We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.

State-space graphical models and the variational autoencoder framework provide a principled apparatus for learning dynamical systems from data. State-of-the-art probabilistic approaches are often able to scale to large problems at the cost of flexibility of the variational posterior or expressivity of the dynamics model. However, those consolidations can be detrimental if the ultimate goal is to learn a generative model capable of explaining the spatiotemporal structure of the data and making accurate forecasts. We introduce a low-rank structured variational autoencoding framework for nonlinear Gaussian state-space graphical models capable of capturing dense covariance structures that are important for learning dynamical systems with predictive capabilities. Our inference algorithm exploits the covariance structures that arise naturally from sample based approximate Gaussian message passing and low-rank amortized posterior updates - effectively performing approximate variational smoothing with time complexity scaling linearly in the state dimensionality. In comparisons with other deep state-space model architectures our approach consistently demonstrates the ability to learn a more predictive generative model. Furthermore, when applied to neural physiological recordings, our approach is able to learn a dynamical system capable of forecasting population spiking and behavioral correlates from a small portion of single trials.

Microsoft has begun testing a new power-saving technology within Windows, as well as assigning AI actions to a right-click menu within File Explorer. Microsoft is also tweaking the way in which widgets are laid out, letting Copilot handle the decisions itself. Microsoft published the changes as part of the Windows 11 Insider Preview Build 26120.4151 By testing these features, Microsoft doesn't necessarily have to commit to eventually rolling them out, although many appear to be under consideration for a more general release. Under the hood, Microsoft said that it's testing out what it calls User Interaction-Aware CPU Power Management, "an OS-level enhancement that helps reduce power consumption and extend your battery life."

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K and M are short for thousand and million respectively. True_neg denotes whether it includes true negative feedback. We only show the statistics of the QK-video (QKV) and QK-article (QKA) in this table. We show the difference between Tenrec and other popular recommendation datasets in Table1. First, most datasets contain only a single scenario. Without overlapped users and items, it is difficult to develop and evaluate transfer learning recommendation methods. In addition, Tenrec contains very rich positive user feedback, which can be used to evaluate the multi-task learning and preference-level transfer learning tasks. Third, compared with most recommendation datasets, Tenrec has true negative examples, which can be used to evaluate more realistic CTR prediction task.

Rodriguez, the President of the National Hispanic Christian Leadership Conference, spoke at Trump's first presidential inauguration in 2017. Moore, who is also the founder of the public relations firm Kairos, served on Trump's Evangelical executive board during his first presidential candidacy. The letter is a sign of growing ties between religious and AI safety groups, which share some of the same worries. It was shared with journalists by representatives of the Future of Life Institute--an AI safety organization that campaigns to reduce what it sees as the existential risk posed by advanced AI systems. The world's biggest tech companies now all believe that it is possible to create so-called "artificial general intelligence"--a form of AI that can do any task better than a human expert. Some researchers have even invoked this technology in religious terms--for example, OpenAI's former chief scientist Ilya Sutskever, a mystical figure who famously encouraged colleagues to chant "feel the AGI" at company gatherings.

The optimal transport (OT) problem (a.k.a. the Monge problem) is to find an optimal map T

Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used K-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the Euclidean space, centroid-based and distance-based formulations of the K-means are equivalent. In modern machine learning applications, data often arise as probability distributions and a natural generalization to handle measure-valued data is to use the optimal transport metric. Due to non-negative Alexandrov curvature of the Wasserstein space, barycenters suffer from regularity and nonrobustness issues. The peculiar behaviors of Wasserstein barycenters may make the centroid-based formulation fail to represent the within-cluster data points, while the more direct distance-based K-means approach and its semidefinite program (SDP) relaxation are capable of recovering the true cluster labels. In the special case of clustering Gaussian distributions, we show that the SDP relaxed Wasserstein K-means can achieve exact recovery given the clusters are well-separated under the 2-Wasserstein metric. Our simulation and real data examples also demonstrate that distance-based K-means can achieve better classification performance over the standard centroid-based K-means for clustering probability distributions and images.

In this section, we give the details of the full optimization cycle and discuss differences between the single-modality baseline and our multi-modal models. As discussed in [1], SDC may converge to trivial solutions, corresponding to empty clusters or encoder parameterizations, where the classifier predicts the same label regardless of the input. DeepCluster proposes workarounds to tackle these issues, involving reassigning empty cluster centers and sampling training images uniformly over the cluster assignments. While these strategies mitigate the issues, they do not fix the main cause of the problem: SDC learns a discriminative classifier on the same input from which it learns the labels. On the other hand, our multi-modal deep clustering models are less prone to trivial solutions because they learn the discriminative classifier on one modality and obtain the labels from a different modality.

Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.