@MrStickman

Hey! The EML function made the rounds recently on the internet as a “cool trick” that allows for the representation of all elementary functions through composition. As a mathematical curiosity, we prove a universal approximation theorem for EML(-type) trees. Intuitively, one expects that if elementary functions can be presented by compositions of EMLs, then so too can polynomials, and polynomials are dense in other functional spaces (like continuous functions or certain Sobolev spaces), then one expects to be able to approximate (to desired accuracy) any function (in a reasonably general space) through an EML tree (with an upper bound on size and depth). One of the key steps in the proof (detailed in the appendix) is an explicit construction of EML(-type) representation of binary operations, polynomials, hyperbolic tangent, and approximate partitions of unity, and subsequently using them as “LEGO” blocks to get more complex functions. There are some technical difficulties that need to be dealt with in the proof, especially in what relates to the the ill-definedness of the natural logarithm for nonpositive inputs, which prompts us to do some “sign-based decompositions” in Theorem1.Step 5 and a suitable affine map in Corollary 1. Comments are welcome! Paper: https://arxiv.org/pdf/2606.23179 (Note: I use the term “EML(-type)” in the above description because, due to some theoretical and practical reasons detailed in the paper, we generalize the original EML function by adding some learnable parameters.) submitted by /u/JoeGermany [link] [Kommentare]

Hey guys Im 33 tried starting a buisness looks like wont work out the way i wanted few paying customers but meh wont become a millionaire from it What can I do can I place my money on a smaller cyrpto market and make millions from it Im not going back to my normal job I have over 200k saved what can i do to make it millions asap? submitted by /u/Prior_Night_985 [link] [Kommentare]

A day in AI now feels like a year in any other industry. TSMC, Vera Rubin VR NVL72: V for Value

The full effects of the ban may not be clear for a decade.

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Whether you’re a fan of crypto or not, it’s obvious that it’s driven by speculative money. Believers in the tech are the minority. Put it this way, if BTC never rose past $10, almost none of us would be here. Speculative gain is the fundamental fuel that keeps crypto alive. Without it, everything goes the way of NFTs. But now, that fundamental fuel is gone. Speculative interest has moved to AI. People aren’t waiting 4 years with crypto, when they can get rich in 4 weeks with AI and chips. That’s also why crypto has decoupled from the market and keeps going down no matter how the wider market moves. It’s also why the 4 year cycle isn’t valid anymore. FTX and previous dips were different. Those dips were fuelled by risk and fear. But risk and fear have never stopped speculators. It’s the reason why they are speculators in the first place. Crypto could recover from those dips, because people still wanted to get rich quick, and crypto was the best way. This time is fundamentally different because there is a better and faster way for people to be greedy. Crypto is no longer the best way to be greedy. Crypto can survive fear, but it cannot survive greed. And AI isn’t going away. The smartest people and biggest companies in the world aren’t investing trillions in AI for nothing. They are going all in because AI is obviously here to stay. submitted by /u/interstellar_nips [link] [Kommentare]

Over 100 companies and government agencies are reportedly authorized to use Mythos 5, including their non-American employees.

A conjectural theory of cognitive inequality