text:
Winemaking at Chamisal Vineyards
The winemaking team at Chamisal Vineyards, led by winemaker Brianne Engles, is dedicated to continuous improvement, experimentation, and isn't afraid to try innovative new techniques in the pursuit of making better wines.
In one of a series of "firsts", the team Chamisal Vineyards, was one of the first producers in California to make an unoaked style of Chardonnay that took more inspiration from the vineyards of Chablis than Napa, and set the tone for a new style that quickly took hold among wine drinkers seeking an alternative to the buttery and oaky style that had become popular.
We continue to innovate with the recent release of our Amphora Chardonnay, aged on its skins in traditional clay amphorae without added yeasts or SO2, and the inaugural vintage of our Estate Sparkling Wine in 2021.
Inspired by the fresh coastal crispness of the ocean air in which our vineyard thrives, our wines are marked by a hallmark style that balances the bright and fresh side of our cool-climate with the layers of complexity and a depth of intensity that comes from our long growing season and extended ripening period.
Our winemaking team is incredibly hands-on in the vineyard, guiding and coaxing each vineyard block to produce fruit that is the most expressive of place and time; allowing for a "less is more" approach in the cellar intended to amplify the voice of the vineyard. Our winemaking team takes a minimalist approach and strives to use as little intervention in the cellar as possible – each decision is weighed carefully and thoughtfully, and every decision about what to add to the wine is as painstakingly made as what not to add.
The art of winemaking is in the details; in the time spent walking each row of vines, in each handful of dirt run through fingers, and in every berry sampled for ripeness and flavor. Each vintage is a culmination of the vintages before it, a patient and persistent progression of tinkering, experiments, and adjustments in the cellar to nudge each wine closer to its fullest and highest expression.


text:
\section{Chirality Nets}
\label{sec:app}

In the following we first provide the  problem formulation for human pose regression, before defining   chirality nets,  equivariance and the chirality transform. Subsequently we discuss how to develop typical layers such as the fully connected layer, the convolution, \etc, which make up chirality nets.

The Pytorch implementation and unit-tests of the proposed layers are part of the supplementary material. We have also included a short Jupyter notebook demo to illustrate the key concepts.

\subsection{Problem Formulation}
Chirality nets can be applied to regression tasks on  coordinates of joints for human pose related task, \ie, the input corresponds to 2D or 3D coordinates of human joints. For readability, we introduce the input and output representations for a single frame. Note that for our experiments we generalize chirality nets  to multiple frames by introducing a time dimension.

We let ${\mathbf{x}} \in \mathbb{R}^{|J^{\tt in}|\cdot|D^{\tt in}|}$ denote the chirality net input, where $J^{\tt in}$ is the set of all joints and $D^{\tt in}$ is the dimension index set for an input coordinate. For example, $J^{\tt in} = \{\text{`right wrist'},  \text{`right shoulder'}, \ldots\}$ and $D^{\tt in} = \{0, 1\}$, for 2D  input joint coordinates.  Similarly, we let  ${\mathbf{y}} \in \mathbb{R}^{|J^{\tt out}|\cdot|D^{\tt out}|}$ refer to the chirality net output. Note that the dimension of the spatial coordinates at the input and output may be different, \eg, prediction from 2D to 3D. Also, the  number of joints may differ, \eg, when mapping between different key-point sets.

For human pose regression, the task is to learn the parameters $\theta$ of a model $F_\theta$ by minimizing a loss function, $\cL(\theta) = \sum_{({\mathbf{x}}, {\mathbf{y}}) \in \cD} \ell(F_\theta({\mathbf{x}}), {\mathbf{y}})$ over the training dataset $\cD$. Hereby, sample loss $\ell(F_\theta({\mathbf{x}}), {\mathbf{y}})$ compares prediction $F_\theta$ to ground-truth ${\mathbf{y}}$.

\subsection{Chirality Nets, Chirality Equivariance, and Chirality Transforms}\label{seq:eq_def}

Chirality nets exhibit chirality equivariance, \ie, their output is transformed in a ``predefined manner'' given that the chirality transform is applied at the input. Note that the input and output dimensions $D^{\tt in}$ and $D^{\tt out}$ may differ. To define this chirality equivariance, we hence  need to consider a pair of transformations, one for the input data, $\mathcal{T}^{\tt in}$, and one for the output data, $\mathcal{T}^{\tt out}$. The corresponding equivariance map is illustrated in \figref{fig:equi_prop} for the task of 2D to 3D pose estimation. Formally,  we say a function $F_\theta$ is chirality equivariant \wrt $(\mathcal{T^{\tt in}, T^{\tt out}})$ if
$$\mathcal{T}^{\tt out}(F_\theta({\mathbf{x}})) = F_\theta(\mathcal{T}^{\tt in}({\mathbf{x}})) \;\; \forall {\mathbf{x}} \in \mathbb{R}^{|J^{\tt in}||D^{\tt in}|}.$$
To define the chirality transform on the input data, \ie, $\mathcal{T}^{\tt in}$, we split the set of joints $J^{\tt in}$ into \emph{ordered tuples} of ${J}^{\tt in}_{\tt l}$, ${J}^{\tt in}_{\tt r}$, and ${J}^{\tt in}_{\tt c}$, each denoting left, right and center joints of the input.
Importantly, these tuples are sorted such that the corresponding left/right joints are at corresponding positions in the tuple.  We also split the dimension index set $D^{\tt in}$  into $D^{\tt in}_{\tt n}$ and $D^{\tt in}_{\tt p}:=  D^{\tt in}  \backslash D^{\tt in}_{\tt n}$,  indicating the coordinates to, or not to, negate.

For readability and without loss of generality, assume the dimensions of the input ${\mathbf{x}}$
follow the order of ${J}^{\tt in}_{\tt l}$, ${J}^{\tt in}_{\tt r}$, ${J}^{\tt in}_{\tt c}$, \ie,  ${\mathbf{x}} = [{\mathbf{x}}_{\tt l}, {\mathbf{x}}_{\tt r}, {\mathbf{x}}_{\tt c}]$. Within each vector ${\mathbf{x}}_{(\cdot)}$, we place the coordinates in the set $D^{\tt in}_{\tt n}$  before the remaining ones, \ie, ${\mathbf{x}}_{\tt l} = [{\mathbf{x}}_{\tt ln}, {\mathbf{x}}_{\tt lp}]$.

Given this construction of the input ${\mathbf{x}}$, the reflection illustrated in step (1) of \figref{fig:sym_prop} is a matrix multiplication with a $(|{J}^{\tt in}||D^{\tt in}|) \times (|{J}^{\tt in}||D^{\tt in}|)$ diagonal matrix $T^{\tt in}_{\tt neg}$, defined as follows:
$$T_{\tt neg}^{\tt in} = {\tt diag (
[
{\bf -1}_{|{J}^{\tt in}_{\tt l}|\cdot |D^{\tt in}_{\tt n}|},  {\bf 1}_{|{J}^{\tt in}_{\tt l}|\cdot |D^{\tt in}_{\tt p}|},
{\bf -1}_{|{J}^{\tt in}_{\tt r}|\cdot |D^{\tt in}_{\tt n}|},  {\bf 1}_{|{J}^{\tt in}_{\tt r}|\cdot |D^{\tt in}_{\tt p}|},
{\bf -1}_{|{J}^{\tt in}_{\tt c}|\cdot |D^{\tt in}_{\tt n}|},  {\bf 1}_{|{J}^{\tt in}_{\tt c}|\cdot |D^{\tt in}_{\tt p}|}
])},$$
where ${\bf 1}_{K}$ indicates a vector of ones of length $K$.

The switch operation illustrated in step (2) of \figref{fig:sym_prop} is a matrix multiplication with a permutation matrix of dimension $(|{J}^{\tt in}||D^{\tt in}|) \times (|{J}^{\tt in}||D^{\tt in}|)$, defined as follows:
$$T^{\tt in}_{\tt swi}  = \begin{bmatrix}
\bf 0 & \mathbf{I}_{|{J}^{\tt in}_{\tt l}|\cdot |D^{\tt in}|} & \bf 0 \\
\mathbf{I}_{|{J}^{\tt in}_{\tt l}|\cdot |D^{\tt in}|}  & \bf 0 & \bf 0\\
\bf 0 & \bf 0 & \mathbf{I}_{|{J}^{\tt in}_{\tt c}|\cdot |D^{\tt in}|}
\end{bmatrix},$$
where ${\bf I}_{K}$ denotes an identity matrix of size $K \times K$.

Given those matrices, the chirality transform of the input $\mathcal{T^{\tt in}}({\mathbf{x}})$ is obtained via $\mathcal{T^{\tt in}}({\mathbf{x}}) = T^{\tt in}_{\tt neg} T^{\tt in}_{\tt swi} {\mathbf{x}}$. The chirality transform of the output, $\mathcal{T^{\tt out}}$, is defined similarly, replacing ``${\tt in}$'' with ``${\tt out}$''.

In the following, we  introduce layers that satisfy the $(\mathcal{T^{\tt in}, T^{\tt out}})$ chirality equivariance property. This enables to construct a chirality net $F_\theta$, as the composition of equivariant layers remains equivariant.  Note that $(\mathcal{T^{\tt in}, T^{\tt out}})$ chirality equivariance can be specified separately for every deep net layer which provides additional flexibility.
In the following we discuss how to construct  layers which satisfy chirality equivariance.

