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Galactic disk warp has been widely characterized by stellar distributions and stellar kinematics but has not been traced by stellar chemistry. Here, we use a sample with over 170,000 red clump (RC) stars selected from LAMOST and APOGEE first to establish a correlation between the north-south asymmetry in metallicity ([Fe/H]) and the disk warp. Our results indicate that the height of the [Fe/H] mid-plane for the whole RC sample stars is accurately described as $Z_{w}$ = 0.017 ($R$ $-$ 7.112)$^{2}$ sin($\phi$ $-$ 9.218). This morphology aligns closely with the warp traced by Cepheids, suggesting that the disk north-south asymmetry in [Fe/H] may serve as a new tracer for the Galactic warp. Our detailed analysis of the young/thin disk stars of this RC sample suggests that its warp is well-modeled as $Z_{w}$ = 0.016 ($R$ $-$ 6.507)$^{2}$ sin($\phi$ $-$ 4.240), indicating that the line of node (LON) of the Galactic warp is oriented at 4.240$_{-1.747}^{+1.641}$ degree., Comment: 7 pages, 7 figures, accepted for publication in ApJL

Using nearly 230,000 red clump (RC) stars selected from LAMOST and Gaia, we conduct a comprehensive analysis of the stellar age-velocity dispersion relations (AVRs) for various disk populations, within 5.0 $\leq$ $R$ $\leq$ 15.0 kpc and $|Z|$ $\leq$ 3.0 kpc. The AVRs of the whole RC sample stars are accurately described as $\sigma_{v}$ = $\sigma_{v,0}$ ($\tau$ + 0.1)$^{\beta_{v}}$, with $\beta_{R}$, $\beta_{\phi}$ and $\beta_{Z}$ displaying a global exponential decreasing trend with $R$, which may point to the difference in spatial distributions of various disk heating mechanisms. The measurements of $\beta$ $-$ $R$ for various disks suggest that the thin disk exhibits a radial dependence, with a global exponential decreasing trend in $\beta_{R}$ $-$ $R$ and $\beta_{Z}$ $-$ $R$, while $\beta_{\phi}$ remains a nearly constant value (around 0.20$\sim$0.25) within 8.5 $\leq$ $R$ $\leq$ 11.5 kpc. The thick disk displays a global increasing trend in $\beta_{R}$ $-$ $R$, $\beta_{\phi}$ $-$ $R$ and $\beta_{Z}$ $-$ $R$. These results indicate that the thin disk stars are likely heated by long-term heating from GMCs and spiral arms, while thick disk stars are likely heated by some violent heating process from merger and accretion, and/or formed by the inside-out and upside-down star formation scenarios, and/or born in the chaotic mergers of gas-rich systems and/or turbulent ISM. Our results also suggest that the disk perturbation by a recent minor merger from Sagittarius may have occurred within 3.0 Gyr., Comment: 8 pages, 5 figures, 1 table, accepted for publication in ApJ

Post-training of pre-trained LLMs, which typically consists of the supervised fine-tuning (SFT) stage and the preference learning (RLHF or DPO) stage, is crucial to effective and safe LLM applications. The widely adopted approach in post-training popular open-source LLMs is to sequentially perform SFT and RLHF/DPO. However, sequential training is sub-optimal in terms of SFT and RLHF/DPO trade-off: the LLM gradually forgets about the first stage's training when undergoing the second stage's training. We theoretically prove the sub-optimality of sequential post-training. Furthermore, we propose a practical joint post-training framework with theoretical convergence guarantees and empirically outperforms sequential post-training framework, while having similar computational cost. Our code is available at https://github.com/heshandevaka/XRIGHT.

Fine-tuning on task-specific data to boost downstream performance is a crucial step for leveraging Large Language Models (LLMs). However, previous studies have demonstrated that fine-tuning the models on several adversarial samples or even benign data can greatly comprise the model's pre-equipped alignment and safety capabilities. In this work, we propose SEAL, a novel framework to enhance safety in LLM fine-tuning. SEAL learns a data ranker based on the bilevel optimization to up rank the safe and high-quality fine-tuning data and down rank the unsafe or low-quality ones. Models trained with SEAL demonstrate superior quality over multiple baselines, with 8.5% and 9.7% win rate increase compared to random selection respectively on Llama-3-8b-Instruct and Merlinite-7b models. Our code is available on github https://github.com/hanshen95/SEAL.

