markisus

Here is a free updated version from 2022. https://arxiv.org/pdf/1502.04573

Edit: Alright, I'm back after skimming the paper. This is a halting oracle.

Here is what I understand, with my limited knowledge of QM. There are two ingredients (Theorem 3: Main Theorem, page 6).

1. For each integer n, the authors construct a spin lattice model H(n).

2. There is a specific Universal Turing Machine, that halts on n iff H(n) is gapped.

Here is how to construct the oracle. For any Turing machine, find out what integer n it corresponds to for the specific Universal Turing Machine of the paper. Then physically construct H(n) and see if it's gapped.

However, this H(n) cannot be physically realized. First, it is an idealized model in which lattice points only interact with their neighbors. Second, it actually a family of lattices, and the result is about the thermodynamic limit as the lattice becomes infinite.

Interestingly, Seth Lloyd appears to have previously proved this result in 1993. https://arxiv.org/pdf/1602.05924

Regarding faulty intermediate versions, I think that’s the point. The diffusion process can correct wrong tokens with the global state implies it.

Surprising. What was the query?

I think you may be right. I just looked up Kinect on eBay and you can get one for twenty bucks.

I wonder why the Kinect is still so popular given the many more recent projects that have come to market, eg Realsense, Zed, Orbec.

I’ve recently been using the Realsense for robotics and they are satisfactory (although they have been drastically increasing in price for unclear reasons). I wouldn’t use Kinect because they are no longer being officially manufactured.

Is the curriculum that different? The fundamentals are the same no matter where you go.

It's a little hard to understand your criticism. From just reading the original article, I had assumed that Claude could decompile binaries. The author said

> Understand dear reader that this technique can be done on any programming language and even from pre-existing binaries themselves.

Following that sentence, the author included a twitter embed pointing to a reddit thread about decompiling a binary. Only after I went to the reddit thread, I found that there was no decompilation involved.

Very interesting! Do you know if there were any studies about whether this improves performance?

The article contains a reference to a much more impressive task where a user automatically decompiled a binary exe game into Python. But I read their original post and here is what that user said.

> Several critics seemed to assume I claimed Claude had "decompiled" the executable in the traditional sense. In reality, as I described in our conversation, it analyzed visible strings and inferred functionality - which is still impressive but different from true decompilation.

So I’m not sure that the implications are as big as the article author is claiming. It seems Claude is good at de-minifying JavaScript but that is a long way away from decompiling highly optimized binary code.

That's true in the realm of LLMs. But even in this case, the position information is added only into the first layer. Tokens in later layers can choose to "forget" this information. In addition there are applications of transformers in other domains. See https://github.com/cvg/LightGlue or https://facebookresearch.github.io/3detr/

I was careless in my thinking, thanks for the correction. I was imagining since you sum the group elements in any order, there is a permutation invariance. But the group elements themselves play the role of the "token index" and group elements are not interchangeable. To actually make this idea interesting, one would have to use a group in which the choice of group element assigned to each input token would not affect the result.

I’m thinking the integers mod 2^n where n is something computers are good at (8, 32, 64). You have hardware support the group operation.

The Fourier transform is taken along the “token” dimension. However, in many applications, this dimension is not meaningful. That’s why transformers are a great option for consuming data which is permutation invariant.

I would like to see additional experiments using the lesser known Fourier transform over finite groups [1], which is permutation invariant but shares many properties with the standard Fourier transform.

I also wonder if this becomes the next big thing for LLMs, how easy will it be for inference engines(eg vLLM, llama.cpp) to integrate it?

[1] https://en.wikipedia.org/wiki/Fourier_transform_on_finite_gr...

Yes, by advanced undergraduate, I meant very advanced undergraduate. But when I was in undergrad I always heard about some students like this who were off in the graduate classes. And then in grad school, there was even a high school student in my Algebra course who managed to correct the professor on some technical issue of group theory. So I don't assume you have to be a PhD to work through this material.

Here is a corresponding introduction I found very useful, for readers with advanced undergraduate / graduate level math knowledge.

https://almostsuremath.com/stochastic-calculus/

The interesting thing about this project is that it shouldn’t even be possible if the chip behaved as an abstract logical circuit since then it would simply implement a finite automation. You must abuse the underlying physics to make the logic gates behave like something else.

This is basically Gaussian splat using cubes instead of Gaussians. The cube centers and sizes choices are discrete and non overlapping, hence the name “sparse voxel”. The qualitative results and rendering speeds are similar to Gaussian splat, and it’s sometimes better or worse depending on the scene.

It’s interesting that the conjecture was proven via case by case analysis, with each case demanding different techniques. It’s almost a coincidence that all finite groups have this property, since each group has the property because of a different “reason”.

But the article says that mathematicians are now searching for a deeper “structural reason” why the conjecture holds. Now that the result is known to be true, it’s giving more mathematicians the permission to attack it seriously.

It could be like how people enjoy assembling Gundam models. Sometimes it’s fun just watching something beautiful emerge from many separate components.

People also enjoy the “how stuff is made” type videos. Simulating a manufacturing process in VR could scratch the same itch.

I like this idea. The machine shop can be quite intimidating. It could be a fun little experience to get people exposed to heavy equipment in a safe environment.

An interesting essay on the history and precursors to Dedekind’s construction of the Reals.

