bandwidth and system scalability has outpaced the capabilities of electrical interconnects and computing units. Large-scale heterogeneous electronic-photonic integrated chiplets (EPICs) provide a promising solution, but their practical adoption is limited by the lack of a unified, fabrication-aware physical design automation stack. At the same time, inverse-designed ultra-compact photonic devices offer orders-of-magnitude improvements in spatial and spectral density, yet remain constrained by insufficient design-for-manufacturing support and yield optimization. In this work, we present OptoSynthesizer, an end-to-end physical design automation flow for yield-optimized, inverse-designed EPICs. It integrates three key components across the physical design pipeline: (1) OptoSynthesizer-InvDes, a physical-AI-augmented, digital-twin-assisted photonic inverse design and photonics-aware inverse lithography framework; (2) OptoSynthesizer-Place, a GPU-accelerated routing-informed EPIC placer for large-scale routability-optimized layout; and (3) OptoSynthesizer-Route, a hierarchical curvy-aware waveguide router with global-planning-assisted electrical-optical co-routing. Together, these toolkits form a seamless flow from EPIC netlists to fabrication-ready, yield-robust GDS layouts. We demonstrate how this framework enables compact large-scale photonic tensor cores and high-bandwidth interconnect fabrics for heterogeneous EPIC platforms, providing a practical foundation for manufacturable large-scale EPICs in next-generation AI systems.

physics.optics↗

arXiv2026

Harnessing Photonics for Machine Intelligence

The exponential growth of machine-intelligence workloads is colliding with the power, memory, and interconnect limits of the post-Moore era, motivating compute substrates that scale beyond transistor density alone. Integrated photonics is emerging as a candidate for artificial intelligence (AI) acceleration by exploiting optical bandwidth and parallelism to reshape data movement and computation. This review reframes photonic computing from a circuits-and-systems perspective, moving beyond building-block progress toward cross-layer system analysis and full-stack design automation. We synthesize recent advances through a bottleneck-driven taxonomy that delineates the operating regimes and scaling trends where photonics can deliver end-to-end sustained benefits. A central theme is cross-layer co-design and workload-adaptive programmability to sustain high efficiency and versatility across evolving application domains at scale. We further argue that Electronic-Photonic Design Automation (EPDA) will be pivotal, enabling closed-loop co-optimization across simulation, inverse design, system modeling, and physical implementation. By charting a roadmap from laboratory prototypes to scalable, reproducible electronic-photonic ecosystems, this review aims to guide the CAS community toward an automated, system-centric era of photonic machine intelligence.

physics.optics↗

arXiv2026

ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity

Diffractive optical neural networks (DONNs) have demonstrated unparalleled energy efficiency and parallelism by processing information directly in the optical domain. However, their computational expressivity is constrained by static, passive diffractive phase masks that lack efficient nonlinear responses and reprogrammability. To address these limitations, we introduce the Recurrent Diffractive Optical Neural Processor (ReDON), a novel architecture featuring reconfigurable, recurrent self-modulated nonlinearity. This mechanism enables dynamic, input-dependent optical transmission through in-situ electro-optic self-modulation, providing a highly efficient and reprogrammable approach to optical computation. Inspired by the gated linear unit (GLU) used in large language models, ReDON senses a fraction of the propagating optical field and modulates its phase or intensity via a lightweight parametric function, enabling effective nonlinearity with minimal inference overhead. As a non-von Neumann architecture in which the primary weighting elements (metasurfaces) remain fixed, ReDON substantially extends the nonlinear representational capacity and task adaptability of conventional DONNs through recurrent optical hardware reuse and dynamically tunable nonlinearity. We systematically investigate various self-modulation configurations to characterize the trade-offs between hardware efficiency and computational expressivity. On image recognition and segmentation benchmarks, ReDON improves test accuracy and mean intersection-over-union (mIoU) by up to 20% compared with prior DONNs employing either optical or digital nonlinearities at comparable model complexity and negligible additional power consumption. This work establishes a new paradigm for reconfigurable nonlinear optical computing, uniting recurrence and self-modulation within non-von Neumann analog processors.

physics.optics↗

arXiv2026

SKYLIGHT: A Scalable Hundred-Channel 3D Photonic In-Memory Tensor Core Architecture for Real-time AI Inference

