What is the difference between presence penalty and frequency penalty in OpenAI?

Both subtract from a token's logit before sampling, but differently. presence_penalty subtracts its full value once if the token has appeared at all, no matter how often. frequency_penalty subtracts its value for every prior occurrence, so it grows with the count. Presence discourages reusing any seen token; frequency specifically fights heavy repetition.

What range should frequency_penalty and presence_penalty be set to?

Both accept values from -2.0 to 2.0. In practice, small positive values of 0.1 to 1.0 reduce repetition without derailing the text; 1.5 to 2.0 can make output incoherent. Negative values do the opposite — they encourage the model to reuse tokens. The default for both is 0 (no penalty).

Does frequency penalty scale with how many times a token appears?

Yes. The frequency term subtracts frequency_penalty × count from the logit, so a token seen five times is penalised five times as hard as one seen once. Presence does not scale — it applies the same one-off subtraction whether the token appeared once or fifty times. That is the core distinction between the two.

How does presence penalty affect the softmax probability of a token?

It lowers the token's logit, which lowers its share after softmax. Because softmax is relative, penalising one token also nudges every other token's probability up. Enter your tokens above and the tool shows the exact before/after probabilities and whether the most likely next token changes.

Is repetition penalty the same as frequency penalty?

No. HuggingFace's repetition_penalty is multiplicative — it divides positive logits (or multiplies negative ones) by a factor, typically around 1.1 to 1.3. OpenAI's frequency_penalty is additive and count-scaled, in the range -2 to 2. They target the same problem but with different math, so a value from one does not transfer to the other.

Why did the most likely next token change when I raised the penalties?

Penalties subtract from the logits of tokens that have already appeared. If a favoured token has been used before, its logit drops while an unused alternative stays put. Once the gap closes past the crossover point, the alternative overtakes it after softmax. The tool flags this flip in the results header.

Does temperature interact with these penalties?

Penalties are applied to the logits first; temperature then divides the adjusted logits before softmax. Lower temperature sharpens the distribution and can exaggerate a penalty-driven flip; higher temperature flattens it. This tool applies the same temperature to the before and after distributions so the comparison isolates the penalty effect.

Are these logit and probability numbers from a real model?

No — you supply illustrative logits and counts so you can see the mechanism clearly. Real logits come from the model at inference and are not exposed by the Chat Completions API. This is a teaching and planning tool for choosing penalty values, not a way to read a live model's internal scores.

AI · LLM sampling

Presence vs Frequency Penalty Calculator (OpenAI)

Enter a few candidate tokens with their logits and how often each has appeared, then drag the presence and frequency penalty sliders to watch the adjusted logits and softmax probabilities update — and see when the most likely next token flips. Uses OpenAI's exact additive formula, runs fully in your browser, no signup.

By Induwara Ashinsana— Executive Director, Ryzera TechnologiesUpdated Jul 10, 2026

Presence & frequency penaltylogits → softmax

OpenAI additive formula

Candidate tokens

TokenBase logitPrior count

Presence penalty0.00

Subtracted once from any token already used (count > 0).

Frequency penalty0.00

Subtracted per prior occurrence — scales with the count.

Temperature1.00

Softmax sharpness. Applied to both before and after.

Presets

Most likely — before

the

62.85%

Most likely — after

the

62.85%

Winner

Unchanged

Penalties did not change the top token

Before vs after probability

thetop62.85% → 62.85%

cat23.12% → 23.12%

dog14.02% → 14.02%

Per-token breakdown

Token	Logit	Count	Adj logit	P before	P after	Δ
the	3	4	3	62.85%	62.85%	0%
cat	2	0	2	23.12%	23.12%	0%
dog	1.5	1	1.5	14.02%	14.02%	0%

Probabilities verified two ways (max softmax difference < 1e-9).

How “the” was adjusted

ℓ' = ℓ − presence·1[count>0] − frequency·count

= 3 − 0·1 − 0·4 = 3

softmax(ℓ' ÷ T=1) over all 3 tokens

P(“the”): 62.85% → 62.85% (0 pts)

Presence is a one-off nudge (any repeat costs the same); frequency compounds with every occurrence. Both are additive on the logit and bounded to [-2, 2] — unlike HuggingFace's multiplicative repetition_penalty.

Additive penalty formula and [-2, 2] range from OpenAI.

How it works

OpenAI's Chat Completions API exposes two sampling controls that look alike but behave differently: presence_penalty and frequency_penalty. Both accept a value from -2.0 to 2.0 and both nudge the model away from (or toward) repeating itself — but they touch the token logits in distinct ways. This tool applies the exact adjustment documented by OpenAI so you can see the effect token by token, without spending API credits to experiment.

For each candidate token j with base logit ℓ_j and a prior occurrence count c_j, the API adjusts the logit before sampling:

ℓ'_j = ℓ_j − frequency_penalty · c_j − presence_penalty · 1[c_j> 0]

The presence term subtracts the full presence_penalty once if the token has appeared at all (c_j> 0), regardless of how many times. It is a flat “have we used this already?” switch.
The frequency term subtracts frequency_penalty × c_j, so it grows linearly with the count. A token used five times is penalised five times as hard as one used once.

After the adjustment the tool converts logits to probabilities the same way the model samples them: divide each adjusted logit by the temperature T, then apply softmax, p_j = e^(z_j) / Σ e^(z_k), computed with max-subtraction for numerical stability. The “before” probabilities use the un-penalised logits ÷ T, so the comparison isolates the penalty effect rather than mixing in a temperature change. As a self-check the tool also recomputes the softmax through the identity p_j = 1 / Σ e^(z_k − z_j) and reports the (near-zero) difference between the two paths.

Because softmax is relative, lowering one token's logit raises every other token's probability. When a previously-favoured but already-repeated token drops far enough, an unused alternative overtakes it — the tool highlights this flip. Note that OpenAI's additive penalties are not the same as HuggingFace's multiplicative repetition_penalty; the two use different math and their values do not transfer.

Worked examples

Presence + frequency flip the winner — presence 0.5, frequency 0.3, T = 1

Token A: logit 2.0, count 3 → adj = 2.0 − 0.5·1 − 0.3·3 = 0.6
Token B: logit 1.5, count 0 → adj = 1.5 − 0 − 0 = 1.5
Before: P(A) = e^2.0 / (e^2.0 + e^1.5) = 62.25%, P(B) = 37.75%
After: P(A) = e^0.6 / (e^0.6 + e^1.5) = 28.91%, P(B) = 71.09%
The already-repeated favourite A loses to the unused token B.

Frequency dominates for heavy repeats — presence 0.2, frequency 0.4

Token "the": logit 3.0, count 5
adj = 3.0 − 0.2·1 − 0.4·5 = 3.0 − 0.2 − 2.0 = 0.8
Total reduction 2.2 = 0.2 presence + 2.0 frequency
For a token seen 5×, the frequency part is 10× the presence part.

The count = 0 vs count = 1 boundary — presence 1.0, frequency 0

Token X: logit 2.0, count 0 → presence part 0 → adj = 2.0
Token Y: logit 2.0, count 1 → presence part 1.0 → adj = 1.0
The presence switch fires only once the count crosses from 0 to 1.
This off-by-one boundary is where presence_penalty first bites.

Frequently asked questions

Sources & references

The additive formula and the [-2, 2] parameter range were last cross-checked against the OpenAI API reference (presence_penalty / frequency_penalty) on 2026-07-10. The two worked examples above (28.91% / 71.09% and adjusted logit 0.8) are reproduced exactly by the calculator.

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