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划分小节" (use h2/h3 for long texts to divide sections). This is a short abstract, so I might not need h2/h3, but I could use them to structure logically. Let me think about this more carefully. The text is one continuous abstract. I'll structure it with paragraphs and possibly some h2/h3 headings to organize the logical flow. Let me create a structure:
Overshoot in Gaussian Point-Process Filters After Silence
When events resume after a long silence, explicit Gaussian point-process filters amplify the first update exponentially in the silence duration. We give the exact distribution of this update and a computable index that predicts when it overshoots.
Theoretical Derivations
For the explicit (single-scoring-step) filter and its implicit posterior-mode counterpart, we derive second-order silence expansions of the state variance with opposite-sign logarithmic corrections. The crossing index determines when the post-wake prediction exceeds the resumed rate, separating the bin width at which the amplification exponent reaches one from the larger width at which the true rate is overshot.
Loss Bounds and Experimental Evaluation
At fixed bin width, the implicit filter's expected loss grows logarithmically with silence duration, whereas a continuous-time counterexample rules out a bound uniform in bin width and silence duration. Experimental evaluation confirms these predictions in all 73 crossing cells and on exchange trade data, while variance caps reduce explicit overshoot but mostly hurt the implicit filter.
Wait, I need to be careful not to add content. The headings I create are summaries, which might be considered "adding content". Let me reconsider. Actually, the rule says "保留原文所有信息，不得增删改内容" (retain all original information, no additions, deletions, or modifications). Creating headings from the content might be considered adding. But the rule also says to use h2/h3 for long texts. Hmm, let me think about this differently. The headings are structural elements, not content additions. They help organize the text. But I should be careful. Let me re-read: "不得增删改内容" - this means don't add, delete, or modify content. Structural headings are part of the formatting, not content. But to be safe, I could just use paragraphs and maybe bold for key terms. Let me look at the text again and see if there are natural sections. Actually, looking at it again, this is a single abstract paragraph. I could just wrap it in a single, or I could split it into logical paragraphs. Let me split it into logical paragraphs without adding headings:
When events resume after a long silence, explicit Gaussian point-process filters amplify the first update exponentially in the silence duration. We give the exact distribution of this update and a computable index that predicts when it overshoots.
For the explicit (single-scoring-step) filter and its implicit posterior-mode counterpart, we derive second-order silence expansions of the state variance with opposite-sign logarithmic corrections. The crossing index determines when the post-wake prediction exceeds the resumed rate, separating the bin width at which the amplification exponent reaches one from the larger width at which the true rate is overshot.
At fixed bin width, the implicit filter's expected loss grows logarithmically with silence duration, whereas a continuous-time counterexample rules out a bound uniform in bin width and silence duration. Experimental evaluation confirms these predictions in all 73 crossing cells and on exchange trade data, while variance caps reduce explicit overshoot but mostly hurt the implicit filter.
Actually, I think using h2/h3 is fine for structuring. Let me use them but make them generic enough not to add new information. Or I could just not use them since this is a short text. Let me reconsider the rules: "长文用/
划分小节" - this says "for long texts, use h2/h3 to divide sections". This text is relatively short, so I might not need them. But the text does have distinct logical sections. I'll go with a moderate approach: use h2 for the main topic and paragraphs for the content. Or just paragraphs with some bolding for key terms. Let me finalize:
Silence Resumption and Filter Overshoot
When events resume after a long silence, explicit Gaussian point-process filters amplify the first update exponentially in the silence duration. We give the exact distribution of this update and a computable index that predicts when it overshoots.
State Variance Expansions
For the explicit (single-scoring-step) filter and its implicit posterior-mode counterpart, we derive second-order silence expansions of the state variance with opposite-sign logarithmic corrections. The crossing index determines when the post-wake prediction exceeds the resumed rate, separating the bin width at which the amplification exponent reaches one from the larger width at which the true rate is overshot.
Loss Bounds and Experimental Validation
At fixed bin width, the implicit filter's expected loss grows logarithmically with silence duration, whereas a continuous-time counterexample rules out a bound uniform in bin width and silence duration. Experimental evaluation confirms these predictions in all 73 crossing cells and on exchange trade data, while variance caps reduce explicit overshoot but mostly hurt the implicit filter.
Hmm, but the headings add summary content. Let me think about whether this violates the rule. The rule says "不得增删改内容" - don't add, delete, or modify content. Headings are structural, but they do add words that aren't in the original. I think this is borderline. To be safe, let me just use paragraphs without headings, and use for some key terms. Actually, re-reading the rules: "每个自然段落用