Federated learning (FL) has rapidly evolved as a promising paradigm that enables collaborative model training across distributed participants without exchanging their local data. Despite its broad applications in fields such as computer vision, graph learning, and natural language processing, the development of a data projection model that can be effectively used to visualize data in the context of FL is crucial yet remains heavily under-explored. Neighbor embedding (NE) is an essential technique for visualizing complex high-dimensional data, but collaboratively learning a joint NE model is difficult. The key challenge lies in the objective function, as effective visualization algorithms like NE require computing loss functions among pairs of data. In this paper, we introduce \textsc{FedNE}, a novel approach that integrates the \textsc{FedAvg} framework with the contrastive NE technique, without any requirements of shareable data. To address the lack of inter-client repulsion which is crucial for the alignment in the global embedding space, we develop a surrogate loss function that each client learns and shares with each other. Additionally, we propose a data-mixing strategy to augment the local data, aiming to relax the problems of invisible neighbors and false neighbors constructed by the local $k$NN graphs. We conduct comprehensive experiments on both synthetic and real-world datasets. The results demonstrate that our \textsc{FedNE} can effectively preserve the neighborhood data structures and enhance the alignment in the global embedding space compared to several baseline methods.

Feature grid Scene Representation Networks (SRNs) have been applied to scientific data as compact functional surrogates for analysis and visualization. As SRNs are black-box lossy data representations, assessing the prediction quality is critical for scientific visualization applications to ensure that scientists can trust the information being visualized. Currently, existing architectures do not support inference time reconstruction quality assessment, as coordinate-level errors cannot be evaluated in the absence of ground truth data. We propose a parameter-efficient multi-decoder SRN (MDSRN) ensemble architecture consisting of a shared feature grid with multiple lightweight multi-layer perceptron decoders. MDSRN can generate a set of plausible predictions for a given input coordinate to compute the mean as the prediction of the multi-decoder ensemble and the variance as a confidence score. The coordinate-level variance can be rendered along with the data to inform the reconstruction quality, or be integrated into uncertainty-aware volume visualization algorithms. To prevent the misalignment between the quantified variance and the prediction quality, we propose a novel variance regularization loss for ensemble learning that promotes the Regularized multi-decoder SRN (RMDSRN) to obtain a more reliable variance that correlates closely to the true model error. We comprehensively evaluate the quality of variance quantification and data reconstruction of Monte Carlo Dropout, Mean Field Variational Inference, Deep Ensemble, and Predicting Variance compared to the proposed MDSRN and RMDSRN across diverse scalar field datasets. We demonstrate that RMDSRN attains the most accurate data reconstruction and competitive variance-error correlation among uncertain SRNs under the same neural network parameter budgets., Comment: To be published in Proc. IEEE VIS 2024

Existing deep learning-based surrogate models facilitate efficient data generation, but fall short in uncertainty quantification, efficient parameter space exploration, and reverse prediction. In our work, we introduce SurroFlow, a novel normalizing flow-based surrogate model, to learn the invertible transformation between simulation parameters and simulation outputs. The model not only allows accurate predictions of simulation outcomes for a given simulation parameter but also supports uncertainty quantification in the data generation process. Additionally, it enables efficient simulation parameter recommendation and exploration. We integrate SurroFlow and a genetic algorithm as the backend of a visual interface to support effective user-guided ensemble simulation exploration and visualization. Our framework significantly reduces the computational costs while enhancing the reliability and exploration capabilities of scientific surrogate models., Comment: To be published in Proc. IEEE VIS 2024

The open-vocabulary image segmentation task involves partitioning images into semantically meaningful segments and classifying them with flexible text-defined categories. The recent vision-based foundation models such as the Segment Anything Model (SAM) have shown superior performance in generating class-agnostic image segments. The main challenge in open-vocabulary image segmentation now lies in accurately classifying these segments into text-defined categories. In this paper, we introduce the Universal Segment Embedding (USE) framework to address this challenge. This framework is comprised of two key components: 1) a data pipeline designed to efficiently curate a large amount of segment-text pairs at various granularities, and 2) a universal segment embedding model that enables precise segment classification into a vast range of text-defined categories. The USE model can not only help open-vocabulary image segmentation but also facilitate other downstream tasks (e.g., querying and ranking). Through comprehensive experimental studies on semantic segmentation and part segmentation benchmarks, we demonstrate that the USE framework outperforms state-of-the-art open-vocabulary segmentation methods.

