I think it's good to continually remind oneself that these are next-word/token-predictors...you can wrap them up in a harness, you can feed them into each other, you can influence the likelyhood of a given word through weights and system prompts...but that's literally all they can do. They can't reason, but they can predict what reasoning looks like.
None of this means they can't be useful tools, but when they fall down, we should remind ourselves of why that is, and be honest with ourselves about what they could ultimately be capable of.
It’s equally useful to continually remind yourself that a Turing machine is just a spool of tape with a magnetic head, and that a human brain is just fatty lipids in a chemical bath.
When you use "next word predictor", it sounds like slow process, like each word take few seconds to minute to be generated. Why not call it "sentence predictor", or "paragraph predictor" ? i would argue it's the same in principle.
It's like calling a video clip a "picture sequencer".
It's literally what a LLM is, and it's not even a word it's a token which is about 2/3'rds of a word. It has nothing to do with speed of producing tokens. Others are not responsible for correcting your bad understanding of a true statement.
we don't know how the brain works yet, and I don't see a thread on hackernews "new paper describes how brain works by mannytv" with 1000 comments so don't talk out of your ass
LLMs are bad for rating or scoring anything because they have the sensibilities of the average person. Unfortunately, the average person has poor taste.
This is a tough one to explain because some people think the average person has good taste by definition. I used to think that way but over the years I've realized that a lot of what the average person likes is derivative 'slop' - This was true before AI and still true with AI.
Once you start deducting points for lack of originality, you will realize that people have really poor taste... Very narrow taste. Most people literally consume trashy variations of the same thing over and over. We have to start deducting points for this because the more intelligent among us can't take it anymore! We're tired of being exposed to thousands of variants of the same slop... It might be sufficiently different to fool the average pleb's simple mind but to us it's like eating the exact same dish every meal of every day with different amounts of salt and pepper.
This comes through when you ask an LLM to rate/score something. It's frustratingly conventional and not based on first principles thinking and it ADDS extra points for being derivative instead of SUBTRACTING as it should. We can see it play out in the workplace. LLMs have poor judgement. It's the one area where they lag behind.
In my own words - you can't calibrate confidence of a model without a calibration set. Confidence is relative to some labeled dataset. Some tasks look similar, but change one word and it turns from easy to very hard. I don't think a single step classifier can predict it without calibration work.
Whilst general self-reporting of confidence will be hard to achieve (we can't even do it as humans), I'm sceptical of the notion that we can't train models to give some confidence scores accurately. I think over the past year that with the correct RL, models can showcase some pretty insane capabilities. If reporting the correct confidence was a RL training target say for predicting weather events or a game outcome that is supported by real RL environment or simulated data, then I suspect LLMs will develop a strong intuition for confidence similar to how the recent JEV and decision models are trained.
I got a degree in statistics, and what I remember from those times is that we spent maybe 10% of our time learning how to build the model and 90% of the time correctly interpreting the model output.
When we start using big datasets where n went into the millions we kinda stopped bothering because margins were so small it was effectively certain you found the mean of some range. However I think in that time we forget what confidence scoring actually is and how quickly multiplied alpha can balloon on you.
From my time building ML models (2016-2023) evaluation and interpretation was a large chunk of it. I often used "brute force" interpretation methods but there were others like SHAP [1] and LIME [2]. The other large chunk of ML work focused on feature engineering and data prep. Today in the LLM agentics era this is out the window. There are "evals" but no one does it seriously, and interpretation is often propagated to the consumer.
I am happy to hear high quality evaluations are out of fashion. That will make the competition so much less hard in the EU where evaluation is a regulatory requirement.
On the other hand, it’s kind of expected that the hard part of the job in AI/ML engineering gets neglected over that part people can brag on social media about. Deeply concerning but sadly understandable.
Its embarrassing how much people are larping as ML folks and just building things that manifestly have no evidence that they work. I have seen it the last 3 places I have worked and most of the folks seem to have no interest in learning how to get consistently good results, just ship it and focus on the next thing.
It’s like an investment banking/consultant career plan: make money with anything, leave before anyone knows if it’s any good. I have inherited my share of such things, partially shipped and/or deployed. Making career-models perform to even the most minimal quality standard is just insane. Often even the most basic fundamentals are missing and if you have a portfolio of these they naturally all work differently.
