Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.
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In online advertisement, ad campaigns are sequentially displayed to users. Both users and campaigns have inherent features, and the former is eligible to the latter if they are ``similar enough''. We model these interactions as a bipartite geometric random graph: the features of the $2N$ vertices ($N$ users and $N$ campaigns) are drawn independently in a metric space and an edge is present between a campaign and a user node if the distance between their features is smaller than $c/N$, where $c>0$ is the parameter of the model. Our contributions are two-fold. In the one-dimensional case, with uniform distribution over the segment $[0,1]$, we derive the size of the optimal offline matching in these bipartite random geometric graphs, and we build an algorithm achieving it (as a benchmark), and analyze precisely its performance. We then turn to the online setting where one side of the graph is known at the beginning while the other part is revealed sequentially. We study the number of matches of the online algorithm closest, which matches any incoming point to its closest available neighbor. We show that its performances can be compared to its fluid limit, completely described as the solution of an explicit PDE. From the latter, we can compute the competitive ratio of closest.
Self-supervised learning models have been shown to learn rich visual representations without requiring human annotations. However, in many real-world scenarios, labels are partially available, motivating a recent line of work on semi-supervised methods inspired by self-supervised principles. In this paper, we propose a conceptually simple yet empirically powerful approach to turn clustering-based self-supervised methods such as SwAV or DINO into semi-supervised learners. More precisely, we introduce a multi-task framework merging a supervised objective using ground-truth labels and a self-supervised objective relying on clustering assignments with a single cross-entropy loss. This approach may be interpreted as imposing the cluster centroids to be class prototypes. Despite its simplicity, we provide empirical evidence that our approach is highly effective and achieves state-of-the-art performance on CIFAR100 and ImageNet.
Previous methods solve feature matching and pose estimation using a two-stage process by first finding matches and then estimating the pose. As they ignore the geometric relationships between the two tasks, they focus on either improving the quality of matches or filtering potential outliers, leading to limited efficiency or accuracy. In contrast, we propose an iterative matching and pose estimation framework (IMP) leveraging the geometric connections between the two tasks: a few good matches are enough for a roughly accurate pose estimation; a roughly accurate pose can be used to guide the matching by providing geometric constraints. To this end, we implement a geometry-aware recurrent attention-based module which jointly outputs sparse matches and camera poses. Specifically, for each iteration, we first implicitly embed geometric information into the module via a pose-consistency loss, allowing it to predict geometry-aware matches progressively. Second, we introduce an \textbf{e}fficient IMP, called EIMP, to dynamically discard keypoints without potential matches, avoiding redundant updating and significantly reducing the quadratic time complexity of attention computation in transformers. Experiments on YFCC100m, Scannet, and Aachen Day-Night datasets demonstrate that the proposed method outperforms previous approaches in terms of accuracy and efficiency.
Among randomized numerical linear algebra strategies, so-called sketching procedures are emerging as effective reduction means to accelerate the computation of Krylov subspace methods for, e.g., the solution of linear systems, eigenvalue computations, and the approximation of matrix functions. While there is plenty of experimental evidence showing that sketched Krylov solvers may dramatically improve performance over standard Krylov methods, many features of these schemes are still unexplored. We derive new theoretical results that allow us to significantly improve our understanding of sketched Krylov methods, and to identify, among several possible equivalent formulations, the most suitable sketched approximations according to their numerical stability properties. These results are also employed to analyze the error of sketched Krylov methods in the approximation of the action of matrix functions, significantly contributing to the theory available in the current literature.
Meta-learning aims to extract useful inductive biases from a set of related datasets. In Bayesian meta-learning, this is typically achieved by constructing a prior distribution over neural network parameters. However, specifying families of computationally viable prior distributions over the high-dimensional neural network parameters is difficult. As a result, existing approaches resort to meta-learning restrictive diagonal Gaussian priors, severely limiting their expressiveness and performance. To circumvent these issues, we approach meta-learning through the lens of functional Bayesian neural network inference, which views the prior as a stochastic process and performs inference in the function space. Specifically, we view the meta-training tasks as samples from the data-generating process and formalize meta-learning as empirically estimating the law of this stochastic process. Our approach can seamlessly acquire and represent complex prior knowledge by meta-learning the score function of the data-generating process marginals instead of parameter space priors. In a comprehensive benchmark, we demonstrate that our method achieves state-of-the-art performance in terms of predictive accuracy and substantial improvements in the quality of uncertainty estimates.
