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Or:. Your friend Ben is also pretty good, but he’s had a bit too much to drink. His darts are all over, but he loudly points out that on average he’s hitting the bull’s-eye. (Maybe he should have been a statistician.) This is the low-bias, high-variance case, shown in the bottom right corner. Ben’s girlfriend, Ashley, is very steady, butshe has a tendency to aim too high and to the right. She has low variance and high bias (top left corner). Cody, who’s visiting from out of town and has never played darts before, is both all over and off center. He has both high bias and high variance (top right).. One such rule is:If Socrates is human, then he’s mortal. This does the job, but is not very useful because it’s specific to Socrates. But now we apply Newton’s principle and generalize the rule to all entities:If an entity is human, then it’s mortal. Or, more succinctly:All humans are mortal. Of course, it would be rash to induce this rule from Socrates alone, but we know similar facts about other humans:. In symbolist learning, there is a one-to-one correspondence between symbols and the concepts they represent. In contrast, connectionist representations are distributed: each concept is represented by many neurons, and each neuron participates in representing many different concepts. Neurons that excite one another form what Hebb called a cell assembly. Concepts and memories are represented in the brain by cell assemblies. Each of these can include neurons from different brain regions and overlap with other assemblies. The cell assembly for“leg” includes the one for “foot,” which includes assemblies for the image of a foot and the sound of the wordfoot. If you ask a symbolist system where the concept“New York” is represented, it can point to the precise location in memory where it’s stored. In a connectionist system, the answer is “it’s stored a little bit everywhere.”. The S curve is not just important as a model in its own right; it’s also the jack-of-all-trades of mathematics. If you zoom in on its midsection, it approximates a straight line. Many phenomena we think of as linear are in fact S curves, because nothing can grow without limit. Because of relativity, andcontra Newton, acceleration does not increase linearly with force, but follows an S curve centered at zero. So does electric current as a function of voltage in the resistors found in electronic circuits, or in a light bulb (until the filament melts, which is itself another phase transition). If you zoom out from an S curve, it approximates a step function, with the output suddenly changing from zero to one at the threshold. So depending on the input voltages, the same curve represents the workings of a transistor in both digital computers and analog devices like amplifiers and radio tuners. The early part of an S curve is effectively an exponential, and near the saturation point it approximates exponential decay. When someone talks about exponential growth, ask yourself: How soon will it turn into an S curve? When will the population bomb peter out, Moore’s law lose steam, or the singularity fail to happen? Differentiate an S curve and you get a bell curve: slow, fast, slow becomes low, high, low. Add a succession of staggered upward and downward S curves, and you get something close to a sine wave. In fact, every function can be closely approximated by a sum of S curves: when the function goes up, you add an S curve; when it goes down, you subtract one. Children’s learning is not a steady improvement but an accumulation of S curves. So is technological change. Squint at the New York City skyline and you can see a sum of S curves unfolding across the horizon, each as sharp as a skyscraper’s corner.. Robotic Park is a massive robot factory surrounded by ten thousand square miles of jungle, urban and otherwise. Ringing that jungle is the tallest, thickest wall ever built, bristling with sentry posts, searchlights, and gun turrets. The wall has two purposes: to keep trespassers out and the park’s inhabitants-millions of robots battling for survival and control of the factory-within. The winning robots get to spawn, their reproduction accomplished by programming the banks of 3-D printers inside. Step-by-step, the robots become smarter, faster-and deadlier. Robotic Park is run by the US Army, and its purpose is to evolve the ultimate soldier.. Evolutionaries and connectionists have something important in common: they both design learning algorithms inspired by nature. But then they part ways. Evolutionaries focus on learning structure; to them, fine-tuning an evolved structure by optimizing parameters is of secondary importance. In contrast, connectionists prefer to take a simple, hand-coded structure with lots of connections and let weight learning do all the work. This is machine learning’s version of the nature versus nurture controversy, and there are good arguments on both sides.. On the other hand, you may be wondering why we’re not done at this point. Surely if we’ve combined nature’s two master algorithms, evolution and the brain, that’s all we could ask for. Unfortunately, what we have so far is only a very crude cartoon of how nature learns, good enough for a lot of applications but still a pale shadow of the real thing. For example, the development of the embryo is a crucial part of life, but there’s no analog of it in machine learning: the “organism” is a very straightforward function of the genome, and we may be missing something important there. But another reason is that we wouldn’t be satisfied even if we had completely figured out how nature learns. For one thing, it’s too slow. Evolution takes billions of years to learn, and the brain takes a lifetime. Culture is better: I can distill a lifetime of learning into a book, and you can read it in a few hours. But learning algorithms should be able to learn in minutes or seconds. He who learns fastest wins, whether it’s the Baldwin effect speeding up evolution, verbal communication speeding up human learning, or computers discovering patterns at the speed of light. Machine learning is the latest chapter in the arms race of life on Earth, and swifter hardware is only half the equation. The other half is smarter software.. