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Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems, where small steps are required not for reasons of numerical accuracy but for the sake of stability. This issue is greatly alleviated in semi-linear problems by the probabilistic exponential integrators developed in this paper. By including the fast, linear dynamics in the prior, we arrive at a class of probabilistic integrators with favorable properties. Namely, they are proven to be L-stable, and in a certain case reduce to a classic exponential integrator -- with the added benefit of providing a probabilistic account of the numerical error. The method is also generalized to arbitrary non-linear systems by imposing piece-wise semi-linearity on the prior via Jacobians of the vector field at the previous estimates, resulting in probabilistic exponential Rosenbrock methods. We evaluate the proposed methods on multiple stiff differential equations and demonstrate their improved stability and efficiency over established probabilistic solvers. The present contribution thus expands the range of problems that can be effectively tackled within probabilistic numerics.

We propose Diffusion Noise Optimization (DNO), a new method that effectively leverages existing motion diffusion models as motion priors for a wide range of motion-related tasks. Instead of training a task-specific diffusion model for each new task, DNO operates by optimizing the diffusion latent noise of an existing pre-trained text-to-motion model. Given the corresponding latent noise of a human motion, it propagates the gradient from the target criteria defined on the motion space through the whole denoising process to update the diffusion latent noise. As a result, DNO supports any use cases where criteria can be defined as a function of motion. In particular, we show that, for motion editing and control, DNO outperforms existing methods in both achieving the objective and preserving the motion content. DNO accommodates a diverse range of editing modes, including changing trajectory, pose, joint locations, or avoiding newly added obstacles. In addition, DNO is effective in motion denoising and completion, producing smooth and realistic motion from noisy and partial inputs. DNO achieves these results at inference time without the need for model retraining, offering great versatility for any defined reward or loss function on the motion representation.

We propose a framework for applying reinforcement learning to contextual two-stage stochastic optimization and apply this framework to the problem of energy market bidding of an off-shore wind farm. Reinforcement learning could potentially be used to learn close to optimal solutions for first stage variables of a two-stage stochastic program under different contexts. Under the proposed framework, these solutions would be learned without having to solve the full two-stage stochastic program. We present initial results of training using the DDPG algorithm and present intended future steps to improve performance.

Re-training a deep learning model each time a single data point receives a new label is impractical due to the inherent complexity of the training process. Consequently, existing active learning (AL) algorithms tend to adopt a batch-based approach where, during each AL iteration, a set of data points is collectively chosen for annotation. However, this strategy frequently leads to redundant sampling, ultimately eroding the efficacy of the labeling procedure. In this paper, we introduce a new AL algorithm that harnesses the power of a Gaussian process surrogate in conjunction with the neural network principal learner. Our proposed model adeptly updates the surrogate learner for every new data instance, enabling it to emulate and capitalize on the continuous learning dynamics of the neural network without necessitating a complete retraining of the principal model for each individual label. Experiments on four benchmark datasets demonstrate that this approach yields significant enhancements, either rivaling or aligning with the performance of state-of-the-art techniques.

We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of autoencoder to identify the unobserved latent random variables. In our approach, we design an encoding function to discover the latent variables, which are modeled as unit Gaussian, and a decoding function to reconstruct the future states of the system. Both the encoder and decoder are expressed as deep neural networks (DNNs). Once the DNNs are trained by the trajectory data, the decoder serves as a predictive model for the unknown stochastic system. Through an extensive set of numerical examples, we demonstrate that the method is able to produce long-term system predictions by using short bursts of trajectory data. It is also applicable to systems driven by non-Gaussian noises.

Graph Neural Networks (GNNs) demonstrate their significance by effectively modeling complex interrelationships within graph-structured data. To enhance the credibility and robustness of GNNs, it becomes exceptionally crucial to bolster their ability to capture causal relationships. However, despite recent advancements that have indeed strengthened GNNs from a causal learning perspective, conducting an in-depth analysis specifically targeting the causal modeling prowess of GNNs remains an unresolved issue. In order to comprehensively analyze various GNN models from a causal learning perspective, we constructed an artificially synthesized dataset with known and controllable causal relationships between data and labels. The rationality of the generated data is further ensured through theoretical foundations. Drawing insights from analyses conducted using our dataset, we introduce a lightweight and highly adaptable GNN module designed to strengthen GNNs' causal learning capabilities across a diverse range of tasks. Through a series of experiments conducted on both synthetic datasets and other real-world datasets, we empirically validate the effectiveness of the proposed module.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.