Deep Manifold
Through the lens of manifold covers, we open a mathematical window into neural networks. At its core lies something unexpectedly simple: inequality, integration, and differentiation.
| Platform |  | Pricing | Only free issues | Publishes | Daily |
|---|---|---|---|---|---|
| Issues | 140 | Founded | 2 years ago | Last Issue | 7 days ago |
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神经学习的喜剧
English Edition: The Comedy of Neural Learning
当数学说“不”
阻碍理论与 Kan 扩张
阻碍理论从一个相当谦逊的问题开始：这个局部的、弱的、不完整的，或从别处搬运过来的结构，能不能被提升成某种完整、严格、全局而且体面的东西？然后，数学会给出它一贯令人安心的回答：也许可以——前提是我们先准确找出它为什么根本做不到。所谓阻碍，就是对失败的正式记录。某个东西无法延拓，某个图就是不肯交换，某个在局部看起来完全无害的结构，一...
The Comedy of Neural Learning
Chinese Edition: 神经学习的喜剧
When Mathematics Says No
Obstruction Theory and Kan Extension
Obstruction theory begins with a modest question: can this partial, weak, local, or transported structure be lifted into something complete, stric...
The Myth of Reasoning
Chinese Edition: 推理的误区
Observable Reasoning and Human Confidence
Human reasoning has been classified into familiar forms such as deduction, induction, analogy, causality, and intuition. But an LLM is not required to follow these cate...
推理的误区
English Edition: The Myth of Reasoning
可观察推理与人类信心
人类推理通常被划分为演绎、归纳、类比、因果和直觉等熟悉的形式。但大语言模型在内部并不必然遵循这些类别。在预训练过程中，它可能形成许多人类无法识别、甚至尚不知道如何描述的计算路径。当这些路径产生有用答案时，我们往往只能在事后将其解释为捷径、直觉、模式识别或潜意识式推理，因为我们缺乏更准确的语言来描述其中实际发生了什么。
Click the image to vie...
单标几何 07:注意力
English Edition: Single Token Geometry 07: Attention
高中数学错误
Transformer 注意力常常被描述成一种相似性机制。一个单标产生 Query，与其他单标的 Key 进行比较，然后利用这个结果决定信息应该流向哪里。在这种解释中，注意力听起来几乎像一个干净的几何操作：一个单标提出问题，另一个单标提供匹配，最高的分数就代表最强的关系。
但这种解释隐藏了一个基本的坐标问题。Query、Key 和 Value...
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Through the lens of manifold covers, we open a mathematical window into neural networks. At its core lies something unexpectedly simple: inequality, integration, and differentiation.
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