The growing computational demands of artificial intelligence (AI) are challenging conventional electronics, making photonic computing a promising alternative. However, existing photonic architectures face fundamental scalability and reliability barriers. This paper introduces SKYLIGHT, a scalable 3D photonic in-memory tensor core architecture designed for real-time AI inference. By co-designing its topology, wavelength routing, accumulation, and programming in a 3D stack, SKYLIGHT overcomes key limitations. Its innovations include a low-loss 3D Si/SiN crossbar topology, a thermally robust non-micro-ring resonator (MRR)-based wavelength-division multiplexing (WDM) component, a hierarchical signal accumulation using a multi-port photodetector (PD), and optically programmed non-volatile phase-change material (PCM) weights. Importantly, SKYLIGHT enables in-situ weight updates that support label-free, layer-local learning (e.g., forward-forward local updates) in addition to inference. Using SimPhony for system-level modeling, we show that a single 144 x 256 SKYLIGHT core is feasible within a single reticle and delivers 342.1 TOPS at 23.7 TOPS/W, enabling ResNet-50 inference at 1212 FPS with 27 mJ per image, and achieves 84.17 FPS/W end-to-end (1.61 x higher than an NVIDIA RTX PRO 6000 Blackwell GPU) under the same workload in real-time measurements. System-level evaluations on four representative machine learning tasks, including unsupervised local self-learning, demonstrate SKYLIGHT's robustness to realistic hardware non-idealities (low-bit quantization and signal-proportional analog noise capturing modulation, PCM programming, and readout variations). With noise-aware training, SKYLIGHT maintains high task accuracy, validating its potential as a comprehensive solution for energy-efficient, large-scale photonic AI accelerators.

cs.ET↗

arXiv2026

CC-VQA: Conflict- and Correlation-Aware Method for Mitigating Knowledge Conflict in Knowledge-Based Visual Question Answering

Knowledge-based visual question answering (KB-VQA) demonstrates significant potential for handling knowledge-intensive tasks. However, conflicts arise between static parametric knowledge in vision language models (VLMs) and dynamically retrieved information due to the static model knowledge from pre-training. The outputs either ignore retrieved contexts or exhibit inconsistent integration with parametric knowledge, posing substantial challenges for KB-VQA. Current knowledge conflict mitigation methods primarily adapted from language-based approaches, focusing on context-level conflicts through engineered prompting strategies or context-aware decoding mechanisms. However, these methods neglect the critical role of visual information in conflicts and suffer from redundant retrieved contexts, which impair accurate conflict identification and effective mitigation. To address these limitations, we propose \textbf{CC-VQA}: a novel training-free, conflict- and correlation-aware method for KB-VQA. Our method comprises two core components: (1) Vision-Centric Contextual Conflict Reasoning, which performs visual-semantic conflict analysis across internal and external knowledge contexts; and (2) Correlation-Guided Encoding and Decoding, featuring positional encoding compression for low-correlation statements and adaptive decoding using correlation-weighted conflict scoring. Extensive evaluations on E-VQA, InfoSeek, and OK-VQA benchmarks demonstrate that CC-VQA achieves state-of-the-art performance, yielding absolute accuracy improvements of 3.3\% to 6.4\% compared to existing methods. Code is available at https://github.com/cqu-student/CC-VQA.

cs.CV↗

arXiv2026

H3PIMAP: A Heterogeneity-Aware Multi-Objective DNN Mapping Framework on Electronic-Photonic Processing-in-Memory Architectures

The future of artificial intelligence (AI) acceleration demands a paradigm shift beyond the limitations of purely electronic or photonic architectures. Photonic analog computing delivers unmatched speed and parallelism but struggles with data movement, robustness, and precision, while electronic processing-in-memory (PIM) enables energy-efficient computing by co-locating storage and computation but suffers from endurance and reconfiguration constraints, limiting it to static weight mapping. Neither approach alone achieves the balance needed for adaptive, efficient AI. To break this impasse, we study a hybrid electronic-photonic-PIM computing architecture and introduce H3PIMAP, a heterogeneity-aware mapping framework that seamlessly orchestrates workloads across electronic and optical tiers. By optimizing workload partitioning through a two-stage multi-objective exploration method, H3PIMAP harnesses light speed for high-throughput operations and PIM efficiency for memory-bound tasks. In system-level evaluations, H3PIMAP delivers a 3.32x latency reduction across language and vision models and, on large language models, achieves 77.0% lower latency with 14.6% lower energy at matched quality, outperforming homogeneous and naive mapping strategies. This proposed framework lays the foundation for hybrid AI accelerators, bridging the gap between electronic and photonic computation for next-generation efficiency and scalability.

cs.AR↗

arXiv2026

Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures

Reinforcement learning (RL) has catalyzed the emergence of Large Reasoning Models (LRMs) that have pushed reasoning capabilities to new heights. While their performance has garnered significant excitement, exploring the internal mechanisms driving these behaviors has become an equally critical research frontier. This paper provides a comprehensive survey of the mechanistic understanding of LRMs, organizing recent findings into three core dimensions: 1) training dynamics, 2) reasoning mechanisms, and 3) unintended behaviors. By synthesizing these insights, we aim to bridge the gap between black-box performance and mechanistic transparency. Finally, we discuss under-explored challenges to outline a roadmap for future mechanistic studies, including the need for applied interpretability, improved methodologies, and a unified theoretical framework.

