**Deformable convolutions** add 2D offsets to the regular grid sampling locations in the standard [convolution](https://paperswithcode.com/method/convolution). It enables free form deformation of the sampling grid. The offsets are learned from the preceding feature maps, via additional convolutional layers. Thus, the deformation is conditioned on the input features in a local, dense, and adaptive manner.

**TD_INLINE_MATH_1** is a generalisation of **TD_INLINE_MATH_2** reinforcement learning algorithms, but it employs an [eligibility trace](https://paperswithcode.com/method/eligibility-trace) $\lambda$ and $\lambda$-weighted returns. The eligibility trace vector is initialized to zero at the beginning of the episode, and it is incremented on each time step by the value gradient, and then fades away by $\gamma\lambda$:

$$ \textbf{z}\_{-1} = \mathbf{0} $$
$$ \textbf{z}\_{t} = \gamma\lambda\textbf{z}\_{t-1} + \nabla\hat{v}\left(S\_{t}, \mathbf{w}\_{t}\right), 0 \leq t \leq T$$

The eligibility trace keeps track of which components of the weight vector contribute to recent state valuations. Here $\nabla\hat{v}\left(S\_{t}, \mathbf{w}\_{t}\right)$ is the feature vector.

The TD error for state-value prediction is:

$$ \delta\_{t} = R\_{t+1} + \gamma\hat{v}\left\(S\_{t+1}, \mathbf{w}\_{t}\right) - \hat{v}\left(S\_{t}, \mathbf{w}\_{t}\right) $$

In **TD_INLINE_MATH_1**, the weight vector is updated on each step proportional to the scalar TD error and the vector eligibility trace:

$$ \mathbf{w}\_{t+1} = \mathbf{w}\_{t} + \alpha\delta\mathbf{z}\_{t}  $$

Source: Sutton and Barto, Reinforcement Learning, 2nd Edition

TD Lambda

Deformable Convolution

Deformable Convolutional Networks

**GAGNN**, or **Group-aware Graph Neural Network**, is a hierarchical model for nationwide city air quality forecasting. The model constructs a city graph and a city group graph to model the spatial and latent dependencies between cities, respectively. GAGNN introduces differentiable grouping network to discover the latent dependencies among cities and generate city groups. Based on the generated city groups, a group correlation encoding module is introduced to learn the correlations between them, which can effectively capture the dependencies between city groups. After the graph construction, GAGNN implements message passing mechanism to model the dependencies between cities and city groups.

Source	Deformable Convolutional Networks
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com