markisus

In Gaussian Splatting, a first order approximation takes ellipsoids in camera space to ellipses in image space. This works ok for pigeonhole cameras where straight lines remain straight and more generally conic sections are taken to other conic sections. For high distortion models like fisheye, this approximation probably breaks. However this method presumably does not rely on approximation since it is ray traced.

Thanks for bringing this to my attention. It’s a bit hard for me to understand the legal intricacies but the point of the article [1] looks like this sentence.

> For developers, this means you need to be cautious about who you interact with and where your contributions come from.

I guess this may prevent USA affiliated developers from collaborating with certain designated foreign developers.

It’s possible that the DeepSeek team or other top foreign developers may become sanctioned by OFAC. Then forking their models may be considered transacting. This would certainly be disastrous for US researchers, if the pace of progress out of foreign teams continues.

But then again I’m not sure why the powers that be would effect such an own-goal.

> If the U.S. continues to stymie open source, China will come to dominate this part of the supply chain and many businesses will end up using models that reflect China’s values much more than America’s.

I'm not sure the U.S. as a whole is stymying open source -- or at least there don't seem to be governmental pressures to keep things closed source. Take the llama models, for instance.

I think there is still a geometric viewpoint you can bring to the multiplicative structure of C. For example there is the extremely natural homeomorphism between unit C and SO(2). And C minus origin to (R+, SO(2)). It’s completely intuitive for mathematicians to say that 1 and i are separated by 90 degrees.

I’m having a hard time with this one as a human.

Spring has sprung, grass has risen. I wonder where the birdies are? The bird is on the wing! Isn’t that absurd? I always heard the wing was on the bird!

Not sure what it means that the bird is on the wing.

This project generates synthetic computer vision training data. The arxiv paper has more detail including some cool pictures of random creatures it can generate. The images are nice but all of them are nature settings so I assume one would have to supplement this type of data with another data set for training a computer vision model.

I remember in the beginning twitter was supportive of third party developers using it for all sorts of different things using its free API. I guess they decided they didn’t just want to be the protocol and closed off access.

Last time I used ROS, it forced you to use its build system. Catkin or something? It was a layer on top of Cmake.

I had to think about this. It’s actually your own skin providing the frictional force that holds your pants up!

I don’t understand this. Wouldn’t the optimal solution be a constant color over the whole image?

Yes you are right. According to Wikipedia it was proven in 1893. https://en.wikipedia.org/wiki/Finite_field

I’m dubious of this project.

I’m also unsure where finite fields are coming into play. Finite fields have orders that are prime powers, and the author is talking about a “finite field” of order 7x9x11. But if we aren’t dealing with fields, why is the author mentioning plans for implementing division? It definitely needs more explanation but I’m not sure if the idea is coherent.

I was sort of puzzled by the meaning of "axiom for boolean algebra" as well, and I looked into this more.

The way I learned boolean algebra was by associating certain operations (AND, NOT, OR, etc) to truth tables. In this framework, proving a theorem of boolean algebra would just involve enumerating all possible truth assignments to each variable and computing that the equation holds.

There is another framework for boolean algebra that does not involve truth tables. This is the axiomatic approach [1]. It puts forth a set of axioms (eg "a OR b = b OR a"). The symbol "OR" is not imbued with any special meaning except that it satisfies the specified axioms. These axioms, taken as a whole, implicitly define each operator. It then becomes possible to prove what the truth tables of each operator must be.

One can ask how many axioms are needed to pin down the truth table for NAND. As you know, this is enough to characterize boolean algebra, since we can define all other operators in terms of NAND. It turns out only one axiom is needed. It is unclear to me whether this was first discovered by Wolfram, or the team of William McCune, Branden Fitelson, and Larry Wos. [2]

[1] https://en.wikipedia.org/wiki/Boolean_algebra_(structure)

[2] https://en.wikipedia.org/wiki/Minimal_axioms_for_Boolean_alg...,.

