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We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, structure-preserving properties, predictive capabilities, and cost reductions of the proposed method.

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling SDEs by utilizing a score-based diffusion model to approximate their stochastic flow map. Unlike the existing methods, this technique is based on an analytically derived closed-form exact score function, which can be efficiently estimated by Monte Carlo method using the trajectory data, and eliminates the need for neural network training to learn the score function. By generating labeled data through solving the corresponding reverse ordinary differential equation, the approach enables supervised learning of the flow map. Extensive numerical experiments across various SDE types, including linear, nonlinear, and multi-dimensional systems, demonstrate the versatility and effectiveness of the method. The learned models exhibit significant improvements in predicting both short-term and long-term behaviors of unknown stochastic systems, often surpassing baseline methods like GANs in estimating drift and diffusion coefficients.

We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. These parameter distributions are developed in the context of non-parametric regression models based on shallow neural networks, and compare favorably to well-established uniform random feature models based on conventional weight initialization. We address the cases of Heaviside and ReLU activation functions, and their smooth approximations (sigmoid and softplus), and use recent results on the harmonic analysis and sparse representation of neural networks resulting from fully trained optimal networks. Extending analytic results that give exact representation, we obtain densities that concentrate in regions of the parameter space corresponding to neurons that are well suited to model the local derivatives of the unknown function. Based on these results, we suggest simplifications of these exact densities based on approximate derivative data in the input points that allow for very efficient sampling and lead to performance of random feature models close to optimal networks in several scenarios.

Click-through rate (CTR) prediction is one of the fundamental tasks in the industry, especially in e-commerce, social media, and streaming media. It directly impacts website revenues, user satisfaction, and user retention. However, real-world production platforms often encompass various domains to cater for diverse customer needs. Traditional CTR prediction models struggle in multi-domain recommendation scenarios, facing challenges of data sparsity and disparate data distributions across domains. Existing multi-domain recommendation approaches introduce specific-domain modules for each domain, which partially address these issues but often significantly increase model parameters and lead to insufficient training. In this paper, we propose a Multi-domain Low-Rank Adaptive network (MLoRA) for CTR prediction, where we introduce a specialized LoRA module for each domain. This approach enhances the model's performance in multi-domain CTR prediction tasks and is able to be applied to various deep-learning models. We evaluate the proposed method on several multi-domain datasets. Experimental results demonstrate our MLoRA approach achieves a significant improvement compared with state-of-the-art baselines. Furthermore, we deploy it in the production environment of the Alibaba.COM. The online A/B testing results indicate the superiority and flexibility in real-world production environments. The code of our MLoRA is publicly available., Comment: 11 pages. Accepted by RecSys'2024, full paper

To cater to users' desire for an immersive browsing experience, numerous e-commerce platforms provide various recommendation scenarios, with a focus on Trigger-Induced Recommendation (TIR) tasks. However, the majority of current TIR methods heavily rely on the trigger item to understand user intent, lacking a higher-level exploration and exploitation of user intent (e.g., popular items and complementary items), which may result in an overly convergent understanding of users' short-term intent and can be detrimental to users' long-term purchasing experiences. Moreover, users' short-term intent shows uncertainty and is affected by various factors such as browsing context and historical behaviors, which poses challenges to user intent modeling. To address these challenges, we propose a novel model called Deep Uncertainty Intent Network (DUIN), comprising three essential modules: i) Explicit Intent Exploit Module extracting explicit user intent using the contrastive learning paradigm; ii) Latent Intent Explore Module exploring latent user intent by leveraging the multi-view relationships between items; iii) Intent Uncertainty Measurement Module offering a distributional estimation and capturing the uncertainty associated with user intent. Experiments on three real-world datasets demonstrate the superior performance of DUIN compared to existing baselines. Notably, DUIN has been deployed across all TIR scenarios in our e-commerce platform, with online A/B testing results conclusively validating its superiority., Comment: Accepted at CIKM 2024

The weather and climate domains are undergoing a significant transformation thanks to advances in AI-based foundation models such as FourCastNet, GraphCast, ClimaX and Pangu-Weather. While these models show considerable potential, they are not ready yet for operational use in weather forecasting or climate prediction. This is due to the lack of a data assimilation method as part of their workflow to enable the assimilation of incoming Earth system observations in real time. This limitation affects their effectiveness in predicting complex atmospheric phenomena such as tropical cyclones and atmospheric rivers. To overcome these obstacles, we introduce a generic real-time data assimilation framework and demonstrate its end-to-end performance on the Frontier supercomputer. This framework comprises two primary modules: an ensemble score filter (EnSF), which significantly outperforms the state-of-the-art data assimilation method, namely, the Local Ensemble Transform Kalman Filter (LETKF); and a vision transformer-based surrogate capable of real-time adaptation through the integration of observational data. The ViT surrogate can represent either physics-based models or AI-based foundation models. We demonstrate both the strong and weak scaling of our framework up to 1024 GPUs on the Exascale supercomputer, Frontier. Our results not only illustrate the framework's exceptional scalability on high-performance computing systems, but also demonstrate the importance of supercomputers in real-time data assimilation for weather and climate predictions. Even though the proposed framework is tested only on a benchmark surface quasi-geostrophic (SQG) turbulence system, it has the potential to be combined with existing AI-based foundation models, making it suitable for future operational implementations.

