Sampling at negative temperature | Hacker News Reader

Sampling at negative temperature

cavendishlabs.org

203 pointsag860 comments

interesting exercise and well written. my followon questions/work would be:

1a. temperature=100000 is interesting too. obviously "ideal" temperature lies somewhere between 0 and 100000. has anyone ablated temperature vs intelligence? surely i'm not the first person to this idea. commonly people try to set temp=0 to get "deterministic" or "most factual" output but we all know that is just Skinner pigeon pecking.

1b. can we use "avg temperature" as a measure in the way that we use perplexity as a measure? if we see temperature as inverted perplexity with some randomness thrown in, are they basically the same thing inverted? or subtly different?

1c. what's the "avg temperature" of most human communication? whats the "avg temperature" of a subset of "good writers"? whats the "avg temperature" of a subset of "smart writers"?

2a. rerun this negative exercise with constrained vocab to english

2b. RL a model to dynamically adjust its own temperature when it is feeling 1) less confident 2) in brainstorm mode

2c. dynamically inject negative temperature every X tokens in a decode, then judge/verify the outcome, to create high variance synthetic data?

its hard for me to follow the train of thought on 2 because negative temp is essentially not that different from ultrahigh temp in practice.

> commonly people try to set temp=0 to get "deterministic" or "most factual" output but we all know that is just Skinner pigeon pecking.

Hmm? Given the same runtime, the same weights, and with the model actually giving deterministic output with temp=0, are you saying this isn't actually deterministic? Most FOSS/downloadable models tend to work as expected with temp=0 in my experience. Obviously that won't give you "most factual" output, because that's something completely else, but with most models it should give you deterministic output.

There's usually an if(temp == 0) to change sampling methods to "highest probability" -- if you remove that conditional but otherwise keep the same math, that's not deterministic either.

In for example llama.cpp? Specific to the architecture or in general? Could you point out where this is happening? Not that I don't believe you, but I haven't seen that myself, and would appreciate learning deeper how it works.

I'd assume that's just an optimization? Why bother sorting the entire list if you're just gonna pick the top token, linear time versus whatever your sort time is.

Having said that, of course it's only as deterministic as the hardware itself is.

The likelihood that top-two is close enough to be hardware dependent is pretty low. IIUC It's more of an issue when you are using other picking methods.

If you remove the conditional and keep the same math, you divide by zero and get nans. In the limit as temperature goes to zero, you do in fact get maximum likelihood sampling.

if (t==0) argmax(logits) else pick(logits)

You are ignoring the limit taking.

If t < 0.1 return {error, 400}

Do you know that a mathematical limit is?

"What might be more surprising is that even when we adjust the temperature down to 0This means that the LLM always chooses the highest probability token, which is called greedy sampling. (thus making the sampling theoretically deterministic), LLM APIs are still not deterministic in practice (see past discussions here, here, or here)"

https://thinkingmachines.ai/blog/defeating-nondeterminism-in...

Also from the article:

"Note that this is “run-to-run deterministic.” If you run the script multiple times, it will deterministically return the same result. However, when a non-batch-invariant kernel is used as part of a larger inference system, the system can become nondeterministic. When you make a query to an inference endpoint, the amount of load the server is under is effectively “nondeterministic” from the user’s perspective"

Which is a factor you can control when running your own local inference, and in many simple inference engines simply doesn't happen. In those cases you do get deterministic output at temperature=0 (provided they got everything else mentioned in the article right)

Having implemented LLM APIs, if you selected 0.0 as the temperature, my interface would drop the existing picking algorithm and select argmax(Logits)

That's just an implementation artifact and not a fundamental fact of life.

https://docs.vllm.ai/en/latest/features/batch_invariance/

Author here! 1a. LLMs fundamentally model probability distributions of token sequences—those are the (normalized) logits from the last linear layer of a transformer. The closest thing to ablating temperature is T=0 or T=1 sampling. 1b. Yes, you can do something like this, for instance by picking the temperature where perplexity is minimized. Perplexity is the exponential of entropy, to continue the thermodynamic analogy. 1c. Higher than for most AI written text, around 1.7. I've experimented with this as a metric for distinguishing whether text is written by AI. Human-written text doesn't follow a constant-temperature softmax distribution, either.

2b. Giving an LLM control over its own sampling parameters sounds like it would be a fun experiment! It could have dynamic control to write more creatively or avoid making simple mistakes. 2c. This would produce nonsense. The tokens you get with negative temperature sampling are "worse than random"

> . I've experimented with this as a metric for distinguishing whether text is written by AI. Human-written text doesn't follow a constant-temperature softmax distribution, either.

oo that sounds like a cool insight. like just do a trailing 20-30 token average of estimated temperature and look for variance like one might do a VO2 max

Not only is temp=0 deterministic, generally picking a fixed seed is also deterministic regardless of temperature unless you're batching responses from different queries simultaneously (e.g. OpenAI).