\subsection{Chirality Layers}

\textbf{Fully connected layer.}
A fully connected layer performs the mapping ${\mathbf{y}} = f_{\text{FC}}({\mathbf{x}} ; W, b) := W{\mathbf{x}} + b$.
We achieve equivariance through parameter sharing and odd symmetry:

$
W \!=\! \begin{bmatrix}
{\color{lb}
\begin{bmatrix}
W_{\tt ln, ln} & W_{\tt ln, lp} \\
W_{\tt lp, ln} & W_{\tt lp, lp}\\
\end{bmatrix}
}
&
{\color{lr}
\begin{bmatrix}
W_{\tt ln, rn} & W_{\tt ln, rp} \\
W_{\tt lp,rn} & W_{\tt lp, rp}\\
\end{bmatrix}
}
&
{\color{dy}
\begin{bmatrix}
W_{\tt ln, cn} & W_{\tt ln, cp} \\
W_{\tt lp, cn} & W_{\tt lp, cp}\\
\end{bmatrix}
}\\
{\color{lr}
\begin{bmatrix}
W_{\tt ln, rn} & -W_{\tt ln, rp} \\
-W_{\tt lp,rn} & W_{\tt lp, rp}\\
\end{bmatrix}
}
&
{\color{lb}
\begin{bmatrix}
W_{\tt ln, ln} & -W_{\tt ln, lp} \\
-W_{\tt lp, ln} & W_{\tt lp, lp}\\
\end{bmatrix}
}
&
{\color{dy}
\begin{bmatrix}
W_{\tt ln, cn} & -W_{\tt ln, cp} \\
-W_{\tt lp, cn} & W_{\tt lp, cp}\\
\end{bmatrix}
}\\
{\color{black}
\begin{bmatrix}
W_{\tt cn, ln} & W_{\tt cn, lp} \\
\bf 0 & W_{\tt cp, lp}\\
\end{bmatrix}
}
&
{\color{black}
\begin{bmatrix}
W_{\tt cn, ln} & -W_{\tt cn, lp} \\
\bf 0 & W_{\tt cp, lp}\\
\end{bmatrix}
}
&
{\color{dg}
\begin{bmatrix}
W_{\tt cn, cn} & \bf 0\\
\bf 0 & W_{\tt cp, cp}\\
\end{bmatrix}
}\\
\end{bmatrix}
$,
$b = \begin{bmatrix}
\begin{bmatrix}
\color{lr}
b_{\tt ln} \\
\color{lr}
b_{\tt lp}
\end{bmatrix} \\
\begin{bmatrix}
\color{lr}
-b_{\tt ln} \\
\color{lr}
b_{\tt lp}
\end{bmatrix} \\
\begin{bmatrix} \bf 0 \\
b_{\tt cp}\end{bmatrix}\\
\end{bmatrix}\!.
$

We  color code the shared parameters using identical colors. Each $W_{(\cdot), (\cdot)}$ denotes a matrix, where the first and the second subscript characterize the dimensions of the output and the input. For example, $W_{{\tt ln},{\tt rp}}$ computes the output's left ($\tt l$) joint's negated ($\tt n$) dimensions, from the input's right ($\tt r$) joint's non-negated, \ie, positive ($\tt p$), dimensions. Note that $W_{{\tt ln},{\tt rp}}$ is a matrix of dimension $|J^{\tt out}_{\tt l}| \cdot |D_{\tt n}^{\tt out}| \times |J^{\tt in}_{\tt r}| \cdot |D_{\tt p}^{\tt in}|$. We refer to this layer as the chiral fully connected layer.

\textbf{1D convolution layers~\cite{waibel1995phoneme, lecun1999object}.}
Pose symmetric 1D convolution layers can be based on fully connected layers. A 1D convolution is a fully connected layer with shared parameters across the time dimension, \ie, at each time step the computation is the sum of fully connected layers over a window:
$${\mathbf{y}}_t = \sum\limits_{\tau} W_{\tau}{\mathbf{x}}_{t-\tau} + b = \sum\limits_{\tau}  f_{\text{FC}}({\mathbf{x}}_{t-\tau}; W_{\tau}, b).$$
Consequently, we  enforce equivariance at each time step by employing the  symmetry pattern of fully connected layers at each time slice.

\textbf{Element-wise nonlinearities.} Nonlinearities are applied element-wise and do not contain parameters.  These operations maintain the input dimension, therefore, $\mathcal{T^{\tt out}}$ and $\mathcal{T^{\tt in}}$ are identical. A nonlinearity $f$ that is an odd function, \ie, $ f(-x) = -f(x)$,
such as tanh,  hardtanh, or soft-sign satisfies the equivariance property. See the following proof:
\bea\nonumber
\mathcal{T^{\tt out}}( f({\mathbf{x}})) =& T^{\tt out}_{\tt neg}T^{\tt out}_{\tt swi} (f({\mathbf{x}})) \overset{\text{elementwise } f}{=}  T^{\tt out}_{\tt neg}f(T^{\tt out}_{\tt swi}{\mathbf{x}})) \\
\overset{\text{odd func. } f}{=}& f(T^{\tt out}_{\tt neg}T^{\tt out}_{\tt swi}  {\mathbf{x}})
= f(\mathcal{T}^{\tt in}({\mathbf{x}})) \;\; \forall {\mathbf{x}} \in \mathbb{R}^{|J^{\tt in}||D^{\tt in}|}. \nonumber
\eea
\textbf{LSTM and GRU layers~\cite{hochreiter1997long, cho2014learning}.}

LSTM and GRU modules which satisfy chirality can be obtained from fully connected layers.

However, na\"ively setting all matrix multiplies within an LSTM to satisfy the equivariance property will not lead to an equivariant LSTM because gates are elementwise \textit{multiplied} with the cell state. If both  gate and cell  preserve the negation then the product will not. Therefore, we  change the weight sharing scheme for the gates. We set $D_{n}^{\tt out}$ for the gates to be the empty set, \ie,  the gates will be invariant to negation at the input, $T^{\tt in}_{\tt neg}$, but still equivariant to the switch operation, $T^{\tt in}_{\tt swi}$. With this setup, the product of the gates and the cell's output will preserve the sign, as the gates are invariant to negation and passed through a Sigmoid to be within the range of $(0,1)$.  GRU modules are modified  in the same manner.

\textbf{Batch-normalization~\cite{ioffe2015batch}.}
A batch normalization layer performs an element-wise standardization, followed by an element-wise affine layer (with learnable parameters $\gamma$ and $\beta$).
For $\gamma$ and $\beta$, we follow the
the principle applied to fully connected layers.

Equivariance for $\mu$, and $\sigma$ is obtained by
computing the mean and standard deviation on the ``augmented batch'' and by keeping track of its running average.

\textbf{Dropout~\cite{srivastava2014dropout}.}
At test time, dropout scales the input by $p$, where $p$ is the dropout probability. The equivariance property is satisfied because of  the associativity property of a scalar multiplication.

\subsection{Reduction in model parameters, FLOPS, and training/test details}
\textbf{Model parameters.} Our model shares parameters between dimensions representing the left and right joints. For each layer, the number of parameters are reduced by a factor of
$\frac{|(|J_{l}^{\tt in}| + |J_{\tt c}^{\tt in}|) \cdot (|J_{\tt l}^{\tt out}| + |J_{\tt c}^{\tt out}|)}{|J^{\tt in}|\cdot |J^{\tt out}|}$. Recall $|J^{\tt in}| = |J_{\tt l}^{\tt in}| + |J_{\tt r}^{\tt in}| + |J_{\tt c}^{\tt in}|$. The output dimension size is computed similarly.

\textbf{FLOPS.} Chirality nets  also have lower FLOPS.  Due to the symmetry, instead of multiplying and adding each of the elements independently, we  add the symmetric values first before applying a single multiplication per symmetric pair.
{
Concretely, consider $\mathbf{w} = [w_1, w_1]$, $\mathbf{x} = [x_1, x_2]$, and their inner product $\mathbf{w}^{T}\mathbf{x}$. Instead of  computing $w_1\cdot x_1 + w_1\cdot x_2$, we exploit symmetry and use instead  $w_1 \cdot (x_1 + x_2)$, which removes one multiplication operation.
}
This is a common speed up trick used in symmetric FIR filters~\cite{note1998implementing, yeh2016stable}. The number of multiplications reduces by a factor of $\frac{|J_{l}^{\tt in}| + |J_{c}^{\tt in}|}{|J^{\tt in}|}$. Additionally, baseline models utilize test-time augmentation, which requires two forward passes through the network for each input, whereas the proposed nets only use a single forward pass.

\textbf{Training and test details.}
During training it is important to apply the chirality transform for data-augmentation, \ie, with 50\% probability we apply $\mathcal{T}^{\tt in}$ and $\mathcal{T}^{\tt out}$ to  input and label. This  ensures that the mini-batch statistics match our assumption on the chirality, \ie, poses that form a chiral pair are both valid, which is important for the batch-normalization layer.
Moreover, during training we use a standard dropout layer. While we could impose  dropped units to be chiral equivariant, we found this lead to over-fitting in practice. This is expected as imposing chirality on the added noise reduces the randomness.
Importantly, during test no data-augmentation is performed and a single forward pass is sufficient to obtain an `averaged' result.

\section{Conclusion}
\label{sec:conc}
We introduce  chirality equivariance for pose regression tasks and develop deep net layers that satisfy this property. Through parameter sharing and odd/even symmetry, we design equivariant versions of  commonly used layers in deep nets, including fully connected, 1D convolution, LSTM/GRU cells, and batch normalization layers. With these equivariant layers at hand, we build Chirality Nets, which guarantee  equivariance from the input to the output. Our models naturally lead to a reduction in trainable parameters and computation due to symmetry. Our experimental results on three human pose regression tasks over four datasets demonstrate state-of-the-art performance and the wide practical impact of the proposed layers.
\section{Experiments}
\label{sec:exp}
{
We evaluate our approach on a variety of tasks, including 2D to 3D pose estimation, 2D pose forecasting, and skeleton based action recognition. For each task, we describe the dataset, metric, and implementation before discussing the results.
}

\input{results/2d_3d_results}
\input{results/human_eva_and_limited_results.tex}
\subsection{2D to 3D pose estimation}
\textbf{Task.} 3D human pose estimation can be decoupled into the tasks of 2D keypoint detection and 2D to 3D pose estimation. We focus on the latter task, \ie, given a sequence of 2D keypoints, the task is to estimate the corresponding 3D human pose. See \figref{fig:task_ill} (a) for an illustration.

