Right, and what happens at that limit is most exciting! A model that has a cross entropy at that limit for a data stream of text, produces a stream of text that is both theoretically and practically indistinguishable from the original stream.
And so if the datastream has been produced by something intelligent, the resulting model is indistinguishable from that intelligence. That is the whole compression idea behind artificial intelligence.
> for LLMs, because in practice floating point inaccuracies (in particular after exponentiation) prevent values from being exactly equal.
In one thinking trace of 10k tokens, with fp16 or bf16 logits, I don't reckon a collision is rare? There are only 65k floating point numbers with that accuracy. And an agent can quickly rake up 100k tokens, so while not every token will have such a collision of equiprobable logits, it is not rare.
If RL was used to train the model, the model will have been trained on its own sequences. Those will have been generated with a temperature of 1.0. They must be, otherwise you would get a premature collapse or explosion of your entropy if the temperature was respectively lower or higher.
After that RL step, you want to stick to the RL distribution, and so keep a temperature of 1.0. Other temperatures will drive the model out-of-distribution.
That is why the sampling step for agents or thinking LLMs are usually kept at a temperature of 1.0.
> Look at the softmax function and take the limit as T->0. It becomes a dirac-delta function.
In pure math, it does not always do that. It becomes a dirac-delta comb with equal weight on every maximum. There can be more than 1 maximum. Setting the temperature to zero turns into greedy sampling, but greedy sampling is not necessarily deterministic as you can have multiple equally optimal options.
> so in principle, setting temperature to 0 _should_ result in deterministic outputs
It is a common misconception, but it is not true even in principle. If I have 2 or more logits which are equal to the maximum of my logits, I will sample uniformly random from them with any temperature, even zero. Sampling from softmax([1, 0, 1]) is still stochastic at temperature 0, because the limit is to sample uniformly from the first or the last element.
Anyway: "GPUs don't do deterministic matrix multiplications" is the biggest source of randomness in LLMs. GPUs put the associativity of the sums in matrix multiplications in arbitrary order, and this has a huge impact on the logits coming out of the neural network.
I mean, he looks uncomfortable, but you would be surprised at how much people can tolerate when there is no alternative. Here is an interview I found [0].
I think he looks better than every 90 year old. But he also mentions that it still is terminal.
It's been used, along with every other divergence and distance you can think of.
In practice, which divergence you use doesn't seem to be very important. The KL is the one with the most theoretic foundation though, i.e. will work with infinite data. The important aspect seems to be that neural networks are Lipschitz bound, and that that is the most important constraint preventing collapse.
> To get there, you often need to slow down your brain's electrical activity, moving from active Beta waves into Alpha or Theta waves through meditation or deep focus. This blurs the boundary between the inner "self" and the outer world.
Quantum Mysticism, a.k.a what if we write about spirituality as if we would report pop-science.
It's been a while since I came across one as flagrant as this article.
If you want to read more: the concept is called "the dual state" [1] after the eponymous book [0]
I agree that the phrase is somewhat contradictory, but it is the best way to describe what was going on. As long as you were within the confines of the normative state, you experienced a rule of law. But as soon as you stepped into the prerogative state, anything could happen. So a "rule of law", except that it didn't apply to everybody, but only to most people. And importantly, the existence of the prerogative state is mostly hidden when you're in the normative state (so unlike a king, which everybody knew was outside of the law)
Not sure if it matters, but that is at least not true for nazi-style fascism. In there, they had a very strong rule of law for most people. But, there was a dual, a parallel system where there was no law at all, it operated outside of the legal system. You could win a trial and be exhonorated, only to be taken away by the gestapo at the door of the courtroom.
It was important for the nazis to keep businesses running, and have most people continue their lives without noticing major changes. Most people would not come into contact with the second system, and barely knew it existed. But if you entered the second system, you often would not come out alive.
This way, they could transit into an authoritarian system without hurting the economy. They knew this and planned it, and it turned out to be correct.