I've been looking at papers involving a lot of 'controlling for confounders' recently and am unsure about how much weight to give their results.
Does anyone have recommendations about how to judge the robustness of these kind of studies?
Also, I was considering doing some tests of my own based on random causal graphs, testing what happens to regressions when you control for a limited subset of confounders, varying the size/depth of graph and so on. I can't seem to find any similar papers but I don't know the area, does anyone know of similar work?
This employee has 100 million dollars, approximately 10,000x fewer resources than the hedge fund. Even if the employee engaged in unethical business practices to achieve a 2x higher yearly growth rate than their former employer, it would take 13 years for them to have a similar amount of capital.
I think it's worth being explicit here about whether increases in resources under control are due to appreciation of existing capital or allocation of new capital.
If you're talking about appreciation, then if the firm earns 5% returns on average and the rogue... (read more)
Cheers for the post, I find the whole series fascinating.
One thing I was particularly curious about is how these 'proposals' are made. Do you have a picture of what kind of embedding is used to present a potential action?
For example, is a proposal encoded in the activations of set of neurons that are isomorphic to the motor neurons and it could then propose tightening a set of finger muscles through specific neurons? Or is the embedding jointly learned between the two in some large unstructured connection, or smaller latent space, or something completely different?
Another little update, speed issue solved for now by adding SymPy's fortran wrappers to the derivative calculations - calculating the SVD isn't (yet?) the bottleneck. Can now quickly get results from 1,000+ step simulations of 100s of particles.
Unfortunately, even for the pretty stable configuration below, the values are indeed exploding. I need to go back through the program and double check the logic but I don't think it should be chaotic, if anything I would expect the values to hit zero.
It might be that there's some kind of quasi-chaotic behaviou... (read more)
Been a while but I thought the idea was interesting and had a go at implementing it. Houdini was too much for my laptop, let alone my programming skills, but I found a simple particle simulation in pygame which shows the basics, can see below.
Planned next step is to work on the run-time speed (even this took a couple of minutes run, calculating the frame-to-frame Jacobian is a pain, probably more than necessary) and then add some utilities for creatin... (read more)
Reading this after Steve Byrnes' posts on neuroscience gives a potentially unfortunate view on this.
The general impression is that the a lot of our general understanding of the world is carried in the neocortex which is running a consistent statistical algorithm and the fact that humans converge on similar abstractions about the world could be explained by the statistical regularities of the world as discovered by this system. At the same time, the other parts of the brain have a huge variety of structures and have functions which are the products of evolu... (read more)
I agree that this is the biggest concern with these models, and the GPT-n series running out of steam wouldn't be a huge relief. It looks likely that we'll have the first human-scale (in terms of parameters) NNs before 2026 - Metaculus, 81% as of 13.08.2020.
Does anybody know of any work that's analysing the rate at which, once the first NN crosses the n-parameter barrier, other architectures are also tried at that scale? If no-one's done it yet, I'll have a look at scraping the data from Papers With Code's databases on e.g. I... (read more)
Hey Daniel, don't have time for a proper reply right now but am interested in talking about this at some point soon. I'm currently in UK Civil Service and will be trying to speak to people in their Office for AI at some point soon to get a feel for what's going on there, perhaps plant some seeds of concern. I think some similar things apply.
I think this this points to the strategic supremacy of relevant infrastructure in these scenarios. From what I remember of the battleship era, having an advantage in design didn't seem to be a particularly large advantage - once a new era was entered, everyone with sufficient infrastructure switches to the new technology and an arms race starts from scratch.
This feels similar to the AI scenario, where technology seems likely to spread quickly through a combination of high financial incentive, interconnected social networks, state-sponsored espionage e... (read more)
Apologies if this is not the discussion you wanted, but it's hard to engage with comparability classes without a framework for how their boundaries are even minimally plausible.
Would you say that all types of discomfort are comparable with higher quantities of themselves? Is there always a marginally worse type of discomfort for any given negative experience? So long as both of these are true (and I struggle to deny them) then transitivity seems to connect the entire spectrum of negative experience. Do you think there is a way to remove the transitivity of comparability and still have a coherent system? This, to me, would be the core requirement for making dust specks and torture incomparable.
I've realised that you've gotta be careful with this method because when you find a trichromatic subtriangle of the original, it won't necessarily have the property of only having points of two colours along the edges, and so may not in fact contain a point that maps to the centre.
This isn't a problem if we just increase the number n by which we divide the whole triangle instead of recursively dividing subtriangles. Unfortunately now we're not reducing the range of co-ords where this fixed point must be, only finding a triad of ar... (read more)
Cleanest solution I can find for #8:
Also, if we have a proof for #6 there's a pleasant method for #7 that should work in any dimension:
We take our closed convex set S that has the bounded function h:S→S . We take a triangle T that covers S so that any point in S is also in T .
Now we define a new function h′:T→T such that h′(x)=h(cs(x)) where cs(x) is the function that maps x to the nearest point in S.
By #6 we know that h′ has a fixed point, since cs is continuous. We know that the fixed point of h′ cannot lie outside S because th... (read more)
On my approach:
I constructed a large triangle around the convex shape with the center somewhere in the interior. I then projected each point in the convex shape from the center towards the edge of the triangle in a proportional manner. ie. The center stays where it is, the points on the edge of the convex shape are projected to the edge of the triangle and a point 1/x of the distance from the center to the edge of the convex shape is 1/x of the distance from the center to the edge of the triangle.
Yeah agreed, in fact I don't think you even need to continually bisect, you can just increase n indefinitely. Iterating becomes more dangerous as you move to higher dimensions because an n dimensional simplex with n+1 colours that has been coloured according to analogous rules doesn't necessarily contain the point that maps to zero.
On the second point, yes I'd been assuming that a bounded function had a bounded gradient, which certainly isn't true for say sin(x^2), the final step needs more work, I like the way you did it in the proof below.
Here's a messy way that at least doesn't need too much exhaustive search:
First let's separate all of the red nodes into groups so that within each group you can get to any other node in that group only passing through red nodes, but not to red nodes in any other group.
Now, we trace out the paths that surround these groups - they immediately look like the paths from Question 1 so this feels like a good start. More precisely, we draw out the paths such that each vertex forms one side of a triangle that has a blue node at its opposite corner. ... (read more)
I was able to get at least (I think) close to proving 2 using Sperner's Lemma as follows:
You can map the continuous function f(x) to a path of the kind found in Question 1 of length n+1 by evaluating f(x) at x=0, x=1 and n-1 equally spaced divisions between these two points and setting a node as blue if f(x) < 0 else as green.
By Sperner's Lemma there is an odd, and therefore non-zero number of b-g vertices. You can then take any b-g pair of nodes as the starting points for a new path and repeat the process. After k iterations you have two v... (read more)
I'm having trouble understanding why we can't just fix n=2 in your proof. Then at each iteration we bisect the interval, so we wouldn't be using the "full power" of the 1-D Sperner's lemma (we would just be using something close to the base case).
Also if we are only given that f is continuous, does it make sense to talk about the gradient?