发表机构
Carnegie Mellon University; Sakana AI（卡内基梅隆大学; Sakana AI）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出神经场适应几何概念，通过元学习与切线核分析，证明神经场权重编码适应成本及历史信息，超越单纯重建能力。
AI 中文摘要
神经场通常根据其重建观测的效果来评估。我们表明，这忽略了拟合网络的两个有用属性：它适应新观测的容易程度，以及其权重从早期观测中保留了哪些信息。我们将这些属性作为适应几何来研究。对于图像，我们元学习类特定的初始化，将每个初始化适应到新图像，并测量网络为拟合它而必须改变的程度。一个简单的局部线性模型能紧密预测这种适应成本，而用另一个网络的切线核替换一个网络的切线核则会显著恶化预测。因此，适应取决于拟合网络的局部几何，而不仅仅是其当前的重建。对于物理场，我们反复将同一网络拟合到来自一个序列的观测。其权重随后保留关于该历史的信息。当两个波历史恰好结束于相同的观测时，最终权重以68.6%的准确率恢复波速度的符号，而仅当前观测不包含此类信息，给出50%的准确率。这两个现象在数量上相关联：切线核特征值既预测哪些变化容易学习，也预测它们被后续拟合覆盖的速度。总之，这些结果表明神经场包含超出其当前重建的有用信息：在于它们如何变化以及它们如何到达那里。
英文摘要
Neural fields are usually evaluated by how well they reconstruct an observation. We show that this misses two useful properties of a fitted network: how easily it can adapt to new observations, and what its weights retain from earlier ones. We study these properties as adaptation geometry. For images, we meta-learn class-specific initializations, adapt each one to a new image, and measure how much the network must change to fit it. A simple local linear model closely predicts this adaptation cost, while replacing one network's tangent kernel with another's substantially worsens the prediction. Adaptation thus depends on the local geometry of the fitted network, not only on its current reconstruction. For physical fields, we repeatedly fit the same network to observations from a sequence. Its weights then retain information about that history. When two wave histories end at exactly the same observation, the final weights recover the sign of the wave velocity with 68.6% accuracy, whereas the current observation alone contains no such information and gives 50%. These two phenomena are quantitatively linked: tangent-kernel eigenvalues predict both which changes are easy to learn and how quickly they are overwritten by later fitting. Together, these results show that neural fields contain useful information beyond what they currently reconstruct: in how they can change and in how they got there.
Comments24 pages, 2 figures. Extended version of work accepted at the NeurIPS 2026 Workshop on Symmetry and Geometry in Neural Representations (NeurReps)
