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One way of viewing planning is as an outer-loop on decision theory.

My approach to the general problem of planning skills was to start with decision theory and build up. In my Guild of the Rose Decision Theory courses was to spend time focusing on slowly building the most fundamental skills of decision theory. This included practicing manipulation of probabilities and utilities via decision trees, and practicing all these steps in a variety of both real and synthetic scenarios, to build an intuition regarding the nuances of how to set up decision problems on paper. The ultimate goal was to get the practitioners to the point where they usually don't need to draw up a decision tree on paper, but rather to leverage those intuitions to quickly solve decision problems mentally, and/or recognize when a decision problem is actually tricky enough to merit breaking out the spreadsheet or Guesstimate project.

In my experience, even long-time rationalists are so incredibly bad at basic decision theory that trying to skip the step of learning to correctly set up a basic decision tree might actually be counterproductive. So my inclination is to focus on really mastering this art before attempting planning.

Another way of viewing planning is that planning is search. 

For computationally bounded agents like us, search involves a natural tradeoff of breadth versus depth. Breadth is essentially idea generation, depth is idea selection and refinement. The tricky think about planning, in general, is that if 100x solutions exist, then those solutions are going to be found by spending the majority of the time on breadth-search, i.e. blue sky brainstorming for ways that the plan could look wildly different from the default approach, but that most situations don't admit 100x plans. Most things in life, especially in our technological civilization, are already sort of optimized, because there is some existing refined solution that has already accommodated the relevant tradeoffs. I could get to work faster if I flew there in a helicopter, but considering in costs, the Pareto optimum is still driving my car on the freeway. Most things look like this. Well-considered Pareto solutions to real-world problems tend to look boring!

Therefor, if you spend a lot of time looking for 100x solutions, you will waste a lot of time, because these solutions usually won't exist. Then, after failing to find a truly galaxy-brain solution, you will spend some amount of time refining the probably-already-obvious plan, realize that there are a lot of unknown-unknowns, and that the best way to get clarity on these is to just start working. Then you will realize that you would have been better off if you had just started working immediately and not bothered with "planning" at all, and you will either be Enlightened or depressed.

It gives me no pleasure to say this! Ten years ago I was all fired up on the idea that rationalists would Win and take over the world by finding these clever HPJEV-esque lateral thinking solutions. I have since realized that one creative rationalist is usually no match for tens of thousands of smart people exploring the manifold through natural breadth-first and then refining on the best solutions organically.

I am not actually completely blackpilled on the idea of scenario planning. Clearly there are situations for which scenario planning is appropriate. Massive capital allocations and long-term research programs might be two good examples. Even for these types of problems, it's worth remembering that the manifold probably only admits to marginal optimizations, not 100x optimizations, so you shouldn't spend too much time looking for them.

Well, there’s your problem!

HardwarePrecisionTFLOPSPrice ($)TFLOPS/$
Nvidia GeForce RTX 4090FP882.58$1,600 0.05161
AMD RX 7600FP821.5$270 0.07963
TPU v5eINT8393$4730*0.08309
H100FP161979$30,6030.06467
H100FP83958$30,6030.12933
* Estimated, sources suggest $3000-6000  

From my notes. Your statement about RTX 4090 leading the pack in flops per dollar does not seem correct based on these sources, perhaps you have a better source for your numbers than I do. 

I did not realize that H100 had >3.9 PFLOPS at 8-bit precision until you prompted me to look, so I appreciate that nudge. That does put the H100 above the TPU v5e in terms of FLOPS/$. Prior to that addition, you can see why I said TPU v5e was taking the lead. Note that the sticker price for TPU v5e is estimated, partly from a variety of sources, partly from my own estimate calculated from the lock-in hourly usage rates.

Note that FP8 and INT8 are both 8-bit computations and are in a certain sense comparable if not necessarily equivalent.

Could you lay that out for me, a little bit more politely? I’m curious.

Does Roodman’s model concern price-performance or raw performance improvement? I can’t find the reference and figured you might know. In either case, price-performance only depends on Moore’s law-like considerations in the numerator, while the denominator (price) is a a function of economics, which is going to change very rapidly as returns to capital spent on chips used for AI begins to grow.

As I remarked in other comments on this post, this is a plot of price-performance. The denominator is price, which can become cheap very fast. Potentially, as the demand for AI inference ramps up over the coming decade, the price of chips falls fast enough to drive this curve without chip speed growing nearly as fast. It is primarily an economic argument, not a purely technological argument.

For the purposes of forecasting, and understanding what the coming decade will look like, I think we care more about price-performance than raw chip speed. This is particularly true in a regime where both training and inference of large models benefit from massive parallelism. This means you can scale by buying new chips, and from a business or consumer perspective you benefit if those chips get cheaper and/or if they get faster at the same price.

A couple of things:

  1. TPUs are already effectively leaping above the GPU trend in price-performance. It is difficult to find an exact cost for a TPU because they are not sold retail, but my own low-confidence estimates for the price of a TPU v5e place its price-performance significantly above the GPU given in the plot. I would expect that the front runner in price-performance cease to be what we think of as GPUs and thus intrinsic architectural limitations of GPUs cease to be the critical bottleneck.
  2. Expecting price-performance to improve doesn't mean we necessarily expect hardware to improve, just that we become more efficient at making hardware. Economies of scale and refinements in manufacturing technology can dramatically improve price-performance by reducing manufacturing costs, without any improvement in the underlying hardware. Of course, in reality we expect both the hardware to become faster and the price of manufacturing it to fall. This is even more true as the sheer quantity of money being poured into compute manufacturing goes parabolic.

The graph was showing up fine before, but seems to be missing now. Perhaps it will come back. The equation is simply an eyeballed curve fit to Kurzweil's own curve. I tried pretty hard to convey that the 1000x number is approximate:
 > Using the super-exponential extrapolation projects something closer to 1000x improvement in price-performance. Take these numbers as rough, since the extrapolations depend very much on the minutiae of how you do your curve fit. Regardless of the details, it is a difference of orders of magnitude.

The justification for putting the 1000x number in the post instead of precisely calculating a number from the curve fit is that the actual trend is pretty wobbly over the years, and my aim here is not to pretend at precision. If you just look at the plot, it looks like we should expect "about 3 orders of magnitude" which really is the limit of the precision level that I would be comfortable with stating. I would guess not lower than two orders of magnitude. Certainly not as low as one order of magnitude, as would be implied by the exponential extrapolation, and would require that we don't have any breakthroughs or new paradigms at all.

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