Ukraine's drone industry is rapidly expanding, with hidden factories near Lviv producing kamikaze drones and interceptor systems to counter Iranian-designed Shahed drones.

Ukraine's bet on drone swarms. Lyiv, Ukraine - Hundreds of AI-controlled robots operating in unison, talking to each other to autonomously attack targets -- a dystopian vision of the future of war that Ukraine's defense industry wants to make a reality. Four years into the Russian invasion, the idea -- known as drone swarms -- is one of the hottest topics in military tech in a country that describes itself as the world-leader in drone warfare. There is a huge interest, military expert Yury Fedorenko told a recent Drone Autonomy conference, held in an undisclosed location in the western Ukrainian city of Lviv. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' 'One of the longest' Russian attacks kills at least six people in Ukraine At least six people have been killed and dozens injured in "one of the longest, massive Russian attacks against Ukraine", according to Ukrainian President Volodymyr Zelenskyy, despite renewed claims from the Russian and United States presidents that the war may be nearing an end. Zelenskyy said the barrage began on Wednesday morning and lasted for hours, striking Kyiv, the western city of Lviv near the Polish border and the Black Sea port of Odesa, among other areas. In the southern region of Kherson, Governor Oleksandr Prokudin said a woman was killed when a Russian drone struck a bus in the town of Bilozerka. Another drone attack in the western region of Rivne killed three people and injured four, according to Governor Oleksandr Koval. In the Kharkiv region in northeastern Ukraine, authorities said a 60-year-old man was killed when Russian forces attacked a community near the city of Zolochiv with first-person view drones.

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training and retrieve it at inference. Existing theoretical analyses typically study transformers under idealized assumptions such as infinite data or orthogonal embeddings. In realistic settings, however, models are trained on finite datasets with non-orthogonal (random) embeddings. We address this gap by analyzing a single-layer transformer with random embeddings trained with (empirical) gradient descent on a simple token-retrieval task, where the model must identify an informative token within a length-$L$ sequence and learn a one-to-one mapping from tokens to labels. Our analysis tracks the ``early phase'' of gradient descent and yields explicit formulas for the model's storage capacity -- revealing a multiplicative dependence between sample size $N$, embedding dimension $d$, and sequence length $L$. We validate these scalings numerically and further complement them with a lower bound for the underlying statistical problem, demonstrating that this multiplicative scaling is intrinsic under non-orthogonal embeddings.

Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' Ukrainian President Volodymyr Zelenskyy said that a state of emergency was being declared for Ukraine's energy sector, after repeated Russian attacks destroyed electricity and heat infrastructure. Zelenskyy said he asked the government to review curfew restrictions during "this extremely cold weather".

Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' Russian drone attack kills 4 in Ukraine's Kharkiv as peace remains elusive A Russian drone attack on Ukraine's northeastern city of Kharkiv has killed at least four people and wounded six, officials have said, just hours after Washington accused Moscow of "dangerous and inexplicable escalation" of the war and as a peace deal remains distant. Kharkiv Regional Governor Oleh Syniehubov said Tuesday that the death toll from the attack on the outskirts of the frequently targeted city, just 30km (19 miles) from the border, had risen to four.

Romance and parenthood feel remote in Ukraine: 'I haven't had a date since before the war' Sitting in a wine bar in Kyiv on a Saturday night, Daria, 34, opens a dating app, scrolls, then puts her phone away. After spending more than a decade in committed relationships she's been single for a long time. I haven't had a proper date since before the war, she says. Four years of war have forced Ukrainians to rethink nearly every aspect of daily life. Increasingly that includes decisions about relationships and parenthood - and these choices are, in turn, shaping the future of a country in which both marriage and birth rates are falling.

Russia used its hypersonic Oreshnik missile in an attack on Ukrainian infrastructure. Ukrainian President Volodymyr Zelenskyy called for an international response.

Service members take part in what the Russian Defense Ministry said was the deployment of a nuclear-capable hypersonic Oreshnik missile system in Belarus, in a still image taken from a video released on Dec. 30. Russia's military says it has fired its hypersonic Oreshnik missile at a target in Ukraine in response to what it described as an attempted Ukrainian drone strike on one of Russian President Vladimir Putin's residences, something Kyiv has called a lie. It is the second time that Russia has used the intermediate-range Oreshnik, a missile that Putin has boasted is impossible to intercept because of its reported velocity of more than 10 times the speed of sound. The missile is capable of carrying nuclear warheads as well as conventional ones, but there was no suggestion that the one used in the overnight attack had been fitted with anything other than a conventional warhead. The Russian Defense Ministry said the strike had targeted critical infrastructure in Ukraine. It said Russia had also used attack drones and high-precision long-range land and sea-based weapons.

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