The modeling of users' behaviors is crucial in modern recommendation systems. A lot of research focuses on modeling users' lifelong sequences, which can be extremely long and sometimes exceed thousands of items. These models use the target item to search for the most relevant items from the historical sequence. However, training lifelong sequences in click through rate (CTR) prediction or personalized search ranking (PSR) is extremely difficult due to the insufficient learning problem of ID embedding, especially when the IDs in the lifelong sequence features do not exist in the samples of training dataset. Additionally, existing target attention mechanisms struggle to learn the multi-modal representations of items in the sequence well. The distribution of multi-modal embedding (text, image and attributes) output of user's interacted items are not properly aligned and there exist divergence across modalities. We also observe that users' search query sequences and item browsing sequences can fully depict users' intents and benefit from each other. To address these challenges, we propose a unified lifelong multi-modal sequence model called SEMINAR-Search Enhanced Multi-Modal Interest Network and Approximate Retrieval. Specifically, a network called Pretraining Search Unit (PSU) learns the lifelong sequences of multi-modal query-item pairs in a pretraining-finetuning manner with multiple objectives: multi-modal alignment, next query-item pair prediction, query-item relevance prediction, etc. After pretraining, the downstream model restores the pretrained embedding as initialization and finetunes the network. To accelerate the online retrieval speed of multi-modal embedding, we propose a multi-modal codebook-based product quantization strategy to approximate the exact attention calculati, Comment: 9 pages,code released

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) operates in the event mode. Time-of-flight (TOF) information about each detected neutron is collected separately and saved as a descriptive entry in a database enabling unprecedented accuracy of the collected experimental data. Nevertheless, the common data processing pipeline still involves the binning of data to perform analysis and feature extraction. For weak reflections, improper binning leads to sparse histograms with low signal-to-noise ratios, rendering them uninformative. In this study, we propose the Bayesian approach for the identification of Bragg peaks in TOF diffraction data. The method is capable of adaptively handling the varying sampling rates found in different regions of the reciprocal space. Unlike histogram fitting methods, our approach focuses on estimating the true neutron flux function. We accomplish this by employing a profile fitting algorithm based on the event-level likelihood, along with a multiresolution histogram-level prior. By using this approach, we ensure that there is no loss of information due to data reduction in strong reflections and that the search space is appropriately restricted for weak reflections. To demonstrate the effectiveness of our proposed model, we apply it to real experimental data collected at the TOPAZ single crystal diffractometer at SNS.

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed \textit{Ensemble Score Filter (EnSF)} is completely training-free and can efficiently generate a set of analysis ensemble members. In this study, we apply the EnSF to a surface quasi-geostrophic model and compare its performance against the popular Local Ensemble Transform Kalman Filter (LETKF), which makes Gaussian assumptions on the posterior distribution. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that EnSF achieves competitive performance relative to LETKF in the case of linear observations, but leads to significant advantages when the state is nonlinearly observed and the numerical model is subject to unexpected shocks. A spectral decomposition of the analysis results shows that the largest improvements over LETKF occur at large scales (small wavenumbers) where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity is very encouraging, and motivates further developments of the algorithm for more realistic problems.

We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling approaches usually focus on approximating the deterministic component of physical model. However, this strategy necessitates knowledge of noise and resorts to auxiliary sampling methods for quantifying inverse uncertainty propagation. In this work, we develop the conditional pseudo-reversible normalizing flow model to directly learn and efficiently generate samples from the conditional probability density functions. The training process utilizes dataset consisting of input-output pairs without requiring prior knowledge about the noise and the function. Our model, once trained, can generate samples from any conditional probability density functions whose high probability regions are covered by the training set. Moreover, the pseudo-reversibility feature allows for the use of fully-connected neural network architectures, which simplifies the implementation and enables theoretical analysis. We provide a rigorous convergence analysis of the conditional pseudo-reversible normalizing flow model, showing its ability to converge to the target conditional probability density function using the Kullback-Leibler divergence. To demonstrate the effectiveness of our method, we apply it to several benchmark tests and a real-world geologic carbon storage problem.

This paper presents a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world applications. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. Numerical experiments validate the efficacy and accuracy of our algorithm, showcasing its high efficiency in solving feedback optimal control problems with partial observation., Comment: arXiv admin note: substantial text overlap with arXiv:2201.10600

In Federated Learning (FL), the data in each client is typically assumed fixed or static. However, data often comes in an incremental manner in real-world applications, where the data domain may increase dynamically. In this work, we study catastrophic forgetting with data heterogeneity in Federated Incremental Learning (FIL) scenarios where edge clients may lack enough storage space to retain full data. We propose to employ a simple, generic framework for FIL named Re-Fed, which can coordinate each client to cache important samples for replay. More specifically, when a new task arrives, each client first caches selected previous samples based on their global and local importance. Then, the client trains the local model with both the cached samples and the samples from the new task. Theoretically, we analyze the ability of Re-Fed to discover important samples for replay thus alleviating the catastrophic forgetting problem. Moreover, we empirically show that Re-Fed achieves competitive performance compared to state-of-the-art methods.

Text matching systems have become a fundamental service in most searching platforms. For instance, they are responsible for matching user queries to relevant candidate items, or rewriting the user-input query to a pre-selected high-performing one for a better search experience. In practice, both the queries and items often contain multiple attributes, such as the category of the item and the location mentioned in the query, which represent condensed key information that is helpful for matching. However, most of the existing works downplay the effectiveness of attributes by integrating them into text representations as supplementary information. Hence, in this work, we focus on exploring the relationship between the attributes from two sides. Since attributes from two ends are often not aligned in terms of number and type, we propose to exploit the benefit of attributes by multiple-intent modeling. The intents extracted from attributes summarize the diverse needs of queries and provide rich content of items, which are more refined and abstract, and can be aligned for paired inputs. Concretely, we propose a multi-intent attribute-aware matching model (MIM), which consists of three main components: attribute-aware encoder, multi-intent modeling, and intent-aware matching. In the attribute-aware encoder, the text and attributes are weighted and processed through a scaled attention mechanism with regard to the attributes' importance. Afterward, the multi-intent modeling extracts intents from two ends and aligns them. Herein, we come up with a distribution loss to ensure the learned intents are diverse but concentrated, and a kullback-leibler divergence loss that aligns the learned intents. Finally, in the intent-aware matching, the intents are evaluated by a self-supervised masking task, and then incorporated to output the final matching result., Comment: 9 pages

