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  1. Climate change is one of the greatest challenges facing humanity, and we, as machine learning (ML) experts, may wonder how we can help. Here we describe how ML can be a powerful tool in reducing greenhouse gas emissions and helping society adapt to a changing climate. From smart grids to disaster management, we identify high impact problems where existing gaps can be filled by ML, in collaboration with other fields. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the ML community to join the global effort against climate change. 
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  2. Great claims have been made about the benefits of dematerialization in a digital service economy. However, digitalization has historically increased environmental impacts at local and planetary scales, affecting labor markets, resource use, governance, and power relationships. Here we study the past, present, and future of digitalization through the lens of three interdependent elements of the Anthropocene: ( a) planetary boundaries and stability, ( b) equity within and between countries, and ( c) human agency and governance, mediated via ( i) increasing resource efficiency, ( ii) accelerating consumption and scale effects, ( iii) expanding political and economic control, and ( iv) deteriorating social cohesion. While direct environmental impacts matter, the indirect and systemic effects of digitalization are more profoundly reshaping the relationship between humans, technosphere and planet. We develop three scenarios: planetary instability, green but inhumane, and deliberate for the good. We conclude with identifying leverage points that shift human–digital–Earth interactions toward sustainability. 
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  3. In 1943, McCulloch and Pitts introduced a discrete recurrent neural network as a model for computation in brains. The work inspired breakthroughs such as the first computer design and the theory of finite automata. We focus on learning in Hopfield networks, a special case with symmetric weights and fixed-point attractor dynamics. Specifically, we explore minimum energy flow (MEF) as a scalable convex objective for determining network parameters. We catalog various properties of MEF, such as biological plausibility, and then compare to classical approaches in the theory of learning. Trained Hopfield networks can perform unsupervised clustering and define novel error-correcting coding schemes. They also efficiently find hidden structures (cliques) in graph theory. We extend this known connection from graphs to hypergraphs and discover n-node networks with robust storage of 2Ω(n1−ϵ) memories for any ϵ>0. In the case of graphs, we also determine a critical ratio of training samples at which networks generalize completely. 
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