Ahhh! Yes, this is very helpful! Thanks for the explanation.
Optimization Process
Karma: 654
Question: if I’m considering an isolated system (~= “the entire universe”), you say that I can swap between state-vector-format and matrix-format via
. But later, you say...
If is uncoupled to its environment (e.g. we are studying a carefully vacuum-isolated system), then we still have to replace the old state vector picture by a (possibly rank ) density matrix …
But if , how could it ever be rank>1?
(Perhaps more generally: what does it mean when a state is represented as a rank>1 density matrix? Or: given that the space of possible s is much larger than the space of possible s, there are sometimes (always?) multiple s that correspond to some particular ; what’s the significance of choosing one versus another to represent your system’s state?)
That is… a very interesting and attractive way of looking at it. I’ll chew on your longer post and respond there!
I have an Anki deck in which I’ve half-heartedly accumulated important quantities. Here are mine! (I keep them all as log10(value in kilogram/meter/second/dollar/whatever seems natural), to make multiplication easy.)
Quantity Value Electron mass -30 Electron charge -18.8 Gravitational constant -10.2 Reduced Planck constant -34 Black body radiation peak wavelength -2.5 Mass of the earth 24.8 Moon-Earth distance 8.6 Earth-sun distance 11.2 log10( 1 ) 0 log10( 2 ) 0.3 log10( 3 ) 0.5 log10( 4 ) 0.6 log10( 5 ) 0.7 log10( 6 ) 0.8 log10( 7 ) 0.85 log10( 8 ) 0.9 log10( 9 ) 0.95 Boltzmann constant -22.9 1 amu -26.8 1 mi 3.2 1 in -1.6 Earth radius 6.8 1 ft -0.5 1 lb -0.3 world population 10 US federal budget 2023 12.8 SWE wage (per sec) -1.4 Seattle min wage (per sec) 2024 -2.3 1 hr 3.6 1 work year 6.9 1 year 7.5 federal min wage (per sec) -2.7 1 acre 3.6
I thank you for your effort! I am currently missing a lot of the mathematical background necessary to make that post make sense, but I will revisit it if I find myself with the motivation to learn!
This is a good point! I’ll send you $20 if you send me your PayPal/Venmo/ETH/??? handle. (In my flailings, I’d stumbled upon this “fractional step” business, but I don’t think I thought about it as hard as it deserved.)
How are you defining “basically equivalent”
Nyeeeh, unfortunately, sort of “I know it when I see it.” It’s kinda neat being able to take a fractional step of a classical elementary CA, but I’m dissatisfied because… ah, because the long-run behavior of the fractional-step operator is basically indistinguishable from the long-run behavior of the corresponding classical CA.
So, tentative operationalization of “basically equivalent”: is “basically equivalent” to a classical elementary CA if the long-run behavior of is very close to the long-run behavior of some , i.e., uh,
...but I can already think of at least one flaw in this operationalization, so, uh, I’m not sure. (Sorry! This being so fuzzy in my head is why I’m asking for help!)
I was imagining the tape wraps around! (And hoping that whatever results fell out would port straightforwardly to infinite tapes.)
I’ve never been familiar enough with group-theory stuff to memorize the names (which, warning, also might mean that it will take you a lot of time to write a sufficiently-dumbed-down version), but the internet suggests is related to… the Minkowski metric? I would be flabbergasted to learn that something so specific-to-our-universe was relevant to this toy mathematical contraption.
I think compared to the literature you’re using an overly restrictive and nonstandard definition of quantum cellular automata.
That makes sense! I’m searching for the simplest cellular-automaton-like thing that’s still interesting to study. I may have gone too far in the “simple” direction; but I’d like to understand why this highly-restricted subset of QCAs is too simple.
Specifically, it only makes sense to me to write as a product of operators like you have if all of the terms are on spatially disjoint regions.
Hmm! That’s not obvious to me; if there’s some general insight like “no operator containing two ~‘partially overlapping’ terms like can be unitary,” I’d happily pay for that!
Things have coalesced near the amphitheater. When the music kicks off again, we’ll go northeast to… approximately here. 47.6309473, −122.3165802 JMJM+99F Seattle, Washington
Announcement 1: I, the organizer, will be 5-10min late. Announcement 2: apparently there’s some music thing happening at the amphitheater! I’ll set up somewhere northeast of the amphitheater when I get there, and post more precise coordinates when I have.
$10 bounty for anybody coming / passing through Capitol Hill: pick up a blind would-be attendee outside the Zeek’s Pizza by 19th and Mercer. DM me your contact information, and I’ll put you in touch, and I’ll pay you on your joint arrival.
Update: the library is unexpectedly closed due to staffing issues. The event is now at Fuel Coffee, one block south and across the street.
If the chance of rain is dissuading you: fear not, there’s a newly constructed roof over the amphitheater!
Hey, folks! PSA: looks like there’s a 50% chance of rain today. Plan A is for it to not rain; plan B is to meet in the rain.
See you soon, I hope!
You win both of the bounties I precommitted to!
Lovely! Yeah, that rhymes and scans well enough for me!
Here are my experiments; they’re pretty good, but I don’t count them as “reliably” scanning. So I think I’m gonna count this one as a win!
(I haven’t tried testing my chess prediction yet, but here it is on ASCII-art mazes.)
I found this lens very interesting!
Upon reflection, though, I begin to be skeptical that “selection” is any different from “reward.”
Consider the description of model-training:To motivate this, let’s view the above process not from the vantage point of the overall training loop but from the perspective of the model itself. For the purposes of demonstration, let’s assume the model is a conscious and coherent entity. From it’s perspective, the above process looks like:
Waking up with no memories in an environment.
Taking a bunch of actions.
Suddenly falling unconscious.
Waking up with no memories in an environment.
Taking a bunch of actions.
and so on.....
The model never “sees” the reward. Each time it wakes up in an environment, its cognition has been altered slightly such that it is more likely to take certain actions than it was before.
What distinguishes this from how my brain works? The above is pretty much exactly what happens to my brain every millisecond:
It wakes up in an environment, with no memories[1]; just a raw causal process mapping inputs to outputs.
It receives some inputs, and produces some outputs.
It’s replaced with a new version—almost identical to the old version, but with some synapse weights and activation states tweaked via simple, local operations.
It wakes up in an environment...
and so on...
Why say that I “see” reward, but the model doesn’t?
- ^
Is it cheating to say this? I don’t think so. Both I and GPT-3 saw the sentence “Paris is the capital of France” in the past; both of us had our synapse weights tweaked as a result; and now both of us can tell you the capital of France. If we’re saying that the model doesn’t “have memories,” then, I propose, neither do I.
Oh, this is genius. I love this.