The application of mixture-of-experts (MoE) is gaining popularity due to its ability to improve model's performance. In an MoE structure, the gate layer plays a significant role in distinguishing and routing input features to different experts. This enables each expert to specialize in processing their corresponding sub-tasks. However, the gate's routing mechanism also gives rise to narrow vision: the individual MoE's expert fails to use more samples in learning the allocated sub-task, which in turn limits the MoE to further improve its generalization ability. To effectively address this, we propose a method called Mixture-of-Distilled-Expert (MoDE), which applies moderate mutual distillation among experts to enable each expert to pick up more features learned by other experts and gain more accurate perceptions on their original allocated sub-tasks. We conduct plenty experiments including tabular, NLP and CV datasets, which shows MoDE's effectiveness, universality and robustness. Furthermore, we develop a parallel study through innovatively constructing "expert probing", to experimentally prove why MoDE works: moderate distilling knowledge can improve each individual expert's test performances on their assigned tasks, leading to MoE's overall performance improvement., Comment: Accepted by AAAI-24

The transient signal available for hyperpolarized (HP) 13C imaging limits the image spatial resolution. This paper demonstrates a method of increasing spatial resolution by post-processing the HP 13C metabolic map using a corresponding anatomic image as a high-resolution example. The proposed method is tested with a Shepp-Logan digital phantom and for an MR image of a tumor in a mouse brain acquired at 3 Tesla using 13C Chemical Shift Imaging. The results are compared to the results of standard image rescaling methods using peak-signal-to-noise ratio and structural similarity index (SSIM) image quality metrics. In vivo, the method reduced blur resulting in a better match between the metabolite biodistribution and the anatomy. It is concluded that the image quality of hyperpolarized 13C MRI in vivo images can be improved with single image superresolution using the anatomic image as an example.

The impressive expressive power of deep neural networks (DNNs) underlies their widespread applicability. However, while the theoretical capacity of deep architectures is high, the practical expressive power achieved through successful training often falls short. Building on the insights gained from Neural ODEs, which explore the depth of DNNs as a continuous variable, in this work, we generalize the traditional fully connected DNN through the concept of continuous width. In the Generalized Deep Neural Network (GDNN), the traditional notion of neurons in each layer is replaced by a continuous state function. Using the finite rank parameterization of the weight integral kernel, we establish that GDNN can be obtained by employing the Integral Activation Transform (IAT) as activation layers within the traditional DNN framework. The IAT maps the input vector to a function space using some basis functions, followed by nonlinear activation in the function space, and then extracts information through the integration with another collection of basis functions. A specific variant, IAT-ReLU, featuring the ReLU nonlinearity, serves as a smooth generalization of the scalar ReLU activation. Notably, IAT-ReLU exhibits a continuous activation pattern when continuous basis functions are employed, making it smooth and enhancing the trainability of the DNN. Our numerical experiments demonstrate that IAT-ReLU outperforms regular ReLU in terms of trainability and better smoothness., Comment: 26 pages, 6 figures

This paper tackles the intricate task of jointly estimating state and parameters in data assimilation for stochastic dynamical systems that are affected by noise and observed only partially. While the concept of ``optimal filtering'' serves as the customary approach to estimate the state of the target dynamical system, traditional methods such as Kalman filters and particle filters encounter significant challenges when dealing with high-dimensional and nonlinear problems. When we also consider the scenario where the model parameters are unknown, the problem transforms into a joint state-parameter estimation endeavor. Presently, the leading-edge technique known as the Augmented Ensemble Kalman Filter (AugEnKF) addresses this issue by treating unknown parameters as additional state variables and employing the Ensemble Kalman Filter to estimate the augmented state-parameter vector. Despite its considerable progress, AugEnKF does exhibit certain limitations in terms of accuracy and stability. To address these challenges, we introduce an innovative approach, referred to as the United Filter. This method amalgamates a remarkably stable and efficient ensemble score filter (EnSF) for state estimation with a precise direct filter dedicated to online parameter estimation. Utilizing the EnSF's generative capabilities grounded in diffusion models, the United Filter iteratively fine-tunes both state and parameter estimates within a single temporal data assimilation step. Thanks to the robustness of the EnSF, the proposed method offers a promising solution for enhancing our comprehension and modeling of dynamical systems, as demonstrated by results from numerical experiments.

Given the enormous number of users and items, industrial cascade recommendation systems (RS) are continuously expanded in size and complexity to deliver relevant items, such as news, services, and commodities, to the appropriate users. In a real-world scenario with hundreds of thousands requests per second, significant computation is required to infer personalized results for each request, resulting in a massive energy consumption and carbon emission that raises concern. This paper proposes GreenFlow, a practical computation allocation framework for RS, that considers both accuracy and carbon emission during inference. For each stage (e.g., recall, pre-ranking, ranking, etc.) of a cascade RS, when a user triggers a request, we define two actions that determine the computation: (1) the trained instances of models with different computational complexity; and (2) the number of items to be inferred in the stage. We refer to the combinations of actions in all stages as action chains. A reward score is estimated for each action chain, followed by dynamic primal-dual optimization considering both the reward and computation budget. Extensive experiments verify the effectiveness of the framework, reducing computation consumption by 41% in an industrial mobile application while maintaining commercial revenue. Moreover, the proposed framework saves approximately 5000kWh of electricity and reduces 3 tons of carbon emissions per day.