While I agree the autoregressive training is poor at calibrating a model, it's clear that LLMs encode a kind of world model to be able to reason, do mathematics, programming, and logic. They are certainly imperfect, but the emergent internal representations go beyond mere "what text comes next" even though LLMs typically simply use tokens.
By analogy to your 'Measuring confidence' section: a function estimator (neural nets can be good at this) and a bunch of past observations could be pretty calibrated at making weather predictions. An LLM has a wild mix of past observations and random collated opinions from previous text (it might mention months, recency of rain etc.. etc...) so lands somewhere between 'text completion' and 'estimator' with a model of unknown fidelity. It is not 'merely' generating a plausible sentence.
I would never use an LLM for accurate forecasting, and certainly agree they are not calibrated, but I would not dismiss them out of hand.
Recently joined a company that does just this. They are using the LLM to review text and produce a grade and a confidence interval.
I'm no expert in the field but it is clear that the model outputs are not reliable. To my frustration this was designed by "experts" so I originally trusted that this approach was sound.
How does this compare with descriptive confidence? For example, major v.s. minor? Intuition tells me it's a different flavor of the same illusion.
That is the opposite of dumb, you can use the next token likelihood to macgyver together a jev in a pinch exactly that way, you just would also want to take some steps to scramble up the choices to smooth over bias and tokenization artifacts. llms have favorite letters for example. Qwen likes A and D.
You can, but it is also fraught and strange and hard to trust. The logprob on one particular token in light of all previous tokens is just that: a token probability. That’s not really the same thing as an assessment of all the reasoning or chain of thought or whatever that preceded that token.
I was hoping the writer would follow the interesting framing of the quality of an LLM's confidence score with some data on how good it is, rather than just proclaiming it's bad because of sycophancy tendencies. If someone collected the data on something measurable, I would be willing to bet the LLM's confidence number isn't too far off.
I’ve run those experiments. Commercially, so I can’t share data. But I can say what the article describes roughly matches what I’ve seen. How well calibrated the scores are varies by model, application, and subtle wording changes. I’m a little more optimistic than the author in that I have gotten it to work reasonably well. But I would not recommend productizing it with a SaaS LLM because it will break every time your vendor sunsets the model you were using, and getting it working again on a new model will be an unholy PITA.
From that paper, model accuracy is not perfect, but it's overall pretty favourable. There are some encouraging findings in there, too, including that accuracy of model confidence scales with reasoning effort.
I think you're making the wrong takeaway here. LLMs aren't bad because of sycophancy tendencies. Any prediction at all is bad when it isn't based on real data, whether or not it ends up being correct, whether or not it is made by an LLM, a human, or some other thing capable of spitting out a number.
Analogize to basketball here. How confident are you that you can hit a free throw? If you ask someone who has played a thousand hours a year for the past ten years, has recorded their own statistics, and has averaged 70% success rate oer those past ten years, and they tell you they're 70% confident they can hit a free throw, that's a good prediction. If you ask me and I give you any prediction at all, I'm full of shit. I haven't played basketball or taken a free throw in 30 years. I can pull a number out of my ass, I can reason through it, I can do a Fermi, I can assume I'll be the average of all people who have ever tried and do my best to collect whatever data might exist on brand new players with no experience trying to take a free throw for the first time. I can narrow that to people my height, my age. Now we're getting better, but it's still not as good as having a real record of my actual past performance and basing a prediction off of that.
This is just science. Hierarchy of evidence. Epistemology. Sometimes answering a question requires collecting data that doesn't exist yet and waiting a while, in the meantime admitting you don't have an answer. It was already sorely lacking in the world, but in this age of oracles, it's only getting worse.
We've found that you can fine-tune confidence scores for your domain into existing models. I think the way this works is that you basically help the model understand what types of inputs it tends to get right and which ones it tends to get wrong. This seems like a reasonable thing you'd expect a model to be able to learn
The author has used weather prediction confidence as an example. I think it is not analogous to LLM's next-token prediction. LLM's next-token is predicted from a finite statistical model. And for the weather prediction model, there is no finite data-based statistical model.
I was surprised that the author hasn't mentioned Jev-like models. They're quite good for general purpose confidence rating.