\textbf{Dataset and metric.}
We evaluate on two standard datasets, the Human3.6M~\cite{h36m_pami} and the HumanEva-I~\cite{sigal2010humaneva}.
Human3.6M is a large scale dataset of human motion with 3.6 million video frames. The dataset consists of 11 subjects performing 15 different actions. Following prior work~\cite{pavlakos17volumetric, tekin2017learning, martinez2017simple, sun2017compositional, luvizon20182d, pavllo20193d}, each human pose is represented by a 17-joint skeleton. We use the same train and test subject splits. HumanEva-I is a smaller  dataset consisting of four subjects and six actions. To be consistent with prior work~\cite{pavlakos2018ordinal, lee2018propagating, pavllo20193d}, we use the same train and test splits evaluated over the actions of (walk, jog, and box). For both of these datasets, we consider the setting where we train one model for all actions.

We report the two standard metrics used in prior work: Protocol 1 (MPJPE) which is the mean per-joint position error between the prediction and ground-truth~\cite{martinez2017simple, pavlakos17volumetric, pavllo20193d}  and Protocol 2 (P-MPJPE) which is the error, after alignment, between the prediction and ground-truth~\cite{martinez2017simple, sun2017compositional, hossain2018exploiting, pavllo20193d}.

\textbf{Implementation details.} Our model follows the supervised training procedure and network design of~\citet{pavllo20193d}. Our network is the identical temporal convolutional network architecture, where each layer is replaced with its
chiral version, \ie, 1D dilated convolution, batch-normalization, and dropout layers. We also replace ReLU non-linearities with Tanh to achieve equivariance. No additional architecture changes were made. For Human3.6M, we use 2D keypoints extracted from CPN~\cite{chen2018cascaded} with Mask R-CNN~\cite{he2017mask} bounding boxes released by~\citet{pavllo20193d}. For HumanEva-I, we use the 2D keypoint detections from Mask R-CNN released by~\citet{pavllo20193d}.

\textbf{Results.}
In \tabref{tab:human36_results}, we report the performance on the Human3.6M data using Protocol 1 (MPJPE). Our approach outperforms the state-of-the-art~\cite{pavllo20193d} which uses test-time augmentation by 0.1 mm in overall average and achieves the best results in eight out of fifteen sub-categories. For the single-frame models, we observe a more significant reduction in error of 0.4 mm over~\cite{pavllo20193d} with test time augmentation.
Additionally, when comparing without  test-time augmentation, our approach outperforms by 1 mm.
We note that,  test-time augmentation employed by \citet{pavllo20193d} involves running the network twice for each input. In contrast, our approach only requires a single forward pass.

Next, on HumanEva-I dataset, we also observed an increase in performance using Protocol 1.  On average, our approach achieves a 32.2mm error. This is a 0.8mm decrease over the current state-of-the-art of 33.0mm~\cite{pavllo20193d} and a 1.1mm decrease over~\cite{pavllo20193d} without test-time augmentation of 33.3mm.

We also performed evaluation using Protocol 2 (P-MPJPE). On Human3.6M we observe that our approach performs worse than~\citet{pavllo20193d} by 0.3mm. We note that the loss function is chosen to optimize Protocol 1, therefore our models are performing better at what they are optimized for.
In \tabref{tab:human_eva_results}, we
report the performance on HumanEva-I using Protocol 2 (P-MPJPE). Our model achieves a 0.2 mm reduction in error over~\citet{pavllo20193d} on average. Most of the gain is obtained for the boxing action, possibly due to the symmetric nature of the movement.

\textbf{Limited data settings.} A benefit of fewer model parameters is the potential to obtain better models with less  data. To confirm this, we perform experiments by varying the amount of training data, starting from  0.1\% of subject 1 (S1) to using three subjects S1, S5, S6. The results with comparison to~\cite{pavllo20193d} are shown in \figref{fig:limited_data_results}. We observe that our approach consistently out-performs~\cite{pavllo20193d} in this low resource settings, except at S1 0.1\%.
For the reported numbers, we use a batch-size of 64, and all other hyper-parameters are identical between the models.
If we further decrease the batch-size to 32 for S1 0.1\%, our approach improves to 100.4mm where \cite{pavllo20193d} improves to 102.3mm.

\input{results/pose_forecast_results.tex}
\subsection{2D pose forecasting}
\textbf{Task.} 2D pose forecasting is the pose regression task of predicting the future human pose, represented in 2D keypoints, given present and past human pose. See \figref{fig:task_ill} (b) for an illustration.

\textbf{Dataset and metric.}
We evaluate on the Penn Action dataset~\cite{zhang2013actemes}. The dataset consists of  2236 videos with 15 actions. Each frame is annotated with 2D keypoints of 13 human joints. We use the same train and test split as in~\cite{chao2017forecasting, chiu2019action}. Following~\citet{chiu2019action} we consider initial velocity as being part of the input and a single model is used for all actions.
For a fair comparison with prior work, we report  the `Percentage of Correct Keypoint' metric with a 0.05 threshold (PCK@0.05), which assesses the accuracy of the predicted keypoints. A predicted keypoint is considered correct if it is within a 0.05 radius of the ground-truth when considering normalized distance.

\textbf{Implementation details.} Our non-chiral equivariant baseline model is a sequence-to-sequence model based on~\cite{martinez2017human}. We made several modifications to match the hyperparameters in~\cite{chiu2019action}, \ie, we used StackedRNN~\cite{pascanu2014howto} with 2 layers and added dropout layers. Additionally, we utilize teacher forcing~\cite{williams1989learning} during training, while prior work did not. We find this to stabilize training and enable the use of the Adam~\cite{kingma2015adam, ams_grad} optimizer without diverging. We performed data augmentation via the chirality transform, \ie, with 0.5 probability we apply $\mathcal{T}^{\tt in}$ and $\mathcal{T}^{\tt out}$ to the input and the ground-truth correspondingly.
For our pose symmetric model, we replaced all the non-symmetric layers, \eg, fully connected layers and LSTM cells with their corresponding
chiral version.

\textbf{Results.}
In \tabref{tab:penn_action_result}, we report the performance of our models and the state-of-the-art. The baseline model without augmentation outperforms the state-of-the-art~\cite{chiu2019action}. The gain comes from the use of Stacked-LSTM and teacher forcing during training. With  additional  train and test time data-augmentation, our baseline model further improves. In addition our pose symmetric model outperforms the baseline, in terms of average PCK@0.05. We observe more significant improvements for the first ten prediction steps.

\input{results/action_results.tex}
\subsection{Skeleton based action recognition}
\textbf{Task.} Skeleton based action recognition aims at predicting human action based on skeleton sequences. See \figref{fig:task_ill} (c) for an illustration.

\textbf{Dataset and metric.} We use the Kinetics-400 dataset~\cite{kay2017kinetics} in our experiments. The dataset contains 400 action classes and 306,245 clips in total. Following the experimental setup by~\cite{yan2018stgcn}, we use OpenPose~\cite{cao2018openpose} to locate the 18 human body joints. Each joint is represented as $(x,y,c)$, where $x$ and $y$ are the 2D coordinates of the joint and $c$ is the confidence score of the joint given by OpenPose. Following~\cite{kay2017kinetics}, we report the classification accuracy at top-1 and top-5.

\textbf{Implementation details.} Our baseline model, `Ours-Conv,' follows `Temporal-Conv'~\cite{kim2017interpretable}, modified  to have not only temporal convolution but also spatial convolution. The temporal convolution considers the intra-frame information while the spatial convolution considers the inter-frame information. For the recognition task, we need chiral invariance,~\ie, a chiral pair should be classified as the same action class. To this end, we use a chiral invariance layer where we let both $J^{\tt out}_{\tt r}$, $J^{\tt out}_{\tt l}$ as well as $D^{\tt out}_{\tt n}$  be empty sets, which means there are no left and right joints but only center joints and there is no dimension that will be negated in the output of the layer after applying chirality transform. Note that the chirality transform exchanges the left and right joints and negates the dimensions in the dimension index set $D^{\tt out}_{\tt n}$. Given $J^{\tt out}_{\tt r}$, $J^{\tt out}_{\tt l}$ and $D^{\tt out}_{\tt n}$ are all empty, it's trivial that the output will be chiral invariant. For the chiral invariance model, `Ours-Conv-Chiral,' we replace  all the non-symmetric layers before the chiral invariance layer with their corresponding chiral equivariance version. All the layers after the chiral invariance layer remain identical to the `Ours-Conv' model. There are in total 10 layers of spatial and temporal convolution and we put the chiral invariance layer at the fourth layer. We use the SGD optimizer with a momentum of $0.9$ as in~\cite{yan2018stgcn}.

\textbf{Results.} In \tabref{tab:action_results}, we report the action recognition performance of our model and the skeleton-based approaches. We observe that the baseline model `Ours-Conv'  performs on par with ST-GCN~\cite{yan2018stgcn} and the chiral invariant model, `Ours-Conv-Chiral' outperforms both ST-GCN and Ours-Conv on Top-1 and Top-5 accuracy, achieving the state-of-the-art performance on the Kinetics-400 dataset among skeleton based action recognition methods.

\section{Introduction}
\label{sec:intro}
Human pose regression tasks such as human pose estimation, human pose forecasting and skeleton based action recognition, have numerous applications in video understanding, security and human-computer interaction. For instance, collaborative virtual reality applications rely on accurate pose estimation for which significant advances have been reported in recent years.

Specifically, recent state-of-the-art approaches use supervised learning to address pose regression and employ deep nets. Input and output  of those nets depend on the task: inputs are typically 2D or 3D human pose key-points stacked into a vector; the output may represent human pose key-points for pose estimation or a classification probability for activity recognition. To improve accuracy of those tasks, a variety of deep net architectures have been proposed~\cite{martinez2017human, chao2017forecasting, hossain2018exploiting, lee2018propagating, pavllo20193d, si2018skeleton}, generally relying on common deep net building blocks, such as, fully connected, convolutional or recurrent layers. Unlike for image datasets, to enlarge the size of human pose datasets, a  reflection (left-right flipping) of the pose coordinates as illustrated in step (1) of \figref{fig:sym_prop} is not sufficient. The chirality of the human pose requires to additionally switch the labeling of left and right as illustrated in step (2) of \figref{fig:sym_prop}.

