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Over the last two decades, pseudospectral methods based on Lagrange interpolants have flourished in solving trajectory optimization problems and their flight implementations. In a seemingly unjustified departure from these highly successful methods, a new starting point for trajectory optimization is proposed. This starting point is based on the recently-developed concept of universal Birkhoff interpolants. The new approach offers a substantial computational upgrade to the Lagrange theory in completely flattening the rapid growth of the condition numbers from O(N2) to O(1), where N is the number of grid points. In addition, the Birkhoff-specific primal-dual computations are isolated to a well-conditioned linear system even for nonlinear, nonconvex problems. This is part I of a two-part paper. In part I, a new theory is developed on the basis of two hypotheses. Other than these hypotheses, the theoretical development makes no assumptions on the choices of basis functions or the selection of grid points. Several covector mapping theorems are proved to establish the mathematical equivalence between direct and indirect Birkhoff methods. In part II of this paper (with Proulx), it is shown that a select family of Gegenbauer grids satisfy the two hypotheses required for the theory to hold. Numerical examples in part II illustrate the power and utility of the new theory.

Recently, text watermarking algorithms for large language models (LLMs) have been mitigating the potential harms of text generated by the LLMs, including fake news and copyright issues. However, the watermark detection of current text algorithms requires the key from the generation process, making them susceptible to breaches and counterfeiting. In this work, we propose the first private watermarking algorithm, which extends the current text watermarking algorithms by using two different neural networks respectively for watermark generation and detection, rather than using the same key at both stages. Meanwhile, part of the parameters of the watermark generation and detection networks are shared, which makes the detection network achieve a high accuracy very efficiently. Experiments show that our algorithm ensures high detection accuracy with minimal impact on generation and detection speed, due to the small parameter size of both networks. Additionally, our subsequent analysis demonstrates the difficulty of reverting the watermark generation rules from the detection network.

Embedding based Knowledge Graph (KG) Completion has gained much attention over the past few years. Most of the current algorithms consider a KG as a multidirectional labeled graph and lack the ability to capture the semantics underlying the schematic information. In a separate development, a vast amount of information has been captured within the Large Language Models (LLMs) which has revolutionized the field of Artificial Intelligence. KGs could benefit from these LLMs and vice versa. This vision paper discusses the existing algorithms for KG completion based on the variations for generating KG embeddings. It starts with discussing various KG completion algorithms such as transductive and inductive link prediction and entity type prediction algorithms. It then moves on to the algorithms utilizing type information within the KGs, LLMs, and finally to algorithms capturing the semantics represented in different description logic axioms. We conclude the paper with a critical reflection on the current state of work in the community and give recommendations for future directions.

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.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

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.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.