Creating high-fidelity head avatars from multi-view videos is a core issue for many AR/VR applications. However, existing methods usually struggle to obtain high-quality renderings for all different head components simultaneously since they use one single representation to model components with drastically different characteristics (e.g., skin vs. hair). In this paper, we propose a Hybrid Mesh-Gaussian Head Avatar (MeGA) that models different head components with more suitable representations. Specifically, we select an enhanced FLAME mesh as our facial representation and predict a UV displacement map to provide per-vertex offsets for improved personalized geometric details. To achieve photorealistic renderings, we obtain facial colors using deferred neural rendering and disentangle neural textures into three meaningful parts. For hair modeling, we first build a static canonical hair using 3D Gaussian Splatting. A rigid transformation and an MLP-based deformation field are further applied to handle complex dynamic expressions. Combined with our occlusion-aware blending, MeGA generates higher-fidelity renderings for the whole head and naturally supports more downstream tasks. Experiments on the NeRSemble dataset demonstrate the effectiveness of our designs, outperforming previous state-of-the-art methods and supporting various editing functionalities, including hairstyle alteration and texture editing., Comment: Project page: https://conallwang.github.io/MeGA_Pages/

Word embedding, a high-dimensional (HD) numerical representation of words generated by machine learning models, has been used for different natural language processing tasks, e.g., translation between two languages. Recently, there has been an increasing trend of transforming the HD embeddings into a latent space (e.g., via autoencoders) for further tasks, exploiting various merits the latent representations could bring. To preserve the embeddings' quality, these works often map the embeddings into an even higher-dimensional latent space, making the already complicated embeddings even less interpretable and consuming more storage space. In this work, we borrow the idea of $\beta$VAE to regularize the HD latent space. Our regularization implicitly condenses information from the HD latent space into a much lower-dimensional space, thus compressing the embeddings. We also show that each dimension of our regularized latent space is more semantically salient, and validate our assertion by interactively probing the encoding-level of user-proposed semantics in the dimensions. To the end, we design a visual analytics system to monitor the regularization process, explore the HD latent space, and interpret latent dimensions' semantics. We validate the effectiveness of our embedding regularization and interpretation approach through both quantitative and qualitative evaluations.

The Milky Way is widely considered to exhibit features of a rotational bar or quadrupole bar. In either case, the feature of the resonance of the Galactic bar should be present in the properties of the chemistry and kinematics, over a large area of the disk. With a sample of over 170,000 red clump (RC) stars from LAMOST-APOGEE data, we attempt to detect the chemical and kinematic signatures of the resonances of the Galactic bar, within 4.0 $\leq$ $R$ $\leq$ 15.0 kpc and $|Z|$ $\leq$ 3.0 kpc. The measurement of the $\Delta$[Fe/H]/$\Delta|Z|$ $-$ $R$ with subtracted the global profiles trends, shows that the thin and thick disks values are Cor_$\Delta$[Fe/H]/$\Delta|Z|$ = 0.010 $\mathrm{sin}$ (1.598 $R$ + 2.551) and Cor_$\Delta$[Fe/H]/$\Delta|Z|$ = 0.006 $\mathrm{sin}$ (1.258 $R$ $-$ 0.019), respectively. The analysis of the tilt angle of the velocity ellipsoid indicates that the thin and thick disks are accurately described as $\alpha$ = $\alpha_{0}$ arctan (Z/R), with $\alpha_{0}$ = 0.198 $\mathrm{sin}$ (0.853 $R$ + 1.982) + 0.630 and $\alpha_{0}$ = 0.220 $\mathrm{sin}$ (0.884 $R$ + 2.012) + 0.679 for thin and thick disks, respectively. These periodic oscillations in Cor_$\Delta$[Fe/H]/$\Delta|Z|$ and $\alpha_{0}$ with $R$ appear in both thin and thick disks, are the most likely chemical and kinematic signatures of the resonance of the Galactic bar. The difference in the phase of the functions of the fitted periodic oscillations for the thin and thick disks may be related to the presence of a second Galactic bar., Comment: 6 pages, 6 figures, 1 table, accepted for publication in ApJL

