Spectral Signatures of Memorization Basins in Diffusion Trajectories

这个问题是要把给定的纯文本新闻正文排版成语义化的HTML片段，需要遵循几个规则：每个自然段落用

包裹，长文用

/

划分小节，列表内容用

• ，引用用

  ，代码用

  ，重要句子可用，保留原文所有信息，不增删改内容，只输出HTML片段本身，不要文档级标签。首先看正文内容，是一个关于扩散模型记忆盆地的研究摘要，结构上是几个连续的自然段落，没有明显的小节标题，但原文里有“Prior empirical work...”“In this paper...”“We observe...”“This signature appears...”“We further investigate...”“During training...”“At inference...”“We find that...”“Together, our results...”这些部分，不过用户要求的是用
  /
  划分小节，但原文本身没有显式的小节，不过可能需要根据内容逻辑？不对，仔细看原文，其实是一段还是多段？原文里的换行是用户输入的分隔，看内容：“Diffusion models are known to reproduce...”“Recent work demonstrated...”“Prior empirical work on such basins...”“In this paper, we present...”“We observe a characteristic signature...”“This signature appears at two timescales...”“We further investigate whether...”“During training, we suppress...”“At inference, we develop...”“We find that these interventions...”“Together, our results corroborate...”这些是连续的段落吗？不，原文在用户输入里是每句一行，但实际是完整的段落，不过需要看每个自然段落。不过仔细看用户给的正文，其实是一个完整的摘要，分成几个句子，但作为自然段落，可能需要把每个完整的语义段落用
  包裹。不过再看规则，长文用
  /
  划分小节，但原文没有显式的小节，所以可能不需要？不对，再看原文内容，有没有可以划分的小节？比如“Prior empirical work...”是关于之前的研究，“In this paper...”是本文内容，“We observe...”是观察结果，“This signature...”是特征的时间尺度，“We further investigate...”是干预研究，“During training...”和“At inference...”是干预方法，“We find that...”是效果，“Together...”是结论。但用户要求保留原文所有信息，不得增删改，所以不能添加小节标题，因为原文没有。所以只能把每个自然段落用
  包裹。那原文里的每个句子是不是一个自然段落？不对，自然段落是指表达一个完整意思的段落，比如第一句到“downstream use.”是一个段落吗？看原文：“Diffusion models are known to reproduce individual examples from their training data as a form of memorization with implications for generalization, privacy, and downstream use. Recent work demonstrated that memorized training samples reside inside contiguous regions of the data/latent space known as basins of memorization -- once a denoising trajectory enters a basin, under finite perturbations it irreversibly reproduces a memorized example. Prior empirical work on such basins in trained models has primarily focused on classifier-free guidance based detection and mitigation strategies in text-to-image models, leaving basin entry and their formation largely uncharacterized. In this paper, we present a geometric characterization of memorization basins for conditional, unconditional, and rectified-flow-based diffusion models. We observe a characteristic signature in the local spectrum of the function geometry that distinguishes basin entry: the emergence of a dominant singular mode followed by a sharp spectral recovery. This signature appears at two timescales: along denoising trajectories during inference and over the course of training. We further investigate whether these geometric signatures can be used to intervene on memorization. During training, we suppress memorization by acting on the dominant mode. At inference, we develop methods to identify trajectories entering memorization basins and steer them away. We find that these interventions remain effective even with low-dimensional approximations of the underlying geometry, and demonstrate that geometry-informed steering extends to large-scale text-to-image diffusion models. Together, our results corroborate that local spectral geometry provides a common basis for characterizing memorization and for suppressing, detecting, and steering away from it across training and generation.” 这整个是一个段落吗？不，用户输入里的换行是每句一行，但实际作为新闻正文，可能是一个完整的摘要，但需要看自然段落。不过仔细看，原文里的内容是一个连贯的摘要，可能分为几个自然段落？