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.

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.

If you want to know where AI is headed, this year's Google I/O has you covered. The company's annual showcase of next-gen products, which kicked off yesterday, has all of the pomp and pizzazz, the sizzle reels and celebrity walk-ons, that you'd expect from a multimillion dollar marketing event. But it also shows us just how fast this still-experimental technology is being subsumed into a line-up designed to sell phones and subscription tiers. Never before have I seen this thing we call artificial intelligence appear so normal. Last December, Meta announced plans to build a massive 10 billion data center for training its artificial intelligence models in rural northeast Louisiana.

The derivation of the self-consistent stochastic process discussed in the main text can be obtained using tools of statistical physics of disordered systems. In particular, it has been done very recently for a related model, the spherical perceptron with random labels, in [1]. Our derivation extends the known DMFT equations by including structure in the data; a stochastic version of gradient descent as discussed in the main text; the relaxation of the spherical constraint over the weights and the introduction of a Ridge regularization term. There are at least two ways to write the DMFT equations. One is by using field theoretical techniques; otherwise one can employ a dynamical version of the so-called cavity method [2].

Large language models such as GPT, Llama, Claude, and DeepSeek can be so fluent that people feel it as a "you," and it answers encouragingly as an "I." The models can write poetry in nearly any given form, read a set of political speeches and promptly sift out and share all the jokes, draw a chart, code a website. How do they do these and so many other things that were just recently the sole realm of humans? Practitioners are left explaining jaw-dropping conversational rabbit-from-a-hat extractions with arm-waving that the models are just predicting one word at a time from an unthinkably large training set scraped from every recorded written or spoken human utterance that can be found--fair enough--or a with a small shrug and a cryptic utterance of "fine-tuning" or "transformers!" These aren't very satisfying answers for how these models can converse so intelligently, and how they sometimes err so weirdly.