Of course, the count function should be fixed.

Alphabet reports $34.5bn profit and revenue soars 48% in recent quarter as it plans a sharp increase in AI spending Google's parent company, Alphabet, beat Wall Street expectations on Wednesday, and is planning a sharp increase in capital spending in 2026 as it continues to invest deeply in AI infrastructure. Alphabet on Wednesday reported profit of $34.5bn in the recently ended quarter, as revenue from cloud computing soared 48%. In an earnings call, investors pressed Alphabet's chief executive, Sundar Pichai, on the significant increase. "We've been supply constrained, even as we've been ramping up our capacity. Obviously, our CapEx spend this year is an eye towards the future," Pichai said, in response.

Google's parent company hit a major financial milestone on Monday, reaching a $4tn valuation for the first time and surpassing Apple to become the second-most valuable company in the world. Alphabet is the fourth company to hit the $4tn milestone after Nvidia, which later hit $5tn, Microsoft and Apple . The spike in share price comes after Apple announced it had chosen Google's Gemini AI model to power a major overhaul of the iPhone maker's digital assistant Siri, which comes installed in every iPhone. Neither company disclosed how much the deal was worth. "After careful evaluation, we determined that Google's technology provides the most capable foundation for Apple Foundation Models," Apple said in a statement to CNBC . As tech stocks continue a years-long meteoric rise, fears of a bubble in the stock market persist; however, Wall Street's excitement for new avenues of investment in AI does as well.

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption renders the problem feasible. We argue that the moment assumption is natural and, in some sense, {\em minimalistic} --- weaker than finite support or tail decay conditions. Under the moment assumption, we provide the first finite-sample entropy estimates for infinite alphabets, nearly recovering the known minimax rates. Moreover, we demonstrate that our empirical bounds are significantly sharper than the state-of-the-art bounds, for various natural distributions and non-trivial sample regimes. Along the way, we give a dimension-free analogue of the Cover-Thomas result on entropy continuity (with respect to total variation distance) for finite alphabets, which may be of independent interest.

Proven methods for teaching the readers who struggle most have been known for decades. Why do we often fail to use them? "There's a window of opportunity to intervene," Mark Seidenberg, a cognitive neuroscientist, said. "You don't want to let that go." In 2024, my niece Caroline received a Ph.D. in gravitational-wave physics. Her research interests include "the impact of model inaccuracies on biases in parameters recovered from gravitational wave data" and "Petrov type, principal null directions, and Killing tensors of slowly rotating black holes in quadratic gravity." I watched a little of her dissertation defense, on Zoom, and was lost as soon as she'd finished introducing herself. She and her husband now live in Italy, where she has a postdoctoral appointment. Caroline's academic achievements seem especially impressive if you know that until third grade she could barely read: to her, words on a page looked like a pulsing mass. She attended a private school in Connecticut, and there was a set time every day when students selected books to read on their own. "I can't remember how long that lasted, but it felt endless," she told me. She hid her disability by turning pages when her classmates did, and by volunteering to draw illustrations during group story-writing projects. One day, she told her grandmother that she could sound out individual letters but when she got to "the end of a row" she couldn't remember what had come before. A psychologist eventually identified her condition as dyslexia. Fluent readers sometimes think of dyslexia as a tendency to put letters in the wrong order or facing the wrong direction, but it's more complicated than that.

Google runs the Gemini AI model and is owned by Alphabet. Google runs the Gemini AI model and is owned by Alphabet. EU opens investigation into Google's use of online content for AI models Tue 9 Dec 2025 05.06 ESTFirst published on Tue 9 Dec 2025 03.48 EST The EU has opened an investigation to assess whether Google is breaching European competition rules in its use of online content from publishers and YouTube creators for artificial intelligence. The European Commission said on Tuesday it will examine whether the US tech company, which runs the Gemini AI model and is owned by Alphabet, is putting rival AI owners at a "disadvantage". "The investigation will notably examine whether Google is distorting competition by imposing unfair terms and conditions on publishers and content creators, or by granting itself privileged access to such content, thereby placing developers of rival AI models at a disadvantage," the commission said.

In this manner we obtain an efficient feed-forward one-shot learner, trained end-to-end by minimizing a one-shot classification objective in a learning to learn formulation. In order to make the construction feasible, we propose a number of factorizations of the parameters of the pupil network.

Many important machine learning tasks are instances of structured prediction problems.

Recent works have shown that tokenisation is NP-complete. However, these works assume tokenisation is applied to inputs with unboundedly large alphabets -- an unrealistic assumption, given that in practice tokenisers operate over fixed-size alphabets, such as bytes or Unicode characters. We close this gap by analysing tokenisation over bounded $n$-ary alphabets, considering two natural variants: bottom-up tokenisation and direct tokenisation, where we must, respectively, select a sequence of merge operations or a vocabulary whose application optimally compresses a dataset. First, we note that proving hardness results for an $n$-ary alphabet proves the same results for alphabets of any larger size. We then prove that even with binary alphabets, both variants are not only NP-complete, but admit no polynomial-time approximation scheme (unless P=NP). We further show that direct tokenisation remains NP-complete even when applied to unary alphabets. While unary alphabets may not be practically useful, this result establishes that the computational intractability of tokenisation is not an artifact of large alphabets or complex constructions, but a fundamental barrier. Overall, our results explain why practical algorithms such as BPE and UnigramLM are heuristic, and points toward approximation algorithms being an important path going forward for tokenisation research.