比如：“Diffusion models are known to reproduce individual examples from their training data as a form of memorization with implications for generalization, privacy, and downstream use. Recent work demonstrated that memorized training samples reside inside contiguous regions of the data/latent space known as basins of memorization -- once a denoising trajectory enters a basin, under finite perturbations it irreversibly reproduces a memorized example. Prior empirical work on such basins in trained models has primarily focused on classifier-free guidance based detection and mitigation strategies in text-to-image models, leaving basin entry and their formation largely uncharacterized.” 这是一个段落，讲背景和之前的研究。然后“In this paper, we present a geometric characterization of memorization basins for conditional, unconditional, and rectified-flow-based diffusion models. We observe a characteristic signature in the local spectrum of the function geometry that distinguishes basin entry: the emergence of a dominant singular mode followed by a sharp spectral recovery. This signature appears at two timescales: along denoising trajectories during inference and over the course of training.” 是第二个段落，讲本文的方法和观察。然后“We further investigate whether these geometric signatures can be used to intervene on memorization. During training, we suppress memorization by acting on the dominant mode. At inference, we develop methods to identify trajectories entering memorization basins and steer them away.” 第三个段落，讲干预研究。然后“We find that these interventions remain effective even with low-dimensional approximations of the underlying geometry, and demonstrate that geometry-informed steering extends to large-scale text-to-image diffusion models. Together, our results corroborate that local spectral geometry provides a common basis for characterizing memorization and for suppressing, detecting, and steering away from it across training and generation.” 第四个段落，讲效果和结论。不过需要确认原文的自然段落划分，用户输入里的换行是每句一行，但实际原文可能是一个段落还是多个？不过根据新闻排版的习惯，摘要可能是一个段落，但用户要求每个自然段落用
  包裹，所以需要看原文是否有自然段落的分隔。不过再仔细看用户给的正文，其实是一个完整的文本，没有明显的段落分隔，但每句之间用换行，可能是用户输入的格式问题。不过根据规则，保留原文所有信息，不得增删改，所以应该把原文中的每个句子作为
  吗？不对，自然段落是指表达一个完整意思的段落，比如第一句和后面的句子如果是一个意思，应该放在一个
  里。但可能更准确的是，原文中的每一个完整的句子作为
  ？不，不对，比如第一句：“Diffusion models are known to reproduce individual examples from their training data as a form of memorization with implications for generalization, privacy, and downstream use.” 是一个段落？然后第二句：“Recent work demonstrated that memorized training samples reside inside contiguous regions of the data/latent space known as basins of memorization -- once a denoising trajectory enters a basin, under finite perturbations it irreversibly reproduces a memorized example.” 是第二个段落？但这样可能太碎了。不过再看用户给的正文，其实是用户输入时每句一行，但实际原文可能是一个段落，不过需要看内容。不过可能更简单的方式是，原文中的每一个句子作为一个
  ？但这样不符合自然段落的定义。或者，可能原文中的整个内容是一个段落，但用户输入时换行，所以需要把它作为一个
  ？不对，再看规则，“每个自然段落用
  包裹”，自然段落是指作者写作时的段落，比如摘要通常是一个段落，但如果是新闻正文，可能有多个段落。不过根据用户给的正文内容，其实是一个完整的摘要，没有明显的段落分隔，所以可能只需要一个
  ？但不对，再看原文，有“Prior empirical work...”“In this paper...”等部分，可能作者写作时是分段的。不过可能更准确的是，按照用户输入的换行，把每个句子作为
  ？但这样可能不符合自然段落。或者，可能用户输入的换行只是为了分隔，实际原文是一个段落，所以用一个
  包裹？不过再仔细看原文内容，比如：“Diffusion models are known to reproduce individual examples from their training data as a form of memorization with implications for generalization, privacy, and downstream use. Recent work demonstrated that memorized training samples reside inside contiguous regions of the data/latent space known as basins of memorization -- once a denoising trajectory enters a basin, under finite perturbations it irreversibly reproduces a memorized example. Prior empirical work on such basins in trained models has primarily focused on