However, while this two-step data augmentation is conceptually easy to employ during training, we argue that even better accuracy is possible for human pose regression tasks if this pose symmetry is directly built into the deep net. In particular, if confronted with either of the poses illustrated on the left or right hand side of \figref{fig:sym_prop} the  output of a  deep net should be equivariant to the transformation, \ie, the output is also transformed in a ``predefined way.''  For example, if the network's output is also a human pose, the output pose should follow the same transformation. On the other hand, for an activity recognition task, the output probability should remain unchanged. The equivariant map, for pose estimation, is illustrated in \figref{fig:equi_prop} and we make the equivariance property more precise  later.

To encode this form of equivariance for human pose regression tasks, we propose ``chirality nets.'' Specifically, the output of a chirality net is guaranteed to be equivariant \wrt a transformation composed of reflections and label switching. To build chirality nets, we develop
chirality equivariant versions of  commonly used layers. Specifically, we design and prove equivariance for versions of fully connected, convolutional, batch-normalization, dropout, and LSTM/GRU layers and element-wise non-linearities such as tanh or soft-sign.
 The main common design principle for chirality equivariant layers is  odd and even symmetric sharing of model parameters. Hence, in addition to being equivariant, transforming a typical deep net into its chiral counterpart results in a reduction of the number of trainable parameters, and lower computation complexity due to the symmetry in the model weights.  We find a smaller number of trainable parameters reduces the sample complexity, \ie, the models need less training data.

We demonstrate the generalization and effectiveness of our approach on three pose regression tasks over four datasets: 3D pose estimation on the Human3.6m~\cite{h36m_pami} and HumanEva dataset~\cite{sigal2010humaneva}, 2D pose estimation on the Penn Action dataset~\cite{zhang2013actemes} and skeleton-based action recognition on Kinetics-400 dataset~\cite{kay2017kinetics}. Our approach achieves state-of-the-art results with guarantees on equivariance, lower number of parameters, and robustness in low-resource settings.

\section{Related Work}
\label{sec:rel}
First we briefly review invariance and equivariance in machine learning and computer vision as well as human pose regression tasks.

\textbf{Invariant and equivariant representation.}
Hand-crafted invariant and equivariant representations have been utilized widely in computer vision systems for decades, \eg, scale invariance of SIFT~\cite{lowe1999object}, orientation invariance of HOG~\cite{dalal2005histograms}, affine invariance of the Harris detector~\cite{mikolajczyk2004scale}, shift-invariant systems in image processing~\cite{vetterli2014foundations}, \etc.

These properties have also been adapted  to learned representations. A widely known property is the translation equivariance of convolutional neural nets (CNN)~\cite{lecun1999object}: through spatial or temporal parameter sharing, a shifted input leads to a shifted output. Group-equivariant CNNs extend the equivariance to rotation, mirror reflection and translation~\cite{cohen2016group} by replacing the shift operation with a more general set of transformations. Other representations for building equivariance into deep nets have also been proposed, \eg, the Symmetric Network~\cite{gens2014deep}, the Harmonic Network~\cite{worrall2017harmonic} and the Spherical CNN~\cite{cohen2018spherical}.

The aforementioned works focus on deep nets where the input are images. While related, they are not directly applicable to human pose. For example, a reflection with respect to the y-axis in the image domain corresponds to a permutation of the pixel locations, \ie, swapping the pixel intensity between each pixel's reflected counterpart. In contrast, for human pose, where the input is a vector representing the   human joints' spatial coordinates, a reflection corresponds to the \textit{negation of the value} for each of the joints  reflected dimension.

The input representation of deep nets for human pose is more similar to pointsets. Prior work has explored building  permutation equivariant deep nets, \ie,  any permutation of input elements  results in the same permutation of output elements.

In~\cite{zaheer2017deep, qi2017pointnet}. Both works utilize parameter sharing to achieve permutation equivariance. Following these works, graph nets generalize the family of permutation equivariant networks and demonstrate success on numerous applications~\cite{scarselli2009graph, kipf2017semi, hamilton2017representation, gilmer2017neural, battaglia2018relational, kipf2018neural, Yeh_2019_CVPR, Liu_2019_CORL}.

For human pose,  equivariance to \emph{all permutations} is too strong of a property. Recall, our aim is to build models equivariant to the chiral symmetry, which only involves \textit{a specific permutation}, \eg, the switch between left and right joints, shown in step (2) of \figref{fig:sym_prop}.

Most relevant to our approach is work by~\citet{ravanbakhsh2017equivariance}. \citet{ravanbakhsh2017equivariance}  explore which type of equivariance can be achieved through parameter sharing. Their approach captures one specific permutation in the pose symmetric transform, but does not capture the negation from the reflection, shown in \figref{fig:sym_prop} step (1). In contrast, our approach considers both operations (1) and (2) jointly, which leads to a different formulation. Lastly, to the best of our knowledge,~\cite{ravanbakhsh2017equivariance} only discusses theoretically  the construction of equivariant networks. In this work, we design and implement a variety of building blocks for deep nets and demonstrate the benefits on a wide range of practical applications in human pose regression tasks.

\textbf{Human pose applications.} For 3D pose estimation from images, recent approaches utilize a two-step approach: (1) 2D pose keypoints are predicted given a video; (2) 3D keypoints are estimated given 2D joint locations. The 2D to 3D estimation is formulated as a regression task via deep nets~\cite{pavlakos17volumetric, tekin2017learning, martinez2017simple, sun2017compositional, fang2018learning, pavlakos2018ordinal, yang20183d, luvizon20182d, hossain2018exploiting, lee2018propagating, pavllo20193d}. Capturing the temporal information is crucial and has been explored in 3D pose estimation~\cite{hossain2018exploiting,lee2018propagating} as well as in action recognition~\cite{tran2018closer,Hussein_2019_CVPR}, video segmentation\cite{hu_nips_2017,hu_eccv_2018a} and learning object dynamics~\cite{martinez2017human,minderer2019unsupervised}. Most recently, \citet{pavllo20193d} propose to use temporal convolutions to better capture the temporal information for 3D pose estimation over previous RNN based methods. They also performed train and test time augmentation based on the chiral-symmetric transformation. For test time augmentation, they compute the output for both the original input and the transformed input, using the average outputs as the final prediction.  In contrast to our work, we note that \citet{pavllo20193d} need to transform the output of the transformed input  back to the original pose. To carefully assess the benefits of chirality nets, in this work, we closely follow the experiment setup of \citet{pavllo20193d}.

For 2D keypoint forecasting, we follow the setup of standard temporal modeling: conditioning on past observations to predict the future. To improve temporal modeling, recent works, have utilized different sequence to sequence models  for this task~\cite{martinez2017human, chao2017forecasting, chiu2019action}. In this work, we closely follow the experiment setup of \citet{chiu2019action}.

For action recognition, skeleton based methods have been explored extensively recently~\cite{yan2018stgcn,zhang2018adding,li2018co,si2018skeleton} due to robustness to illumination changes and cluttered background. Here we closely follow the experimental setup of~\citet{yan2018stgcn}.

\section{Code and Test Cases}
In the supplemental materials, we have included Pytorch implementation of the proposed layers. Each layer also comes with unit-tests validating the chirality-equivaraince. Please read the \texttt{README.md} for directory structures, usage and required dependencies. There is also a Jupyter notebook and it's HTML output visualizing the concepts introduced in the paper.

\section{Additional Description for Equivariant Layers}\label{extra_layers}

\subsection{Equivariant fully connected layers}
\input{supp_linear_proof}

\subsection{Equivariant 1D convolution layers}
{
\textbf{1D convolution layers~\cite{waibel1995phoneme, lecun1999object}.}
}
Pose symmetric 1D convolution layers can be based on fully connected layers. A 1D convolution is a fully connected layer with shared parameters across the time dimension, \ie, at each time step the computation is the sum of fully connected layers over a window:
$${\mathbf{y}}_t = \sum\limits_{\tau} W_{\tau}{\mathbf{x}}_{t-\tau} + b = \sum\limits_{\tau}  f_{\text{FC}}({\mathbf{x}}_{t-\tau}; W_{\tau}, b).$$
Consequently, we  enforce equivariance at each time step by employing the  symmetry pattern of fully connected layers at each time slice.
$$
W_{\tau} = \begin{bmatrix}
{\color{lb}
\begin{bmatrix}
W_{\tt ln, ln, \tau} & W_{\tt ln, lp, \tau} \\
W_{\tt lp, ln, \tau} & W_{\tt lp, lp, \tau}\\
\end{bmatrix}
}
&
{\color{lr}
\begin{bmatrix}
W_{\tt ln, rn, \tau} & W_{\tt ln, rp, \tau} \\
W_{\tt lp,rn, \tau} & W_{\tt lp, rp, \tau}\\
\end{bmatrix}
}
&
{\color{dy}
\begin{bmatrix}
W_{\tt ln, cn, \tau} & W_{\tt ln, cp, \tau} \\
W_{\tt lp, cn, \tau} & W_{\tt lp, cp, \tau}\\
\end{bmatrix}
}\\
{\color{lr}
\begin{bmatrix}
W_{\tt ln, rn, \tau} & -W_{\tt ln, rp, \tau} \\
-W_{\tt lp,rn, \tau} & W_{\tt lp, rp, \tau}\\
\end{bmatrix}
}
&
{\color{lb}
\begin{bmatrix}
W_{\tt ln, ln, \tau} & -W_{\tt ln, lp, \tau} \\
-W_{\tt lp, ln, \tau} & W_{\tt lp, lp, \tau}\\
\end{bmatrix}
}
&
{\color{dy}
\begin{bmatrix}
W_{\tt ln, cn, \tau} & -W_{\tt ln, cp, \tau} \\
-W_{\tt lp, cn, \tau} & W_{\tt lp, cp, \tau}\\
\end{bmatrix}
}\\
{\color{black}
\begin{bmatrix}
W_{\tt cn, ln, \tau} & W_{\tt cn, lp, \tau} \\
\bf 0 & W_{\tt cp, lp, \tau}\\
\end{bmatrix}
}
&
{\color{black}
\begin{bmatrix}
W_{\tt cn, ln, \tau} & -W_{\tt cn, lp, \tau} \\
\bf 0 & W_{\tt cp, lp, \tau}\\
\end{bmatrix}
}
&
{\color{dg}
\begin{bmatrix}
W_{\tt cn, cn, \tau} & \bf 0\\
\bf 0 & W_{\tt cp, cp, \tau}\\
\end{bmatrix}
}\\
\end{bmatrix},
$$
for all $\tau$.
The bias of a 1D convolution is identical to that of a fully connected layer, \ie, the  same bias is added for each time step. Hence the same parameter sharing is used.

