`, long articles use `
`/`
` for sections. 3. Lists use `
- `, quotes use `
`, code uses `
`, important sentences use ``.
4. Preserve *all* original information (no additions or deletions).
5. No document-level tags (``, ``, ``).
2. Analyze the Source Text:
* *Paragraph 1:* "Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass."
* *Paragraph 2:* "Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$."
* *Paragraph 3:* "The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66\% of locked units with $g=6$ stay locked under DRY and 1\% with $g=8$. In free generation with llama.cpp, all 109 loops that survive DRY have $g\le 7$."
* *Paragraph 4:* "We propose DRY-C, which adds a term that grows exponentially with the number of verbatim recurrences, up to its look-back window. With it, none of 720 structured output generations looped to the length limit, and task completion stayed close to DRY's."
3. Determine Structure and Tags:
* The text is a single research paper abstract/summary. It naturally breaks down into logical sections based on the flow of ideas.
* Section 1: Core problem & determinism (Paras 1 & 2). Let's group them or use `` for the main topic and `
` for the paragraphs. Since it's a short article, maybe just `
` for the first part and `
` for the specific method analysis, then `
` for the results? Or just standard paragraphs with `` for key sentences as requested. The prompt says "长文用/
划分小节" (long articles use h2/h3 to divide sections). This text is relatively short but dense. I will structure it logically:
* `
` "核心问题与确定性分析" (Core Problem and Deterministic Analysis) -> Para 1 & 2
* `
` "DRY采样的盲点" (Blind spot in DRY sampler) -> Para 3
* `
` "DRY-C的提出与验证" (Proposal and Verification of DRY-C) -> Para 4
* Wait, the rule says "每个自然段落用
包裹" (every natural paragraph wrapped in `
`). If I use `
`, do I also wrap the following text in `
`? Usually, yes, or the heading stands alone. Let's make headings stand alone and wrap paragraphs in `
`. * Let's refine the structure: * `
` Loop escape conditions
* `
Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass.
`
* `Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$.` (Wait, this is one sentence? No, it's two independent clauses separated by a semone. Let's keep it as one `
`.) * `
` Blind spot in DRY sampler
* `
The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66% of locked units with $g=6$ stay locked under DRY and 1% with $g=8$. In free generation with llama.cpp, all 109 loops that survive DRY have $g\le 7$.
`
* `` DRY-C proposal and validation
* `
We propose DRY-C, which adds a term that grows exponentially with the number of verbatim recurrences, up to its look-back window. With it, none of 720 structured output generations looped to the length limit, and task completion stayed close to DRY's.
`
* Where do I use `
- `, `
`, `
`, ``?
* The prompt requires using these tags if applicable ("列表内容用- ，引用用
，代码用，重要句子可用"). While the source text doesn't explicitly have lists or blockquotes, a good semanticizer might extract key facts or emphasize important sentences.
* Important sentences:
* "Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$." -> Make this ``?
* "A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$." -> Make this ``?
* "On eleven open models, 66% of locked units with $g=6$ stay locked under DRY and 1% with $g=8$." -> Important stats, maybe ``?
* "none of 720 structured output generations looped to the length limit" -> Important result, maybe ``? * Can I create a list from the key points? "核心发现：..." No, the rule says "保留原文所有信息，不得增删改内容" (Preserve all original info, don't add/delete). Creating bullet points might violate "natural paragraph" rules or imply adding structure not explicitly in the text. Better to just use `` for the most critical sentences within the `
` tags. * What about `\$`? The prompt has `$n$`, `$π$`, `$π>1/2$`, `$π$`, `$λb^{g-1-a}$`, `$g=6$`, `$g=8$`, `$g\le 7$`. I must keep these exact LaTeX strings. 4. Drafting the HTML: ```html
Loop Escape Conditions
Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass.
Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$.
Blind Spot in DRY Sampler
The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66% of locked units with $g=6$ stay locked under DRY
`, code uses ``, important sentences use ``. 4. Preserve *all* original information (no additions or deletions). 5. No document-level tags (``, ``, ``). 2. Analyze the Source Text: * *Paragraph 1:* "Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass." * *Paragraph 2:* "Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$." * *Paragraph 3:* "The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66\% of locked units with $g=6$ stay locked under DRY and 1\% with $g=8$. In free generation with llama.cpp, all 109 loops that survive DRY have $g\le 7$." * *Paragraph 4:* "We propose DRY-C, which adds a term that grows exponentially with the number of verbatim recurrences, up to its look-back window. With it, none of 720 structured output generations looped to the length limit, and task completion stayed close to DRY's." 3. Determine Structure and Tags: * The text is a single research paper abstract/summary. It naturally breaks down into logical sections based on the flow of ideas. * Section 1: Core problem & determinism (Paras 1 & 2). Let's group them or use `` for the main topic and `
` for the paragraphs. Since it's a short article, maybe just `
` for the first part and `
` for the specific method analysis, then `
` for the results? Or just standard paragraphs with `` for key sentences as requested. The prompt says "长文用
/
划分小节" (long articles use h2/h3 to divide sections). This text is relatively short but dense. I will structure it logically: * `
` "核心问题与确定性分析" (Core Problem and Deterministic Analysis) -> Para 1 & 2 * `
` "DRY采样的盲点" (Blind spot in DRY sampler) -> Para 3 * `
` "DRY-C的提出与验证" (Proposal and Verification of DRY-C) -> Para 4 * Wait, the rule says "每个自然段落用
包裹" (every natural paragraph wrapped in `
`). If I use `
`, do I also wrap the following text in `
`? Usually, yes, or the heading stands alone. Let's make headings stand alone and wrap paragraphs in `
`. * Let's refine the structure: * `
` Loop escape conditions * `
Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass.
` * `Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$.` (Wait, this is one sentence? No, it's two independent clauses separated by a semone. Let's keep it as one `
`.) * `
` Blind spot in DRY sampler * `
The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66% of locked units with $g=6$ stay locked under DRY and 1% with $g=8$. In free generation with llama.cpp, all 109 loops that survive DRY have $g\le 7$.
` * `` DRY-C proposal and validation * `
We propose DRY-C, which adds a term that grows exponentially with the number of verbatim recurrences, up to its look-back window. With it, none of 720 structured output generations looped to the length limit, and task completion stayed close to DRY's.
` * Where do I use `
- `, `
`, ``, ``? * The prompt requires using these tags if applicable ("列表内容用
- ，引用用
，代码用，重要句子可用"). While the source text doesn't explicitly have lists or blockquotes, a good semanticizer might extract key facts or emphasize important sentences. * Important sentences: * "Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$." -> Make this ``? * "A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$." -> Make this ``? * "On eleven open models, 66% of locked units with $g=6$ stay locked under DRY and 1% with $g=8$." -> Important stats, maybe ``? * "none of 720 structured output generations looped to the length limit" -> Important result, maybe ``? * Can I create a list from the key points? "核心发现：..." No, the rule says "保留原文所有信息，不得增删改内容" (Preserve all original info, don't add/delete). Creating bullet points might violate "natural paragraph" rules or imply adding structure not explicitly in the text. Better to just use `` for the most critical sentences within the `` tags. * What about `\$`? The prompt has `$n$`, `$π$`, `$π>1/2$`, `$π$`, `$λb^{g-1-a}$`, `$g=6$`, `$g=8$`, `$g\le 7$`. I must keep these exact LaTeX strings. 4. Drafting the HTML: ```html
Loop Escape Conditions
Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass.
Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$.
Blind Spot in DRY Sampler
The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66% of locked units with $g=6$ stay locked under DRY