Uplift modeling is widely used in performance marketing to estimate effects of promotion campaigns (e.g., increase of customer retention rate). Since it is impossible to observe outcomes of a recipient in treatment (e.g., receiving a certain promotion) and control (e.g., without promotion) groups simultaneously (i.e., counter-factual), uplift models are mainly trained on instances of treatment and control groups separately to form two models respectively, and uplifts are predicted by the difference of predictions from these two models (i.e., two-model method). When responses are noisy and the treatment effect is fractional, induced individual uplift predictions will be inaccurate, resulting in targeting undesirable customers. Though it is impossible to obtain the ideal ground-truth individual uplifts, known as Individual Treatment Effects (ITEs), alternatively, an average uplift of a group of users, called Average Treatment Effect (ATE), can be observed from experimental deliveries. Upon this, similar to Multiple Instance Learning (MIL) in which each training sample is a bag of instances, our framework sums up individual user uplift predictions for each bag of users as its bag-wise ATE prediction, and regularizes it to its ATE label, thus learning more accurate individual uplifts. Additionally, to amplify the fractional treatment effect, bags are composed of instances with adjacent individual uplift predictions, instead of random instances. Experiments conducted on two datasets show the effectiveness and universality of the proposed framework., Comment: short paper of CIKM22(full version)

Nowadays, the rapid development of mobile economy has promoted the flourishing of online marketing campaigns, whose success greatly hinges on the efficient matching between user preferences and desired marketing campaigns where a well-established Marketing-oriented Knowledge Graph (dubbed as MoKG) could serve as the critical "bridge" for preference propagation. In this paper, we seek to carefully prompt a Large Language Model (LLM) with domain-level knowledge as a better marketing-oriented knowledge miner for marketing-oriented knowledge graph construction, which is however non-trivial, suffering from several inevitable issues in real-world marketing scenarios, i.e., uncontrollable relation generation of LLMs,insufficient prompting ability of a single prompt, the unaffordable deployment cost of LLMs. To this end, we propose PAIR, a novel Progressive prompting Augmented mIning fRamework for harvesting marketing-oriented knowledge graph with LLMs. In particular, we reduce the pure relation generation to an LLM based adaptive relation filtering process through the knowledge-empowered prompting technique. Next, we steer LLMs for entity expansion with progressive prompting augmentation,followed by a reliable aggregation with comprehensive consideration of both self-consistency and semantic relatedness. In terms of online serving, we specialize in a small and white-box PAIR (i.e.,LightPAIR),which is fine-tuned with a high-quality corpus provided by a strong teacher-LLM. Extensive experiments and practical applications in audience targeting verify the effectiveness of the proposed (Light)PAIR.

Aligning language models to human expectations, e.g., being helpful and harmless, has become a pressing challenge for large language models. A typical alignment procedure consists of supervised fine-tuning and preference learning. Most preference learning methods, such as RLHF and DPO, depend on pairwise preference data, which inadequately address scenarios where human feedback is point-wise, leading to potential information loss and suboptimal performance. Addressing this gap, we introduce Point-wise Direct Preference Optimization, a novel preference learning method designed to harness point-wise feedback effectively. Our work also uncovers a novel connection between supervised fine-tuning and point-wise preference learning, culminating in Unified Language Model Alignment, a single-step method that unifies the alignment with human demonstrations and point-wise preferences. Extensive experiments on point-wise preference datasets with binary or continuous labels validate the effectiveness of our methods. Our code and a new dataset with high-quality demonstration samples on harmlessness are released.

Dense retrieval methods have been mostly focused on unstructured text and less attention has been drawn to structured data with various aspects, e.g., products with aspects such as category and brand. Recent work has proposed two approaches to incorporate the aspect information into item representations for effective retrieval by predicting the values associated with the item aspects. Despite their efficacy, they treat the values as isolated classes (e.g., "Smart Homes", "Home, Garden & Tools", and "Beauty & Health") and ignore their fine-grained semantic relation. Furthermore, they either enforce the learning of aspects into the CLS token, which could confuse it from its designated use for representing the entire content semantics, or learn extra aspect embeddings only with the value prediction objective, which could be insufficient especially when there are no annotated values for an item aspect. Aware of these limitations, we propose a MUlti-granulaRity-aware Aspect Learning model (MURAL) for multi-aspect dense retrieval. It leverages aspect information across various granularities to capture both coarse and fine-grained semantic relations between values. Moreover, MURAL incorporates separate aspect embeddings as input to transformer encoders so that the masked language model objective can assist implicit aspect learning even without aspect-value annotations. Extensive experiments on two real-world datasets of products and mini-programs show that MURAL outperforms state-of-the-art baselines significantly., Comment: Accepted by WSDM2024, update

To help merchants/customers to provide/access a variety of services through miniapps, online service platforms have occupied a critical position in the effective content delivery, in which how to recommend items in the new domain launched by the service provider for customers has become more urgent. However, the non-negligible gap between the source and diversified target domains poses a considerable challenge to cross-domain recommendation systems, which often leads to performance bottlenecks in industrial settings. While entity graphs have the potential to serve as a bridge between domains, rudimentary utilization still fail to distill useful knowledge and even induce the negative transfer issue. To this end, we propose PEACE, a Prototype lEarning Augmented transferable framework for Cross-domain rEcommendation. For domain gap bridging, PEACE is built upon a multi-interest and entity-oriented pre-training architecture which could not only benefit the learning of generalized knowledge in a multi-granularity manner, but also help leverage more structural information in the entity graph. Then, we bring the prototype learning into the pre-training over source domains, so that representations of users and items are greatly improved by the contrastive prototype learning module and the prototype enhanced attention mechanism for adaptive knowledge utilization. To ease the pressure of online serving, PEACE is carefully deployed in a lightweight manner, and significant performance improvements are observed in both online and offline environments., Comment: Accepted by WSDM 2024

