Shibo Li

Shibo Li, Xin Yu, Wei Xing et al.

Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can be a costly bottleneck in practice, because it often demands expensive physical simulations. To overcome this problem, we propose Multi-Resolution Active learning of FNO (MRA-FNO), which can dynamically select the input functions and resolutions to lower the data cost as much as possible while optimizing the learning efficiency. Specifically, we propose a probabilistic multi-resolution FNO and use ensemble Monte-Carlo to develop an effective posterior inference algorithm. To conduct active learning, we maximize a utility-cost ratio as the acquisition function to acquire new examples and resolutions at each step. We use moment matching and the matrix determinant lemma to enable tractable, efficient utility computation. Furthermore, we develop a cost annealing framework to avoid over-penalizing high-resolution queries at the early stage. The over-penalization is severe when the cost difference is significant between the resolutions, which renders active learning often stuck at low-resolution queries and inferior performance. Our method overcomes this problem and applies to general multi-fidelity active learning and optimization problems. We have shown the advantage of our method in several benchmark operator learning tasks. The code is available at https://github.com/shib0li/MRA-FNO.

Shikai Fang, Madison Cooley, Da Long et al.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student $t$ mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at \url{https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE}.

Shikai Fang, Xin Yu, Shibo Li et al.

Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects' representation. More important, we lack an effective approach to capture such evolution from streaming data, which is common in real-world applications. To address these issues, we propose Streaming Factor Trajectory Learning for temporal tensor decomposition. We use Gaussian processes (GPs) to model the trajectory of factors so as to flexibly estimate their temporal evolution. To address the computational challenges in handling streaming data, we convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE). We develop an efficient online filtering algorithm to estimate a decoupled running posterior of the involved factor states upon receiving new data. The decoupled estimation enables us to conduct standard Rauch-Tung-Striebel smoothing to compute the full posterior of all the trajectories in parallel, without the need for revisiting any previous data. We have shown the advantage of SFTL in both synthetic tasks and real-world applications. The code is available at {https://github.com/xuangu-fang/Streaming-Factor-Trajectory-Learning}.

Shikai Fang, Xin Yu, Zheng Wang et al.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at \url{https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition}.

Zheng Wang, Shikai Fang, Shibo Li et al.

Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the structural knowledge within the sparsely observed tensor entries. To overcome these limitations and to better capture the underlying temporal structure, we propose Dynamic EMbedIngs fOr dynamic Tensor dEcomposition (DEMOTE). We develop a neural diffusion-reaction process to estimate dynamic embeddings for the entities in each tensor mode. Specifically, based on the observed tensor entries, we build a multi-partite graph to encode the correlation between the entities. We construct a graph diffusion process to co-evolve the embedding trajectories of the correlated entities and use a neural network to construct a reaction process for each individual entity. In this way, our model can capture both the commonalities and personalities during the evolution of the embeddings for different entities. We then use a neural network to model the entry value as a nonlinear function of the embedding trajectories. For model estimation, we combine ODE solvers to develop a stochastic mini-batch learning algorithm. We propose a stratified sampling method to balance the cost of processing each mini-batch so as to improve the overall efficiency. We show the advantage of our approach in both simulation study and real-world applications. The code is available at https://github.com/wzhut/Dynamic-Tensor-Decomposition-via-Neural-Diffusion-Reaction-Processes.

Shibo Li, Zheng Wang, Robert M. Kirby et al.

Multi-fidelity modeling and learning are important in physical simulation-related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation while still achieving good performance. While existing approaches only model finite, discrete fidelities, in practice, the fidelity choice is often continuous and infinite, which can correspond to a continuous mesh spacing or finite element length. In this paper, we propose Infinite Fidelity Coregionalization (IFC). Given the data, our method can extract and exploit rich information within continuous, infinite fidelities to bolster the prediction accuracy. Our model can interpolate and/or extrapolate the predictions to novel fidelities, which can be even higher than the fidelities of training data. Specifically, we introduce a low-dimensional latent output as a continuous function of the fidelity and input, and multiple it with a basis matrix to predict high-dimensional solution outputs. We model the latent output as a neural Ordinary Differential Equation (ODE) to capture the complex relationships within and integrate information throughout the continuous fidelities. We then use Gaussian processes or another ODE to estimate the fidelity-varying bases. For efficient inference, we reorganize the bases as a tensor, and use a tensor-Gaussian variational posterior to develop a scalable inference algorithm for massive outputs. We show the advantage of our method in several benchmark tasks in computational physics.

