71–80 of 123 posts
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Nitpick of the nitpick... Temperature is actually an intensive quantity, i.e. combining two subsystems with the same temperature yields a bigger system with the same temperature, not twice bigger.
This is why the "thermodynamic beta" is really useful. https://en.wikipedia.org/wiki/Thermodynamic_beta
Nitpick in the article conclusion: >Heat flows from hot to cold because the number of ways in which the system can be non-uniform in temperature is much lower than the number of ways it can be uniform in temperature ... Should probably say "thermal energy" instead of "temperature" if we want to be really precise with our thermodynamics terms. Temperature is not a direct measure of energy, rather it is an extensive pr…
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Probability is a bunch of numbers that add to 1. Sometimes you can use this to represent subjective beliefs. Sometimes you can use it to represent objectively existing probability distributions. For example, an LLM is a probability distribution on a following token given previous tokens. If two "observers" disagree about an LLM's probability assigned to some token, then only at most one of them can be correct. So the…
> If two "observers" disagree about an LLM's probability assigned to some token, then only at most one of them can be correct. The observer who knows the implementation in detail and the state of the pseudo-random number generator can predict the next token with certainty. (Or almost certainty, if we consider flip-switching cosmic rays, etc.)
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> If two "observers" disagree about an LLM's probability assigned to some token, then only at most one of them can be correct. The observer who knows the implementation in detail and the state of the pseudo-random number generator can predict the next token with certainty. (Or almost certainty, if we consider flip-switching cosmic rays, etc.)
That’s the probability to observe a token given the prompt and the seed. The probability assigned to a token given the prompt alone is a separate thing, which is objectively defined independent of any observer and can be found by reading out the model logits.
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That’s the probability to observe a token given the prompt and the seed. The probability assigned to a token given the prompt alone is a separate thing, which is objectively defined independent of any observer and can be found by reading out the model logits.
Yes, that’s a purely mathematical abstract concept that exists outside of space and time. The labels “objective” and “subjective” are usually used to talk about probabilities in relation to the physical world.
Earlier quoted context omitted.
That’s the probability to observe a token given the prompt and the seed. The probability assigned to a token given the prompt alone is a separate thing, which is objectively defined independent of any observer and can be found by reading out the model logits.
Yes, that’s a purely mathematical abstract concept that exists outside of space and time. The labels “objective” and “subjective” are usually used to talk about probabilities in relation to the physical world.
I don’t see Sean Carroll’s musings mentioned yet, so repeating my previous comment: Entropy got a lot more exciting to me after hearing Sean Carroll talk about it. He has a foundational/philosophical bent and likes to point out that there are competing definitions of entropy set on different philosophical foundations, one of them seemingly observer dependent: - https://youtu.be/x9COqqqsFtc?si=cQkfV5IpLC039Cl5 - https…
Half a year after that talk Wolfram appeared on a popular podcast [1] to discuss his book on the Second Law of Thermodynamics [2]. That discussion contained the best one-sentence description of entropy I've ever heard: > Entropy is the logarithm of the number of states that are consistent with what you know about a system. [1]: Mystery of Entropy FINALLY Solved After 50 Years? (Stephen Wolfram) - Machine Learning Str…
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Yes, that’s a purely mathematical abstract concept that exists outside of space and time. The labels “objective” and “subjective” are usually used to talk about probabilities in relation to the physical world.
An LLM distribution exists in the physical world, just as much as this comment does. It didn’t exist before the model was trained. It has relation to the physical world: it assigns probabilities to subword units of text. It has commercial value that it wouldn’t have if its objective probability values were different.
How is that probability assignment linked to the physical world exactly? In the physical world the computer will produce a token. You rejected before that it was about predicting the token that would be produced.
Over the last few months, I've been developing an unorthodox perspective on entropy [1] . It defines the phenomenon in much more detail, allowing for a unification of all forms of entropy. It also defines probability through the same lens. I define both concepts fundamentally in relation to priors and possibilities: - Entropy is the relationship between priors and ANY possibility, relative to the entire space of poss…