**Temporal Pyramid Network**, or **TPN**, is a pyramid level module for action recognition at the feature-level, which can be flexibly integrated into 2D or 3D backbone networks in a plug-and-play manner. The source of features and the fusion of features form a feature hierarchy for the backbone so that it can capture action instances at various tempos. In the TPN, a Backbone Network is used to extract multiple level features, a Spatial Semantic Modulation spatially downsamples features to align semantics, a Temporal Rate Modulation temporally downsamples features to adjust relative tempo among levels, Information Flow aggregates features in various directions to enhance and enrich level-wise representations and Final Prediction rescales and concatenates all levels of pyramid along channel dimension.

**GradientDICE** is a density ratio learning method for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. It optimizes a different objective from [GenDICE](https://arxiv.org/abs/2002.09072) by using the Perron-Frobenius theorem and eliminating GenDICE’s use of divergence, such that nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation.

GradientDICE

GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values

Temporal Pyramid Network for Action Recognition

**Rectified Adam**, or **RAdam**, is a variant of the [Adam](https://paperswithcode.com/method/adam) stochastic optimizer that introduces a term to rectify the variance of the adaptive learning rate. It seeks to tackle the bad convergence problem suffered by Adam. The authors argue that the root cause of this behaviour is that the adaptive learning rate has undesirably large variance in the early stage of model training, due to the limited amount of training samples being used. Thus, to reduce such variance, it is better to use smaller learning rates in the first few epochs of training - which justifies the warmup heuristic. This heuristic motivates RAdam which rectifies the variance problem:

$$g\_{t} = \nabla\_{\theta}f\_{t}\left(\theta\_{t-1}\right) $$

$$v\_{t} = 1/\beta\_{2}v\_{t-1} + \left(1-\beta\_{2}\right)g^{2}\_{t} $$

$$m\_{t} = \beta\_{1}m\_{t-1} + \left(1-\beta\_{1}\right)g\_{t} $$

$$ \hat{m\_{t}} = m\_{t} / \left(1-\beta^{t}\_{1}\right) $$

$$ \rho\_{t} = \rho\_{\infty} - 2t\beta^{t}\_{2}/\left(1-\beta^{t}\_{2}\right) $$

$$\rho_{\infty} = \frac{2}{1-\beta_2} - 1$$ 

If the variance is tractable - $\rho\_{t} > 4$ then:

...the adaptive learning rate is computed as:

$$ l\_{t} = \sqrt{\left(1-\beta^{t}\_{2}\right)/v\_{t}}$$

...the variance rectification term is calculated as:

$$ r\_{t} = \sqrt{\frac{(\rho\_{t}-4)(\rho\_{t}-2)\rho\_{\infty}}{(\rho\_{\infty}-4)(\rho\_{\infty}-2)\rho\_{t}}}$$

...and we update parameters with adaptive momentum:

$$ \theta\_{t} = \theta\_{t-1} - \alpha\_{t}r\_{t}\hat{m}\_{t}l\_{t} $$

If the variance isn't tractable we update instead with:

$$ \theta\_{t} = \theta\_{t-1} - \alpha\_{t}\hat{m}\_{t} $$

Source	Temporal Pyramid Network for Action Recognition
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com