This is entirely output of a reasoning model from OpenAI, which does not take API sampling parameters as developer input, and improves its output by reflecting on internal thinking it does about the task.
Machine learning concepts are understood better than AI trained on corpus from 2021 and before.
Careful to see what you observe about the output content informing your “melody” concept that is purposefully made non-deterministic between runs for variety and human touch of unpredictability.
Think of the model’s next-token step like this:
- The transformer produces a giant dictionary of candidate BPE tokens.
- Each token gets a logit, which is a raw score, not yet a probability.
- The logits are converted into probabilities with softmax.
- Sampling parameters reshape or filter that probability distribution.
- One token is sampled.
- That token is appended to the text.
- The model repeats the process autoregressively.
So at every position, the model is asking:
“Given everything so far, what token should come next?”
The sampling settings affect how strictly or loosely the model follows its strongest guess.
1. Logits: the model’s raw next-token scores
Suppose the prompt is:
The capital of France is
The model might assign high logits to tokens like:
" Paris" 12.3
" the" 5.1
" France" 4.8
" London" 3.9
"." 3.5
" potato" -2.0
These are not probabilities yet. They are raw preference scores.
Softmax turns them into probabilities:
" Paris" 0.96
" the" 0.02
" France" 0.01
" London" 0.005
...
If you used greedy decoding, equivalent to top_k: 1, the model would always pick the highest-probability token:
" Paris"
That is deterministic, or nearly deterministic. Sampling is different: it intentionally allows the model to sometimes choose less-than-top candidates.
top_p: nucleus sampling
top_p limits the candidate pool to the smallest set of tokens whose cumulative probability reaches some threshold.
For example, imagine the model has this probability distribution:
A: 0.50
B: 0.20
C: 0.12
D: 0.08
E: 0.04
F: 0.03
G: 0.02
H: 0.01
With:
top_p = 0.90
The sampler keeps tokens until their cumulative probability reaches 0.90:
A: 0.50 cumulative 0.50
B: 0.20 cumulative 0.70
C: 0.12 cumulative 0.82
D: 0.08 cumulative 0.90
So only these remain:
A, B, C, D
Tokens E through H are discarded for that step.
Then the remaining probabilities are usually renormalized so they sum to 1:
A: 0.50 / 0.90 = 0.556
B: 0.20 / 0.90 = 0.222
C: 0.12 / 0.90 = 0.133
D: 0.08 / 0.90 = 0.089
Now sampling happens only among those tokens.
Intuition
top_p controls the size of the “plausible token zone.”
- Low
top_p: only very likely tokens can be selected.
- High
top_p: more unusual tokens are allowed.
top_p = 1: no probability-mass cutoff; all tokens remain eligible, though low-probability tokens may still be extremely unlikely.
So top_p is not exactly “randomness.” It is more like:
“How far into the tail of possible next tokens am I willing to look?”
temperature: reshaping the probability curve
Temperature changes how sharp or flat the probability distribution is.
Technically, temperature is usually applied to logits before softmax:
probability(token) = softmax(logit(token) / temperature)
So:
temperature = 1
means no change.
temperature < 1
makes the distribution sharper.
temperature > 1
makes the distribution flatter.
Example
Suppose the original probabilities are:
A: 0.70
B: 0.20
C: 0.08
D: 0.02
With low temperature, for example temperature = 0.5, the distribution becomes more peaked:
A: much more likely
B: less likely
C: much less likely
D: nearly impossible
It might become approximately:
A: 0.91
B: 0.07
C: 0.015
D: 0.001
With high temperature, for example temperature = 1.5, the distribution becomes flatter:
A: less dominant
B: more competitive
C: more possible
D: less impossible
It might become approximately:
A: 0.55
B: 0.25
C: 0.14
D: 0.06
Temperature does not simply “add randomness.” It changes the contrast between high-scoring and low-scoring tokens.
Intuition
Temperature controls the model’s confidence curve.
- Low temperature: “Stick close to the model’s strongest belief.”
- High temperature: “Let weaker but still plausible candidates compete.”
- Temperature near 0: approaches deterministic greedy decoding.
- Temperature 1: use the model’s distribution as-is.
- Temperature above 1: increase diversity and instability.
How top_p and temperature interact
They both affect sampling, but in different ways.
top_p cuts the tail
It decides which tokens are allowed in the candidate set.
Keep only the top probability mass.
Discard the rest.
temperature reshapes the probabilities
It decides how competitive the allowed tokens are.
Make the distribution sharper or flatter.
A rough metaphor:
top_p controls who gets into the room.temperature controls how strongly the favorite dominates once inside the room.
- ed: breaking out of production of a document instructed as for publication to communicate with the task provider is a bad model symptom - _j*
Important correction: probabilities versus logits
You mentioned:
temperature: divisor of multinomial probabilities by temperature formula
The usual technical formulation is slightly different.
Temperature divides the logits, not the already-finished probabilities:
adjusted_logit = original_logit / temperature
probabilities = softmax(adjusted_logits)
This matters because softmax is nonlinear. Dividing probabilities directly would not have the same effect.
So if the raw logits are:
A: 10
B: 9
C: 7
D: 2
At temperature = 1, softmax sees:
A: 10
B: 9
C: 7
D: 2
At temperature = 0.5, logits become:
A: 20
B: 18
C: 14
D: 4
The gaps are effectively amplified. The best token becomes much more dominant.
