Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply diffusion models to the discretized data. While such approaches are practically appealing, the performance of the resulting algorithms typically deteriorates as discretization parameters are refined. In this paper, we instead directly formulate diffusion-based generative models in infinite dimensions and apply them to the generative modeling of functions. We prove that our formulations are well posed in the infinite-dimensional setting and provide dimension-independent distance bounds from the sample to the target measure. Using our theory, we also develop guidelines for the design of infinite-dimensional diffusion models. For image distributions, these guidelines are in line with the canonical choices currently made for diffusion models. For other distributions, however, we can improve upon these canonical choices, which we show both theoretically and empirically, by applying the algorithms to data distributions on manifolds and inspired by Bayesian inverse problems or simulation-based inference.
Lattice-linear systems allow nodes to execute asynchronously. We introduce eventually lattice-linear algorithms, where lattices are induced only among the states in a subset of the state space. The algorithm guarantees that the system transitions to a state in one of the lattices. Then, the algorithm behaves lattice linearly while traversing to an optimal state through that lattice. We present a lattice-linear self-stabilizing algorithm for service demand based minimal dominating set (SDMDS) problem. Using this as an example, we elaborate the working of, and define, eventually lattice-linear algorithms. Then, we present eventually lattice-linear self-stabilizing algorithms for minimal vertex cover (\mvc), maximal independent set (\mis), graph colouring (\gc) and 2-dominating set problems (\tds). Algorithms for SDMDS, \mvc and \mis converge in 1 round plus $n$ moves (within $2n$ moves), \gc in $n+4m$ moves, and \tds in 1 round plus $2n$ moves (within $3n$ moves). These results are an improvement over the existing literature. We also present experimental results to show performance gain demonstrating the benefit of lattice-linearity.
In task-oriented dialogue, a system often needs to follow a sequence of actions, called a workflow, that complies with a set of guidelines in order to complete a task. In this paper, we propose the novel problem of multi-step workflow action prediction, in which the system predicts multiple future workflow actions. Accurate prediction of multiple steps allows for multi-turn automation, which can free up time to focus on more complex tasks. We propose three modeling approaches that are simple to implement yet lead to more action automation: 1) fine-tuning on a training dataset, 2) few-shot in-context learning leveraging retrieval and large language model prompting, and 3) zero-shot graph traversal, which aggregates historical action sequences into a graph for prediction. We show that multi-step action prediction produces features that improve accuracy on downstream dialogue tasks like predicting task success, and can increase automation of steps by 20% without requiring as much feedback from a human overseeing the system.
Consider an active learning setting in which a learner has a training set with few labeled examples and a pool set with many unlabeled inputs, while a remote teacher has a pre-trained model that is known to perform well for the learner's task. The learner actively transmits batches of unlabeled inputs to the teacher through a constrained communication channel for labeling. This paper addresses the following key questions: (i) Active batch selection: Which batch of inputs should be sent to the teacher to acquire the most useful information and thus reduce the number of required communication rounds? (ii) Batch encoding: How do we encode the batch of inputs for transmission to the teacher to reduce the communication resources required at each round? We introduce Communication-Constrained Bayesian Active Knowledge Distillation (CC-BAKD), a novel protocol that integrates Bayesian active learning with compression via a linear mix-up mechanism. Bayesian active learning selects the batch of inputs based on their epistemic uncertainty, addressing the "confirmation bias" that is known to increase the number of required communication rounds. Furthermore, the proposed mix-up compression strategy is integrated with the epistemic uncertainty-based active batch selection process to reduce the communication overhead per communication round.
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs, and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motif mining holds promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge intersections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least correlated with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most correlated with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation.
Standard contrastive learning approaches usually require a large number of negatives for effective unsupervised learning and often exhibit slow convergence. We suspect this behavior is due to the suboptimal selection of negatives used for offering contrast to the positives. We counter this difficulty by taking inspiration from support vector machines (SVMs) to present max-margin contrastive learning (MMCL). Our approach selects negatives as the sparse support vectors obtained via a quadratic optimization problem, and contrastiveness is enforced by maximizing the decision margin. As SVM optimization can be computationally demanding, especially in an end-to-end setting, we present simplifications that alleviate the computational burden. We validate our approach on standard vision benchmark datasets, demonstrating better performance in unsupervised representation learning over state-of-the-art, while having better empirical convergence properties.
Recent advances in representation learning have demonstrated an ability to represent information from different modalities such as video, text, and audio in a single high-level embedding vector. In this work we present a self-supervised learning framework that is able to learn a representation that captures finer levels of granularity across different modalities such as concepts or events represented by visual objects or spoken words. Our framework relies on a discretized embedding space created via vector quantization that is shared across different modalities. Beyond the shared embedding space, we propose a Cross-Modal Code Matching objective that forces the representations from different views (modalities) to have a similar distribution over the discrete embedding space such that cross-modal objects/actions localization can be performed without direct supervision. In our experiments we show that the proposed discretized multi-modal fine-grained representation (e.g., pixel/word/frame) can complement high-level summary representations (e.g., video/sentence/waveform) for improved performance on cross-modal retrieval tasks. We also observe that the discretized representation uses individual clusters to represent the same semantic concept across modalities.
Federated learning enables multiple parties to collaboratively train a machine learning model without communicating their local data. A key challenge in federated learning is to handle the heterogeneity of local data distribution across parties. Although many studies have been proposed to address this challenge, we find that they fail to achieve high performance in image datasets with deep learning models. In this paper, we propose MOON: model-contrastive federated learning. MOON is a simple and effective federated learning framework. The key idea of MOON is to utilize the similarity between model representations to correct the local training of individual parties, i.e., conducting contrastive learning in model-level. Our extensive experiments show that MOON significantly outperforms the other state-of-the-art federated learning algorithms on various image classification tasks.
Invariant approaches have been remarkably successful in tackling the problem of domain generalization, where the objective is to perform inference on data distributions different from those used in training. In our work, we investigate whether it is possible to leverage domain information from the unseen test samples themselves. We propose a domain-adaptive approach consisting of two steps: a) we first learn a discriminative domain embedding from unsupervised training examples, and b) use this domain embedding as supplementary information to build a domain-adaptive model, that takes both the input as well as its domain into account while making predictions. For unseen domains, our method simply uses few unlabelled test examples to construct the domain embedding. This enables adaptive classification on any unseen domain. Our approach achieves state-of-the-art performance on various domain generalization benchmarks. In addition, we introduce the first real-world, large-scale domain generalization benchmark, Geo-YFCC, containing 1.1M samples over 40 training, 7 validation, and 15 test domains, orders of magnitude larger than prior work. We show that the existing approaches either do not scale to this dataset or underperform compared to the simple baseline of training a model on the union of data from all training domains. In contrast, our approach achieves a significant improvement.
The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.
Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.