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Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the $L^2$ loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an $L^2$ bound on the approximation error and a certain regularity condition on the data distributions.

In this paper, we consider the problem of learning a linear regression model on a data domain of interest (target) given few samples. To aid learning, we are provided with a set of pre-trained regression models that are trained on potentially different data domains (sources). Assuming a representation structure for the data generating linear models at the sources and the target domains, we propose a representation transfer based learning method for constructing the target model. The proposed scheme is comprised of two phases: (i) utilizing the different source representations to construct a representation that is adapted to the target data, and (ii) using the obtained model as an initialization to a fine-tuning procedure that re-trains the entire (over-parameterized) regression model on the target data. For each phase of the training method, we provide excess risk bounds for the learned model compared to the true data generating target model. The derived bounds show a gain in sample complexity for our proposed method compared to the baseline method of not leveraging source representations when achieving the same excess risk, therefore, theoretically demonstrating the effectiveness of transfer learning for linear regression.

Multi-robot motion planning (MRMP) is the problem of finding collision-free paths for a set of robots in a continuous state space. The difficulty of MRMP increases with the number of robots and is exacerbated in environments with narrow passages that robots must pass through, like warehouse aisles where coordination between robots is required. In single-robot settings, topology-guided motion planning methods have shown improved performance in these constricted environments. In this work, we extend an existing topology-guided single-robot motion planning method to the multi-robot domain to leverage the improved efficiency provided by topological guidance. We demonstrate our method's ability to efficiently plan paths in complex environments with many narrow passages, scaling to robot teams of size up to 25 times larger than existing methods in this class of problems. By leveraging knowledge of the topology of the environment, we also find higher-quality solutions than other methods.

Image fusion plays a key role in a variety of multi-sensor-based vision systems, especially for enhancing visual quality and/or extracting aggregated features for perception. However, most existing methods just consider image fusion as an individual task, thus ignoring its underlying relationship with these downstream vision problems. Furthermore, designing proper fusion architectures often requires huge engineering labor. It also lacks mechanisms to improve the flexibility and generalization ability of current fusion approaches. To mitigate these issues, we establish a Task-guided, Implicit-searched and Meta-initialized (TIM) deep model to address the image fusion problem in a challenging real-world scenario. Specifically, we first propose a constrained strategy to incorporate information from downstream tasks to guide the unsupervised learning process of image fusion. Within this framework, we then design an implicit search scheme to automatically discover compact architectures for our fusion model with high efficiency. In addition, a pretext meta initialization technique is introduced to leverage divergence fusion data to support fast adaptation for different kinds of image fusion tasks. Qualitative and quantitative experimental results on different categories of image fusion problems and related downstream tasks (e.g., visual enhancement and semantic understanding) substantiate the flexibility and effectiveness of our TIM. The source code will be available at //github.com/LiuZhu-CV/TIMFusion.

We study a generalization of the online binary prediction with expert advice framework where at each round, the learner is allowed to pick $m\geq 1$ experts from a pool of $K$ experts and the overall utility is a modular or submodular function of the chosen experts. We focus on the setting in which experts act strategically and aim to maximize their influence on the algorithm's predictions by potentially misreporting their beliefs about the events. Among others, this setting finds applications in forecasting competitions where the learner seeks not only to make predictions by aggregating different forecasters but also to rank them according to their relative performance. Our goal is to design algorithms that satisfy the following two requirements: 1) $\textit{Incentive-compatible}$: Incentivize the experts to report their beliefs truthfully, and 2) $\textit{No-regret}$: Achieve sublinear regret with respect to the true beliefs of the best fixed set of $m$ experts in hindsight. Prior works have studied this framework when $m=1$ and provided incentive-compatible no-regret algorithms for the problem. We first show that a simple reduction of our problem to the $m=1$ setting is neither efficient nor effective. Then, we provide algorithms that utilize the specific structure of the utility functions to achieve the two desired goals.