Considering the field of functional data analysis, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our approach uses latent variables, allowing an adaptive selection since it can determine the number of variables and which ones should be selected for a function-on-scalar regression model. Simulation studies show the proposed method's main properties, such as its accuracy in estimating the coefficients and high capacity to select variables correctly. Furthermore, we conducted comparative studies with the main competing methods, such as the BGLSS method as well as the group LASSO, the group MCP and the group SCAD. We also used a COVID-19 dataset and some socioeconomic data from Brazil for real data application. In short, the proposed Bayesian variable selection model is extremely competitive, showing significant predictive and selective quality.
Radiologists are in short supply globally, and deep learning models offer a promising solution to address this shortage as part of clinical decision-support systems. However, training such models often requires expensive and time-consuming manual labeling of large datasets. Automatic label extraction from radiology reports can reduce the time required to obtain labeled datasets, but this task is challenging due to semantically similar words and missing annotated data. In this work, we explore the potential of weak supervision of a deep learning-based label prediction model, using a rule-based labeler. We propose a deep learning-based CheXpert label prediction model, pre-trained on reports labeled by a rule-based German CheXpert model and fine-tuned on a small dataset of manually labeled reports. Our results demonstrate the effectiveness of our approach, which significantly outperformed the rule-based model on all three tasks. Our findings highlight the benefits of employing deep learning-based models even in scenarios with sparse data and the use of the rule-based labeler as a tool for weak supervision.
Offline reinforcement learning (RL) seeks to derive an effective control policy from previously collected data. To circumvent errors due to inadequate data coverage, behavior-regularized methods optimize the control policy while concurrently minimizing deviation from the data collection policy. Nevertheless, these methods often exhibit subpar practical performance, particularly when the offline dataset is collected by sub-optimal policies. In this paper, we propose a novel algorithm employing in-sample policy iteration that substantially enhances behavior-regularized methods in offline RL. The core insight is that by continuously refining the policy used for behavior regularization, in-sample policy iteration gradually improves itself while implicitly avoids querying out-of-sample actions to avert catastrophic learning failures. Our theoretical analysis verifies its ability to learn the in-sample optimal policy, exclusively utilizing actions well-covered by the dataset. Moreover, we propose competitive policy improvement, a technique applying two competitive policies, both of which are trained by iteratively improving over the best competitor. We show that this simple yet potent technique significantly enhances learning efficiency when function approximation is applied. Lastly, experimental results on the D4RL benchmark indicate that our algorithm outperforms previous state-of-the-art methods in most tasks.
We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with different initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDE, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE's final state without simulating trajectories. Existing normalizing flows for SDEs depend on the initial distribution, meaning the model needs to be re-trained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. We provide a rigorous convergence analysis of the pseudo-reversible normalizing flow model to the target probability density function in the Kullback-Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.
Seeking the equivalent entities among multi-source Knowledge Graphs (KGs) is the pivotal step to KGs integration, also known as \emph{entity alignment} (EA). However, most existing EA methods are inefficient and poor in scalability. A recent summary points out that some of them even require several days to deal with a dataset containing 200,000 nodes (DWY100K). We believe over-complex graph encoder and inefficient negative sampling strategy are the two main reasons. In this paper, we propose a novel KG encoder -- Dual Attention Matching Network (Dual-AMN), which not only models both intra-graph and cross-graph information smartly, but also greatly reduces computational complexity. Furthermore, we propose the Normalized Hard Sample Mining Loss to smoothly select hard negative samples with reduced loss shift. The experimental results on widely used public datasets indicate that our method achieves both high accuracy and high efficiency. On DWY100K, the whole running process of our method could be finished in 1,100 seconds, at least 10* faster than previous work. The performances of our method also outperform previous works across all datasets, where Hits@1 and MRR have been improved from 6% to 13%.
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