**Deep Stereo Geometry Network** is a 3D object detection pipeline that relies on space transformation from 2D features to an effective 3D structure, called 3D geometric volume (3DGV). The whole neural network consists of four components. (a) A 2D image
feature extractor for capture of both pixel- and high-level feature. (b) Constructing the plane-sweep volume and 3D geometric volume. (c) Depth Estimation on the plane-sweep volume. (d) 3D object detection on 3D geometric volume.

A **Kernel Activation Function** is a non-parametric activation function defined as a one-dimensional kernel approximator:

$$ f(s) = \sum_{i=1}^D \alpha_i \kappa( s, d_i) $$

where:

1. The dictionary of the kernel elements $d_0, \ldots, d_D$ is fixed by sampling the $x$-axis with a uniform step around 0.
2. The user selects the kernel function (e.g., Gaussian, [ReLU](https://paperswithcode.com/method/relu), [Softplus](https://paperswithcode.com/method/softplus)) and the number of kernel elements $D$ as a hyper-parameter. A larger dictionary leads to more expressive activation functions and a larger number of trainable parameters.
3. The linear coefficients are adapted independently at every neuron via standard back-propagation.

In addition, the linear coefficients can be initialized using kernel ridge regression to behave similarly to a known function in the beginning of the optimization process.

Kafnets: kernel-based non-parametric activation functions for neural networks

DSGN

DSGN: Deep Stereo Geometry Network for 3D Object Detection

**Temporal Distribution Characterization**, or **TDC**, is a module used in the [AdaRNN](https://paperswithcode.com/method/adarnn) architecture to characterize the distributional information in a time series.

Based on the principle of maximum entropy, maximizing the utilization of shared knowledge underlying a times series under temporal covariate shift can be done by finding periods which are most dissimilar to each other, which is also considered as the worst case of temporal covariate shift since the cross-period distributions are the most diverse. TDC achieves this goal for splitting the time-series by solving an optimization problem whose objective can be formulated as:

$$
\max \_{0<K \leq K\_{0}} \max \_{n\_{1}, \cdots, n\_{K}} \frac{1}{K} \sum_{1 \leq i \neq j \leq K} d\left(\mathcal{D}\_{i}, \mathcal{D}\_{j}\right) 
$$

$$
\text { s.t. } \forall i, \Delta_{1}<\left|\mathcal{D}\_{i}\right|<\Delta_{2} ; \sum_{i}\left|\mathcal{D}\_{i}\right|=n
$$

where $d$ is a distance metric, $\Delta\_{1}$ and $\Delta\_{2}$ are predefined parameters to avoid trivial solutions (e.g., very small values or very large values may fail to capture the distribution information), and $K\_{0}$ is the hyperparameter to avoid over-splitting. The metric $d(\cdot, \cdot)$ above can be any distance function, e.g., Euclidean or Editing distance, or some distribution-based distance / divergence, like MMD [14] and KL-divergence.

The learning goal of the optimization problem (1) is to maximize the averaged period-wise distribution distances by searching $K$ and the corresponding periods so that the distributions of each period are as diverse as possible and the learned prediction model has better a more generalization ability.

Source	DSGN: Deep Stereo Geometry Network for 3D Object Detection
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com