A recent goal in the theory of deep learning is to identify how neural networks can escape the "lazy training," or Neural Tangent Kernel (NTK) regime, where the network is coupled with its first order Taylor expansion at initialization. While the NTK is minimax optimal for learning dense polynomials (Ghorbani et al, 2021), it cannot learn features, and hence has poor sample complexity for learning many classes of functions including sparse polynomials. Recent works have thus aimed to identify settings where gradient based algorithms provably generalize better than the NTK. One such example is the "QuadNTK" approach of Bai & Lee (2020), which analyzes the second-order term in the Taylor expansion. Bai & Lee (2020) show that the second-order term can learn sparse polynomials efficiently; however, it sacrifices the ability to learn general dense polynomials.In this paper, we analyze how gradient descent on a two-layer neural network can escape the NTK regime by utilizing a spectral characterization of the NTK (Montanari & Zhong, 2020) and building on the QuadNTK approach.

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Ukraine has branded Russia's presidency of the UN Security Council for the month of April "a symbolic blow," joining a chorus of outrage from Western countries. Moscow assumes the presidency as part of its monthly rotation between the Security Council's 15 member states, with ties with the West at their lowest point since the Cold War over Russia's invasion of Ukraine. Andriy Yermak, the Ukrainian president's chief of staff, said Russia's tenure was a "symbolic blow." It is another symbolic blow to the rules-based system of international relations," he wrote on Twitter. Ukraine's Foreign Minister Dmytro Kuleba said Russia assuming the presidency was "a slap in the face to the international community". "I urge the current UNSC members to thwart any Russian attempts to abuse its presidency," he wrote on Twitter on Saturday, calling Russia "an outlaw on the UNSC". Moscow last chaired the council in February 2022, the same month it invaded Ukraine – prompting Kyiv to call for Russia's removal from the council. Russia will hold little influence on decisions but will be in charge of the agenda. Moscow has said Foreign Minister Sergey Lavrov is planning to chair a UN Security Council meeting this month on "effective multilateralism". Russian foreign ministry spokeswoman Maria Zakharova also said that Lavrov would lead a debate on the Middle East on April 25. The Kremlin said on Friday it planned to "exercise all its rights" in the role. The White House urged Russia to "conduct itself professionally" when it assumes the role, saying there was no means to block Moscow from the post. "A country that flagrantly violates the UN Charter and invades its neighbour has no place on the UN Security Council," White House spokesperson Karine Jean-Pierre said on Friday. "Unfortunately, Russia is a permanent member of the Security Council and no feasible international legal pathway exists to change that reality," she added, calling the presidency "a largely ceremonial position". The Baltic states also expressed their concern. Estonia's UN envoy Rein Tammsaar, speaking also on behalf of Latvia and Lithuania, warned the Security Council Friday as it met to discuss Russia's plans to deploy tactical nuclear weapons in neighbouring Belarus. "Isn't it telling that tomorrow, on the anniversary of the Bucha killings, Russia will assume the Presidency of the UN Security Council?

NaaS Technology one of the largest and fastest growing electric vehicle charging service providers in China, recently announced the launch of its first self-developed automatic charging robot with features including active vehicle locating, smart charging, and automatic payment settlement to meet the rising demand for mobile charging of electric vehicles ("EV"). With the future popularization of self-driving vehicles, compatible automatic charging robots will become indispensable infrastructure. During an automatic charging session, robots with mechanical arms will automatically dock with the ports of EVs and complete the charging and settlement processes in one go. Empowered by deep learning, 5G, V2X, simultaneous localization and mapping, and other underlying technologies, NaaS' waterproof and shock-proof charging robot brings science fiction to life with one-click ordering, active vehicle locating, precise self-parking, automatic docking, charging and undocking via mechanical arms, and automatic return and recharging functions. It is available in various charging power and battery capacity configurations and can connect with major OEMs seamlessly through an open API, enabling EV owners to enjoy unmanned service anywhere, around the clock, saving much time and effort.