End users face a choice between privacy and efficiency in current Large Language Model (LLM) service paradigms. In cloud-based paradigms, users are forced to compromise data locality for generation quality and processing speed. Conversely, edge device paradigms maintain data locality but fail to deliver satisfactory performance. In this work, we propose a novel LLM service paradigm that distributes privacy-sensitive computation on edge devices and shared computation in the cloud. Only activations are transmitted between the central cloud and edge devices to ensure data locality. Our core innovation, PrivateLoRA, addresses the challenging communication overhead by exploiting the low rank of residual activations, achieving over 95% communication reduction. Consequently, PrivateLoRA effectively maintains data locality and is extremely resource efficient. Under standard 5G networks, PrivateLoRA achieves throughput over 300% of device-only solutions for 7B models and over 80% of an A100 GPU for 33B models. PrivateLoRA also provides tuning performance comparable to LoRA for advanced personalization. Our approach democratizes access to state-of-the-art generative AI for edge devices, paving the way for more tailored LLM experiences for the general public. To our knowledge, our proposed framework is the first efficient and privacy-preserving LLM solution in the literature.

LoRA achieves remarkable resource efficiency and comparable performance when adapting LLMs for specific tasks. Since ChatGPT demonstrated superior performance on various tasks, there has been a growing desire to adapt one model for all tasks. However, the explicit low-rank of LoRA limits the adaptation performance in complex multi-task scenarios. LoRA is dominated by a small number of top singular vectors while fine-tuning decomposes into a set of less important unitary transforms. In this paper, we propose MultiLoRA for better multi-task adaptation by reducing the dominance of top singular vectors observed in LoRA. MultiLoRA scales LoRA modules horizontally and change parameter initialization of adaptation matrices to reduce parameter dependency, thus yields more balanced unitary subspaces. We unprecedentedly construct specialized training data by mixing datasets of instruction follow, natural language understanding, world knowledge, to cover semantically and syntactically different samples. With only 2.5% of additional parameters, MultiLoRA outperforms single LoRA counterparts and fine-tuning on multiple benchmarks and model scales. Further investigation into weight update matrices of MultiLoRA exhibits reduced dependency on top singular vectors and more democratic unitary transform contributions.

Memory-augmented Large Language Models (LLMs) have demonstrated remarkable performance in long-term human-machine interactions, which basically relies on iterative recalling and reasoning of history to generate high-quality responses. However, such repeated recall-reason steps easily produce biased thoughts, \textit{i.e.}, inconsistent reasoning results when recalling the same history for different questions. On the contrary, humans can keep thoughts in the memory and recall them without repeated reasoning. Motivated by this human capability, we propose a novel memory mechanism called TiM (Think-in-Memory) that enables LLMs to maintain an evolved memory for storing historical thoughts along the conversation stream. The TiM framework consists of two crucial stages: (1) before generating a response, a LLM agent recalls relevant thoughts from memory, and (2) after generating a response, the LLM agent post-thinks and incorporates both historical and new thoughts to update the memory. Thus, TiM can eliminate the issue of repeated reasoning by saving the post-thinking thoughts as the history. Besides, we formulate the basic principles to organize the thoughts in memory based on the well-established operations, (\textit{i.e.}, insert, forget, and merge operations), allowing for dynamic updates and evolution of the thoughts. Furthermore, we introduce Locality-Sensitive Hashing into TiM to achieve efficient retrieval for the long-term conversations. We conduct qualitative and quantitative experiments on real-world and simulated dialogues covering a wide range of topics, demonstrating that equipping existing LLMs with TiM significantly enhances their performance in generating responses for long-term interactions.

Artificial Intelligence (AI) has achieved significant advancements in technology and research with the development over several decades, and is widely used in many areas including computing vision, natural language processing, time-series analysis, speech synthesis, etc. During the age of deep learning, especially with the arise of Large Language Models, a large majority of researchers' attention is paid on pursuing new state-of-the-art (SOTA) results, resulting in ever increasing of model size and computational complexity. The needs for high computing power brings higher carbon emission and undermines research fairness by preventing small or medium-sized research institutions and companies with limited funding in participating in research. To tackle the challenges of computing resources and environmental impact of AI, Green Computing has become a hot research topic. In this survey, we give a systematic overview of the technologies used in Green Computing. We propose the framework of Green Computing and devide it into four key components: (1) Measures of Greenness, (2) Energy-Efficient AI, (3) Energy-Efficient Computing Systems and (4) AI Use Cases for Sustainability. For each components, we discuss the research progress made and the commonly used techniques to optimize the AI efficiency. We conclude that this new research direction has the potential to address the conflicts between resource constraints and AI development. We encourage more researchers to put attention on this direction and make AI more environmental friendly., Comment: 113 pages, 18 figures

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require to use reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the UCI repository.