\subsection{Equivariant LSTM and GRU layers}
LSTM and GRU modules which satisfy chirality can be obtained from fully connected layers.
However, na\"ively setting all matrix multiplies within an LSTM to satisfy the equivariance property will not lead to an equivariant LSTM because gates are elementwise \textit{multiplied} with the cell state. If both  gate and cell  preserve the negation then the product will not. Therefore, we  change the weight sharing scheme for the gates. We set $D_{n}^{\tt out}$ for the gates to be the empty set, \ie,  the gates will be invariant to negation at the input, $T^{\tt in}_{\tt neg}$, but still equivariant to the switch operation, $T^{\tt in}_{\tt swi}$. With this setup, the product of the gates and the cell's output will preserve the sign, as the gates are invariant to negation and passed through a Sigmoid to be within the range of $(0,1)$.  GRU modules are modified  in the same manner.

More formally, the computation in an LSTM module are as follows:
\begin{center}
\begin{tabular}{lc}
 $i_t = \sigma(W^\text{ii} x_t + b^\text{ii} + W^\text{hi} h_{(t-1)} + b^\text{hi})$ & (Input Gate)\\
 $o_t = \sigma(W^\text{io} x_t + b^\text{io} + W^\text{ho} h_{(t-1)} + b^\text{ho})$ & (Output  Gate)\\
 $f_t = \sigma(W^\text{if} x_t + b^\text{if} + W^\text{hf} h_{(t-1)} + b^\text{hf})$ & (Forget Gate) \\
 $g_t = \tanh(W^\text{ig} x_t + b^\text{ig} + W^\text{hg} h_{(t-1)} + b^\text{hg})$ &  (Cell State) \\
 $ c_t = f_t \cdot c_{(t-1)} + i_t \cdot g_t$ & \\
 $h_t = o_t \cdot \tanh(c_t)$ & (Recurrent State)\\
\end{tabular},
\end{center}
where $\sigma$ denotes an element-wise sigmoid non-linearity.

Observe that the LSTM operations consist of fully connected layers. For the cell state's parameters, \eg, $W^\text{ig}, W^\text{hg}, b^\text{ig}, b^\text{hg}$, we  follow the weight sharing scheme discussed for fully connected layers.

Due the to multiplication in the cell state, we redesigned the parameter sharing for the input, output and forget gate, to be invariant to $T^{\tt in}_{\tt neg}$, by setting $D_{n}^{\tt out}$  to be the empty set: no negation is needed for all dimension. This results in the following parameter sharing scheme for the parameters $W^\text{ii}, b^\text{ii}, W^\text{hi}, b^\text{hi}, W^\text{io}, b^\text{io}, W^\text{ho}, b^\text{ho}, W^\text{if}, b^\text{if}, W^\text{hf}, b^\text{hf}$:
\begin{center}
$
W = \begin{bmatrix}
{\color{lb}
\begin{bmatrix}
W_{\tt lp, ln} & W_{\tt lp, lp}\\
\end{bmatrix}
}
&
{\color{lr}
\begin{bmatrix}
W_{\tt lp,rn} & W_{\tt lp, rp}\\
\end{bmatrix}
}
&
{\color{dy}
\begin{bmatrix}
W_{\tt lp, cn} & W_{\tt lp, cp}\\
\end{bmatrix}
}\\
{\color{lr}
\begin{bmatrix}
-W_{\tt lp,rn} & W_{\tt lp, rp}\\
\end{bmatrix}
}
&
{\color{lb}
\begin{bmatrix}
-W_{\tt lp, ln} & W_{\tt lp, lp}\\
\end{bmatrix}
}
&
{\color{dy}
\begin{bmatrix}
-W_{\tt lp, cn} & W_{\tt lp, cp}\\
\end{bmatrix}
}\\
{\color{black}
\begin{bmatrix}
\bf 0 & W_{\tt cp, lp}\\
\end{bmatrix}
}
&
{\color{black}
\begin{bmatrix}
\bf 0 & W_{\tt cp, lp}\\
\end{bmatrix}
}
&
{\color{dg}
\begin{bmatrix}
\bf 0 & W_{\tt cp, cp}\\
\end{bmatrix}
}\\
\end{bmatrix}
$,
$b = \begin{bmatrix}
\begin{bmatrix}
\color{lr}
\color{lr}
b_{\tt lp}
\end{bmatrix} \\
\begin{bmatrix}
\color{lr}
\color{lr}
b_{\tt lp}
\end{bmatrix} \\
\begin{bmatrix}
b_{\tt cp}\end{bmatrix}\\
\end{bmatrix}
$.
\end{center}
This LSTM is chirality equivariant, as  the computation of the cell state is equivariant. Other computations are linear combinations of chirality equivariant operations, which remains equivariant. We note that the chirality equivariant GRU module  is modified by following the same sharing scheme for the gates.

\subsection{Equivariant batch-norm layers}
A batch normalization layer performs an element-wise standardization, followed by an element-wise affine layer (with learnable parameters $\gamma$ and $\beta$):
$$
{\mathbf{y}} = f_{\text{BN}}({\mathbf{x}}):= \gamma \cdot \frac{{\mathbf{x}} - \mu}{\sqrt{\sigma^2 + \epsilon}} + \beta.
$$
\textit{Equivariance for $\gamma$, and $\beta$} is obtained by
following the  principle applied to fully connected layers: we achieve equivariance via parameter sharing and odd symmetry:
\begin{center}
$\gamma =
\begin{bmatrix}
\color{lr}
\begin{bmatrix}
\gamma_{\tt ln} & \gamma_{\tt lp}
\end{bmatrix} &
\color{lr}
\begin{bmatrix}
\gamma_{\tt ln} & \gamma_{\tt 1p}
\end{bmatrix} &
\begin{bmatrix}
\gamma_{\tt cn} & \gamma_{\tt cp}
\end{bmatrix}
\end{bmatrix}^T$
and
$\beta = \begin{bmatrix}
\color{lr}
\begin{bmatrix}
\beta_{\tt ln} & \beta_{\tt lp}
\end{bmatrix}&
\color{lr}
\begin{bmatrix}-\beta_{\tt ln} & \beta_{\tt lp}
\end{bmatrix}&
\begin{bmatrix}
\bf 0 & \beta_{\tt cp}
\end{bmatrix}\\
\end{bmatrix}^{T}$.
\end{center}

\textit{Equivariance for $\mu$, and $\sigma$} is obtained by
computing the mean and standard deviation on the ``augmented batch'' and by keeping track of its running average. Formally, given a batch $\mathcal{B}$ of data,
\begin{center}
$\mu = \frac{1}{2|\mathcal{B}|} \sum_{{\mathbf{x}} \in \mathcal{B}} {\mathbf{x}} + \mathcal{T}^{\tt in}({\mathbf{x}})$, \hspace{0.1cm} $\sigma =  \sqrt{\frac{\sum_{{\mathbf{x}} \in \mathcal{B}} ({\mathbf{x}} - \mu)^2 + (\mathcal{T}^{\tt in}({\mathbf{x}})- \mu)^2}{2 |\mathcal{B}|}}$.
\end{center}
\subsection{Dropout.}
At test time, dropout scales the input by $p$, where $p$ is the dropout probability. The equivariance property is satisfied because of  the associativity property of a scalar multiplication.
The input and output dimension and symmetry of a dropout layer are identical. Therefore, $\mathcal{T^{\tt out}}$ and $\mathcal{T^{\tt in}}$ are identical. From the definition:
$$
\mathcal{T}^{\tt out}( p \cdot {\mathbf{x}})  = \mathcal{T^{\tt in}}(p \cdot {\mathbf{x}}) = T^{\tt in}_{\tt neg}T^{\tt in}_{\tt swi} (p \cdot {\mathbf{x}}) = p \cdot (T^{\tt in}_{\tt neg}T^{\tt in}_{\tt swi}{\mathbf{x}})
=p \cdot (\mathcal{T}^{\tt in}({\mathbf{x}})) \;\; \forall {\mathbf{x}} \in \mathbb{R}^{|J^{\tt in}||D^{\tt in}|}.$$
Hence, a dropout layer naturally satisfies the equivariance property. At training-time, we do not enforce equivariance for the dropped units, \ie, we do not jointly drop symmetric units  as we found this to prevent overfitting. This is likely application dependent.

