Brewing byproduct may be a key sustainable secret ingredient. Breakthroughs, discoveries, and DIY tips sent every weekday. Brewing beer relies on a very simple living thing-brewer's yeast. The microorganisms thrive on mashed grains, converting sugars into both alcohol and carbon dioxide along the way. But there's not much use for yeast after the pints are poured .

Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts to design communication-compressed algorithms for decentralized nonconvex optimization, where the clients are only allowed to communicate a small amount of quantized information (aka bits) with their neighbors over a predefined graph topology. Despite significant efforts, the state-of-the-art algorithm in the nonconvex setting still suffers from a slower rate of convergence $O((G/T)^{2/3})$ compared with their uncompressed counterpart, where $G$ measures the data heterogeneity across different clients, and $T$ is the number of communication rounds. This paper proposes BEER, which adopts communication compression with gradient tracking, and shows it converges at a faster rate of $O(1/T)$. This significantly improves over the state-of-the-art rate, by matching the rate without compression even under arbitrary data heterogeneity. Numerical experiments are also provided to corroborate our theory and confirm the practical superiority of beer in the data heterogeneous regime.

Breakthroughs, discoveries, and DIY tips sent every weekday. Humans have a long history with alcohol--we've been making and consuming it for over ten thousand years, about as long as we've had agriculture. That's a long time for people to come up with all kinds of ideas about the drug and how it works. So, not surprisingly, some of them are wrong. Here are a few common myths about alcohol, debunked by scientific research.

In this section, we review closely related literature on decentralized optimization, communication-efficient algorithms, and communication compression. Both categories have received significant attention in recent years. Here, (7) is referred as the Cauchy-Schwarz inequality, (8) and (9) are referred as Y oung's inequality. Specifically, we have the following lemma. Proof: We first prove (11) by induction.

The user then decides weather to try (i.e., consume) the beer (

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Only four bottles of Asahi Super Dry beer are left on the shelves of Ben Thai, a cosy restaurant in the Tokyo suburb of Sengawacho. Its owner, Sakaolath Sugizaki, expects to get a few more soon, but she says her supplier is keeping the bulk of its stock for bigger customers. That's because Asahi, the maker of Japan's best-selling beer, was forced to halt production at most of its 30 factories in the country at the end of last month after being hit by a cyber-attack. While all of its facilities in Japan - including six breweries - have now partially reopened, its computer systems are still down. That means it has to process orders and shipments manually - using pen, paper and fax machines - resulting in much fewer shipments than before the attack.

In a classic paper, Conant and Ashby claimed that "every good regulator of a system must be a model of that system." Artificial Life has produced many examples of systems that perform tasks with apparently no model in sight; these suggest Conant and Ashby's theorem doesn't easily generalise beyond its restricted setup. Nevertheless, here we show that a similar intuition can be fleshed out in a different way: whenever an agent is able to perform a regulation task, it is possible for an observer to interpret it as having "beliefs" about its environment, which it "updates" in response to sensory input. This notion of belief updating provides a notion of model that is more sophisticated than Conant and Ashby's, as well as a theorem that is more broadly applicable. However, it necessitates a change in perspective, in that the observer plays an essential role in the theory: models are not a mere property of the system but are imposed on it from outside. Our theorem holds regardless of whether the system is regulating its environment in a classic control theory setup, or whether it's regulating its own internal state; the model is of its environment either way. The model might be trivial, however, and this is how the apparent counterexamples are resolved.