Shibo Li, Jeff M. Phillips, Xin Yu et al.

Learning functions with high-dimensional outputs is critical in many applications, such as physical simulation and engineering design. However, collecting training examples for these applications is often costly, e.g. by running numerical solvers. The recent work (Li et al., 2022) proposes the first multi-fidelity active learning approach for high-dimensional outputs, which can acquire examples at different fidelities to reduce the cost while improving the learning performance. However, this method only queries at one pair of fidelity and input at a time, and hence has a risk to bring in strongly correlated examples to reduce the learning efficiency. In this paper, we propose Batch Multi-Fidelity Active Learning with Budget Constraints (BMFAL-BC), which can promote the diversity of training examples to improve the benefit-cost ratio, while respecting a given budget constraint for batch queries. Hence, our method can be more practically useful. Specifically, we propose a novel batch acquisition function that measures the mutual information between a batch of multi-fidelity queries and the target function, so as to penalize highly correlated queries and encourages diversity. The optimization of the batch acquisition function is challenging in that it involves a combinatorial search over many fidelities while subject to the budget constraint. To address this challenge, we develop a weighted greedy algorithm that can sequentially identify each (fidelity, input) pair, while achieving a near $(1 - 1/e)$-approximation of the optimum. We show the advantage of our method in several computational physics and engineering applications.

Zheng Wang, Yiming Xu, Conor Tillinghast et al.

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound) of the sparsity ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction, and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.

Jun Li, Shibo Li, Ying Hu et al.

Automatic radiology report generation is essential to computer-aided diagnosis. Through the success of image captioning, medical report generation has been achievable. However, the lack of annotated disease labels is still the bottleneck of this area. In addition, the image-text data bias problem and complex sentences make it more difficult to generate accurate reports. To address these gaps, we pre-sent a self-guided framework (SGF), a suite of unsupervised and supervised deep learning methods to mimic the process of human learning and writing. In detail, our framework obtains the domain knowledge from medical reports with-out extra disease labels and guides itself to extract fined-grain visual features as-sociated with the text. Moreover, SGF successfully improves the accuracy and length of medical report generation by incorporating a similarity comparison mechanism that imitates the process of human self-improvement through compar-ative practice. Extensive experiments demonstrate the utility of our SGF in the majority of cases, showing its superior performance over state-of-the-art meth-ods. Our results highlight the capacity of the proposed framework to distinguish fined-grained visual details between words and verify its advantage in generating medical reports.

Shibo Li, Michael Penwarden, Yiming Xu et al.

Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, apply different PINNs to solve the problem in each subdomain, and stitch the subdomains at the interface. Thereby, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of multi-domain PINNs is sensitive to the choice of the interface conditions. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine appropriate interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit (MAB) models. The first one applies to the entire training course, and online updates a Gaussian process (GP) reward that given the PDE parameters and interface conditions predicts the performance. We prove a sub-linear regret bound for both UCB and Thompson sampling, which in theory guarantees the effectiveness of our MAB. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP reward for each phase to enable different condition selections at the two stages to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.

Zheng Wang, Shibo Li, Shikai Fang et al.

Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly reduces the cost of data collection. Despite the variety of existing methods, they all build a model to map the input parameters outright to the solution output. Inspired by the recent breakthrough in generative models, we take an alternative view and consider the solution output as generated from random noises. We develop a diffusion-generative multi-fidelity (DGMF) learning method based on stochastic differential equations (SDE), where the generation is a continuous denoising process. We propose a conditional score model to control the solution generation by the input parameters and the fidelity. By conditioning on additional inputs (temporal or spacial variables), our model can efficiently learn and predict multi-dimensional solution arrays. Our method naturally unifies discrete and continuous fidelity modeling. The advantage of our method in several typical applications shows a promising new direction for multi-fidelity learning.

Shibo Li, Zhuoran Hou, Liang Chu et al.