\section{Additional Results}\label{extra_results}
\subsection{3D pose estimation}
In \tabref{tab:supp_eva_quan}, we report the HumanEva-I for multi-action models evaluated on Protocol 1 (MPJPE). Our approach have benefits the most from the Boxing action while maintaing the performance on other actions. We also provide qualitative evaluation in \figref{fig:supp_eva_walk} and \figref{fig:supp_eva_box}. We observe that our model successfully estimates 3D poses from 2D key-points. We have also attached animations in the supplemental.

\begin{table}[t]
\centering
\begin{tabular}{l|ccc|ccc|ccc|c}
\specialrule{.15em}{.05em}{.05em}
 &  \multicolumn{3}{c|}{Walk} & \multicolumn{3}{c|}{Jog} & \multicolumn{3}{c|}{Box} & Avg.\\
App. & S1 & S2 & S3 & S1 & S2 & S3 & S1 & S2 & S3 & -\\
\hline
\hline
Pavllo~\cite{pavllo20193d} & 17.6 & 12.5 & 37.6  & 28.1 & 19.1 & 19.2 & 29.5 & 44.0 & 43.1 & 33.3\\
Pavllo~\cite{pavllo20193d} ($\ddagger$) & \bf 17.5 & 12.3 & 37.4 & \bf 27.7 & 19.0 & 19.0 & 27.7 & 43.4& 42.5 & 33.0\\
\hline
Ours & 18.9 & \bf 12.3 & 38.1 & 28.5 & \bf 18.1 & \bf 18.2 & \bf 27.1 & \bf 40.9 & \bf 40.2 & \bf 32.2\\
\specialrule{.15em}{.05em}{.05em}
\end{tabular}
\caption{Results on HumanEva-I for multi-action (MA) models reported in Protocol 1 (MPJPE), lower the better. $\ddagger$ indicates test time augmentation.}
\label{tab:supp_eva_quan}
\end{table}

\begin{figure}[t]
\centering
\includegraphics[scale=0.3]{supp_fig/eva/w1}
\includegraphics[scale=0.3]{supp_fig/eva/w2}
\includegraphics[scale=0.3]{supp_fig/eva/w3}
\caption{Qualitative visualization of 2D to 3D pose estimation for the action ``Walking" on HumanEva-I dataset.}
\label{fig:supp_eva_walk}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[scale=0.3]{supp_fig/eva/b1}
\includegraphics[scale=0.3]{supp_fig/eva/b2}
\includegraphics[scale=0.3]{supp_fig/eva/b3}
\caption{Qualitative visualization of 2D to 3D pose estimation for the action ``Boxing" on HumanEva-I dataset.}
\label{fig:supp_eva_box}
\end{figure}

\subsection{Skeleton based action recognition}
In~\figref{fig:supp_action}, we show the visualization of the input skeleton sequences computed by OpenPose~\cite{cao2018openpose} and the predicted action class by our chiral invariant skeleton based action recognition model.
\input{fig_sup_action}

\section{Implementation Details}\label{extra_implement}
\subsection{3D pose estimation}
\textbf{Implementation details.}
Our model follows the temporal convolutional architecture proposed by~\citet{pavllo20193d}, and replaced all layers with their chiral versions; code for the layers are attached in the supplemental as well.
We also changed ReLU to tanh to achieve chiral equivariance. For the temporal models, we follow their 4 blocks design which has the receptive field of 243. For the single frame model, we follow their 3 blocks design. These models all contains 1020 hidden dimensions so it is a factor the number of joints, 17, this is slightly smaller than the 1024 used in~\cite{pavllo20193d}. We also use their data processing and batching stragety as described in Section 5 and Appendix A.5 of~\cite{pavllo20193d}. For training the model, we utilized the Adam optimizer with beta1=0.9 and beta2=0.9999. We decay the batch-normalizations' momentum as suggested in~\cite{pavllo20193d}. Other details follows the publicly available implementation by~\citet{pavllo20193d}.  We enforced chiral equivariance by choosing the $|D_n^{\tt out}|$ to be $\frac{1}{3}$ of the hidden dimension. The $|D_n^{\tt in}|$ for the input layer is 17 and the $|D_n|^{\tt out}$ for the output layer is 17, as one for each joint.

\subsection{2D pose forecasting}
\textbf{Implementation details.}
The non-chiral equivariant baseline is a seq2seq model consisting of an encoder and decoder, which are stacked-LSTMs with hidden size of 1040 and 2 stacked layers. We trained using teacher forcing with the Adam optimizer. The batch-size is 256, and we trained for 30 epochs. Dropout is applied to the LSTMs' hidden layer with drop probability of 0.5. Following prior works, we use max norm gradient clipping of 5, a learning rate of 0.005 with a decay of 0.95 every 2 epochs. The data processing and evaluation setting follows~\cite{chiu2019action}. Other details follows the publicly available implementation by~\citet{chiu2019action}. We enforced chiral equivariance by choosing the $|D_n^{\tt out}|$ to be $\frac{1}{2}$ of the hidden dimension, as the output is two dimensional per joint.

\subsection{Skeleton-based action recognition}
\textbf{Implementation details.}
The non-chiral version of the model, Ours-Conv, follows Temporal-Conv~\cite{kim2017interpretable} while we modified the model to have not only temporal convolution but also spatial convolution. There are ten spatial-temporal convolution blocks and each block we first perform spatial convolution and then temporal convolution. The temporal convolution considers the intra-frame information while the spatial convolution considers the inter-frame information. For the recognition task, we need chiral invariance,~\ie, a chiral pair should be classified as the same action class. To this end, we use a chiral invariance layer where we let both $J^{\tt out}_{\tt r}$, $J^{\tt out}_{\tt l}$ as well as $D^{\tt out}_{\tt n}$ to be empty sets, which means there are no left and right joints but only center joints and there is no dimension that will be negated in the output of the layer after applying the chirality transform. Note that the chiral transformation exchange the left and right joints and negate the dimension in the index set $D^{\tt out}_{\tt n}$. Given $J^{\tt out}_{\tt r}$, $J^{\tt out}_{\tt l}$ and $D^{\tt out}_{\tt n}$ are all empty, it's obvious that the output will be chiral invariance. For the chiral invariance model, Ours-Conv-Chiral, we replace the all the non-symmetric layers before the chiral invariance layer with their corresponding chiral equivariance version. All the layers after the chiral invariance layer remains the same as in the Ours-Conv model. Similar to~\cite{kim2017interpretable}, there are in total 10 convolution blocks in Ours-Conv and we put the chiral invariance layer at the fourth layer. Also, we gradually reduce the ratio of the dimension to be negated ($|{D^{\tt out}_{\tt n}}|/|{D^{\tt out}}|$) from $\frac{1}{3}$ to $\frac{1}{6}$ at the first layer, from $\frac{1}{6}$ to $\frac{1}{12}$ at the second layer and from $\frac{1}{12}$ to $0$ at the third layer. We use the SGD optimizer with a momentum of $0.9$ as in~\cite{yan2018stgcn} with a batch size of 256. We train the model for 90 epochs.

redpajama_set_name: RedPajamaArXiv


Home Again: Big White Shares Olympic Spirit!
The Olympic Spirit is being felt everywhere.
''Top Five Family Ski Resorts in the World''.
The feeling of the Olympic spirit is truly alive at Big White!!!
just to let you know we're up here and loving the snow.
I think the Olympics should of been at Big White.
hauling snow from Manning Park..
I have decided to stay inside and learn how to post from my Notebook.
The words Big White describe the visibility today.
Vision is extremely poor and it's claustrophobic for me.
I can't even see the trees.
We've had some fantastic days..
do I dare cancel meetings at home and ski????
for the Canadian mogul competitions held in Calgary.
gearing up for some Gold medals.
We need to keep BELIEVING!!!
Thanks for the link to the snow party. It reminds me so much of growing up on the farm and riding behind my dad's tractor. We would even go on the roads around the country. It got even more fun when we got snow mobiles to get us back up the hill after sledding. Nothing is more fun! Your Olympic photos look so pretty. What a great opportunity for you!
I say "forget the meetings" and stay in that divine place. The pictures are awesome and make anyone want to take time out to enjoy the good life. Enjoy!
Oh my goodness! You've got snow! That's GREAT!!! I've been visiting Koralee at Bluebird Notes (she's from Vancouver) ~she's been wishing for snow for the Olympics.
The kids will love 'meeting' all the mascots!
Forget the meetings...and ski to your heart's delight! The only snow you will find at home is imported from elsewhere.
Your pictures are making me a little envious. I am almost climbing walls because I'm craving some snow! Have a wonderful, restful trip.
I hope. .hope .. .hope that we are the most hospitable country ever. That one aspect we have complete control over.
Yesterday as we walked about Vancouver. . .we smiled and chatted it up with anyone who gave us notice. It was very fun.
Take the day off. . it's beautiful up there.
Marg, you are so cute! I say you did you work on you new notebook... go skiing when you can.
I can't wait to watch the Olympics.
I'd forget the meetings and ski.
Your pics are great! I love the darkness against the snow. I feel like I need to ski on over to see you. I feel like I miss you!!!! I will climb over the snow to get to you!


All of us at Gradoni & Associates would like to congratulate George Parnham and Wendell Odom, two of our favorite clients, for being selected as Harris County Criminal Defense Lawyers of the Year for their representation of Andrea Yates.
Having had the privilege to work with both attorneys on the Yates case, we certainly know first hand all of the time, money and energy expended by both George, Wendell and their staff in Andrea's defense.
I can certainly attest that both George and Wendell poured their hearts and souls into this case.
The case was certainly an uphill battle, which left all of the defense team with newfound knowledge about mental illness, hospitals that provide mental care and psychiatric services.
Yvonne Parks, a graduate of the University of Houston with a degree in Political Science has recently joined our staff. Yvonne will be handling case work in the Fort Bend County area.
Yvonne hails from Fort Bend County and has worked with a number of Fort Bend County attorneys working in criminal and civil practices. Yvonne is working on her Masters Degree in Criminal Justice.
Terrance Levi, a graduate of SW Louisiana College with a Criminal Justice degree has recently joined our staff working in the surveillance unit. Terrance has over 17 years of experience in mobile video surveillance undercover corporate investigations. Terrance is an expert in the covert work of identifying theft rings, fraud and drugs in the work place.
Both are welcomed additions to our staff.
Clay Buckner is our profiled Investigator in this issue. Clay is recognized as a valuable team member of Gradoni & Associates because of his versatile abilities.
Clay is the mainstay of our surveillance team, but also has a great deal of experience in interviewing witnesses and conducting background investigations.
Clay grew up in the Houston area, attending Cy-Creek High School. Clay joined our firm in January 1992 after his Honorable Discharge from the United States Marine Corp, serving in Desert Storm.
Clay has been responsible for many surveillance successes, which has included filming suspected fraud, workman's compensation claimants from heavy brush in full camouflage attire, filming people who claim they are unable to drive while following behind them at high rates of speed and utilizing our undercover camera to catch individuals claiming disability at work.
Clay returned to college on a part time basis in order to complete his degree program. Clay is currently a senior at the University of Houston, majoring in computer science and mathematics. Clay's work ethic and attitude embodies our core function to provide the best possible work product for all of our clients.
We are proud to have Clay as a member of our team.
Everyone on the staff at Gradoni & Associates would like to say goodbye and good luck to Elizabeth Congos, our lead word processor who has been with our firm since August of 1992. We will miss Elizabeth, who is moving to Dallas to further her education.
Elizabeth is a typing wizard, who can type over 110 words per minute. We will probably have to hire two replacements in order to not lose the pace Elizabeth provides on our work product.
For all of our friends in the Criminal Defense arena, we will again be attending the upcoming Rusty Duncan Seminar in San Antonio on June 6th and 7th as an exhibitor. We look forward to seeing many of you. Please stop and say hello.


text:
Clement Dowd (* 27. August 1832 in Richland Creek, Moore County, North Carolina; † 15. April 1898 in Charlotte, North Carolina) war ein US-amerikanischer Politiker.

