Graph learning architectures based on the k-dimensional Weisfeiler-Leman (k-WL) hierarchy offer a theoretically well-understood expressive power. However, such architectures often fail to deliver solid predictive performance on real-world tasks, limiting their practical impact. In contrast, global attention-based models such as graph transformers demonstrate strong performance in practice, but comparing their expressive power with the k-WL hierarchy remains challenging, particularly since these architectures rely on positional or structural encodings for their expressivity and predictive performance. To address this, we show that the recently proposed Edge Transformer, a global attention model operating on node pairs instead of nodes, has at least 3-WL expressive power. Empirically, we demonstrate that the Edge Transformer surpasses other theoretically aligned architectures regarding predictive performance while not relying on positional or structural encodings.
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Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learnt from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment, however, the data distribution may (and often does) vary, causing domain adaptation/generalization issues. In this paper we lay the foundations for a `credal' theory of learning, using convex sets of probabilities (credal sets) to model the variability in the data-generating distribution. Such credal sets, we argue, may be inferred from a finite sample of training sets. Bounds are derived for the case of finite hypotheses spaces (both assuming realizability or not) as well as infinite model spaces, which directly generalize classical results.
We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. We derive several new algorithms for dynamic programming and temporal-difference learning based on this framework, provide asymptotic convergence theory, and examine the empirical performance of the algorithms on a suite of tabular tasks. Further, we show that this approach can be straightforwardly combined with deep reinforcement learning, and obtain a new deep RL agent that improves over baseline distributional approaches on the Arcade Learning Environment.
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
Large Transformer models are capable of implementing a plethora of so-called in-context learning algorithms. These include gradient descent, classification, sequence completion, transformation, and improvement. In this work, we investigate whether large language models (LLMs), which never explicitly encountered the task of black-box optimization, are in principle capable of implementing evolutionary optimization algorithms. While previous works have solely focused on language-based task specification, we move forward and focus on the zero-shot application of LLMs to black-box optimization. We introduce a novel prompting strategy, consisting of least-to-most sorting of discretized population members and querying the LLM to propose an improvement to the mean statistic, i.e. perform a type of black-box recombination operation. Empirically, we find that our setup allows the user to obtain an LLM-based evolution strategy, which we call `EvoLLM', that robustly outperforms baseline algorithms such as random search and Gaussian Hill Climbing on synthetic BBOB functions as well as small neuroevolution tasks. Hence, LLMs can act as `plug-in' in-context recombination operators. We provide several comparative studies of the LLM's model size, prompt strategy, and context construction. Finally, we show that one can flexibly improve EvoLLM's performance by providing teacher algorithm information via instruction fine-tuning on previously collected teacher optimization trajectories.
Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.
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.
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-called meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
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.
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