cs.CL↗

arXiv2025

Toward Large-Scale Photonics-Empowered AI Systems: From Physical Design Automation to System-Algorithm Co-Exploration

In this work, we identify three considerations that are essential for realizing practical photonic AI systems at scale: (1) dynamic tensor operation support for modern models rather than only weight-static kernels, especially for attention/Transformer-style workloads; (2) systematic management of conversion, control, and data-movement overheads, where multiplexing and dataflow must amortize electronic costs instead of letting ADC/DAC and I/O dominate; and (3) robustness under hardware non-idealities that become more severe as integration density grows. To study these coupled tradeoffs quantitatively, and to ensure they remain meaningful under real implementation constraints, we build a cross-layer toolchain that supports photonic AI design from early exploration to physical realization. SimPhony provides implementation-aware modeling and rapid cross-layer evaluation, translating physical costs into system-level metrics so architectural decisions are grounded in realistic assumptions. ADEPT and ADEPT-Z enable end-to-end circuit and topology exploration, connecting system objectives to feasible photonic fabrics under practical device and circuit constraints. Finally, Apollo and LiDAR provide scalable photonic physical design automation, turning candidate circuits into manufacturable layouts while accounting for routing, thermal, and crosstalk constraints.

physics.optics↗

arXiv2025

Democratizing Electronic-Photonic AI Systems: An Open-Source AI-Infused Cross-Layer Co-Design and Design Automation Toolflow

Photonics is becoming a cornerstone technology for high-performance AI systems and scientific computing, offering unparalleled speed, parallelism, and energy efficiency. Despite this promise, the design and deployment of electronic-photonic AI systems remain highly challenging due to a steep learning curve across multiple layers, spanning device physics, circuit design, system architecture, and AI algorithms. The absence of a mature electronic-photonic design automation (EPDA) toolchain leads to long, inefficient design cycles and limits cross-disciplinary innovation and co-evolution. In this work, we present a cross-layer co-design and automation framework aimed at democratizing photonic AI system development. We begin by introducing our architecture designs for scalable photonic edge AI and Transformer inference, followed by SimPhony, an open-source modeling tool for rapid EPIC AI system evaluation and design-space exploration. We then highlight advances in AI-enabled photonic design automation, including physical AI-based Maxwell solvers, a fabrication-aware inverse design framework, and a scalable inverse training algorithm for meta-optical neural networks, enabling a scalable EPDA stack for next-generation electronic-photonic AI systems.

physics.optics↗

arXiv2025

Sketch-in-Latents: Eliciting Unified Reasoning in MLLMs

While Multimodal Large Language Models (MLLMs) excel at visual understanding tasks through text reasoning, they often fall short in scenarios requiring visual imagination. Unlike current works that take predefined external toolkits or generate images during thinking, however, humans can form flexible visual-text imagination and interactions during thinking without predefined toolkits, where one important reason is that humans construct the visual-text thinking process in a unified space inside the brain. Inspired by this capability, given that current MLLMs already encode visual and text information in the same feature space, we hold that visual tokens can be seamlessly inserted into the reasoning process carried by text tokens, where ideally, all visual imagination processes can be encoded by the latent features. To achieve this goal, we propose Sketch-in-Latents (SkiLa), a novel paradigm for unified multi-modal reasoning that expands the auto-regressive capabilities of MLLMs to natively generate continuous visual embeddings, termed latent sketch tokens, as visual thoughts. During multi-step reasoning, the model dynamically alternates between textual thinking mode for generating textual think tokens and visual sketching mode for generating latent sketch tokens. A latent visual semantics reconstruction mechanism is proposed to ensure these latent sketch tokens are semantically grounded. Extensive experiments demonstrate that SkiLa achieves superior performance on vision-centric tasks while exhibiting strong generalization to diverse general multi-modal benchmarks. Codes will be released at https://github.com/TungChintao/SkiLa.

cs.CV↗

arXiv2025

Refining Genetic Discoveries of Group Knockoffs via A Feature-level Filter

Identifying variants that carry substantial information on the trait of interest remains a core topic in genetic studies. In analyzing the EADB-UKBB dataset to identify genetic variants associated with Alzheimer's disease (AD), however, we recognize that both existing marginal association tests and conditional independence tests using existing knockoff filters suffer either power loss or lack of informativeness, especially when strong correlations exist among variants. To address these limitations, we propose a new feature-versus-group (FVG) filter that achieves balance between the power and precision in identifying important features from a set of strongly correlated features using group knockoffs. In extensive simulation studies, the FVG filter controls the expected proportion of false discoveries and identifies important features in smaller catching sets without large power loss. Applying the proposed method to the EADB-UKBB dataset, we discover important variants from 89 loci (similar to the most powerful group knockoff filter) with catching sets of substantially smaller size and higher purity and verify the biological informativeness of our discoveries.

stat.AP↗