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up, if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes.. Everything is connected, but not directly. The most important question in any analogical learner is how to measure similarity. It could be as simple as Euclidean distance between data points, or as complex as a whole program with multiple levels of subroutines whose final output is a similarity value. Either way, the similarity function controls how the learner generalizes from known examples to new ones. It’s where we insert our knowledge of the problem domain into the learner, making it the analogizers’ answer to Hume’s question. We can apply analogical learning to all kinds of objects, not just vectors of attributes, provided we have a way of measuring the similarity between them. For example, we can measure the similarity between two molecules by the number of identical substructures they contain. Methane and methanol are similar because they have three carbon-hydrogen bonds in common and differ only in the replacement of a hydrogen atom by a hydroxyl group:. We flip the“on” switch, and Robby’s video eyes open for the very first time. At once he’s flooded with what William James memorably called the “blooming, buzzing confusion” of the world. With new images streaming in at a rate of dozens per second, one of the first things he must do is learn to organize them into larger chunks. The real world is made up of objects that persist over time, not random pixels changing arbitrarily from one moment to the next. Mommy isn’t replaced by a smaller Mommy when she walks away. Putting a dish on the table doesn’t make a white hole in it. A young baby is not surprised if a teddy bear passes behind a screen and reemerges as an airplane, but a one-year-old is. Somehow, he’s figured out that teddy bears are different from airplanes and don’t spontaneously transmute. Soon afterward, he’ll figure out that some objects are more alike than others and start forming categories. Given a pile of toy horses and pencils to play with, a nine-month-old doesn’t think to sort them into separate piles of horses and pencils, but an eighteen-month-old does.. Online dating is in fact a tough example because chemistry is hard to predict. Two people who hit it off on a date may wind up falling in love and believing passionately that they were made for each other, but if their initial conversation takes a different turn, they might instead find each other annoying and never want to meet again. What a really sophisticated learner would do is run a thousand Monte Carlo simulations of a date between each pair of plausible matches and rank the matches by the fraction of dates that turned out well. Short of that, dating sites can organize parties and invite people who are each a likely match for many of the others, letting them accomplish in a few hours what would otherwise take weeks.. Even more interesting, the process doesn’t end when you find a car, a house, a doctor, a date, or a job. Your digital half is continually learning from its experiences, just as you would. It figures out what works and doesn’t, whether it’s in job interviews, dating, or real-estate hunting. It learns about the people and organizations it interacts with on your behalf and then (even more important) from your real-world interactions with them. It predicted Alice would be a great date for you, but you had an awkward time, so it hypothesizes possible reasons, which it will test on your next round of dating. It shares its most important findings with you. (“You believe you like X, but in reality you tend to go for Y.”) Comparing your experiences of various hotels with their reviews on TripAdvisor, it figures out what the really telling tidbits are and looks for them in the future. It learns not just which online merchantsare more trustworthy but how to decode what the less trustworthy ones say. Your digital half has a model of the world: not just of the world in general but of the world as it relates to you. At the same time, of course, everyone else also has a continually evolving model of his or her world. Every party to an interaction learns from it and applies what it’s learned to its next interactions. You have your model of every person and organization you interact with, and they each have their model of you. As the models improve, their interactions become more and more like the ones you would have in the real world-except millions of times faster and in silicon. Tomorrow’s cyberspace will be a vast parallel world that selects only the most promising things to try out in the real one. It will be like a new, global subconscious, the collective id of the human race.. Three Algorithms for the Scientists under the sky,.