> The only hope I have is to try something completely novel

I don’t think this is true. Neural networks were not completely novel when they started to work. Someone just used a novel piece — the gpu. Whatever the next thing is, it will probably be a remix of preexisting components.

Maybe if you take Alice and Bob to be two separate alien species it could make more sense. Alice’s species has no measurement devices capable of detecting Bob’s version of entropy, and therefore Alice is not able to extract any useful work from Bob’s system and vice versa. Therefore any objective definition of entropy needs to include the capabilities of the measurer. Which is just the same as what you were saying about macrostates.

Maybe the experimental apparatus is not objective. The quantities we choose to measure are dictated by our psychological and physiological limitations. The volume of a container is not objectively defined. An organism which lives at a faster time scale will see the walls of the container vibrating and oscillating. You must convince the organism to average these measurements over a certain time scale. This averaging throws away information. This is the same with other thermodynamic quantities.

1080p at 30 fps is nuts. I had assumed that this kind of thing would eventually be accomplished with Gaussian splats but it looks like this new approach is a twist on the older multi plane image technique.

This sounds about right, having spent my share of time prepping robot systems for big PR and investor demos.

I’m pretty sure most modern mathematics research takes place on pencil and paper or chalkboard. It’s too tedious to typeset everything in the research phase. It’s also way harder to draw little diagrams or new invented notations on the computer.

I assumed that the algorithm only uses the RGB sensor and the depth is ignored. I bought two d455 within the past year and they are quite nice.

A proof is basically a directed graph where nodes are propositions, and edges are deductive rules. One only needs to check that the starting nodes are axioms and that each edge is one of a finite set of deduction rules in the system. So the time to check a proof is linear in the number of edges.

Not a lot of substance to back up the author’s ideas. The author tries to explain why many East Asian countries stand out on different metrics like standardized testing and birth rates. He rejects “Confucius of the gaps” which is a cultural explanation while at the same positing a genetic disposition towards increased conformity and lack of ability to go off script. This is a “genetics of the gaps” explanation. There is no further genomic evidence put forward. Rather, the author creates many just-so stories to justify the data.

Funnily, it seems that any way the data goes, the author can create a story. Here is what the author said after finding data that contradicted his prediction that Asian countries would have fewer traffic incidents.

> I suppose we can save race science by invoking more race science. Asians are low on non-conforming behavior, but they’re also bad drivers, and maybe the impact of the latter is more important.

The authors hypothesize at the bottom of page 3 that linear layers can combine to form nonlinear functions. This is wrong, but maybe I’m misunderstanding what they are trying to say.

In the hypothetical above, you won’t have any way to know which libraries are actually being used unless you read through the source code. Many libraries will transitively include protobuf, but most functions will not call protobuf.

Thanks for bringing up the intricacies involved. I shouldn’t have used the word “just” as it implies that the solution is easy.

Unfortunately you cannot extend this approach much beyond this simple example if you are writing a physics simulation. There is no known closed form solution, for example, for the famous three body problem, so a some sort of numerical integration is absolutely required. At that point, you should just decouple the numerical integration timestep from the monitor refresh rate, or mandate a refresh rate that will be acceptable to the player.

We know neural networks cannot solve the halting problem. But isn’t the question whether they can learn the transition table for game of life? Since each cell depends only on neighbors, this is as easy as memorizing how each 3x3 tile transitions.

Contextually of dimension even exists within a specific scientific theory. In relativity, the direction you call time might contain some component of the direction I call space. This implies notions like simultaneity are not well defined in a universal context.

It’s extremely strong almost to the point of absurdity to say that transformers are the optimal architecture. As far as we know, human minds are not transformer networks and outperform them in many respects. And it’s even absurd to me to say that the human mind has optimal architecture even though we haven’t seen a better one in billions of years.

Yeah sometimes compression ratio is not the right question when there are other practical concerns like disk space or user experience.

But I do want to point out that almost everyone installs at least one multigigabyte file to decompress other files, and that is the OS.