In modern commercial search engines and recommendation systems, data from multiple domains is available to jointly train the multi-domain model. Traditional methods train multi-domain models in the multi-task setting, with shared parameters to learn the similarity of multiple tasks, and task-specific parameters to learn the divergence of features, labels, and sample distributions of individual tasks. With the development of large language models, LLM can extract global domain-invariant text features that serve both search and recommendation tasks. We propose a novel framework called S\&R Multi-Domain Foundation, which uses LLM to extract domain invariant features, and Aspect Gating Fusion to merge the ID feature, domain invariant text features and task-specific heterogeneous sparse features to obtain the representations of query and item. Additionally, samples from multiple search and recommendation scenarios are trained jointly with Domain Adaptive Multi-Task module to obtain the multi-domain foundation model. We apply the S\&R Multi-Domain foundation model to cold start scenarios in the pretrain-finetune manner, which achieves better performance than other SOTA transfer learning methods. The S\&R Multi-Domain Foundation model has been successfully deployed in Alipay Mobile Application's online services, such as content query recommendation and service card recommendation, etc., Comment: CIKM 2023,6 pages

We study the budget allocation problem in online marketing campaigns that utilize previously collected offline data. We first discuss the long-term effect of optimizing marketing budget allocation decisions in the offline setting. To overcome the challenge, we propose a novel game-theoretic offline value-based reinforcement learning method using mixed policies. The proposed method reduces the need to store infinitely many policies in previous methods to only constantly many policies, which achieves nearly optimal policy efficiency, making it practical and favorable for industrial usage. We further show that this method is guaranteed to converge to the optimal policy, which cannot be achieved by previous value-based reinforcement learning methods for marketing budget allocation. Our experiments on a large-scale marketing campaign with tens-of-millions users and more than one billion budget verify the theoretical results and show that the proposed method outperforms various baseline methods. The proposed method has been successfully deployed to serve all the traffic of this marketing campaign., Comment: WSDM 23, Best Paper Candidate

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses a mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves a tremendous amount of time spent on training neural networks. High-dimensional Lorenz-96 systems are used to demonstrate the performance of our method. EnSF provides surprising performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter method, in reliably and efficiently tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimensions) with highly nonlinear observation processes., Comment: arXiv admin note: text overlap with arXiv:2306.09282

Click-through rate (CTR) prediction is a crucial issue in recommendation systems. There has been an emergence of various public CTR datasets. However, existing datasets primarily suffer from the following limitations. Firstly, users generally click different types of items from multiple scenarios, and modeling from multiple scenarios can provide a more comprehensive understanding of users. Existing datasets only include data for the same type of items from a single scenario. Secondly, multi-modal features are essential in multi-scenario prediction as they address the issue of inconsistent ID encoding between different scenarios. The existing datasets are based on ID features and lack multi-modal features. Third, a large-scale dataset can provide a more reliable evaluation of models, fully reflecting the performance differences between models. The scale of existing datasets is around 100 million, which is relatively small compared to the real-world CTR prediction. To address these limitations, we propose AntM$^{2}$C, a Multi-Scenario Multi-Modal CTR dataset based on industrial data from Alipay. Specifically, AntM$^{2}$C provides the following advantages: 1) It covers CTR data of 5 different types of items, providing insights into the preferences of users for different items, including advertisements, vouchers, mini-programs, contents, and videos. 2) Apart from ID-based features, AntM$^{2}$C also provides 2 multi-modal features, raw text and image features, which can effectively establish connections between items with different IDs. 3) AntM$^{2}$C provides 1 billion CTR data with 200 features, including 200 million users and 6 million items. It is currently the largest-scale CTR dataset available. Based on AntM$^{2}$C, we construct several typical CTR tasks and provide comparisons with baseline methods. The dataset homepage is available at https://www.atecup.cn/home.

Model-free RL-based recommender systems have recently received increasing research attention due to their capability to handle partial feedback and long-term rewards. However, most existing research has ignored a critical feature in recommender systems: one user's feedback on the same item at different times is random. The stochastic rewards property essentially differs from that in classic RL scenarios with deterministic rewards, which makes RL-based recommender systems much more challenging. In this paper, we first demonstrate in a simulator environment where using direct stochastic feedback results in a significant drop in performance. Then to handle the stochastic feedback more efficiently, we design two stochastic reward stabilization frameworks that replace the direct stochastic feedback with that learned by a supervised model. Both frameworks are model-agnostic, i.e., they can effectively utilize various supervised models. We demonstrate the superiority of the proposed frameworks over different RL-based recommendation baselines with extensive experiments on a recommendation simulator as well as an industrial-level recommender system., Comment: SIGIR '23

Instruction tuning is instrumental in enabling Large Language Models~(LLMs) to follow user instructions to complete various open-domain tasks. The success of instruction tuning depends on the availability of high-quality instruction data. Owing to the exorbitant cost and substandard quality of human annotation, recent works have been deeply engaged in the exploration of the utilization of powerful closed-source models to generate instruction data automatically. However, these methods carry potential risks arising from the usage requirements of powerful closed-source models, which strictly forbid the utilization of their outputs to develop machine learning models. To deal with this problem, in this work, we explore alternative approaches to generate high-quality instruction data that do not rely on closed-source models. Our exploration includes an investigation of various existing instruction generation methods, culminating in the integration of the most efficient variant with two novel strategies to enhance the quality further. Evaluation results from two benchmarks and the GPT-4 model demonstrate the effectiveness of our generated instruction data, which can outperform Alpaca, a method reliant on closed-source models. We hope that more progress can be achieved in generating high-quality instruction data without using closed-source models.

We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this issue, we adopt the diffusion model framework to solve the nonlinear filtering problem. In stead of storing the information of the filtering density in finite number of Monte Carlo samples, in the score-based filter we store the information of the filtering density in the score model. Then, via the reverse-time diffusion sampler, we can generate unlimited samples to characterize the filtering density. Moreover, with the powerful expressive capabilities of deep neural networks, it has been demonstrated that a well trained score in diffusion model can produce samples from complex target distributions in very high dimensional spaces. Extensive numerical experiments show that our score-based filter could potentially address the curse of dimensionality in very high dimensional problems.