Dowd studierte Jura an der University of North Carolina in Chapel Hill und erhielt 1856 seinen Abschluss. 1857 und 1858 war er als Lehrer tätig. 1859 wurde er in die Anwaltschaft aufgenommen und praktizierte in Charlotte. Während des Bürgerkrieges diente er in der Konföderiertenarmee. Nach Ende des Krieges wurde er wieder in seinem früheren Beruf tätig. Von 1869 bis 1871 bekleidete Dowd das Amt des Bürgermeisters von Charlotte. Danach wurde er von 1871 bis 1874 Präsident der Merchants & Farmers' National Bank und von 1874 bis 1880 Präsident der Commercial National Bank of Charlotte.

Dowd wurde als Demokrat in den Kongress gewählt und vertrat dort vom 4. März 1881 bis zum 3. März 1885 den Bundesstaat North Carolina im US-Repräsentantenhaus. Bei den Wahlen von 1884 kandidierte er nicht mehr. Er starb 1898 in Charlotte und wurde auf dem Elmwood Cemetery beigesetzt.

Weblinks

Mitglied des Repräsentantenhauses der Vereinigten Staaten für North Carolina
Bürgermeister (Charlotte, North Carolina)
Mitglied der Demokratischen Partei (Vereinigte Staaten)
US-Amerikaner
Geboren 1832
Gestorben 1898
Mann

redpajama_set_name: RedPajamaWikipedia


The online catalog is the primary tool for discovering all the library's holdings, including rare books, manuscripts, maps, works of art on paper and the modern reference collection.
Organized by format (manuscripts, maps, etc.), the Digital Library contains images of and brief information on highlights of the collections, as well as material most popular with the library's researchers.
Finding aids for large manuscript and archival collections, such as the Records of the Society of the Cincinnati and the Anderson Family Papers, can be found online through the Digital Library.


My thanks to all of you who expressed you concern about what happened to the digests since Monday, 22Jan96. I have been away, attending the annual winter USENIX technical conference. The winter USENIX conference always attracts the "who's who" of the Unix community, and for me, is not to be missed.
They always have terminals set up connected to the Internet, so I figured I'd just log in and edit the digest from there. It turned out that there was so much useful going on, until late at night, that I never got to it. To make matters worse, _THIS_ digest, which was ready to send before I left on my tavels, did not get transmitted due to an oversight. Consequently the "outage" when I got back was actually longer than I thought.
I'm going to send the digests (although late) with the correct dates on them for their content. I'll try to get two (or more) out each day until we get caught up.
Thanks again for all of your interest and concern.


text:
Introduction to CMM Arms 362
"Introduction to CMM Arms" provides an overview of the components and functions of a portable coordinate measuring machine arm, or CMM arm. Portable CMM arms are used to measure workpiece features and record their coordinate locations with software. CMM arms measure using either contact or noncontact methods and can be used in most environments on the production floor.
CMM arms are used for many applications in manufacturing, including inspection, rapid prototyping, and reverse engineering processes. After taking this class, users will be able to describe CMM arms and best practices for using them.
details Other tabs
Class Name:
Portable CMMs
CMM Arms
CMM Arm Applications
Review: CMM Arm Introduction
Parts of a CMM Arm
CMM Coordinate Systems
Review: CMM Parts and Setup
CMM Arm Operation
Data Collection and Output
Describe CMMs.
Distinguish between types of portable CMMs.
Describe CMM arms.
Describe CMM arm applications.
Identify the components of a CMM arm.
Describe CMM coordinate systems.
Describe CMM arm alignment.
Describe part workholding when using a CMM arm.
Describe CMM arm operation.
Describe CMM arm data.
Vocabulary Term
3D Three-dimensional. Having or appearing to have length, breadth, and depth. 3D models show an object's shape better than two-dimensional drawings.
adhesives A chemical material used to bond two objects together. Adhesives are often used to stabilize smaller parts during inspection.
alignment The process of arranging components so that they are lined up. Alignment of a CMM arm occurs when the part coordinate system matches the machine coordinate system.
articulated Consisting of segments connected by joints. Articulated CMM arms move in many directions.
automated Controlled by machines or computers with little human interaction. Automated CMMs can measure parts once programed.
axes An imaginary line or circle that is used to define the position of an object in space. The linear axes are X, Y, and Z.
base The foundation of a machine that supports all other machine components. The base stabilizes the machine and provides it with rigidity.
bridge A machine part that provides support and allows movement. On a CMM, the bridge is a horizontal beam that provides a stable area for movement of the probe.
CAD Computer-aided design. A computer software program that aids in the automated design and technical precision drawing of a part, product, process, or building. CAD software can tell a CMM arm how to inspect a part.
climate-controlled Having artificially regulated air temperature, humidity, and movement. Climate-controlled environments are not necessary for portable CMMs.
CMM arms A portable measuring device consisting of segments connected by joints. CMM arms operate using either contact or noncontact methods.
CMMs Coordinate measuring machines. A sophisticated measuring instrument that uses a suspended probe to measure parts in three-dimensional space. CMMs operate using either contact or noncontact methods.
computer-aided design CAD. A computer software program that aids in the automated design and technical precision drawing of a part, product, process, or building. Computer-aided design software can tell a CMM arm how to inspect a part.
contact probes A type of probe consisting of a synthetic ruby-tipped stylus that makes physical contact with a workpiece. A contact probe records one single point each time it touches a part's surface.
control system A manual or automatic mechanism used to manage dynamic processes. Control systems in CMM arms power and operate the measuring device and record data for inspection.
coordinate measuring machines CMM. A sophisticated measuring instrument that uses a suspended probe to measure parts in three-dimensional space. Coordinate measuring machines operate using either contact or noncontact methods.
coordinate system A system that uses three linear axes to describe the location of an object in three-dimensional space. A coordinate system expresses the location of any point as the distance from it to the origin, or the fixed intersection of axes.
counterbalanced Weighted so as to stabilize opposing force. Counterbalanced linkage arms in a CMM arm increase its stability and ease of operation.
datum A point of reference for machine tools, programs, and fixtures from which measurements are taken. A datum acts as the origin of the part coordinate system.
deviations The difference between a standard and a result. Deviations can lead to parts that do not meet specifications.
distance meter An instrument that uses a laser to accurately determine the distance of an object without contacting it. Distance meters are highly accurate and can measure far distances.
distortion Warpage in a workpiece due to stresses caused by exposure to pressure and other manufacturing forces. Distortion can be prevented through proper use of workholding devices.
fixed CMMs A stationary coordinate measuring machine. Fixed CMMs have a large base with a suspended probe and are operated in a controlled environment.
fixtures A customizable, modular workholding device created by configuring locators, supports, and clamps on a body fixture. Fixtures are common workholding devices for CMM inspection because they allow a part to be accessible while secured in place.
geometry The measurement, properties, and relationships of the lines and points of an object that make up its shape. Geometry is used when measuring and designing parts.
home position The central point from which a machine begins an operation. The home position acts as the origin of the machine coordinate system.
in-process Currently being produced by manufacturing. In-process parts are found throughout the process of turning raw material into finished products.
inspection The examination of a part during or after its creation to confirm that it adheres to specifications. During inspection, defects may be identified and corrected.
joints A place where two things or parts are connected. The joints in a CMM arm allow the device to move freely and to measure several different kinds of parts.
laser A device that generates an intense beam of light that can be precisely aimed and controlled. Lasers are projected on a part's surface to scan position coordinates.
laser scanner A portable measuring device that uses a beam of light to measure an object's geometric shape. Laser scanners are noncontact probes.
laser trackers A portable measuring device that projects a beam of light at a retroreflective target to measure large objects. Laser trackers require a person to hold a target on the object being measured.
linkage arms Separate segments of an articulated arm connected by joints. Linkage arms are lightweight and rotate on the CMM arm's axes.
machine coordinate system A fixed coordinate system that has the machine's home position as its origin. The machine coordinate system's X, Y, and Z axes are mapped to the components of the machine and remain the same for every part.
metrology The science of measurement. Metrology strives for accuracy, precision, and repeatability.
modular wrist A handheld, movable grip at the end of a CMM arm that holds probes. A modular wrist can fully rotate on an axis.
nominal A stated measurement that may not correlate exactly with a physical part. Nominal measurements for a part indicate the size specified in the blueprint, which may differ from the size of the actual part.
noncontact probe A type of probe that consists of a laser or scanning system that does not physically contact the part surface. Noncontact probes are used to streamline surface inspection.
on-machine Relating to or being on a machine. On-machine parts can easily be measured with a CMM arm.
orientation Position in three-dimensional space. Orientation is determined by the vectors in a coordinate system.
origin The fixed, central point in a coordinate system where the axes meet. The origin has a numerical value of zero.
part coordinate system A unique coordinate system that has a feature or datum of a specific workpiece as its origin. A part coordinate system's X, Y, and Z axes are mapped to the features of the specific workpiece.
pistol grip handle A handheld, movable handle with an extra rotating axis at the end of a CMM arm that holds probes. A pistol grip handle can provide better accuracy when scanning an object with a laser scanner.
portable CMMs A coordinate measuring machine that can be easily carried or moved. Portable CMMs can be used on the factory floor.
prints A document that contains the instructions necessary to manufacture and/or assemble a part. Prints include the degree of tolerance necessary for the part to function as intended.
probe A device that gathers measurement data from the workpiece. The probe on the CMM arm is attached to the modular wrist or handle and uses either contact or noncontact methods to measure a part.
quality control A system of managing quality by inspecting finished products to make sure they meet specifications. Quality control relies on error detection and correction.
quality report A document of measurement data used for inspection. Quality reports provide the information needed to determine the dimensional accuracy of parts.
rapid prototyping A product development technique that uses additive manufacturing (AM) to create prototypes for a traditional manufacturing operation. Rapid prototyping allows engineers to quickly create a number of prototypes in a short time period.
restrained Securely held in place so as to limit mobility. Restrained parts are held by fixtures or other workholding to keep them in place during inspection.
retroreflective Reflecting light back in the direction from where it came. Retroreflective targets are used with laser trackers.
reverse engineering A process that captures geometric data of an existing object to convert it to a three-dimensional (3D) computer-aided design (CAD) model. Reverse engineering can be used to create a reproduction based on a part's composition.
rotary encoders A device that translates angular position or motion into a digital signal. Rotary encoders in the joints of a CMM arm detect the incremental lines on a scale to determine positioning.
stylus A precision tip that records measurements. The stylus on the CMM arm is the spherical portion of the contact probe that is mounted to the wrist and makes contact with the part.
three-dimensional 3D. Having or appearing to have length, breadth, and depth. Three-dimensional models show an object's shape better than two-dimensional drawings.
tolerances An unwanted but acceptable variation or deviation from a desired dimension of a part. A part within tolerances will meet specifications and pass inspection.
unrestrained Free of external force or restrictions that would limit movement. Unrestrained parts are large enough or heavy enough to not need workholding during inspection.
vacuum Any device that uses suction. Vacuum-powered stands draw air rapidly, providing a portable CMM with a stable, rigid base.
vectors A set of numbers specifying a direction in 3D space. Vectors are used when determining the exact orientation of a part.
white light scanners A portable measuring device that projects a grid of light on an object and scans an image of it to record 3D surface measurements. White light scanners may take several scans before gathering all the dimensional data.
workholding A device used to secure, support, and locate a workpiece during a manufacturing operation. Workholding helps to ensure that parts are created accurately and with good repeatability.
X axis The linear axis representing side-to-side movement in a device, relative to the origin. A CMM arm uses the X, Y, and Z axes as reference.
Y axis The linear axis representing back-and-forth movement in a device, relative to the origin. A CMM arm uses the X, Y, and Z axes as reference.
Z axis The linear axis that represents up-and-down movement in a device, relative to the origin. A CMM arm uses the X, Y, and Z axes as reference.
Take an Online Class for Free
Choose from our comprehensive catalog.

