Weintroduceaweak versionofexp-concavity; see Assumption (A2). Let 0 2 0 beapointinthegrid 0 minimizing D( , 0).

In the total least squares problem, one is given an m n matrix A, and an m d matrix B, and one seeks to "correct" both A and B, obtaining matrices  and B, so that there exists an X satisfying the equation ÂX = B. Typically the problem is overconstrained, meaning that m max(n, d).

Why was El Paso airspace shut down? A new United States military laser-based anti-drone system led authorities to halt air traffic in and out of El Paso, Texas, after aviation officials raised serious concerns about risks to commercial aircraft. The Federal Aviation Administration (FAA) initially announced a 10-day airspace closure on Wednesday but removed the restriction less than eight hours later, a decision reports said stemmed from miscommunication between the Pentagon and aviation regulators. The FAA and the military had planned to discuss the issue at a February 20 meeting, but the army moved ahead without final FAA approval, prompting the agency to halt flights in El Paso, sources said. What happened when El Paso's airspace was shut down?

Analternativeapproach isto predict instead adistributionp(ˆy|x) = Φˆy(x) over possible values of the annotationy. Theannotators are shown a set of points sampled randomly and uniformly over one of predefined body parts of aperson inan image.

Optimization is an integral part of most machine learning systems and most numerical optimization schemes relyonthecomputation ofderivatives.

Many works have studied neural execution in different domains before [45, 23, 24, 31, 33, 42]. With the rapid development of GNNs in graph representation learning, learning graph algorithms with GNNs has attracted researchers' attention [39, 38, 41]. These works exploit GNNs to approximate certain classes of graph algorithms, such as parallel algorithms (e.g., Breadth-First-Search) and sequential algorithms (e.g., Dijkstra).

However,computing extendedpersistent homologysummaries remainsslowfor large and dense graphs and can be aserious bottleneck for the learning pipeline.

Thisresult shows that visual grounding/feature attribution can be ineffective at resolving shortcuts.