We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with different initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDE, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE's final state without simulating trajectories. Existing normalizing flows for SDEs depend on the initial distribution, meaning the model needs to be re-trained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. We provide a rigorous convergence analysis of the pseudo-reversible normalizing flow model to the target probability density function in the Kullback-Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

With the growing popularity of various mobile devices, user targeting has received a growing amount of attention, which aims at effectively and efficiently locating target users that are interested in specific services. Most pioneering works for user targeting tasks commonly perform similarity-based expansion with a few active users as seeds, suffering from the following major issues: the unavailability of seed users for newcoming services and the unfriendliness of black-box procedures towards marketers. In this paper, we design an Entity Graph Learning (EGL) system to provide explainable user targeting ability meanwhile applicable to addressing the cold-start issue. EGL System follows the hybrid online-offline architecture to satisfy the requirements of scalability and timeliness. Specifically, in the offline stage, the system focuses on the heavyweight entity graph construction and user entity preference learning, in which we propose a Three-stage Relation Mining Procedure (TRMP), breaking loose from the expensive seed users. At the online stage, the system offers the ability of user targeting in real-time based on the entity graph from the offline stage. Since the user targeting process is based on graph reasoning, the whole process is transparent and operation-friendly to marketers. Finally, extensive offline experiments and online A/B testing demonstrate the superior performance of the proposed EGL System., Comment: Accepted by ICDE 2023

Recently, the growth of service platforms brings great convenience to both users and merchants, where the service search engine plays a vital role in improving the user experience by quickly obtaining desirable results via textual queries. Unfortunately, users' uncontrollable search customs usually bring vast amounts of long-tail queries, which severely threaten the capability of search models. Inspired by recently emerging graph neural networks (GNNs) and contrastive learning (CL), several efforts have been made in alleviating the long-tail issue and achieve considerable performance. Nevertheless, they still face a few major weaknesses. Most importantly, they do not explicitly utilize the contextual structure between heads and tails for effective knowledge transfer, and intention-level information is commonly ignored for more generalized representations. To this end, we develop a novel framework GARCIA, which exploits the graph based knowledge transfer and intention based representation generalization in a contrastive setting. In particular, we employ an adaptive encoder to produce informative representations for queries and services, as well as hierarchical structure aware representations of intentions. To fully understand tail queries and services, we equip GARCIA with a novel multi-granularity contrastive learning module, which powers representations through knowledge transfer, structure enhancement and intention generalization. Subsequently, the complete GARCIA is well trained in a pre-training&fine-tuning manner. At last, we conduct extensive experiments on both offline and online environments, which demonstrates the superior capability of GARCIA in improving tail queries and overall performance in service search scenarios., Comment: Accepted by ICDE 2023

Federated learning (FL) is a popular way of edge computing that doesn't compromise users' privacy. Current FL paradigms assume that data only resides on the edge, while cloud servers only perform model averaging. However, in real-life situations such as recommender systems, the cloud server has the ability to store historical and interactive features. In this paper, our proposed Edge-Cloud Collaborative Knowledge Transfer Framework (ECCT) bridges the gap between the edge and cloud, enabling bi-directional knowledge transfer between both, sharing feature embeddings and prediction logits. ECCT consolidates various benefits, including enhancing personalization, enabling model heterogeneity, tolerating training asynchronization, and relieving communication burdens. Extensive experiments on public and industrial datasets demonstrate ECCT's effectiveness and potential for use in academia and industry., Comment: Accepted by Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR '23)

We present a new lite python-based program, CrysFieldExplorer, for fast optimizing crystal electric field (CEF) parameters to fit experimental data. The main novelty of CrysFieldExplorer is the development of a unique loss function, referred to as the Spectrum-Characteristic Loss ($L_{\text{Spectrum}}$), which is defined based on the characteristic polynomial of the Hamiltonian matrix. Particle Swarm Optimization and Covariance matrix adaptation evolution strategy are used to find the minimum of the total loss function. We demonstrate that CrysFieldExplorer can performs direct fitting of CEF parameters to any experimental data such as neutron spectrum, susceptibility, magnetizations etc. CrysFieldExplorer can handle a large amount of none-zero CEF parameters and reveal multiple local and global minimum solutions. Detailed crystal field theory, description of the loss function, implementation and limit of the program are discussed within context of two examples.

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [42], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by a oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. We also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justify the advantage of using moderate or large smoothing radius with the method. Furthermore, if the noise level decays to zero when approaching global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based method in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as its formulation and/or data of its solution for pre-training. In this work, we propose to construct transferable neural feature spaces from purely function approximation perspectives without using PDE information. The construction of the feature space involves re-parameterization of the hidden neurons and uses auxiliary functions to tune the resulting feature space. Theoretical analysis shows the high quality of the produced feature space, i.e., uniformly distributed neurons. Extensive numerical experiments verify the outstanding performance of our method, including significantly improved transferability, e.g., using the same feature space for various PDEs with different domains and boundary conditions, and the superior accuracy, e.g., several orders of magnitude smaller mean squared error than the state of the art methods.

The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from data. However, the fundamental challenges still exist: discovering the exact governing equations from highly noisy data. In present work, we propose a compressive sensing-assisted mixed integer optimization (CS-MIO) method to make a step forward from a modern discrete optimization lens. In particular, we first formulate the problem into a mixed integer optimization model. The discrete optimization nature of the model leads to exact variable selection by means of cardinality constraint, and hereby powerful capability of exact discovery of governing equations from noisy data. Such capability is further enhanced by incorporating compressive sensing and regularization techniques for highly noisy data and high-dimensional problems. The case studies on classical dynamical systems have shown that CS-MIO can discover the exact governing equations from large-noise data, with up to two orders of magnitude larger noise comparing with state-of-the-art method. We also show its effectiveness for high-dimensional dynamical system identification through the chaotic Lorenz 96 system.

