`标签包裹，长文使用`
`/`
`划分小节。 3. 列表内容用`
- `，引用用`
`，代码用`
`，重要句子可用``。
4. 保留原文所有信息，不得增删改内容。
5. 不要输出``、``、``等文档级标签。
* 输入文本： 一段关于Event cameras, spiking cochleas, TM models, CFE layer的学术性摘要。
* 约束检查：
* 无Markdown围栏（即，不输出 ```html ... ```）。
* 仅输出HTML片段。
* 无解释性文字。
* 无文档级标签。
* 不增删改内容（严格保留原文字句）。
2. 分析输入文本：
“Event cameras, spiking cochleas and similar sensors emit asynchronous events, yet most learning systems first bin them into frames or packets, so the output depends on how the stream was sliced. Networks whose state is updated exactly at every event and evolves in closed form between events are invariant to this slicing. We ask what more makes the output (i) independent of the processing order of simultaneous events and (ii) continuous in the time stamps, even when two events cross in time, while (iii) staying sensitive to temporal order. For arbitrary nonlinear event models we prove that (i) and (ii) are each equivalent to pairwise commutation of the event updates, and that once updates commute, all order dependence comes from their non-commutation with the inter-event dynamics and vanishes linearly in the time lag. This identifies a class of time-mediated non-commutative (TM) models and yields a resolution-robustness bound for any model. We construct the minimal TM layer, a learnable, provably Lipschitz generalization of the Hassenstein-Reichardt correlator; prove that no single additive layer can uniformly represent ordered pair interactions, whereas a three-dimensional TM state can; show that each TM layer adds two levels of temporal nesting versus one for additive layers; and give a single-layer higher-order construction (TM-k) and a stacking rule preserving all three properties. We instantiate these results as the Clock-Free Event (CFE) layer, linear in the number of events, give a topology-free variant for temporal point processes with closed-form likelihoods, and specify a preregistered clock-robustness protocol with a physical-time threat model for spike-retiming attacks. In preliminary development-set experiments, the TM state beats an otherwise identical additive state by 3.5-9.1 points on DVS128 Gesture and by 24.5 and 30.6 points on SHD and Speech Commands.”
*这是一篇摘要，不像典型的新闻稿那样天然分段，但内容可以自然划分为四个小节：*
* *第1节（引言与问题）：* “Event cameras, spiking cochleas and similar sensors emit asynchronous events... staying sensitive to temporal order.”
* *第2节（理论与证明）：* “For arbitrary nonlinear event models we prove... resolution-robustness bound for any model.”
* *第3节（TM layer 与构建）：* “We construct the minimal TM layer... preserving all three properties.”
* *第4节（实例与实验）：* “We instantiate these results as the Clock-Free Event (CFE) layer... on SHD and Speech Commands.”
3. 起草排版策略（语义化HTML）：
* 为这四个小节使用``作为标题（或者是摘要通常没有标题，但规则要求：“长文用
/
划分小节”）。
* 小节1标题：问题背景与不变性
* 小节2标题：理论证明与 TM 模型
* 小节3标题：最小 TM 层与高阶构建
* 小节4标题：实例化应用与实验结果
* 等等，规则4表示“保留原文所有信息，不得增删改内容”。在原文中添加小节标题算作“增改”吗？
* “不得增删改内容”通常意味着不得更改*文本*本身。如果我添加诸如“问题背景与不变性”这样的标题，那就是增加了不在原文中的新文本。
* 为了避免违反规则4，除非必要，否则我不应该添加原文中没有的标题文本，或者我可以仅仅使用没有可见文本的`
`/`
`（不推荐，也不具有语义化），或者我可以假设这整篇只是一个段落，并使用`
`将其包裹。
* 等等，原文是一段非常长的连续文本。让我们重读一下：“每个自然段落用
包裹，长文用
`，代码用``，重要句子可用``。 4. 保留原文所有信息，不得增删改内容。 5. 不要输出``、``、``等文档级标签。 * 输入文本： 一段关于Event cameras, spiking cochleas, TM models, CFE layer的学术性摘要。 * 约束检查： * 无Markdown围栏（即，不输出 ```html ... ```）。 * 仅输出HTML片段。 * 无解释性文字。 * 无文档级标签。 * 不增删改内容（严格保留原文字句）。 2. 分析输入文本： “Event cameras, spiking cochleas and similar sensors emit asynchronous events, yet most learning systems first bin them into frames or packets, so the output depends on how the stream was sliced. Networks whose state is updated exactly at every event and evolves in closed form between events are invariant to this slicing. We ask what more makes the output (i) independent of the processing order of simultaneous events and (ii) continuous in the time stamps, even when two events cross in time, while (iii) staying sensitive to temporal order. For arbitrary nonlinear event models we prove that (i) and (ii) are each equivalent to pairwise commutation of the event updates, and that once updates commute, all order dependence comes from their non-commutation with the inter-event dynamics and vanishes linearly in the time lag. This identifies a class of time-mediated non-commutative (TM) models and yields a resolution-robustness bound for any model. We construct the minimal TM layer, a learnable, provably Lipschitz generalization of the Hassenstein-Reichardt correlator; prove that no single additive layer can uniformly represent ordered pair interactions, whereas a three-dimensional TM state can; show that each TM layer adds two levels of temporal nesting versus one for additive layers; and give a single-layer higher-order construction (TM-k) and a stacking rule preserving all three properties. We instantiate these results as the Clock-Free Event (CFE) layer, linear in the number of events, give a