The multi-source electromechanical coupling makes the energy management of fuel cell electric vehicles (FCEVs) relatively nonlinear and complex especially in the types of 4-wheel-drive (4WD) FCEVs. Accurate state observing for complicated nonlinear system is the basis for fantastic energy managing in FCEVs. Aiming at releasing the energy-saving potential of FCEVs, a novel learning-based robust model predictive control (LRMPC) strategy is proposed for a 4WD FCEV, contributing to suitable power distribution among multiple energy sources. The well-designed strategy based on machine learning (ML) translates the knowledge of the nonlinear system to the explicit controlling scheme with superior robust performance. To start with, ML methods with high regression accuracy and superior generalization ability are trained offline to establish the precise state observer for SOC. Then, explicit data tables for SOC generated by state observer are used for grabbing accurate state changing, whose input features include the vehicle status and the states of vehicle components. To be specific, the vehicle velocity estimation for providing future speed reference is constructed by deep forest. Next, the components including explicit data tables and vehicle velocity estimation are combined with model predictive control (MPC) to release the state-of-the-art energy-saving ability for the multi-freedom system in FCEVs, whose name is LRMPC. At last, the detailed assessment is performed in simulation test to validate the advancing performance of LRMPC. The corresponding results highlight the optimal control effect in energy-saving potential and strong real-time application ability of LRMPC.

Sipeng Chen, Junliang Liu, Hewei Tang et al.

The source distribution in conditional flow matching is a design parameter that can be calibrated to data, not a default isotropic prior. We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for parametric PDE solutions: the source is calibrated to the empirical low-to-high-fidelity residual scale with local Gaussian-blur correlation, and the velocity network is conditioned on the low-fidelity solution. Conditioning makes the residual refinement problem substantially easier than unconditional field generation, while residual-calibrated source noise improves the flow-matching training geometry. A multi-resolution cascade applies the same construction independently between adjacent fidelities. After level-wise flow-matching pretraining, we fine-tune the composed cascade end-to-end with a deterministic one-step rollout, which makes one velocity evaluation per cascade level the optimized operating point at inference. The result is a learned analog of multigrid refinement that reaches the finest grid in $L$ deterministic network evaluations per query. We validate MFFM on eight benchmarks: two super-resolution problems and six spatiotemporal forecasting tasks from PDEBench, The Well, and the FNO Navier--Stokes dataset.

Yiren Zheng, Shibo Li, Jiaming Liu et al.

Current multimodal approaches predominantly treat visual generation as an external process, relying on pixel rendering or code execution, thereby overlooking the native visual representation capabilities latent within Large Language Models (LLMs). In this work, we unlock this potential through ASCII art, a compact, efficient, and text-native visual format. We introduce SVE-ASCII, a unified framework designed to elicit and benchmark Symbolic Visual Expression directly within the pure text space. To address the scarcity of systematic resources, we construct ASCIIArt-7K, a high-quality dataset synthesized via a novel "Seed-and-Evolve" pipeline that augments human-curated anchors through in-context stylistic editing. We further implement a unified instruction-tuning strategy that jointly optimizes for both Generation (Text-to-ASCII) and Understanding (ASCII-to-Text). Crucially, our experiments reveal a critical phenomenon regarding task duality: while it is established that perception aids generation, we provide compelling evidence that generative training significantly enhances visual comprehension. This confirms a mutually reinforcing cycle in symbolic visual processing, a relationship previously hypothesized but rarely empirically demonstrated in the visual domain. We release our dataset, the ASCIIArt-Bench benchmark, and the SVE-ASCII model, establishing a robust baseline for native text-based visual intelligence.

Junqi Qu, Yan Zhang, Shangqian Gao et al.

Large Language Models (LLMs) show promise for equation discovery, yet their outputs are highly sensitive to prompt phrasing, a phenomenon we term instruction brittleness. Static prompts cannot adapt to the evolving state of a multi-step generation process, causing models to plateau at suboptimal solutions. To address this, we propose NeuroSymBO, which reframes prompt engineering as a sequential decision problem. Our method maintains a discrete library of reasoning strategies and uses Bayesian Optimization to select the optimal instruction at each step based on numerical feedback. Experiments on PDE discovery benchmarks show that adaptive instruction selection significantly outperforms fixed prompts, achieving higher recovery rates with more parsimonious solutions.