An interpolation method to evaluate magnetic fields given unstructured, scattered magnetic data is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L^2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergence-free condition is incorporated as a constrain in the cost function allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Applications to the computation of Poincar\'e sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Our numerical scheme is based on the direct approximation of the nonlinear Feynman-Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman-Kac representation successfully avoids solving dense linear systems arising from nonlocality operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

The mercury constitutive model predicting the strain and stress in the target vessel plays a central role in improving the lifetime prediction and future target designs of the mercury targets at the Spallation Neutron Source (SNS). We leverage the experiment strain data collected over multiple years to improve the mercury constitutive model through a combination of large-scale simulations of the target behavior and the use of machine learning tools for parameter estimation. We present two interdisciplinary approaches for surrogate-based model calibration of expensive simulations using evolutionary neural networks and sparse polynomial expansions. The experiments and results of the two methods show a very good agreement for the solid mechanics simulation of the mercury spallation target. The proposed methods are used to calibrate the tensile cutoff threshold, mercury density, and mercury speed of sound during intense proton pulse experiments. Using strain experimental data from the mercury target sensors, the newly calibrated simulations achieve 7\% average improvement on the signal prediction accuracy and 8\% reduction in mean absolute error compared to previously reported reference parameters, with some sensors experiencing up to 30\% improvement. The proposed calibrated simulations can significantly aid in fatigue analysis to estimate the mercury target lifetime and integrity, which reduces abrupt target failure and saves a tremendous amount of costs. However, an important conclusion from this work points out to a deficiency in the current constitutive model based on the equation of state in capturing the full physics of the spallation reaction. Given that some of the calibrated parameters that show a good agreement with the experimental data can be nonphysical mercury properties, we need a more advanced two-phase flow model to capture bubble dynamics and mercury cavitation., Comment: 26 pages, 10 figures, 6 tables

Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks. Inspired by the Nonlinear Level set Learning (NLL) method that uses the reversible residual network (RevNet), in this paper we propose a new method of Dimension Reduction via Learning Level Sets (DRiLLS) for function approximation. Our method contains two major components: one is the pseudo-reversible neural network (PRNN) module that effectively transforms high-dimensional input variables to low-dimensional active variables, and the other is the synthesized regression module for approximating function values based on the transformed data in the low-dimensional space. The PRNN not only relaxes the invertibility constraint of the nonlinear transformation present in the NLL method due to the use of RevNet, but also adaptively weights the influence of each sample and controls the sensitivity of the function to the learned active variables. The synthesized regression uses Euclidean distance in the input space to select neighboring samples, whose projections on the space of active variables are used to perform local least-squares polynomial fitting. This helps to resolve numerical oscillation issues present in traditional local and global regressions. Extensive experimental results demonstrate that our DRiLLS method outperforms both the NLL and Active Subspace methods, especially when the target function possesses critical points in the interior of its input domain.

We propose a novel prediction interval (PI) method for uncertainty quantification, which addresses three major issues with the state-of-the-art PI methods. First, existing PI methods require retraining of neural networks (NNs) for every given confidence level and suffer from the crossing issue in calculating multiple PIs. Second, they usually rely on customized loss functions with extra sensitive hyperparameters for which fine tuning is required to achieve a well-calibrated PI. Third, they usually underestimate uncertainties of out-of-distribution (OOD) samples leading to over-confident PIs. Our PI3NN method calculates PIs from linear combinations of three NNs, each of which is independently trained using the standard mean squared error loss. The coefficients of the linear combinations are computed using root-finding algorithms to ensure tight PIs for a given confidence level. We theoretically prove that PI3NN can calculate PIs for a series of confidence levels without retraining NNs and it completely avoids the crossing issue. Additionally, PI3NN does not introduce any unusual hyperparameters resulting in a stable performance. Furthermore, we address OOD identification challenge by introducing an initialization scheme which provides reasonably larger PIs of the OOD samples than those of the in-distribution samples. Benchmark and real-world experiments show that our method outperforms several state-of-the-art approaches with respect to predictive uncertainty quality, robustness, and OOD samples identification.

Nuclear magnetic resonance (NMR) spectroscopy provides detailed information pertaining to dynamic processes through line-shape changes, which have been traditionally limited to equilibrium conditions. However, there is a wealth of information to be gained by studying chemical reactions under off-equilibrium conditions -- e.g., in states that arise upon mixing reactants that subsequently undergo chemical changes -- and in monitoring the formation of reaction products in real time. Herein, we propose and demonstrate a time-resolved kinetic NMR experiment that combines rapid mixing techniques, continuous flow, and single-scan spectroscopic imaging methods, leading in unison to a new 2D spectro-temporal NMR correlation which provides high-quality kinetic information of off-equilibrium dynamics. These kinetic 2D NMR spectra possess a spectral dimension conveying with high resolution the individual chemical sites, correlated with a time-independent, steady-state spatial axis that delivers unique information concerning temporal changes along the chemical reaction coordinate. A comprehensive description of the kinetic and spectroscopic features associated to these spectro-temporal NMR analyses is presented, factoring in the rapid-mixing, the flow and the spectroscopic NMR imaging. An experimental demonstration of this method's novel aspects was carried out using an enzymatically catalyzed reaction, leading to site- and time-resolved kinetic NMR data that are in excellent agreement with control experiments and literature values.

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. Here we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second-order convergence in space, first-order convergence in time, and is straightforward to parallelize. Applications are presented to the advection-diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.