58 lines
1.8 KiB
Markdown
58 lines
1.8 KiB
Markdown
---
|
||
title: "Within-Concept / Between-Concept Axes (概念内/间轴)"
|
||
created: 2026-07-10
|
||
updated: 2026-07-10
|
||
type: concept
|
||
tags: ["representation-geometry", "kernel-methods", "cka", "conceptual-representation"]
|
||
sources: ["[[shared-concept-geometry-2026|Hu et al. (ICML 2026)]]"]
|
||
---
|
||
|
||
# Within-Concept / Between-Concept Axes (概念内/间轴)
|
||
|
||
Hu et al. (ICML 2026) 的概念表示的双轴表征框架。
|
||
|
||
## 双轴定义
|
||
|
||
### 概念内关系（Within-Concept）
|
||
|
||
同一概念跨上下文的点云形状：
|
||
|
||
```
|
||
K_w^{(m)}[i, j] = k(r^{(m)}(w, c_i), r^{(m)}(w, c_j)), c_i, c_j ∈ C
|
||
```
|
||
|
||
测量**上下文可变性**——概念在多大程度上随语境变化。
|
||
|
||
### 概念间关系（Between-Concept）
|
||
|
||
同一上下文内不同概念的相互位置：
|
||
|
||
```
|
||
K_τ^{(m)}[i, j] = k(r^{(m)}(w_i, τ), r^{(m)}(w_j, τ)), w_i, w_j ∈ W
|
||
```
|
||
|
||
测量**概念间关系结构**——概念在共享上下文中的相对几何。
|
||
|
||
## 互补性
|
||
|
||
| 轴 | 问题 | 不变的是 | 变化的是 |
|
||
|-----|------|---------|---------|
|
||
| Within-Concept | 一个概念有多灵活？ | 概念 w | 上下文 c |
|
||
| Between-Concept | 概念间关系多稳定？ | 上下文 τ | 概念 w |
|
||
|
||
## 跨模型对齐
|
||
|
||
两种关系都在模型间显著对齐（CKA + permutation calibration），且对齐程度与**模型能力**（MMLU 分数）正相关。Pythia 等较老模型的对齐较弱。
|
||
|
||
## 上下文特异性
|
||
|
||
- **自然上下文**：within-concept 对齐最强
|
||
- **模板上下文**：between-concept 对齐最强
|
||
- → 这表明跨模型对齐不是语料重叠的表面伪影——打乱上下文会破坏对齐
|
||
|
||
## 参考
|
||
|
||
- [[shared-concept-geometry-2026|Hu et al. (ICML 2026)]]
|
||
- [[concept-point-cloud-manifold|Point-Cloud Manifold]]
|
||
- [[contextual-transformation-field|Contextual Transformation Field]]
|