Of course an LLM does have a latent concept of its own confidence that is not useless, and is perfectly able to articulate it, the author just chose the worst possible way to ask. Using a 0-100 scale for anything is a bad idea with both LLMs and people. Instead of rating it 0-100, split your problem into many dimensions/axes and give each a small and meaningful enum or just a less granular numerical scale (ideally just a binary choice). Then apply weighted scoring to the result. You'll be surprised how much better it becomes at meaningfully expressing its confidence this way.
YouTube removed the 1-5 scale for the same reason, people have no idea what to do with it.
That's very well put. I noticed the issue myself when building my own evals and naturally started drifting into the direction you are describing, but you describe it so succinctly that now I am seeing how it should actually be done. Thank you
Yeah, I agree this approach can produce usable results. The more narrow and well scoped you can make each decision the model has to make (e.g. binary vs 0 to 100) the better the results you'll get (and the easier it is to troubleshoot and tune).
The scale is almost never useful. You cannot quantify most things. Even with humans you get inconsistent results and confusion. As the parent said, a binary (ok/not ok) or ternary (bad/ok/good) choice is what’s appropriate, most of the time. If this is not granular enough, the vast majority of the time it means that you need more axes.
Lets be honest with Youtube's system: it's not about what people really want; it's about whats enough to make them _feel_ in control.
What many people would want it just a complete block on select youtube channels and providers. Just whole hog, rip them out of any of the potential recommendations.
But that's not whats best for Youtube. The point system still stands in ratings, once exposed to the viewer, are gamified. They would however still work if it was a secret vote, but then, again, the user wouldn't be compelled to use it as people want immediate visual cues that they're doing what benefits themselves.
> What many people would want it just a complete block on select YouTube channels
This exists, doesn't it? "Block channel" (or rather, "Don't recommend channel") is probably the feature I use most... I must have thousands of thousands of channels on that list.
The alternative is "Not Interested", but at least on AppleTV you're forced to then choose either "I've already watched the video" or "I don't like the video", and I have literally no idea what to do with those choices. If I've already watched the video then the reason I'm saying I'm not interested is because I didn't like it, so both are true, but I can't select both; and if I just don't like the clickbait thumbnail or title I haven't watched it and I don't know if I like the video itself, so neither is true, but I can't select neither...
Every time I think about YouTube's interface it becomes more obvious it's made by people (?) who's brains just don't work like mine...
You are only talking about what you're feeling. Care to actually make a statement about what you think is true, besides implicitly denigrating someone else?
"LLM" literally converse/compute via statistical inference.
It is given sets of paramaters/data and infers a response based on it's acceptable confidence level. The bottleneck for this is compute power and model/prompt/rails/integrations.
The reason LLM stays consistent/can be somewhat trusted to stay on rails is that it's aware of both it's context/scope and it's confidence about the context.
Anything else would be....original thought and exposition? I guess. You could say that our brains do the same, IE; unconcious statistical analysis leading to inference based on confidence.
> It is given sets of paramaters/data and infers a response based on it's acceptable confidence level. The bottleneck for this is compute power and model/prompt/rails/integrations.
Does the output of the model have insight into those details? Just because our brains function based upon electrical potential doesn't mean we have innate insight into it.
Yes, this is what is user-level marketed as context memory.
Certain models of course force this context memory, some don't, some allow you to toggle it's "trigger level".
For example Anthropic, use haiku for low memory context queries, research. Then Opus/Fable for compiling/analysis/design, which relies on the LLM inference constantly going back into context memory.
Another example is OpenAI/GPT. The "free" tier forces context memory using the "highest available model" per your subscription (or lack thereof), and upon hitting its limit, drops you down to a low context model, and then ultimatley blocking that chat entirely.
(I appreciate this discussion and am not trying to inform you, I'm sure you already know, but typing these things out helps me understand my holes in understanding.)
Excuse my ignorance, but how does context memory provide an insight into a model's inner workings? I mean this:
> It is given sets of paramaters/data and infers a response based on it's acceptable confidence level. The bottleneck for this is compute power and model/prompt/rails/integrations.
Or whatever the LLM claims its confidence is on any given output?
You converse through electrical signals and muscle contractions, but that will not make you an expert in either.
Similarly, a language model trained to emulate speech, follow instructions, and solve problems will not implicitly have an understanding of its own statistics. The research doesn't back that up and it just doesn't make any sense if you think about it.