Zhan Cheng, Bolin Shen, Tianming Sha et al.

Graph Neural Networks (GNNs) have gained traction in Graph-based Machine Learning as a Service (GMLaaS) platforms, yet they remain vulnerable to graph-based model extraction attacks (MEAs), where adversaries reconstruct surrogate models by querying the victim model. Existing defense mechanisms, such as watermarking and fingerprinting, suffer from poor real-time performance, susceptibility to evasion, or reliance on post-attack verification, making them inadequate for handling the dynamic characteristics of graph-based MEA variants. To address these limitations, we propose ATOM, a novel real-time MEA detection framework tailored for GNNs. ATOM integrates sequential modeling and reinforcement learning to dynamically detect evolving attack patterns, while leveraging $k$-core embedding to capture the structural properties, enhancing detection precision. Furthermore, we provide theoretical analysis to characterize query behaviors and optimize detection strategies. Extensive experiments on multiple real-world datasets demonstrate that ATOM outperforms existing approaches in detection performance, maintaining stable across different time steps, thereby offering a more effective defense mechanism for GMLaaS environments.

Shibo Li, Hengliang Cheng, Weihua Li

The widespread application of Electronic Health Records (EHR) data in the medical field has led to early successes in disease risk prediction using deep learning methods. These methods typically require extensive data for training due to their large parameter sets. However, existing works do not exploit the full potential of EHR data. A significant challenge arises from the infrequent occurrence of many medical codes within EHR data, limiting their clinical applicability. Current research often lacks in critical areas: 1) incorporating disease domain knowledge; 2) heterogeneously learning disease representations with rich meanings; 3) capturing the temporal dynamics of disease progression. To overcome these limitations, we introduce a novel heterogeneous graph learning model designed to assimilate disease domain knowledge and elucidate the intricate relationships between drugs and diseases. This model innovatively incorporates temporal data into visit-level embeddings and leverages a time-aware transformer alongside an adaptive attention mechanism to produce patient representations. When evaluated on two healthcare datasets, our approach demonstrated notable enhancements in both prediction accuracy and interpretability over existing methodologies, signifying a substantial advancement towards personalized and proactive healthcare management.

Yifei Sun, Tao Wang, Junqi Qu et al.

Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved computational efficiency they often fail to effectively capture intricate correlations inherent in coupled physical processes To address this limitation we introduce COMPOL a novel coupled multiphysics operator learning framework COMPOL extends conventional operator architectures by incorporating sophisticated recurrent and attentionbased aggregation mechanisms effectively modeling interdependencies among interacting physical processes within latent feature spaces Our approach is architectureagnostic and seamlessly integrates into various neural operator frameworks that involve latent space transformations Extensive experiments on diverse benchmarksincluding biological reactiondiffusion systems patternforming chemical reactions multiphase geological flows and thermohydromechanical processes demonstrate that COMPOL consistently achieves superior predictive accuracy compared to stateoftheart methods.

Yan Zhang, Xuefeng Liu, Sipeng Chen et al.

Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications, including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design, demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.

Sipeng Chen, Yan Zhang, Shibo Li

Implicit Neural Representations (INRs) have emerged as a transformative paradigm in signal processing and computer vision, excelling in tasks from image reconstruction to 3D shape modeling. Yet their effectiveness is fundamentally limited by the absence of principled strategies for optimal configuration - spanning activation selection, initialization scales, layer-wise adaptation, and their intricate interdependencies. These choices dictate performance, stability, and generalization, but current practice relies on ad-hoc heuristics, brute-force grid searches, or task-specific tuning, often leading to inconsistent results across modalities. This work introduces OptiINR, the first unified framework that formulates INR configuration as a rigorous optimization problem. Leveraging Bayesian optimization, OptiINR efficiently explores the joint space of discrete activation families - such as sinusoidal (SIREN), wavelet-based (WIRE), and variable-periodic (FINER) - and their associated continuous initialization parameters. This systematic approach replaces fragmented manual tuning with a coherent, data-driven optimization process. By delivering globally optimal configurations, OptiINR establishes a principled foundation for INR design, consistently maximizing performance across diverse signal processing applications.

