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We propose a way to split a given bivariate P-recursive sequence into a summable part and a non-summable part in such a way that the non-summable part is minimal in some sense. This decomposition gives rise to a new reduction-based creative telescoping algorithm based on the concept of integral bases.

Reasoning on large-scale knowledge graphs has been long dominated by embedding methods. While path-based methods possess the inductive capacity that embeddings lack, their scalability is limited by the exponential number of paths. Here we present A*Net, a scalable path-based method for knowledge graph reasoning. Inspired by the A* algorithm for shortest path problems, our A*Net learns a priority function to select important nodes and edges at each iteration, to reduce time and memory footprint for both training and inference. The ratio of selected nodes and edges can be specified to trade off between performance and efficiency. Experiments on both transductive and inductive knowledge graph reasoning benchmarks show that A*Net achieves competitive performance with existing state-of-the-art path-based methods, while merely visiting 10% nodes and 10% edges at each iteration. On a million-scale dataset ogbl-wikikg2, A*Net not only achieves a new state-of-the-art result, but also converges faster than embedding methods. A*Net is the first path-based method for knowledge graph reasoning at such scale.

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

Designing and analyzing model-based RL (MBRL) algorithms with guaranteed monotonic improvement has been challenging, mainly due to the interdependence between policy optimization and model learning. Existing discrepancy bounds generally ignore the impacts of model shifts, and their corresponding algorithms are prone to degrade performance by drastic model updating. In this work, we first propose a novel and general theoretical scheme for a non-decreasing performance guarantee of MBRL. Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. These discoveries encourage us to formulate a constrained lower-bound optimization problem to permit the monotonicity of MBRL. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns. Motivated by these analyses, we design a simple but effective algorithm CMLO (Constrained Model-shift Lower-bound Optimization), by introducing an event-triggered mechanism that flexibly determines when to update the model. Experiments show that CMLO surpasses other state-of-the-art methods and produces a boost when various policy optimization methods are employed.

Ratings are frequently used to evaluate and compare subjects in various applications, from education to healthcare, because ratings provide succinct yet credible measures for comparing subjects. However, when multiple rating lists are combined or considered together, subjects often have missing ratings, because most rating lists do not rate every subject in the combined list. In this study, we propose analyses on missing value patterns using six real-world data sets in various applications, as well as the conditions for applicability of imputation algorithms. Based on the special structures and properties derived from the analyses, we propose optimization models and algorithms that minimize the total rating discordance across rating providers to impute missing ratings in the combined rating lists, using only the known rating information. The total rating discordance is defined as the sum of the pairwise discordance metric, which can be written as a quadratic function. Computational experiments based on real-world and synthetic rating data sets show that the proposed methods outperform the state-of-the-art general imputation methods in the literature in terms of imputation accuracy.

With recent advancements in natural language processing, Large Language Models (LLMs) have emerged as powerful tools for various real-world applications. Despite their prowess, the intrinsic generative abilities of LLMs may prove insufficient for handling complex tasks which necessitate a combination of task planning and the usage of external tools. In this paper, we first propose a structured framework tailored for LLM-based AI Agents and discuss the crucial capabilities necessary for tackling intricate problems. Within this framework, we design two distinct types of agents (i.e., one-step agent and sequential agent) to execute the inference process. Subsequently, we instantiate the framework using various LLMs and evaluate their Task Planning and Tool Usage (TPTU) abilities on typical tasks. By highlighting key findings and challenges, our goal is to provide a helpful resource for researchers and practitioners to leverage the power of LLMs in their AI applications. Our study emphasizes the substantial potential of these models, while also identifying areas that need more investigation and improvement.

Significant improvements in end-to-end speech translation (ST) have been achieved through the application of multi-task learning. However, the extent to which auxiliary tasks are highly consistent with the ST task, and how much this approach truly helps, have not been thoroughly studied. In this paper, we investigate the consistency between different tasks, considering different times and modules. We find that the textual encoder primarily facilitates cross-modal conversion, but the presence of noise in speech impedes the consistency between text and speech representations. Furthermore, we propose an improved multi-task learning (IMTL) approach for the ST task, which bridges the modal gap by mitigating the difference in length and representation. We conduct experiments on the MuST-C dataset. The results demonstrate that our method attains state-of-the-art results. Moreover, when additional data is used, we achieve the new SOTA result on MuST-C English to Spanish task with 20.8% of the training time required by the current SOTA method.

Learning from demonstration (LfD) provides an efficient way to train robots. The learned motions should be convergent and stable, but to be truly effective in the real world, LfD-capable robots should also be able to remember multiple motion skills. Multi-skill retention is a capability missing from existing stable-LfD approaches. On the other hand, recent work on continual-LfD has shown that hypernetwork-generated neural ordinary differential equation solvers, can learn multiple LfD tasks sequentially, but this approach lacks stability guarantees. We propose an approach for stable continual-LfD in which a hypernetwork generates two networks: a trajectory learning dynamics model, and a trajectory stabilizing Lyapunov function. The introduction of stability not only generates stable trajectories but also greatly improves continual learning performance, especially in the size-efficient chunked hypernetworks. With our approach, we can continually train a single model to predict the position and orientation trajectories of the robot's end-effector simultaneously for multiple real world tasks without retraining on past demonstrations. We also propose stochastic regularization with a single randomly sampled regularization term in hypernetworks, which reduces the cumulative training time cost for $N$ tasks from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ without any loss in performance in real-world tasks. We empirically evaluate our approach on the popular LASA dataset, on high-dimensional extensions of LASA (including up to 32 dimensions) to assess scalability, and on a novel extended robotic task dataset (RoboTasks9) to assess real-world performance. In trajectory error metrics, stability metrics and continual learning metrics our approach performs favorably, compared to other baselines. Code and datasets will be shared after submission.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

Attention mechanism has been used as an ancillary means to help RNN or CNN. However, the Transformer (Vaswani et al., 2017) recently recorded the state-of-the-art performance in machine translation with a dramatic reduction in training time by solely using attention. Motivated by the Transformer, Directional Self Attention Network (Shen et al., 2017), a fully attention-based sentence encoder, was proposed. It showed good performance with various data by using forward and backward directional information in a sentence. But in their study, not considered at all was the distance between words, an important feature when learning the local dependency to help understand the context of input text. We propose Distance-based Self-Attention Network, which considers the word distance by using a simple distance mask in order to model the local dependency without losing the ability of modeling global dependency which attention has inherent. Our model shows good performance with NLI data, and it records the new state-of-the-art result with SNLI data. Additionally, we show that our model has a strength in long sentences or documents.