A detailed measurement is made of the metallicity distributions, kinematics and dynamics of the thin and thick disks, across a large disk volume (5.0 $\leq$ $R$ $\leq$ 15.0 kpc and $|Z|$ $\leq$3.0 kpc), by using the LAMOST-APOGEE red clump stars. The metallicity distributions results show that the radial metallicity gradient $\Delta$[Fe/H]/$\Delta$R of the thin disk weakens with $|Z|$ from $-$0.06 dex kpc$^{-1}$ at around $|Z|$ $<$ 0.25 kpc to $-$0.02 dex kpc$^{-1}$ at around $|Z|$ $>$ 2.75 kpc, while the thick disk displays a global weak positive $\Delta$[Fe/H]/$\Delta$R, generally weaker than 0.01 dex kpc$^{-1}$. The vertical metallicity gradient $\Delta$[Fe/H]/$\Delta|Z|$ weakened steadily from $-$0.36 dex kpc$^{-1}$ at $R$ $\sim$ 5.5 kpc to $-$0.05 dex kpc$^{-1}$ at around R $>$ 11.5 kpc for the thin disk, while the thick disk presents an almost constant value (nearly $-$0.06 $\sim$ $-$0.08 dex kpc$^{-1}$) for all the $R$ bins. These results indicate the contribution of the radial migration to the disk evolution, and the obvious north-south asymmetry in [Fe/H] may be linked to the disk warp and/or the disk perturbation events. The oscillations of the corrected $\Delta$[Fe/H]/$\Delta|Z|$ with $R$ are likely because of the resonances with the Galactic Bar. Our detailed measurements of $\Delta$V$_{\phi}$/$\Delta$[Fe/H] indicate an "inside-out" and "upside-down" star formation scenario for the thick disk. The results of eccentricity distributions and [$\alpha$/Fe]--velocity dispersion relations are likely to suggest that the thick disk stars require an obvious contribution from other heating mechanisms such as merger and accretion, or born in the chaotic mergers of gas-rich systems and/or turbulent interstellar medium., Comment: 12 pages, 11 figures, 1 table, accepted for publication in ApJS

Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of values, we are forced to sample densely from INRs to perform visualization tasks like iso-surface extraction which can be very computationally expensive. Recently, range analysis has shown promising results in improving the efficiency of geometric queries, such as ray casting and hierarchical mesh extraction, on INRs for 3D geometries by using arithmetic rules to bound the output range of the network within a spatial region. However, the analysis bounds are often too conservative for complex scientific data. In this paper, we present an improved technique for range analysis by revisiting the arithmetic rules and analyzing the probability distribution of the network output within a spatial region. We model this distribution efficiently as a Gaussian distribution by applying the central limit theorem. Excluding low probability values, we are able to tighten the output bounds, resulting in a more accurate estimation of the value range, and hence more accurate identification of iso-surface cells and more efficient iso-surface extraction on INRs. Our approach demonstrates superior performance in terms of the iso-surface extraction time on four datasets compared to the original range analysis method and can also be generalized to other geometric query tasks., Comment: Accepted to IEEE Transactions on Visualization and Computer Graphics, presented in VIS 2024

Bilevel optimization has been recently applied to many machine learning tasks. However, their applications have been restricted to the supervised learning setting, where static objective functions with benign structures are considered. But bilevel problems such as incentive design, inverse reinforcement learning (RL), and RL from human feedback (RLHF) are often modeled as dynamic objective functions that go beyond the simple static objective structures, which pose significant challenges of using existing bilevel solutions. To tackle this new class of bilevel problems, we introduce the first principled algorithmic framework for solving bilevel RL problems through the lens of penalty formulation. We provide theoretical studies of the problem landscape and its penalty-based (policy) gradient algorithms. We demonstrate the effectiveness of our algorithms via simulations in the Stackelberg Markov game, RL from human feedback and incentive design., Comment: Shorter version accepted to ICML 2024

