数学不是计算，而是看见结构：柯尔莫哥洛夫没有想到的事
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TL;DR - This essay argues that mathematics, human learning, and large language models share a core process: compressing many examples into reusable structural representations. It frames Kolmogorov complexity as a useful analogy for understanding model generalization while stressing that compression alone does not ensure interpretability, causal understanding, or correctness.
- Modern mathematics studies invariant relationships and structures rather than merely manipulating individual objects.
- Language models compress statistical patterns—including syntax, semantics, code, and reasoning conventions—into parameters through next-token prediction and gradient-based training.
- Generalization is presented as evidence of learned transferable structure, although models can still memorize training details.
- Minimal descriptions may be opaque, erase important exceptions, or capture correlations without causality, so reliable intelligence also requires validation, feedback, and causal reasoning.
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数学不是计算，而是看见结构：柯尔莫哥洛夫没有想到的事
TL;DR - This essay argues that mathematics, human learning, and large language models share a core process: compressing many examples into reusable structural representations. It frames Kolmogorov complexity as a useful analogy for understanding model generalization while stressing that compression alone does not ensure interpretability, causal understanding, or correctness.
- Modern mathematics studies invariant relationships and structures rather than merely manipulating individual objects.
- Language models compress statistical patterns—including syntax, semantics, code, and reasoning conventions—into parameters through next-token prediction and gradient-based training.
- Generalization is presented as evidence of learned transferable structure, although models can still memorize training details.
- Minimal descriptions may be opaque, erase important exceptions, or capture correlations without causality, so reliable intelligence also requires validation, feedback, and causal reasoning.