The only thing LLM produce that could be considered its "confidence" would be its token logit values, but even that is a sketchy connection.
I didn't say anything about expertise, I do not use LLM for work and have a background in statistics/teaching. Also, none of this is related to tokenization. It's just the way the application layer infers response.
Any inference or probability engine, be it an app or a heuristic mental process, is obviously based on categorizing historical data and literally weighing it's confidence around it to form responses.
Confidence intervals and associated indexes/logic are the foundation for most heuristic data models.
This is an incorrect conclusion. Your statement about statistical inference is correct but it doesn't explain why your initial statement, especially "is perfectly able to articulate it".
A good litmus test for this is, typically any artificial neural network, perceptron or even a simple linear regression model do statistical inference based on weights and selection based on confidence level. It's a generic characteristic, which doesn't explain anything specific to LLMs.
> The reason LLM stays consistent/can be somewhat trusted to stay on rails is that it's aware of both it's context/scope and it's confidence about the context.
Post hoc ergo propter hoc.
> I guess. You could say that our brains do the same
I understand that it "feels" the same from a certain perspective, but we don't know that.
LLMs have trouble with open labeling tasks, this was studied.
But, what also was studied is that if you instruct it how to score something, it can do it not so far than a human. If you leave out the instructions, I believe it can be considered an open codebook and therefor it probably wont work well.
I would also like a source for this, I do not believe it is true and founded that "an LLM has a latent concept of its own confidence that is internally consistent".
LLMs generally cannot report the outputs of their own activation functions. Taking the output of softmax as if it were a probability score is considered a first-year PhD student misconception.
They can generally do a decent enough job with a likert scale and a rubric. Which isn’t quite the same thing as a confidence score and won’t be calibrated at all, but may be preferable to users.
Peoper confidence scores on a continuous scale, or even a fine grained discrete scale, are arguably skeuomorphic. It’s worth introspecting on whether that’s what you really needed in the first place, or if it’s just what you’re used to from past experience working with regression-type models.
Exactly my experience: given a set of 3-5 scores a and a sentence or two for each describing what earns that rating is quite effective in getting LLMs to score accurately. Failing to give a rubric doesn't give enough context, and using many values (like 1-100) produces more arbitrary results.
Yes. Though, also, I don't think it's correct to regard that as a confidence score (in the traditional sense) coming from the LLM. Most the value in a good rubric comes from how well the human prompt engineer can clearly and concretely describe the kinds of inputs that would support different confidence levels. Leaving it unspecified and letting the LLM sort it out doesn't lead to satisfactory results IME.
The upshot being, good "confidence" scores reflect good human analysis and prompt engineering, not some sort of introspective capacity on the part of the LLM.
If it is nominally a probability then make sure it’s well calibrated.
If it is something like cosine similarity or SVM scores, which aren’t probabilities or even percentages, then users will misinterpret it if you present it as a number from 0-100 or 0.0-1.0.
>>YouTube removed the 1-5 scale for the same reason, people have no idea what to do with it.
As always, I'm in a minority - I have a VERY clear idea what to do with it :-).
(1/2 - never ever show me crap like this again. 3 - decent mainstream stuff. 4 - This meets my interests, is good, and I'd like more of it please. 5 - this is endorphin analog candy for me. Scott Pilgrim, Hunt for Red October, Neuromancer, Dune grade content :)
I looked at how consistent LLMs are by asking them to forecast events from Polymarket with slight variations in the input, such as negating the question.
An LLM call is just text until you act upon it, so why not send many requests for the exact same prompt and then externally measure the likelihood of a specific tool choice being made?
I'm pretty sure this is how reasoning models work at the big providers. Averaging 10 lunas together likely provides more stable outcomes than one big sol invoke. In any case, you could use the statistical distribution to decide on subsequent inference steps.
Isn’t this what jev training is supposed to improve? They don’t train on predicting the next token but predicting the distribution of next tokens, or something like that.
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[ 1.7 ms ] story [ 41.4 ms ] threadNone of this means they can't be useful tools, but when they fall down, we should remind ourselves of why that is, and be honest with ourselves about what they could ultimately be capable of.
It's like calling a video clip a "picture sequencer".
None of that means they can't be useful tools, but when they fall down, we should remind ourselves of why that is, etc etc.