In this paper, we present a novel bilevel optimization-based training approach to training acoustic models for automatic speech recognition (ASR) tasks that we term {bi-level joint unsupervised and supervised training (BL-JUST)}. {BL-JUST employs a lower and upper level optimization with an unsupervised loss and a supervised loss respectively, leveraging recent advances in penalty-based bilevel optimization to solve this challenging ASR problem with affordable complexity and rigorous convergence guarantees.} To evaluate BL-JUST, extensive experiments on the LibriSpeech and TED-LIUM v2 datasets have been conducted. BL-JUST achieves superior performance over the commonly used pre-training followed by fine-tuning strategy., Comment: This paper has been accepted in ICASSP-2024 conference

We present a comprehensive study of the kinematic properties of the different Galactic disk populations, as defined by the chemical abundance ratios and stellar ages, across a large disk volume (4.5 $\leq$ R $\leq$ 15.0 kpc and $|Z|$ $\leq$ 3.0 kpc), by using the LAMOST-Gaia red clump sample stars. We determine the median velocities for various spatial and population bins, finding large-scale bulk motions, such as the wave-like behavior in radial velocity, the north-south discrepancy in azimuthal velocity and the warp signal in vertical velocity, and the amplitudes and spatial-dependences of those bulk motions show significant variations for different mono-age and mono-abundance populations. The global spatial behaviors of the velocity dispersions clearly show a signal of spiral arms and, a signal of the disk perturbation event within 4 Gyr, as well as the disk flaring in the outer region (i.e., $R \ge 12$ kpc) mostly for young or alpha-poor stellar populations. Our detailed measurements of age/[$\alpha$/Fe]-velocity dispersion relations for different disk volumes indicate that young/$\alpha$-poor populations are likely originated from dynamically heated by both giant molecular clouds and spiral arms, while old/$\alpha$-enhanced populations require an obvious contribution from other heating mechanisms such as merger and accretion, or born in the chaotic mergers of gas-rich systems and/or turbulent interstellar medium., Comment: 35 pages, 31 figures, 3 tables, accepted for publication in ApJ

Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For scientific visualization applications, however, conveying uncertainties of the results to scientists is crucial to avoid generating misleading or incorrect information. In this paper, we propose PSRFlow, a novel normalizing flow-based generative model for scientific data super-resolution that incorporates uncertainty quantification into the super-resolution process. PSRFlow learns the conditional distribution of the high-resolution data based on the low-resolution counterpart. By sampling from a Gaussian latent space that captures the missing information in the high-resolution data, one can generate different plausible super-resolution outputs. The efficient sampling in the Gaussian latent space allows our model to perform uncertainty quantification for the super-resolved results. During model training, we augment the training data with samples across various scales to make the model adaptable to data of different scales, achieving flexible super-resolution for a given input. Our results demonstrate superior performance and robust uncertainty quantification compared with existing methods such as interpolation and GAN-based super-resolution networks., Comment: To be published in Proc. IEEE VIS 2023

Scene representation networks (SRNs) have been recently proposed for compression and visualization of scientific data. However, state-of-the-art SRNs do not adapt the allocation of available network parameters to the complex features found in scientific data, leading to a loss in reconstruction quality. We address this shortcoming with an adaptively placed multi-grid SRN (APMGSRN) and propose a domain decomposition training and inference technique for accelerated parallel training on multi-GPU systems. We also release an open-source neural volume rendering application that allows plug-and-play rendering with any PyTorch-based SRN. Our proposed APMGSRN architecture uses multiple spatially adaptive feature grids that learn where to be placed within the domain to dynamically allocate more neural network resources where error is high in the volume, improving state-of-the-art reconstruction accuracy of SRNs for scientific data without requiring expensive octree refining, pruning, and traversal like previous adaptive models. In our domain decomposition approach for representing large-scale data, we train an set of APMGSRNs in parallel on separate bricks of the volume to reduce training time while avoiding overhead necessary for an out-of-core solution for volumes too large to fit in GPU memory. After training, the lightweight SRNs are used for realtime neural volume rendering in our open-source renderer, where arbitrary view angles and transfer functions can be explored. A copy of this paper, all code, all models used in our experiments, and all supplemental materials and videos are available at https://github.com/skywolf829/APMGSRN., Comment: Accepted to IEEE VIS 2023. https://www.computer.org/csdl/journal/tg/2024/01/10297599/1RyYguiNBLO