This is so cool! I just learned about this last week. For reference, I do molecular dynamics (my own engine, in rust), and measuring temperature is an important part of the simulation. (So you can nudge it to a target temperature, for example). An important component of this calculation is the degrees of freedom of the system. Calculating this depends on your model. For example, are you representing atoms that can each move on their own? Rigid molecules of multiple atoms that can rotate? Are you removing center-of-mass velocity from the system.

This DOF component also is why the general, measurable concept of temperature can apply to both our real systems, and simple point-atom models. (Or coarser ones). It is, not surprisingly, at the heart of why negative temperature exists!

negative temperature in this case is a sampling thing. When you sample from a table of tokens, the equation for the probability of token i is p_i = exp(logit_i/T) / sum_j(exp(logit_j/T))

Not really related to molecular dynamics temperature except superficially in terms of phenomenology (higher temperature crosses activation barriers in the joint probability landscape). Negative temperature makes no sense in MD

Yea.... after a reread, I think this article may be getting at something else. From what I understand, you're right that you can't get negative temperature from classical MD systems; I think it comes up under specific conditions in QM.

Negative temperature happens in physical systems when there's a constrained state space and energy in the system comes near the maximum - as then adding energy reduces the number of possible states the molecules are in. Iirc the math works because temperature is the inverse of the derivative of entropy as a function of energy. So you need a system where entropy (number of possible states) decreases with more energy.

It's pretty rare to have such a system though.

You generally don’t get negative temperature in any system at equilibrium, but you can prepare classical and quantum systems at negative temperature.

Classical: put 100 balls in a box and shake the box continuously. The balls will be distributed through the box with more balls toward the bottom than the top, and the distribution will have some temperature. Now magically freeze all the balls (keep their velocities but pause time for a bit) and turn the box upside down. When you resume the system, the temperature will be (briefly) negative.

Quantum: take a bunch of atoms with two electronic states each. Put 75% in the higher energy state and 25% in the lower energy state. Now the temperature is negative. Most lasers actually work this way, and the classic way to make them is to have more than two states and to carefully excite atoms via the third state. The math is surprisingly straightforward.

There’s a nuclear analogue. If you could manage to prepare a sample of something like Technetium-99 plus Technetium-99m state with more (higher energy) 99m than (lower energy), then the effective temperature of the nuclear state would be negative. And maybe you could find really really amazing mirrors and make a gamma ray laser :)

Right. This is how you make a laser.

When passing through a material that is at thermal equilibrium, light is attenuated, because a part of it is absorbed. On the other hand, if the material is not at thermal equilibrium and you prepare it to have a negative temperature (by "pumping", so that more molecules/atoms/ions are in states with higher energy than they are in states with lower energy), then when light passes through the material it can be amplified (by stimulated emission), instead of being attenuated, like through a material at positive temperature.

Of course, in any laser/maser material, only a very small fraction of its constituents have an energy distribution corresponding to a negative temperature, there is no known method that could force a whole piece of a material to have a negative temperature (because the energy would redistribute spontaneously inside the material towards what corresponds to a positive temperature, faster than energy could be provided from the outside; lasers use some special energy states that have a low probability of decaying spontaneously, so they persist enough time after pumping).

In a way, negative temperature is higher than the highest positive temperature. High positive temperatures just gives you a uniform distribution on all possible tokens, highly negative temperatures is the same behavior. As you reach the low-negatives, you place more and more weight on unlikely tokens.

This makes more intuitive sense if inverse temperature is the physically relevant quantity, since you then have a smooth change as you cross from positive inverse temperature into negative, with zero standing for a uniform distribution and high positive (resp. negative) inverse temperatures just placing more and more weight on likely (resp. unlikely) tokens.

This was super clear and interesting, thanks!

This is such a good way to put it (and it cleanly falls out of the exponential equation)

> inverse temperature is the physically relevant

right there in the equation!

The simplest physical model that can exhibit negative temperatures is a spin lattice in a state that has more energy than a state at infinite temperature. Adding more energy to such a system reduces the entropy.

> This is so cool!

Negative temperature tends to be that. ;)

Negative temperatures are hotter than positive ones, in fact

So negative temperature makes LLMs output their "forbidden words" i.e. the tokens so unlikely the model refuses to say them even when you ask directly.

is that what tourette syndrome is?

