Grammatical inference consists in learning a formal grammar as a finite state machine or as a set of rewrite rules. In this paper, we are concerned with inferring Nondeterministic Finite Automata (NFA) that must accept some words, and reject some other words from a given sample. This problem can naturally be modeled in SAT. The standard model being enormous, some models based on prefixes, suffixes, and hybrids were designed to generate smaller SAT instances. There is a very simple and obvious property that says: if there is an NFA of size k for a given sample, there is also an NFA of size k+1. We first strengthen this property by adding some characteristics to the NFA of size k+1. Hence, we can use this property to tighten the bounds of the size of the minimal NFA for a given sample. We then propose simplified and refined models for NFA of size k+1 that are smaller than the initial models for NFA of size k. We also propose a reduction algorithm to build an NFA of size k from a specific NFA of size k+1. Finally, we validate our proposition with some experimentation that shows the efficiency of our approach.

Understanding player shooting profiles is an essential part of basketball analysis: knowing where certain opposing players like to shoot from can help coaches neutralize offensive gameplans from their opponents; understanding where their players are most comfortable can lead them to developing more effective offensive strategies. An automatic tool that can provide these performance profiles in a timely manner can become invaluable for coaches to maximize both the effectiveness of their game plan as well as the time dedicated to practice and other related activities. Additionally, basketball is dictated by many variables, such as playstyle and game dynamics, that can change the flow of the game and, by extension, player performance profiles. It is crucial that the performance profiles can reflect the diverse playstyles, as well as the fast-changing dynamics of the game. We present a tool that can visualize player performance profiles in a timely manner while taking into account factors such as play-style and game dynamics. Our approach generates interpretable heatmaps that allow us to identify and analyze how non-spatial factors, such as game dynamics or playstyle, affect player performance profiles.

Recent breakthroughs in self supervised training have led to a new class of pretrained vision language models. While there have been investigations of bias in multimodal models, they have mostly focused on gender and racial bias, giving much less attention to other relevant groups, such as minorities with regard to religion, nationality, sexual orientation, or disabilities. This is mainly due to lack of suitable benchmarks for such groups. We seek to address this gap by providing a visual and textual bias benchmark called MMBias, consisting of around 3,800 images and phrases covering 14 population subgroups. We utilize this dataset to assess bias in several prominent self supervised multimodal models, including CLIP, ALBEF, and ViLT. Our results show that these models demonstrate meaningful bias favoring certain groups. Finally, we introduce a debiasing method designed specifically for such large pre-trained models that can be applied as a post-processing step to mitigate bias, while preserving the remaining accuracy of the model.

Coreference resolution models are often evaluated on multiple datasets. Datasets vary, however, in how coreference is realized -- i.e., how the theoretical concept of coreference is operationalized in the dataset -- due to factors such as the choice of corpora and annotation guidelines. We investigate the extent to which errors of current coreference resolution models are associated with existing differences in operationalization across datasets (OntoNotes, PreCo, and Winogrande). Specifically, we distinguish between and break down model performance into categories corresponding to several types of coreference, including coreferring generic mentions, compound modifiers, and copula predicates, among others. This break down helps us investigate how state-of-the-art models might vary in their ability to generalize across different coreference types. In our experiments, for example, models trained on OntoNotes perform poorly on generic mentions and copula predicates in PreCo. Our findings help calibrate expectations of current coreference resolution models; and, future work can explicitly account for those types of coreference that are empirically associated with poor generalization when developing models.

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes barely any progress alternate with intervals of rapid decrease. These successive phases of learning often take place on very different time scales. Finally, models learnt in an early phase are typically `simpler' or `easier to learn' although in a way that is difficult to formalize. Although theoretical explanations of these phenomena have been put forward, each of them captures at best certain specific regimes. In this paper, we study the gradient flow dynamics of a wide two-layer neural network in high-dimension, when data are distributed according to a single-index model (i.e., the target function depends on a one-dimensional projection of the covariates). Based on a mixture of new rigorous results, non-rigorous mathematical derivations, and numerical simulations, we propose a scenario for the learning dynamics in this setting. In particular, the proposed evolution exhibits separation of timescales and intermittency. These behaviors arise naturally because the population gradient flow can be recast as a singularly perturbed dynamical system.

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered efficiently using tensor deflation which consists of successive rank-one approximations, while non-orthogonal components may alter the tensor deflation mechanism, thereby preventing efficient recovery. Relying on recently developed random tensor tools, this paper deals precisely with the non-orthogonal case by deriving an asymptotic analysis of a parameterized deflation procedure performed on an order-three and rank-two spiked tensor. Based on this analysis, an efficient tensor deflation algorithm is proposed by optimizing the parameter introduced in the deflation mechanism, which in turn is proven to be optimal by construction for the studied tensor model. The same ideas could be extended to more general low-rank tensor models, e.g., higher ranks and orders, leading to more efficient tensor methods with a broader impact on machine learning and beyond.

Secretary of Defense Lloyd Austin said during a briefing on Wednesday that the collision of a Russian jet with a U.S. drone follows a "pattern" of unsafe and risky behavior from Russia. Chairman of the Joint Chiefs of Staff Mark Milley said during a briefing on Wednesday that America doesn't seek "armed conflict" with Russia after the collision of a Russian jet and a U.S. drone On Tuesday, a Russian Su-27 fighter plane collided with a U.S. MQ-9 Reaper drone while traveling over the Black Sea, a U.S. defense official told Fox News. The collision occurred in international airspace while over international waters, with the jet in question being one of two Su-27s flying in tandem. The drone's propeller was damaged, forcing it to be ditched in the Black Sea west of Crimea, the defense official said. Secretary of Defense Lloyd Austin described the incident as a continuation of risky behavior from Russia during Tuesday's press briefing.

BRIAN KENNY: Artificial intelligence or AI for short is certainly creating a lot of buzz these days. And although it may seem like this amorphous thing that's somewhere off in our future, it's already very much in our midst. Navigation apps have turned printed maps into relics. Alexa, knows what you need from the grocery store before you do. Google Nest has the house at just the right temperature before you roll out from under the covers. And this is all great, but now you have to wonder if this intro is written by me or chat GPT. Which raises an important question.

Fox News correspondent Mike Tobin has the latest on the Russia-Ukraine war on'Special Report.' Tensions remain between Russia and the United States after a collision in international airspace. U.S. military command officials said Tuesday that a Russian fighter jet dumped fuel on a U.S. drone over the Black Sea, clipped the drone's propeller and forced it into the water. An MQ-9 Reaper remotely piloted aircraft is parked in a hanger at Creech Air Force Base in Indian Springs, Nevada. Russia is now denying that the aircraft touched one another, and accusing the U.S. of unnecessarily escalating the issue.

Fox News Flash top headlines are here. Check out what's clicking on Foxnews.com. The U.K. and Germany scrambled fighter jets to intercept two Russian aircraft flying near Estonia late Tuesday. The Russian aircraft, a Russian Il-78 Midas refueling plane and an Antonov 148 military transport, approached NATO airspace without contacting Estonian authorities. The incident was the first time the U.K. and Germany have conducted a joint air intercept as part of the NATO treaty.