Shibo Li, Yao Zheng

This paper introduces the MPS (Model Prediction Set), a novel framework for online model selection for nonstationary time series. Classical model selection methods, such as information criteria and cross-validation, rely heavily on the stationarity assumption and often fail in dynamic environments which undergo gradual or abrupt changes over time. Yet real-world data are rarely stationary, and model selection under nonstationarity remains a largely open problem. To tackle this challenge, we combine conformal inference with model confidence sets to develop a procedure that adaptively selects models best suited to the evolving dynamics at any given time. Concretely, the MPS updates in real time a confidence set of candidate models that covers the best model for the next time period with a specified long-run probability, while adapting to nonstationarity of unknown forms. Through simulations and real-world data analysis, we demonstrate that MPS reliably and efficiently identifies optimal models under nonstationarity, an essential capability lacking in offline methods. Moreover, MPS frequently produces high-quality sets with small cardinality, whose evolution offers deeper insights into changing dynamics. As a generic framework, MPS accommodates any data-generating process, data structure, model class, training method, and evaluation metric, making it broadly applicable across diverse problem settings.

Damith Chamalke Senadeera, Xiaoyun Yang, Shibo Li et al.

The rapid proliferation of surveillance cameras has increased the demand for automated violence detection. While CNNs and Transformers have shown success in extracting spatio-temporal features, they struggle with long-term dependencies and computational efficiency. We propose Dual Branch VideoMamba with Gated Class Token Fusion (GCTF), an efficient architecture combining a dual-branch design and a state-space model (SSM) backbone where one branch captures spatial features, while the other focuses on temporal dynamics. The model performs continuous fusion via a gating mechanism between the branches to enhance the model's ability to detect violent activities even in challenging surveillance scenarios. We also present a new benchmark by merging RWF-2000, RLVS, SURV and VioPeru datasets in video violence detection, ensuring strict separation between training and testing sets. Experimental results demonstrate that our model achieves state-of-the-art performance on this benchmark and also on DVD dataset which is another novel dataset on video violence detection, offering an optimal balance between accuracy and computational efficiency, demonstrating the promise of SSMs for scalable, near real-time surveillance violence detection.

Shibo Li, Zheng Wang, Akil Narayan et al.

Model Agnostic Meta Learning (MAML) is widely used to find a good initialization for a family of tasks. Despite its success, a critical challenge in MAML is to calculate the gradient w.r.t. the initialization of a long training trajectory for the sampled tasks, because the computation graph can rapidly explode and the computational cost is very expensive. To address this problem, we propose Adjoint MAML (A-MAML). We view gradient descent in the inner optimization as the evolution of an Ordinary Differential Equation (ODE). To efficiently compute the gradient of the validation loss w.r.t. the initialization, we use the adjoint method to construct a companion, backward ODE. To obtain the gradient w.r.t. the initialization, we only need to run the standard ODE solver twice -- one is forward in time that evolves a long trajectory of gradient flow for the sampled task; the other is backward and solves the adjoint ODE. We need not create or expand any intermediate computational graphs, adopt aggressive approximations, or impose proximal regularizers in the training loss. Our approach is cheap, accurate, and adaptable to different trajectory lengths. We demonstrate the advantage of our approach in both synthetic and real-world meta-learning tasks.

Shibo Li, Robert M. Kirby, Shandian Zhe

Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions. To enable a flexible trade-off between the cost and accuracy, many applications allow the function to be evaluated at different fidelities. In order to reduce the optimization cost while maximizing the benefit-cost ratio, in this paper, we propose Batch Multi-fidelity Bayesian Optimization with Deep Auto-Regressive Networks (BMBO-DARN). We use a set of Bayesian neural networks to construct a fully auto-regressive model, which is expressive enough to capture strong yet complex relationships across all the fidelities, so as to improve the surrogate learning and optimization performance. Furthermore, to enhance the quality and diversity of queries, we develop a simple yet efficient batch querying method, without any combinatorial search over the fidelities. We propose a batch acquisition function based on Max-value Entropy Search (MES) principle, which penalizes highly correlated queries and encourages diversity. We use posterior samples and moment matching to fulfill efficient computation of the acquisition function and conduct alternating optimization over every fidelity-input pair, which guarantees an improvement at each step. We demonstrate the advantage of our approach on four real-world hyperparameter optimization applications.