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open problem whether prime numbers can be pseudodeterministically constructed in polynomial time. We provide a positive solution to this question in the infinitely-often regime. In more detail, we give an *unconditional* polynomial-time randomized algorithm $B$ such that, for infinitely many values of $n$, $B(1^n)$ outputs a canonical $n$-bit prime $p_n$ with high probability. More generally, we prove that for every dense property $Q$ of strings that can be decided in polynomial time, there is an infinitely-often pseudodeterministic polynomial-time construction of strings satisfying $Q$. This improves upon a subexponential-time construction of Oliveira and Santhanam. Our construction uses several new ideas, including a novel bootstrapping technique for pseudodeterministic constructions, and a quantitative optimization of the uniform hardness-randomness framework of Chen and Tell, using a variant of the Shaltiel--Umans generator.

Missing values challenge the probabilistic wind power forecasting at both parameter estimation and operational forecasting stages. In this paper, we illustrate that we are allowed to estimate forecasting functions for each missing patterns conveniently, and propose an adaptive quantile regression model whose parameters can adapt to missing patterns. For that, we particularly design a feature extraction block within the quantile regression model, where parameters are set as a function of missingness pattern and only account for observed values. To avoidthe quantile-crossing phenomena, we design a multi-task model to ensure the monotonicity of quantiles, where higher quantiles are derived by the addition between lower quantiles and non-negative increments modeled by neural networks. The proposed approach is distribution-free and applicable to both missing-at-random and missing-not-at-random cases. Case studies demonstrate that the proposed approach achieves the state-of-the-art in terms of the continuous ranked probability score.

Deployment of Internet of Things (IoT) devices and Data Fusion techniques have gained popularity in public and government domains. This usually requires capturing and consolidating data from multiple sources. As datasets do not necessarily originate from identical sensors, fused data typically results in a complex data problem. Because military is investigating how heterogeneous IoT devices can aid processes and tasks, we investigate a multi-sensor approach. Moreover, we propose a signal to image encoding approach to transform information (signal) to integrate (fuse) data from IoT wearable devices to an image which is invertible and easier to visualize supporting decision making. Furthermore, we investigate the challenge of enabling an intelligent identification and detection operation and demonstrate the feasibility of the proposed Deep Learning and Anomaly Detection models that can support future application that utilizes hand gesture data from wearable devices.

Sequential recommendation as an emerging topic has attracted increasing attention due to its important practical significance. Models based on deep learning and attention mechanism have achieved good performance in sequential recommendation. Recently, the generative models based on Variational Autoencoder (VAE) have shown the unique advantage in collaborative filtering. In particular, the sequential VAE model as a recurrent version of VAE can effectively capture temporal dependencies among items in user sequence and perform sequential recommendation. However, VAE-based models suffer from a common limitation that the representational ability of the obtained approximate posterior distribution is limited, resulting in lower quality of generated samples. This is especially true for generating sequences. To solve the above problem, in this work, we propose a novel method called Adversarial and Contrastive Variational Autoencoder (ACVAE) for sequential recommendation. Specifically, we first introduce the adversarial training for sequence generation under the Adversarial Variational Bayes (AVB) framework, which enables our model to generate high-quality latent variables. Then, we employ the contrastive loss. The latent variables will be able to learn more personalized and salient characteristics by minimizing the contrastive loss. Besides, when encoding the sequence, we apply a recurrent and convolutional structure to capture global and local relationships in the sequence. Finally, we conduct extensive experiments on four real-world datasets. The experimental results show that our proposed ACVAE model outperforms other state-of-the-art methods.

Most algorithms for representation learning and link prediction in relational data have been designed for static data. However, the data they are applied to usually evolves with time, such as friend graphs in social networks or user interactions with items in recommender systems. This is also the case for knowledge bases, which contain facts such as (US, has president, B. Obama, [2009-2017]) that are valid only at certain points in time. For the problem of link prediction under temporal constraints, i.e., answering queries such as (US, has president, ?, 2012), we propose a solution inspired by the canonical decomposition of tensors of order 4. We introduce new regularization schemes and present an extension of ComplEx (Trouillon et al., 2016) that achieves state-of-the-art performance. Additionally, we propose a new dataset for knowledge base completion constructed from Wikidata, larger than previous benchmarks by an order of magnitude, as a new reference for evaluating temporal and non-temporal link prediction methods.