This paper aims to prove the emergence of symbolic concepts in well-trained
AI models. We prove that if (1) the high-order derivatives of the model output
w.r.t. the input variables are all zero, (2) the AI model can be used on
occluded samples and will yield higher confidence when the input sample is less
occluded, and (3) the confidence of the AI model does not significantly degrade
on occluded samples, then the AI model will encode sparse interactive concepts.
Each interactive concept represents an interaction between a specific set of
input variables, and has a certain numerical effect on the inference score of
the model. Specifically, it is proved that the inference score of the model can
always be represented as the sum of the interaction effects of all interactive
concepts. In fact, we hope to prove that conditions for the emergence of
symbolic concepts are quite common. It means that for most AI models, we can
usually use a small number of interactive concepts to mimic the model outputs
on any arbitrarily masked samples.

通过证明 AI 模型对不同交互概念的输入输出方式的映射，本研究试图证明，大多数 AI 模型可使用少数交互概念来在任意遮掩样本上模拟模型输出。

AI 模型中稀疏符号概念出现证明的进展

Where We Have Arrived in Proving the Emergence of Sparse Symbolic  Concepts in AI Models

Monocular 3D object detection is an essential component in autonomous driving
while challenging to solve, especially for those occluded samples which are
only partially visible. Most detectors consider each 3D object as an
independent training target, inevitably resulting in a lack of useful
information for occluded samples. To this end, we propose a novel method to
improve the monocular 3D object detection by considering the relationship of
paired samples. This allows us to encode spatial constraints for
partially-occluded objects from their adjacent neighbors. Specifically, the
proposed detector computes uncertainty-aware predictions for object locations
and 3D distances for the adjacent object pairs, which are subsequently jointly
optimized by nonlinear least squares. Finally, the one-stage uncertainty-aware
prediction structure and the post-optimization module are dedicatedly
integrated for ensuring the run-time efficiency. Experiments demonstrate that
our method yields the best performance on KITTI 3D detection benchmark, by
outperforming state-of-the-art competitors by wide margins, especially for the
hard samples.

本文提出了一种考虑成对样本关系来改进单目三维物体检测的方法，包括计算对象对之间的不确定性感知预测和利用非线性最小二乘方法对其进行优化，实验结果表明，该方法在 KITTI 三维检测基准测试中表现最佳。