VTI is different. It literally tracks all public stocks, weighted by market cap so no such manipulation is possible.

If a bunch of people will be forced to buy Space X (QQQ holders), active investors will short the stock in anticipation of market correction and money will flow from those who were forced to buy. I’m sure there are other ways to take advantage of a forced buyer situation.

Total market will be unaffected, assuming efficient market hypothesis / no arbitrage.

But why must retail investors hold this bundle? If I’m holding now, I can sell it and buy a different bundle right? And if I’m not holding it now, I can just continue not to buy it after SpaceX gets included.

> Missing @cython.cdivision(True) inserts a zero-division check before every floating-point divide in the inner loop. Millions of branches that are never taken.

I thought never taken branches were essentially free. Does this mean something in the loop is messing with the branch predictor?

An additional benefit of this style of allocation over malloc/free is that you can get a lot of the same type of objects contiguous in memory so that iteration over them is a lot faster because there are fewer cache misses.

As for the importance of visualization (of the reals), I don't think you can cleanly separate it from formalism (as constructed in set theory).

I think we all have built in pre-mathematical notions of concepts like number, point, and line. For some, the purpose of mathematics is to reify these pre-mathematical ideas into concrete formalism. These formalisms clarify our mental pictures, so that we can make deeper investigations without being led astray by confused intuitions. Zeno could not take his analysis further, because his mental imagery was not detailed enough.

From clarity we gain the ability to formalize even more of our pre-mathematical notions like infinitesimal, connectedness, and even computation. And so we have a feedback loop of visualization, formalism, visualization.

I think the article was saying that Dedekind and Cantor clarified what we should mean when we talk about the number line, and dispelled confusions that existed before then.

I'll try to interpret this sentence.

We all have some mental imagery that comes to mind when we think about the number line. Before Cantor and Dedekind, this image was usually a series of infinitely many dots, arranged along a horizontal line. Each dot corresponds to some quantity like sqrt(2), pi, that arises from mathematical manipulation of equations or geometric figures. If we ever find a gap between two dots, we can think of a new dot to place between them (an easy way is to take their average). However, we will also be adding two new gaps. So this mental image also has infinitely many gaps.

Dedekind and Cantor figured out a way to fill all the gaps simultaneously instead of dot by dot. This method created a new sort of infinity that mathematicians were unfamiliar with, and it was vastly larger than the gappy sort of infinity they were used to picturing.

A contractor may try to negotiate that unilateral shut off ability with the government, and the government should refuse those terms based on democratic principles, as Luckey said.

But suppose the contractor doesn’t want to give up that power. Is it okay for the government to not only reject the contract, but go a step further and label the contractor as a “supply chain risk?” It’s not clear that this part is still about upholding democratic principles. The term “supply chain risk” seems to have a very specific legal meaning. The government may not have the legal authority to make a supply chain risk designation in this case.

> This isn’t a sign of incompetence. It’s a sign that you’re actually doing real work.

> Your value as an engineer isn’t in executing the same playbook forever. It’s in expanding the domain of what’s possible.

> That experience doesn’t produce arrogance. It produces humility.

> They’re not confident that they already have all the answers. They’re confident that they’ll find them.

Using swipe, no space bar after kill: Kill maps Jill myself Jill myself

Using swipe, manually pressing space bar after kill: Kill mussels Kill mussels Kill mussels

It's known that large neural networks can even memorize random data. The number of random datasets is unfathomably large, and the weight space of neural networks trained on random data would probably not live in a low dimensional subspace.

It's only the interesting-to-human datasets, as far as I know, that drive the neural network weights to a low dimensional subspace.

Given 500 fine tune datasets, we could expect the 500 drag directions to span a 500 dimensional space. After all, 500 random vectors in a high dimensional space are likely to be mutually orthogonal.

The paper shows, however, that the 500 drag directions live in a ~40 dimensional subspace.

Another way to say it is that you can compress fine tune weights into a vector of 40 floats.

Imagine if, one day, fine tunes on huggingface were not measured in gigabytes, megabytes, or even kilobytes. Suppose you started to see listings like 160 bytes. Would that be surprising?

I’m leaving out the detail that the basis direction vectors themselves would have to be on your machine and each basis direction is as big as the model itself. And I’m also taking for granted that the subspace dimension will not increase as the number of fine tune datasets increases.

I agree that the authors decision to use random models on hugging face is unfortunate. I’m hopeful that this paper will inspire follow up works that train large models from scratch.