Shibo Li, Robert M. Kirby, Shandian Zhe

Many applications, such as in physical simulation and engineering design, demand we estimate functions with high-dimensional outputs. The training examples can be collected with different fidelities to allow a cost/accuracy trade-off. In this paper, we consider the active learning task that identifies both the fidelity and input to query new training examples so as to achieve the best benefit-cost ratio. To this end, we propose DMFAL, a Deep Multi-Fidelity Active Learning approach. We first develop a deep neural network-based multi-fidelity model for learning with high-dimensional outputs, which can flexibly, efficiently capture all kinds of complex relationships across the outputs and fidelities to improve prediction. We then propose a mutual information-based acquisition function that extends the predictive entropy principle. To overcome the computational challenges caused by large output dimensions, we use multi-variate Delta's method and moment-matching to estimate the output posterior, and Weinstein-Aronszajn identity to calculate and optimize the acquisition function. The computation is tractable, reliable and efficient. We show the advantage of our method in several applications of computational physics and engineering design.

Tao Yang, Shikai Fang, Shibo Li et al.

Leveraging biased click data for optimizing learning to rank systems has been a popular approach in information retrieval. Because click data is often noisy and biased, a variety of methods have been proposed to construct unbiased learning to rank (ULTR) algorithms for the learning of unbiased ranking models. Among them, automatic unbiased learning to rank (AutoULTR) algorithms that jointly learn user bias models (i.e., propensity models) with unbiased rankers have received a lot of attention due to their superior performance and low deployment cost in practice. Despite their differences in theories and algorithm design, existing studies on ULTR usually use uni-variate ranking functions to score each document or result independently. On the other hand, recent advances in context-aware learning-to-rank models have shown that multivariate scoring functions, which read multiple documents together and predict their ranking scores jointly, are more powerful than uni-variate ranking functions in ranking tasks with human-annotated relevance labels. Whether such superior performance would hold in ULTR with noisy data, however, is mostly unknown. In this paper, we investigate existing multivariate scoring functions and AutoULTR algorithms in theory and prove that permutation invariance is a crucial factor that determines whether a context-aware learning-to-rank model could be applied to existing AutoULTR framework. Our experiments with synthetic clicks on two large-scale benchmark datasets show that AutoULTR models with permutation-invariant multivariate scoring functions significantly outperform those with uni-variate scoring functions and permutation-variant multivariate scoring functions.

Shibo Li, Wei Xing, Mike Kirby et al.

Bayesian optimization (BO) is a popular framework to optimize black-box functions. In many applications, the objective function can be evaluated at multiple fidelities to enable a trade-off between the cost and accuracy. To reduce the optimization cost, many multi-fidelity BO methods have been proposed. Despite their success, these methods either ignore or over-simplify the strong, complex correlations across the fidelities, and hence can be inefficient in estimating the objective function. To address this issue, we propose Deep Neural Network Multi-Fidelity Bayesian Optimization (DNN-MFBO) that can flexibly capture all kinds of complicated relationships between the fidelities to improve the objective function estimation and hence the optimization performance. We use sequential, fidelity-wise Gauss-Hermite quadrature and moment-matching to fulfill a mutual information-based acquisition function, which is computationally tractable and efficient. We show the advantages of our method in both synthetic benchmark datasets and real-world applications in engineering design.

Shibo Li, Wei Xing, Mike Kirby et al.

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such structures) over all the outputs and latent functions for posterior approximation, which, however, can miss the strong posterior dependencies among the latent variables and hurt the inference quality. In addition, the updates of the variational parameters are inefficient and can be prohibitively expensive for a large number of outputs. To overcome these limitations, we propose a scalable variational inference algorithm for GPRN, which not only captures the abundant posterior dependencies but also is much more efficient for massive outputs. We tensorize the output space and introduce tensor/matrix-normal variational posteriors to capture the posterior correlations and to reduce the parameters. We jointly optimize all the parameters and exploit the inherent Kronecker product structure in the variational model evidence lower bound to accelerate the computation. We demonstrate the advantages of our method in several real-world applications.