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The same way we feed the variable size sequence of characters or sound samples into this RNN. Instead of raw samples at the 16 kHz rate, we'll have one sequence of 1 sample per second, another sequence of 1 sample per 0.5 seconds and so on. We can go as far as 1 sample per 1/48000 sec, but I don't think it's practical (but this is what these music generators do).
This proof is largely irrelevant in the real world. An interesting question would be how much can be approximated with a model that has 1 MB worth of weights and can use only relu/tanh/softmax activations.
I don't think every continuous function can be approximated this way because we can make an infinitely complex, but continuous function that would have any n-th derivative also continuous. I'm thinking about those weird zeta-riemann-style functions. In order to approximate such a function we'd need a huge model that couldn't be computed or stored even by a universe-size perfect computer.
Of course they can, because an NN can be any function. If we can pick tanh as the "activation" then we can as easily pick arctan as the activation ans say our NN computes arctan. What an achievement! A better question is whether conv+relu based NNs can approximate any function. But that's most likely false because there are many weird functions that are impossible to compute, not even approximate (I'm talking about those curious counter-examples in math).
It's not so much about the density. It's about ludicrous mortgage that they signed up in past and want their house to at least maintain its price.
It's not the corporations, but the current mortgage system. Corp workers with 100-200k pay pair up and put their entire life earnings (30 years) towards a house. Banks back this deal and the couple gets a house they can't really afford. Same with our education system and healthcare. If the gov made a law that mortgage can't exceed 1 year income, prices would adjust to that number.
More like a 2M house and a 120K car. 500K/year isn't enough to live in a 10M house because it's 20 years of work (30, accounting for other expenses) and that assumes no cut in income. To get into a 10M house one needs to start a very successful business, which is quite possible after all the experience at such a job.
The advice that I would give to myself in my early 20s is (1) nobody cares about your career except you: people come and go, change companies and have their own careers; (2) the only way to move up the ranks is by shifting between companies and getting multiple competing offers; this applies even to outstanding devs; so you are expected to move every 3-4 years if you don't want to get stuck at your entry level pay.
It's also far easier for an L4 to get competing offers for amount far exceeding what L5s make. That's also how many (most?) people get the L5 level: they negotiate with HRs when they have the leverage (competing offers). Getting to L5 via the promo committee is probably the hardest way to get there.
650 is L6 which is maybe 5% of the Google's population. The median pay would be around 300.
I don't get this statement. Google doesn't force anyone to work overnight. It doesn't force you to work at all, to be honest. Some people can spend a workday skiing and then arrive at 6 pm for dinner. TC is 400K. And once you're bored or feel undercompensated, you just go to FB, Netflix or Snapchat and get a 30-50% pay rise.
The other option is to realize that in the world of people, your people skills can be even more valuable than your technical skills. I think that L5 is the tipping point where people skills start to dominate.
That's because a decent programmer (especially one working at Google) has many companies fighting for him trying to offer more than others. It's usually easy to leave and that often comes with a hefty raise and it will be your former boss' problem that his direct reports are leaving. Unions are seen from this perspective as bureaucratic organizations run by not very smart people who want to get their piece of the pie by regulating what they don't understand. Unions are good for the opposite market situation when there are too many workers and they have to fight for the limit number of jobs.
I actually think capitalism is the problem. It's the best form we know to organize a society, but it has the serious problem when money tend to stick or gravitate towards bigger chunks of money. I'm making well over 300k and can afford a decent house that I'd have to pay off my entire life. What if I had 30M and was too lazy to start a business? I would just buy 30-40 nice houses in my area and would rent them. 10 years later I would have 60M in assets plus whatever rent I've been paid. Where did those 30M come from? Did I do anything useful to the society? No. I have done nothing useful. It's just the dynamics of capitalism where another 30M sticked to my original 30M by the mere fact of their existence. If I was seriously rich, I could lobby zoning laws to benefit from monopoly and drive my wealth even higher, while giving nothing back to the society.