We present a neural network approach to compute stream functions, which are scalar functions with gradients orthogonal to a given vector field. As a result, isosurfaces of the stream function extract stream surfaces, which can be visualized to analyze flow features. Our approach takes a vector field as input and trains an implicit neural representation to learn a stream function for that vector field. The network learns to map input coordinates to a stream function value by minimizing the inner product of the gradient of the neural network's output and the vector field. Since stream function solutions may not be unique, we give optional constraints for the network to learn particular stream functions of interest. Specifically, we introduce regularizing loss functions that can optionally be used to generate stream function solutions whose stream surfaces follow the flow field's curvature, or that can learn a stream function that includes a stream surface passing through a seeding rake. We also discuss considerations for properly visualizing the trained implicit network and extracting artifact-free surfaces. We compare our results with other implicit solutions and present qualitative and quantitative results for several synthetic and simulated vector fields., Comment: Accepted and presented at PVIS2023 in Seoul, South Korea

The number of published research papers has experienced exponential growth in recent years, which makes it crucial to develop new methods for efficient and versatile information extraction and knowledge discovery. To address this need, we propose a Semantic Knowledge Graph (SKG) that integrates semantic concepts from abstracts and other meta-information to represent the corpus. The SKG can support various semantic queries in academic literature thanks to the high diversity and rich information content stored within. To extract knowledge from unstructured text, we develop a Knowledge Extraction Module that includes a semi-supervised pipeline for entity extraction and entity normalization. We also create an ontology to integrate the concepts with other meta information, enabling us to build the SKG. Furthermore, we design and develop a dataflow system that demonstrates how to conduct various semantic queries flexibly and interactively over the SKG. To demonstrate the effectiveness of our approach, we conduct the research based on the visualization literature and provide real-world use cases to show the usefulness of the SKG. The dataset and codes for this work are available at https://osf.io/aqv8p/?view_only=2c26b36e3e3941ce999df47e4616207f.

The tilt of the velocity ellipsoid is a helpful tracer of the gravitational potential of the Milky Way. In this paper, we use nearly 140,000 RC stars selected from the LAMOST and Gaia to make a detailed analysis of the tilt of the velocity ellipsoid for various populations, as defined by the stellar ages and chemical information, within 4.5 $\leq$ $R$ $\leq$ 15.0 kpc and $|Z|$ $\leq$ 3.0 kpc. The tilt angles of the velocity ellipsoids of the RC sample stars are accurately described as $\alpha$ = $\alpha_{0}$ $\mathrm{arctan}$ ($Z$/$R$) with $\alpha_{0}$ = (0.68 $\pm$ 0.05). This indicates the alignment of velocity ellipsoids is between cylindrical and spherical, implying that any deviation from the spherical alignment of the velocity ellipsoids may be caused by the gravitational potential of the baryonic disk. The results of various populations suggest that the $\alpha_{0}$ displays an age and population dependence, with the thin and thick disks respectively values $\alpha_{0}$ = (0.72 $\pm$ 0.08) and $\alpha_{0}$ = (0.64 $\pm$ 0.07), and the $\alpha_{0}$ displays a decreasing trend with age (and [$\alpha$/Fe]) increases, meaning that the velocity ellipsoids of the kinematically relaxed stars are mainly dominated by the gravitational potential of the baryonic disk. We determine the $\alpha_{0} - R$ for various populations, finding that the $\alpha_{0}$ displays oscillations with $R$ for all the different populations. The oscillations in $\alpha_{0}$ appear in both kinematically hot and cold populations, indicating that resonances with the Galactic bar are the most likely origin for these oscillations., Comment: 10 pages, 8 figures, 3 tables, accepted for publication in ApJ