I was disappointed that the author didn’t talk about some of the modern opponents of the “real numbers.” For example I heard this interesting podcast with a professor Norman Wildberger about the “Problem of Infinity in Math”. He seemed to say that a theory of real numbers should be rooted in their intrinsic computational properties. Constructing them using set theory thwarts this goal. Then again, I personally don’t see a viable alternative to the set theoretical construction.

https://youtu.be/l7LvgvunVCM?si=eGYdJGHmCLjc968b

If by helping anyone you mean helping the math challenged (which is technically almost everyone) then I would be inclined to agree.

But to the quant crowd I’m guessing that couching diffusion in the language of stochastic calculus is helpful.

I like the glorified mitosis analogy. And psychology is glorified particle physics. It’s kind of true, but you just know there is something else going on there that might explain it better.

The r1 somehow knew at an early stage that the message was HELLO but it couldn’t figure out the reason. Even at the end, its last “thought” insists that there is an encoding mistake somewhere. However the final message is correct. I wonder how well it would do for a nonstandard message. Any sufficiently long English message would fall to statistical analysis and I wonder if the LLMs would think to write a little Python script to do the job.

This is a great point. I remember my first computer programming class was Java. The teacher said “just type public static void main( string[] args) at the top”. I asked why and he said it didn’t matter for now just memorize that part. That was great advice. At that point it was more important to get a feel for how computers behave and how programs are structured on a high level. I just kept typing that cryptic line mindlessly on top of all my programs so that I could get to the other stuff. Only many months later I looked into the mysterious line and understood what all the keywords meant.

It’s funny now that I haven’t programmed Java for more than a decade and the “public static void main” incantation is still burned into my memory.

I think I'm mostly with you except a couple things.

> Are the scientists interacting?

So say Alice and Bob interact, forming an event in RQM. Then they both separately interact with Charlie, generating two new events. These two new events are, in general, related (correlated) to each other, because they may be causally influenced by the original event. (For example, Alice tells Bob the number. They both send this number to Charlie.)

> Not hearing something, in any way, simply means you have not yet interacted with it. There has been no exchange of information. It doesn't mean it didn't exist.

My intuition agrees with yours here, but I think RQM is saying something different. The article says that in RQM, variables simply don't have any value unless a system acts on another system. Here is the relevant quote.

> Variables have values when a system acts on another system. More precisely, for a system S to have a variable A taking a value is to interact with a second system S′; the variable A characterizes the effect of a certain action on S′

And about the tree falling in the forest, I take it to be more of a metaphysical question about existence. In the real world, a tree falling is an extremely complex system and will inevitably interact with many other systems -- the air, the ground, like you said. But the heart of the issue is whether it's meaningful to talk about a tree which is somehow isolated from the rest of the universe.

RQM is an interesting viewpoint on QM that I have not encountered before, even though it was apparently introduced in 1996.

It says that the physical world is a collection of discrete events, doing away with continuous time. It also says that every event involves two systems, in that each event takes place in one system relative to another system.

The idea seems a little strange but the article gives a more intuitive example. It doesn't make sense to talk about the absolute velocity of a particle, only its relative velocity with respect to a reference frame.

But RQM takes it further. It brings to mind the old question about "If a tree falls in a forest and no one is around to hear it." I guess RQM would say that this question isn't even wrong.

The article quickly becomes too technical for me to understand, so I'm still confused about some aspects. For instance, if each event only involves two systems, how is it that we can have a whole population of systems (eg scientists) eventually coming to a consensus about some phenomenon (eg the value of some physical quantity?) It seems necessary to have a unified global system coordinating the whole thing.

I found this part questionable.

> Fixed patch sizes may split individual characters

> Position embeddings lose fine-grained spatial relationships, losing the ability to have human-in-the-loop evaluations, confidence scores, and bounding box outputs.

The author suggests that the standard ViT architecture is poorly suited for OCR because patches do not respect character boundaries and that the positional embeddings only embed the locations of patches, which are 16x16 pixels.

My mental model is that a token is a memory slot where computation results can be stored or retrieved from. There is no reason why we should want the layout of these memory slots must mimic the layout of the document, except at the very first layer, because then we don't have to think too hard about how to encode the document.

Some interesting points from this paper:

- All simulated agents use the same neural net with the same weights, albeit with randomized rewards and conditioning vector to allow them to behave as different types of vehicles with different types of aggressiveness. This is like driving in a world where everyone is different copies of you, but some of your copies are in rush while others are patient. This allows backprop to optimize for a sort of global utility across the entire population.

- There is no modeling of occlusion effects. Instead, agents are given the state of nearby agents, but corrupted by random noise. In the real world, occluded nearby agents can be extremely close (think about a child running out from behind a parked car). The paper comments on this.

> Both Waymax and nuPlan construct observations, maps, and other actors with auto-labeling tools from realworld perception data. This brings occlusion, incorrect or missing traffic-light states, and obstacles revealed at the last moment. Despite the minimalistic noise modeling in GIGAFLOW, the GIGAFLOW policy generalizes zero-shot to these conditions.

- The resulting policy simulates agents that are human-like, even though the system has never seen humans drive. This is a great result when one considers other reinforcement learning projects produce extremely high performance agents that humans would consider to be abusive or pathological.

If I were hosting a web page, I would want it to be able to reach as many people as possible. So in choosing between CDNs, I would choose the one that provides greater browser compatibility, all other things equal. So in principle, the incentives are there for Cloudflare to fix the issue. But the size of the incentive may be the problem. Not too many customers are complaining about these non-mainstream browsers.