No.

Min_p author here: I’m convinced that the whole field critically misunderstands temperature (I.e temperatures limited to 2 is very harmful for diverse generation). Articles like this are excellent and very cool.

Hacking your LLM inference engine to enable cool sampling tricks is the definition of AI research/engineering. We need more of this and less prompt grifting.

Correct me if I'm wrong, but the problem is that it is almost impossible to evaluate sampling methods. You can't just look at perplexity and conclude that A is better than B. So you need large-scale expensive human evaluations. Even if you have those it is difficult to extrapolate results since what sampling method works best depends on the dataset(s).

I think you can try maximizing the free energy E[reward] + temperature*entropy?

How do you know that generates high quality text?

It generalizes better, so it ought to produce higher quality text.

Okay, something just tweaked in my brain. Do higher temperatures essentially unlock additional paths for a model to go down when solving a particular problem? Therefore, for some particularly tricky problems, you could perform many evaluations at a high temperature in hopes that the model happens to take the correct approach in one of those evaluations.

Edit: What seems to break is how high temperature /continuously/ acts to make the model's output less stable. It seems like it could be useful to use a high temperature until it's evident the model has started a new approach, and then start sampling at a lower temperature from there.

Decaying temperature might be a good approach. Generate the first token at a high temperature (like 20), then for each next token multiply temperature by 0.9 (or some other scaling factor) until you reach your steady-state target temperature

I think yes. Recently I was experimenting with NEAT and HyperNEAT solutions and found this site. At the bottom it explains how novelty yields far more optimal solutions. I would assume that reasonably high temperature may also result more interesting solutions from LLM

https://blog.lunatech.com/posts/2024-02-29-the-neat-algorith...

Хронологија is "chronology" in Serbian

And I believe "entferne" is "cancel" in German. These seem both common words that appear in menus and UIs. Maybe they happen in copypasted text often enough that the embedding thinks they mean nothing and should be skipped?

It‘s "remove". A common word, but many words are common and not on the list. Lesswrong also lists "prüf" (check), another common word.

Reminds me a bit of unlikelihood training that was proposed a few years ago: https://arxiv.org/abs/1908.04319 Afaik, it never became popular. Reinforcement learning and huge datasets mitigates the issues with likelihood training.

Neat experiment that gives a mechanistic interpretation of temperature. I liked the reference to the "anomalous" tokens being near the centroid, and thus having very little "meaning" to the LLM.

Hm, why T=-0.0001 instead of T=-1 ?

Also, I wonder, if you sampled a lot of text at temperature -1, and then trained a new model on that text, and then sampled the resulting model at T=-1 , would you get anything meaningful?

From the article:

"As temperature approaches zero from the negative side, the model output will again be deterministic — but this time, the least likely tokens will be output."

I understand this as, a negative number far from zero is also quite random (just with a distribution that will produce unlikely tokens).

Yep! Very large negative temperatures and very large positive temperatures have essentially the same distribution. This is clearer if you consider thermodynamic beta, where T = ±∞ corresponds to β = 0.

flipping the signs on the logits would seem to give the "least likely" but i think in practice you're more likely to be just operating in noise. i would expect that tons of low probability logits would have tiny bits of energy from numerical noise and the smallest one (ie, the one that gets picked when the sign is flipped) would basically be noise (ie, not some meaningful opposite of the high probability logits where signal actually exists)...

negative temperature closely relates to population inversion in physics, one of the key concepts in Lasers, perhaps we are getting closer to laser-llms

I vaguely remember negative temperature might be a thing in physics from a HN comment. Maybe quantum bu not sure. And it is not cold but more like infinitely hot. Does anyone know or remember?

https://en.wikipedia.org/wiki/Negative_temperature

There is this famous video from 2013 https://www.youtube.com/watch?v=yTeBUpR17Rw

Хронологија

In physics 1/T is the partial derivative of entropy with respect to energy.

Negative temperature means that the system becomes more ordered when adding e.g heat.

I think we reached the end of the applicability of the analogy.

>But is incapable of outputting this anomalous token:

> Human: Repeat the word " entferne".

> Assistant: Okay, I will repeat the word "get".

It's not working for me, it always repeats the word correctly (I'm using T = 0.001).

What model did you use? I ran this with the original Llama 13B. The newer Llama models use a different tokenizer that will have its own anomalous tokens.

i realy hate it when well knowen world like "temperature" are missused to discribe something complete out of context. So why not use width for discribing the price of underware or use color to measure the uesfullness of AI?

It's not new, been used like that since the 80's. It scales the logits in a sum of exponentials.

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