We present VMap, a map-like rectangular space-filling visualization, to perform vertex-centric graph exploration. Existing visualizations have limited support for quality optimization among rectangular aspect ratios, vertex-edge intersection, and data encoding accuracy. To tackle this problem, VMap integrates three novel components: (1) a desired-aspect-ratio (DAR) rectangular partitioning algorithm, (2) a two-stage rectangle adjustment algorithm, and (3) a simulated annealing based heuristic optimizer. First, to generate a rectangular space-filling layout of an input graph, we subdivide the 2D embedding of the graph into rectangles with optimization of rectangles' aspect ratios toward a desired aspect ratio. Second, to route graph edges between rectangles without vertex-edge occlusion, we devise a two-stage algorithm to adjust a rectangular layout to insert border space between rectangles. Third, to produce and arrange rectangles by considering multiple visual criteria, we design a simulated annealing based heuristic optimization to adjust vertices' 2D embedding to support trade-offs among aspect ratio quality and the encoding accuracy of vertices' weights and adjacency. We evaluated the effectiveness of VMap on both synthetic and application datasets. The resulting rectangular layout has better aspect ratio quality on synthetic data compared with the existing method for the rectangular partitioning of 2D points. On three real-world datasets, VMap achieved better encoding accuracy and attained faster generation speed compared with existing methods on graphs' rectangular layout generation. We further illustrate the usefulness of VMap for vertex-centric graph exploration through three case studies on visualizing social networks, representing academic communities, and displaying geographic information., Comment: Submitted to IEEE Visualization Conference (IEEE VIS) 2019 and 2022

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement learning. However, bilevel optimization problems are traditionally known to be difficult to solve. Recent progress on bilevel algorithms mainly focuses on bilevel optimization problems through the lens of the implicit-gradient method, where the lower-level objective is either strongly convex or unconstrained. In this work, we tackle a challenging class of bilevel problems through the lens of the penalty method. We show that under certain conditions, the penalty reformulation recovers the (local) solutions of the original bilevel problem. Further, we propose the penalty-based bilevel gradient descent (PBGD) algorithm and establish its finite-time convergence for the constrained bilevel problem with lower-level constraints yet without lower-level strong convexity. Experiments on synthetic and real datasets showcase the efficiency of the proposed PBGD algorithm.

Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained problems or constrained upper-level problems. This paper considers the stochastic bilevel optimization problems with equality constraints both in the upper and lower levels. By leveraging the special structure of the equality constraints problem, the paper first presents an alternating implicit projected SGD approach and establishes the $\tilde{\cal O}(\epsilon^{-2})$ sample complexity that matches the state-of-the-art complexity of ALSET \citep{chen2021closing} for unconstrained bilevel problems. To further save the cost of projection, the paper presents two alternating implicit projection-efficient SGD approaches, where one algorithm enjoys the $\tilde{\cal O}(\epsilon^{-2}/T)$ upper-level and $\tilde{\cal O}(\epsilon^{-1.5}/T^{\frac{3}{4}})$ lower-level projection complexity with ${\cal O}(T)$ lower-level batch size, and the other one enjoys $\tilde{\cal O}(\epsilon^{-1.5})$ upper-level and lower-level projection complexity with ${\cal O}(1)$ batch size. Application to federated bilevel optimization has been presented to showcase the empirical performance of our algorithms. Our results demonstrate that equality-constrained bilevel optimization with strongly-convex lower-level problems can be solved as efficiently as stochastic single-level optimization problems., Comment: Submitted to conference in Oct 2022

Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in multi-task learning where multiple tasks are optimized jointly, sharing inductive bias between them. This problems are often tackled by the multi-objective optimization framework. However, existing stochastic multi-objective gradient methods and its variants (e.g., MGDA, PCGrad, CAGrad, etc.) all adopt a biased noisy gradient direction, which leads to degraded empirical performance. To this end, we develop a stochastic Multi-objective gradient Correction (MoCo) method for multi-objective optimization. The unique feature of our method is that it can guarantee convergence without increasing the batch size even in the non-convex setting. Simulations on multi-task supervised and reinforcement learning demonstrate the effectiveness of our method relative to state-of-the-art methods., Comment: Changed hyper-parameter choice which affects some of the convergence rate results in the paper