arXiv:2512.23752cs.LGcs.AI2025-12被引 5

大模型保留贝叶斯推断的几何结构,可读取不确定性分布。

Geometric Scaling of Bayesian Inference in LLMs

  • 发现大模型最后一层值向量沿单一主轴分布,与预测熵强相关。
  • 在特定提示下,模型退化为低维流形,类似小模型的精确贝叶斯结构。
  • 扰动该几何轴会破坏局部不确定性,适合研究模型可信度机制。

近期研究表明,受控训练的小型Transformer可实现精确贝叶斯推断,其训练动态生成低维值流形和逐步正交的键,编码后验结构。本文探究该几何特征是否存在于生产级语言模型中。在Pythia、Phi-2、Llama-3和Mistral系列模型中,我们发现最后一层值表示沿单一主导轴组织,其位置与预测熵高度相关;域限制提示使该结构坍缩至合成设置中观察到的低维流形。通过针对Pythia-410M在上下文学习中对熵对齐轴进行定向干预,发现移除或扰动该轴会特异性破坏局部不确定性几何,而随机轴干预则无影响。然而,单层操作未导致贝叶斯行为成比例下降,表明该几何是不确定性的重要读出方式,而非单一计算瓶颈。结果表明,现代语言模型保留了风洞实验中支持贝叶斯推断的几何基底,并据此组织近似贝叶斯更新。

原文摘要 · Abstract (English)

Recent work has shown that small transformers trained in controlled "wind-tunnel'' settings can implement exact Bayesian inference, and that their training dynamics produce a geometric substrate -- low-dimensional value manifolds and progressively orthogonal keys -- that encodes posterior structure. We investigate whether this geometric signature persists in production-grade language models. Across Pythia, Phi-2, Llama-3, and Mistral families, we find that last-layer value representations organize along a single dominant axis whose position strongly correlates with predictive entropy, and that domain-restricted prompts collapse this structure into the same low-dimensional manifolds observed in synthetic settings. To probe the role of this geometry, we perform targeted interventions on the entropy-aligned axis of Pythia-410M during in-context learning. Removing or perturbing this axis selectively disrupts the local uncertainty geometry, whereas matched random-axis interventions leave it intact. However, these single-layer manipulations do not produce proportionally specific degradation in Bayesian-like behavior, indicating that the geometry is a privileged readout of uncertainty rather than a singular computational bottleneck. Taken together, our results show that modern language models preserve the geometric substrate that enables Bayesian inference in wind tunnels, and organize their approximate Bayesian updates along this substrate.

贝叶斯推理大模型几何结构不确定性建模

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