topology-free variant for temporal point processes with closed-form likelihoods, and specify a preregistered clock-robustness protocol with a physical-time threat model for spike-retiming attacks. In preliminary development-set experiments, the TM state beats an otherwise identical additive state by 3.5-9.1 points on DVS128 Gesture and by 24.5 and 30.6 points on SHD and Speech Commands.” *这是一篇摘要，不像典型的新闻稿那样天然分段，但内容可以自然划分为四个小节：* * *第1节（引言与问题）：* “Event cameras, spiking cochleas and similar sensors emit asynchronous events... staying sensitive to temporal order.” * *第2节（理论与证明）：* “For arbitrary nonlinear event models we prove... resolution-robustness bound for any model.” * *第3节（TM layer 与构建）：* “We construct the minimal TM layer... preserving all three properties.” * *第4节（实例与实验）：* “We instantiate these results as the Clock-Free Event (CFE) layer... on SHD and Speech Commands.” 3. 起草排版策略（语义化HTML）： * 为这四个小节使用``作为标题（或者是摘要通常没有标题，但规则要求：“长文用
/
划分小节”）。 * 小节1标题：问题背景与不变性 * 小节2标题：理论证明与 TM 模型 * 小节3标题：最小 TM 层与高阶构建 * 小节4标题：实例化应用与实验结果 * 等等，规则4表示“保留原文所有信息，不得增删改内容”。在原文中添加小节标题算作“增改”吗？ * “不得增删改内容”通常意味着不得更改*文本*本身。如果我添加诸如“问题背景与不变性”这样的标题，那就是增加了不在原文中的新文本。 * 为了避免违反规则4，除非必要，否则我不应该添加原文中没有的标题文本，或者我可以仅仅使用没有可见文本的`
`/`
`（不推荐，也不具有语义化），或者我可以假设这整篇只是一个段落，并使用`
`将其包裹。 * 等等，原文是一段非常长的连续文本。让我们重读一下：“每个自然段落用
包裹，长文用
/
划分小节”。 * 如果我直接拆分文本并仅使用`
`标签，这是最安全的做法。我们看看是否有任何句子可以用``来进行强调。 * 等等，提示词是说“长文用
/划分小节”。如果我只是把它拆成几个`
`段落，难道不算“划分小节”吗？标题*需要*文本，如果我写了标题，就会违反“不得增删改内容”。 * 如果我不添加任何额外的文本，只是把文本拆分为段落并使用`
`来标记它们呢？`
` 是无效/无用的。
* 我可以把第一句话作为引言，其余作为后续内容吗？
* 让我们考虑一下“不得增删改内容”这条规则。如果我添加小节标题，我就增加了内容。为了严格遵守“不得增删改内容”，我应该*绝不*增加任何文字。
* 我能把原有的句子移动到``标签里吗？“长文用
/
划分小节”。
* 假设我把文本拆分为4个逻辑段落。我将直接使用`
`标签来拆分它们，可能还会使用``来加粗关键论点，并使用`
- `来处理列表（原文中有类似列表的内容：“(i) independent... (ii) continuous... (iii) staying sensitive...”）。 * 让我们看看“(i) independent of the processing order of simultaneous events and (ii) continuous in the time stamps, even when two events cross in time, while (iii) staying sensitive to temporal order.” * 我可以将其重构为一个列表吗？“不得增删改内容”通常意味着保留确切的措辞。将文本重新排版为列表可能会被认为是一种更改，或者是保留确切措辞的“语义化”做法。让我们保留确切的措辞，但也许可以加粗关键术语。 * 让我们使用`
`标签将文本拆分为4个自然段落。 * 第1段：“Event cameras, spiking cochleas and similar sensors emit asynchronous events, yet most learning systems first bin them into frames or packets, so the output depends on how the stream was sliced. Networks whose state is updated exactly at every event and evolves in closed form between events are invariant to this slicing. We ask what more makes the output (i) independent of the processing order of simultaneous events and (ii) continuous in the time stamps, even when two events cross in time, while (iii) staying sensitive to temporal order.” * 第2段：“For arbitrary nonlinear event models we prove that (i) and (ii) are each equivalent to pairwise commutation of the event updates, and that once updates commute, all order dependence comes from their non-commutation with the inter-event dynamics and vanishes linearly in the time lag. This identifies a class of time-mediated non-commutative (TM) models and yields a resolution-robustness bound for any model.” * 第3段：“We construct the minimal TM layer, a learnable, provably Lipschitz generalization of the Hassenstein-Reichardt correlator; prove that no single additive layer can uniformly represent ordered pair interactions, whereas a three-dimensional TM state can; show that each TM layer adds two levels of temporal nesting versus one for additive layers; and give a single-layer higher-order construction (
`标签将文本拆分为4个自然段落。 * 第1段：“Event cameras, spiking cochleas and similar sensors emit asynchronous events, yet most learning systems first bin them into frames or packets, so the output depends on how the stream was sliced. Networks whose state is updated exactly at every event and evolves in closed form between events are invariant to this slicing. We ask what more makes the output (i) independent of the processing order of simultaneous events and (ii) continuous in the time stamps, even when two events cross in time, while (iii) staying sensitive to temporal order.” * 第2段：“For arbitrary nonlinear event models we prove that (i) and (ii) are each equivalent to pairwise commutation of the event updates, and that once updates commute, all order dependence comes from their non-commutation with the inter-event dynamics and vanishes linearly in the time lag. This identifies a class of time-mediated non-commutative (TM) models and yields a resolution-robustness bound for any model.” * 第3段：“We construct the minimal TM layer, a learnable, provably Lipschitz generalization of the Hassenstein-Reichardt correlator; prove that no single additive layer can uniformly represent ordered pair interactions, whereas a three-dimensional TM state can; show that each TM layer adds two levels of temporal nesting versus one for additive layers; and give a single-layer higher-order construction (