张春成

V2

2023/05/21阅读:11主题:默认主题

点集的着色及其生成顺序分析

点集的着色及其生成顺序分析

我们之前在给定图形之内构造了一组致密点云,本文进一步解决如何对这些点进行分类着色的问题,并分析点集的类别与生成顺序之间的关系。如果我们稍微放飞一下自我,也许它可以作为一个 demo,用于解释机器学习中的“涌现”现象。

开源代码位置仍为

Plot population


按区域着色

我们既然能够在给定的范围内构造点云,下一步自然是对这些点进行按区域分类,这样才能更有效地利用这些点。所谓区域分类即是将点的横、纵坐标作为特征,对这些点进行“聚类”操作。本文使用最简单的 kmeans 算法进行,效果如下图所示。另外,如何控制点的分区策略呢?我们可以通过适当调整位置参数的权重来达到这个目的,效果如下图所示。至于使用哪种分区策略,使用者需要自行设计。

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npm: kmeans-engine

顺序分析

下面,我对不同类别的点进行分类统计,统计的对象是该类别的点是在什么时候被“放置”在轮廓中的。下图右侧的横坐标代表这些点的生成时间,这些点周围的颜色深浅代表该时间段内出现的概率密度。由于前文已经发现了点云生长过程中的“自组织”现象,因此不难想见,不同区域类别的点具有不同的“生日”时间,如图中的箭头所示。

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如果我们稍微放飞一下自我,也许它可以作为一个 demo,用于解释机器学习中的“涌现”现象。虽然涌现现象比较复杂,但我不想过分深入地探讨其中的概念,只是将机器学习的过程看作是不断“填满”整个概率空间的过程。那么在这个过程中,梯度算法会自然而然地形成类似本文例子的自组织结构,它像一条大河一样迅速扩张自己的“地盘”,随后再由“支流”渗透每一个角落。

那么,在整个学习过程中,不同的概念就好像是本例中的区域类别一样,随着点的生成过程而逐渐纳入学习范围。因此,在某一个特殊的时间点上有些概念会“涌现”出来,因为大河恰当在这个时刻流淌到这里。

当然,这只是非常感性的认识或者说是比喻,也不知道是否恰当。

附录:AI 给出的“涌现”解释

(English speaking)

Certainly! Emergence is a phenomenon that can occur in machine learning systems, particularly in complex models such as deep neural networks. It refers to the unexpected and often unintuitive behaviors or properties that arise from the interactions of simpler components or elements within the system.

In the context of machine learning, emergence can manifest in various ways. Here are a few examples:

  1. Feature Learning: In deep learning models, lower-level features are learned by individual neurons or small groups of neurons. As information flows through multiple layers, higher-level features emerge, which are combinations or abstractions of the lower-level features. These emergent features capture more complex patterns and concepts, often leading to improved performance in tasks such as object recognition or natural language understanding.
  2. Unsupervised Learning: In unsupervised learning, a model is trained to discover patterns or structures in the data without explicit labels or targets. Emergent properties can arise when the model finds latent factors or clusters in the data that were not explicitly specified. For example, in image clustering, the model may discover groups of visually similar images that correspond to different object categories, even though it was not directly trained on those categories.
  3. Collective Behavior: In certain machine learning systems, such as swarm intelligence algorithms or multi-agent reinforcement learning, emergence can be observed at a higher level of organization. Individual agents or components follow simple rules, but when interacting with each other or their environment, collective behaviors emerge that are not exhibited by any single agent. These emergent behaviors can lead to coordinated actions, problem-solving, or optimization of the system as a whole.

It's important to note that while emergence can bring about useful and insightful behaviors, it can also lead to unintended consequences or unpredictable outcomes. The complexity and non-linear nature of machine learning systems make it challenging to fully understand and control emergent phenomena. Therefore, researchers and practitioners need to carefully analyze and validate the emergent behaviors to ensure they align with the desired objectives and avoid any undesirable effects.


(中文说法)

在机器学习领域中,"涌现"(emergence)是指系统整体表现出超出其个体组成部分的性质或行为的现象。这种现象可能是由于个体之间的交互作用、自组织性质或复杂性导致的。在机器学习中,涌现可以指涉到以下几个方面:

  1. 群体智能涌现:在群体中的个体之间的相互作用和协作可以导致群体整体表现出智能性质。例如,通过群体协作和信息共享,群体可以解决复杂的问题,这些问题可能超出了单个个体的能力。
  2. 模型行为涌现:有时,当训练机器学习模型时,模型可能表现出令人惊讶的行为或性能。这些行为可能是由于模型学习到了数据中的隐含模式或结构,这些模式或结构原本并不明显或被人类难以察觉。
  3. 特征涌现:在特征选择或特征提取过程中,机器学习算法可能会从原始数据中发现新的特征或组合特征,这些特征对于解决给定的任务非常有用。这种涌现的特征可以提供更好的数据表示或更好的判别能力。

涌现现象在机器学习领域的研究中很重要,因为它可以帮助我们理解模型的行为和性能,并为我们提供更深入的洞察力,以改进机器学习算法和系统。

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张春成
V2