This is a tough one to explain because some people think the average person has good taste by definition. I used to think that way but over the years I've realized that a lot of what the average person likes is derivative 'slop' - This was true before AI and still true with AI.
Once you start deducting points for lack of originality, you will realize that people have really poor taste... Very narrow taste. Most people literally consume trashy variations of the same thing over and over. We have to start deducting points for this because the more intelligent among us can't take it anymore! We're tired of being exposed to thousands of variants of the same slop... It might be sufficiently different to fool the average pleb's simple mind but to us it's like eating the exact same dish every meal of every day with different amounts of salt and pepper.
This comes through when you ask an LLM to rate/score something. It's frustratingly conventional and not based on first principles thinking and it ADDS extra points for being derivative instead of SUBTRACTING as it should. We can see it play out in the workplace. LLMs have poor judgement. It's the one area where they lag behind.
When we start using big datasets where n went into the millions we kinda stopped bothering because margins were so small it was effectively certain you found the mean of some range. However I think in that time we forget what confidence scoring actually is and how quickly multiplied alpha can balloon on you.
[1] https://shap.readthedocs.io/en/latest/
[2] https://christophm.github.io/interpretable-ml-book/lime.html
On the other hand, it’s kind of expected that the hard part of the job in AI/ML engineering gets neglected over that part people can brag on social media about. Deeply concerning but sadly understandable.
By analogy to your 'Measuring confidence' section: a function estimator (neural nets can be good at this) and a bunch of past observations could be pretty calibrated at making weather predictions. An LLM has a wild mix of past observations and random collated opinions from previous text (it might mention months, recency of rain etc.. etc...) so lands somewhere between 'text completion' and 'estimator' with a model of unknown fidelity. It is not 'merely' generating a plausible sentence.
I would never use an LLM for accurate forecasting, and certainly agree they are not calibrated, but I would not dismiss them out of hand.
I'm no expert in the field but it is clear that the model outputs are not reliable. To my frustration this was designed by "experts" so I originally trusted that this approach was sound.
How does this compare with descriptive confidence? For example, major v.s. minor? Intuition tells me it's a different flavor of the same illusion.
I know that you can use LLMs to write ascii numbers that represent a "confidence" as in TFA. This is fraught and strange and hard to trust.
But can't you also output the next token likelihood, and rearchitect to represent the output classes as tokens to be predicted from inputs?
I guess I thought that's what decision-like models were doing. (or something like that)
It's thought to work "better" but score calibration is still a problem.
But I agree, I would much rather have some data than reckons.
https://arxiv.org/html/2607.20526v1
From that paper, model accuracy is not perfect, but it's overall pretty favourable. There are some encouraging findings in there, too, including that accuracy of model confidence scales with reasoning effort.
Analogize to basketball here. How confident are you that you can hit a free throw? If you ask someone who has played a thousand hours a year for the past ten years, has recorded their own statistics, and has averaged 70% success rate oer those past ten years, and they tell you they're 70% confident they can hit a free throw, that's a good prediction. If you ask me and I give you any prediction at all, I'm full of shit. I haven't played basketball or taken a free throw in 30 years. I can pull a number out of my ass, I can reason through it, I can do a Fermi, I can assume I'll be the average of all people who have ever tried and do my best to collect whatever data might exist on brand new players with no experience trying to take a free throw for the first time. I can narrow that to people my height, my age. Now we're getting better, but it's still not as good as having a real record of my actual past performance and basing a prediction off of that.
This is just science. Hierarchy of evidence. Epistemology. Sometimes answering a question requires collecting data that doesn't exist yet and waiting a while, in the meantime admitting you don't have an answer. It was already sorely lacking in the world, but in this age of oracles, it's only getting worse.
I was surprised that the author hasn't mentioned Jev-like models. They're quite good for general purpose confidence rating.
YouTube removed the 1-5 scale for the same reason, people have no idea what to do with it.
What many people would want it just a complete block on select youtube channels and providers. Just whole hog, rip them out of any of the potential recommendations.
But that's not whats best for Youtube. The point system still stands in ratings, once exposed to the viewer, are gamified. They would however still work if it was a secret vote, but then, again, the user wouldn't be compelled to use it as people want immediate visual cues that they're doing what benefits themselves.
This exists, doesn't it? "Block channel" (or rather, "Don't recommend channel") is probably the feature I use most... I must have thousands of thousands of channels on that list.