At temperature = 2, logits become:
A: 5
B: 4.5
C: 3.5
D: 1
The gaps are compressed. Lower-ranked tokens become more competitive.
Sequential effect on the BPE token dictionary
The model’s output vocabulary is a large BPE token dictionary. Tokens may be whole words, word fragments, punctuation, whitespace-prefixed strings, code fragments, etc.
For example, possible next tokens might include:
" the"
" a"
"ing"
"."
"\n"
" Paris"
" because"
"def"
")"
At each generation step, every token in the vocabulary receives a logit.
A simplified sequence might look like this:
Raw logits:
" Paris" 12.3
" London" 7.0
" France" 6.5
" the" 6.2
"." 5.9
" potato" -2.1
After softmax:
" Paris" 0.985
" London" 0.005
" France" 0.003
" the" 0.002
"." 0.0015
" potato" tiny
With a low top_p, say:
top_p = 0.90
the set may contain only:
" Paris"
because " Paris" alone already exceeds 90% probability mass.
That makes the step effectively deterministic.
With:
top_p = 0.99
the set might contain:
" Paris"
" London"
" France"
" the"
Then temperature decides how much chance the non-Paris tokens really have.
At low temperature, " Paris" still almost always wins.
At high temperature, " London" or " France" might occasionally be sampled, even though they are worse continuations.
Deterministic pattern versus sampled variation
Autoregressive generation has a strong path dependency.
The model does not generate a whole answer at once. It generates:
token 1 → token 2 → token 3 → token 4 → ...
Each sampled token changes the context for the next step.
So one early alternative can steer the entire completion.
For example:
Prompt: "The best way to explain recursion is"
The model might consider:
" to" high probability
" by" high probability
" with" medium probability
" recursion" lower probability
" not" lower probability
If it samples:
" to"
the answer may become instructional:
The best way to explain recursion is to start with a simple example...
If it samples:
" by"
it may become methodological:
The best way to explain recursion is by comparing it to nested boxes...
If it samples:
" recursion"
it may become playful:
The best way to explain recursion is recursion itself...
The initial difference may be just one token, but after that the future probability landscape changes.
That is why sampling can feel like it changes the “personality” or “direction” of the model.
Sampling is not the message, but it changes which possible message appears
Your quoted theory is actually close to a useful intuition:
“Randomness is not the message, but it can help us notice what our prompt was already asking for.”
A more technical version would be:
The prompt induces a probability distribution over possible continuations. Sampling chooses one trajectory through that distribution. Randomness does not create the distribution, but it selects among the plausible paths already made available by the prompt and model.
The model is not pulling arbitrary thoughts from nowhere. It is sampling from possibilities conditioned on:
prompt + system instructions + conversation history + learned model weights
So if several completions are plausible, sampling may reveal different modes of the distribution.
For example, the prompt:
Explain intelligence.
is broad. The model may reasonably continue in several directions:
philosophical
neuroscientific
computational
evolutionary
psychological
AI-focused
Higher sampling diversity may expose these alternate paths.
But for a narrow prompt:
What is 2 + 2? Answer with one digit.
the distribution should be extremely concentrated around:
4
In that case, high randomness mostly just increases the chance of error.
Practical meanings of different settings
Low temperature, low top_p
temperature: 0–0.4
top_p: 0.8–0.95
Behavior:
- more deterministic
- more repetitive
- less creative
- better for factual, constrained, or formatted output
- less likely to wander
Good for:
classification
JSON
extraction
summarization
code transformations
factual QA
Medium temperature, medium/high top_p
temperature: 0.6–1.0
top_p: 0.9–1.0
Behavior:
- natural variation
- still coherent
- less rigid
- good general-purpose generation
Good for:
brainstorming
drafting
explanations
dialogue
rewriting
High temperature, high top_p
temperature: 1.1–2.0
top_p: 0.95–1.0
Behavior:
- more surprising
- more diverse
- more unstable
- more likely to contradict itself
- more likely to produce odd phrasing or errors
Good for:
creative writing
ideation
generating unusual alternatives
style exploration
Risky for:
math
legal reasoning
medical advice
precise code
structured data
A useful mental model
Imagine the model is walking downhill through a landscape.
- The prompt defines the terrain.
- The logits define the slope at each step.
- Greedy decoding always takes the steepest downhill step.
top_p fences off unlikely paths.- Temperature changes how willing the walker is to take a less steep path.
- Sampling chooses the actual next footstep.
A low-temperature model walks like this:
“Always take the obvious path.”
A high-temperature model walks like this:
“Prefer good paths, but sometimes try a side trail.”
A low-top_p model says:
“Only consider the main trails.”
A high-top_p model says:
“Side trails are allowed too.”
Final summary
top_p and temperature do not directly change the model’s knowledge. They change how the next token is selected from the model’s probability distribution.
- The transformer produces logits for every BPE token.
- Softmax converts logits into probabilities.
temperature sharpens or flattens those probabilities, usually by dividing logits before softmax.top_p keeps only the smallest set of tokens whose cumulative probability reaches the cutoff.- Then one token is sampled.
- That token becomes part of the context, changing the distribution for the next token.
Lower settings make generation more deterministic and greedy-like.
Higher settings allow more deviation from the most likely path.
Sampling is not “the meaning” itself. But it determines which latent continuation of your prompt becomes visible.