The alternative is "Not Interested", but at least on AppleTV you're forced to then choose either "I've already watched the video" or "I don't like the video", and I have literally no idea what to do with those choices. If I've already watched the video then the reason I'm saying I'm not interested is because I didn't like it, so both are true, but I can't select both; and if I just don't like the clickbait thumbnail or title I haven't watched it and I don't know if I like the video itself, so neither is true, but I can't select neither...
Every time I think about YouTube's interface it becomes more obvious it's made by people (?) who's brains just don't work like mine...
Can you provide credible reference for this?
It is given sets of paramaters/data and infers a response based on it's acceptable confidence level. The bottleneck for this is compute power and model/prompt/rails/integrations.
The reason LLM stays consistent/can be somewhat trusted to stay on rails is that it's aware of both it's context/scope and it's confidence about the context.
Anything else would be....original thought and exposition? I guess. You could say that our brains do the same, IE; unconcious statistical analysis leading to inference based on confidence.
Does the output of the model have insight into those details? Just because our brains function based upon electrical potential doesn't mean we have innate insight into it.
Certain models of course force this context memory, some don't, some allow you to toggle it's "trigger level".
For example Anthropic, use haiku for low memory context queries, research. Then Opus/Fable for compiling/analysis/design, which relies on the LLM inference constantly going back into context memory.
Another example is OpenAI/GPT. The "free" tier forces context memory using the "highest available model" per your subscription (or lack thereof), and upon hitting its limit, drops you down to a low context model, and then ultimatley blocking that chat entirely.
(I appreciate this discussion and am not trying to inform you, I'm sure you already know, but typing these things out helps me understand my holes in understanding.)
> It is given sets of paramaters/data and infers a response based on it's acceptable confidence level. The bottleneck for this is compute power and model/prompt/rails/integrations.
Or whatever the LLM claims its confidence is on any given output?
Similarly, a language model trained to emulate speech, follow instructions, and solve problems will not implicitly have an understanding of its own statistics. The research doesn't back that up and it just doesn't make any sense if you think about it.
The only thing LLM produce that could be considered its "confidence" would be its token logit values, but even that is a sketchy connection.
Any inference or probability engine, be it an app or a heuristic mental process, is obviously based on categorizing historical data and literally weighing it's confidence around it to form responses.
Confidence intervals and associated indexes/logic are the foundation for most heuristic data models.
"It's aware" is a big leap and bold original thought, as awareness is not something it has full stop, try different terminology?
A good litmus test for this is, typically any artificial neural network, perceptron or even a simple linear regression model do statistical inference based on weights and selection based on confidence level. It's a generic characteristic, which doesn't explain anything specific to LLMs.
> The reason LLM stays consistent/can be somewhat trusted to stay on rails is that it's aware of both it's context/scope and it's confidence about the context.
Post hoc ergo propter hoc.
> I guess. You could say that our brains do the same
I understand that it "feels" the same from a certain perspective, but we don't know that.
LLMs generally cannot report the outputs of their own activation functions. Taking the output of softmax as if it were a probability score is considered a first-year PhD student misconception.
Peoper confidence scores on a continuous scale, or even a fine grained discrete scale, are arguably skeuomorphic. It’s worth introspecting on whether that’s what you really needed in the first place, or if it’s just what you’re used to from past experience working with regression-type models.
The upshot being, good "confidence" scores reflect good human analysis and prompt engineering, not some sort of introspective capacity on the part of the LLM.
Even a probability?
If it is something like cosine similarity or SVM scores, which aren’t probabilities or even percentages, then users will misinterpret it if you present it as a number from 0-100 or 0.0-1.0.
As always, I'm in a minority - I have a VERY clear idea what to do with it :-).
(1/2 - never ever show me crap like this again. 3 - decent mainstream stuff. 4 - This meets my interests, is good, and I'd like more of it please. 5 - this is endorphin analog candy for me. Scott Pilgrim, Hunt for Red October, Neuromancer, Dune grade content :)
You can see for yourself the results here: https://noisebench.com/
It's basically setting the reasoning mode to 'pro' on OpenAI's API.
I'm pretty sure this is how reasoning models work at the big providers. Averaging 10 lunas together likely provides more stable outcomes than one big sol invoke. In any case, you could use the statistical distribution to decide on subsequent inference steps.