redpajama_set_name: RedPajamaCommonCrawl


Many options Intentionally create a closed system, which can be tedious to move away from once you begin. However, with a stage called Ecwid, you do not need to worry about it. Actually, the whole aim of the business, which started in 2009, would be to quickly and quickly make an internet store system in your present websites.
This raised my Attention, because I understand the struggles that come along with attempting to migrate websites, particularly when it comes to ecommerce. So, I wanted to put together a comprehensive review of this Ecwid system to see whether it is worth the time.
It is rather Remarkable what Ecwid has done since 2009, with over 1 million merchants getting signed up. What is even more cool is that the Ecwid merchants span over 175 distinct countries, showing that this isn't just a platform for most people in the united states or Europe. Even businesses in developing countries have a opportunity to get an online store going, and you don't have to trash your previous website in case you have one.
In addition to The total merchant count, over 20,000 active users are using the Ecwid Shopping Cart for WordPress. The gap between that 20,000 and the 1 million is the simple fact that you don't need a WordPress site to implement Ecwid. So, the 20,000 simply identifies WordPress users with the plugin.
Ecwid is a hosted Solution for building an internet store. Unlike competing products such as Shopify, Bigcommerce and Volusion, which allow you to construct a new site with e-commerce functionality, Ecwid is geared more towards people who already have a website and just wish to add an online store to it.
Much like other E-commerce platforms, Ecwid lets you install'catalogs' of all goods, and add photographs, pricing, weight etc. for each. You are able to define shipping rates, accept credit card payments etc — all of the key things that you'd expect to be able to perform using an e-commerce solution.
However it differs Apart from competing products such as Shopify, Volusion, Squarespace and Bigcommerce since it is not really designed to allow you to produce a fully-featured, standalone e-commerce website; instead, it's intended to enable you add an internet store to an present online presence.
The Product works by providing you a widget which gets placed on other websites — hence the name Ecwid: it's short for'E-commerce Widget'. You receive a few lines of HTML code (the widget) to add into an present website or social networking profile, and your shop is displayed wherever you have added this code.
Ecwid makes Strides in the market by catering to companies which don't need to begin a brand-new site. The main attribute is that you can take your old site and immediately integrate the Ecwid system inside a couple of minutes.
You can also Mirror the machine onto several different sites if you plan on selling elsewhere on the web. Handle all these websites from one location rather than switching between multiple dashboards.
Another nice Attribute is the syncing between multiple devices. Sell on-the-go with your smartphone. This usually means you could visit a tradeshow to generate a few sales and all these earnings are represented onto the back part of your website.
The system is Also made to integrate nicely with social networks, so that you can sell your items on Facebook if desired. 1 part of Ecwid that we particularly enjoy is the delivery facet. With real-time transport integrations you constantly know what is happening with your orders and at which they are being shipped to.
Thanks To Ecwid's point-of-sale (POS) functionality, you may use your Ecwid shop to market not just online but in bodily locations too — in stores, market stalls, in concerts and so on.
Together with Ecwid's POS Performance, regardless of if a customer purchases a product in shop, online, on their phone or via Facebook, everything stays in sync – i.e., the retailer's catalogue, inventory and customer / transaction information.
There is a few ways that you can take advantage of this feature: the simplest is likely to use'Paypal Here.' This involves downloading the Ecwid iOS app from the Apple's App store, linking it to the Paypal Here service, then taking payments using a mobile card reader (pictured above).
If you are located outside That the US / UK, or need to work with another mobile device kind, the good news is that Ecwid also functions with all the Vend, Clover, NCR Silver and Square POS systems. These all facilitate using a wider range of hardware in a physical retail location (full-sized card readers, receipt printers, cash drawers pill stands etc.) and are usable in more nations.
Although you can avail Of the Paypal Here POS choice on most of paid-for plans, you'll need to be to the most expensive'Unlimited' program if you would like to avail of a Vend, Clover, NCR Silver or Square integration.
Ecwid Storefronts are responsive, meaning that they will display properly across apparatus — desktopcomputer, tablet and cellular. In an era where smartphone web browsing is eclipsing desktop surfing, this is vital.
Granted, it is a fairly Basic plan, where features such as discount coupons and service aren't available, and it only lets you sell up to ten products in 2 categories — but this could actually be adequate for some customers, and using it's a good way to try out the system.
However, A vital point to notice about the free plan is that it is not great from an SEO standpoint — you need to be on a paid plan to make certain that your product pages talk to search engines correctly (more on SEO under ).
Ecwid is forward of the Pack in that its storefronts could be mechanically translated into nearly 50 distinct languages — customers can view your store in their own language, without you having to worry about producing alternate versions of this. Ecwid provides this performance by discovering visitors' language mechanically based on their browser preferences / IP address.
Competing products like Shopify And Bigcommerce are yet to provide this sort of functionality — they force you to rely on third party programs, the production of numerous shops or Google Translate to provide different language variations of your store, which is less than perfect. Therefore a definite triumph for Ecwid here.
Search engine Optimisation (SEO) in Ecwid is a fairly straightforward affair. You can edit the name of your page and its own meta description; the relevant fields are pre-populated for you automatically, however you can tweak them to match your SEO objectives.
1 place where Ecwid does not perform so Well on the search engine optimization front involves AMP — accelerated cellular pages. As the name suggests, AMP pages load quicker on mobile devices. This encourages people to stay longer on your webpage, thus increasing'live time' –something that's believed by many SEO experts consider to be rewarded with Google with preferential treatment in search results. Furthermore, Google occasionally highlights AMP webpages in carousels in search results, giving AMP content an extra little boost.
Unfortunately However — and unlike most competing products such as Bigcommerce or Shopify, you can not create AMP versions of your products using Ecwid.
The Export option allows you to export merchandise information, orders and customers (in CSV format) and ensures that should you ever feel the need to migrate your shop to a different e-commerce platform, then you shouldn't have some significant difficulties doing so.
WordPress doesn't Provided any e-commerce performance from this box, so anybody wishing to market on the stage will require a third-party alternative like Ecwid. There's an Ecwid plugin available, so adding an Ecwid shop to your WordPress site is very straightforward — you can get up and running with a couple clicks.
Squarespace comes with Increasingly excellent e-commerce attributes, but the amount of payment gateway options is quite limited — you have to utilize Stripe or Paypal. (And using Stripe only functions if you're selling goods from particular countries). Another main problem with the built-in Squarespace marketing tools is that they don't facilitate dropshipping, and complete export of products is not currently possible.
Integrating Ecwid with Squarespace permits you to bypass these limitations, and adding it to some Squarespace site is very simple: it's a simple matter of including a code block into a webpage and pasting some HTML to it.
As With Squarespace, there's currently no dropshipping choice for Wix users, therefore again Ecwid can provide a good workaround. A dedicated app is provided by Ecwid to enable you incorporate the product on a Wix shop easily.
Ecwid provides a fairly Restricted number integrations with other well-known apps. Integrations do exist with services Mailchimp, Xero and Freshbooks; but to be fair the range of integrations could be more extensive — competing products such as Shopify provide a much broader range of apps. Notable omissions in the Ecwid store comprise Quickbooks and Zendesk, such as (that said, a Quickbooks integration is coming soon).
Ecwid's Interface is rather user friendly. Like most similar online store builders, you receive a vertical menu on the left which lets you access key functionality, and the area on the right is used to display or edit related products, website reports and content.
As with any e-commerce tool, you will have to Spend a fair amount of time getting your head around producing catalogues and product variations, establishing shipping prices and so on…but there is nothing that should represent too a lot of a learning curve.
I'm not a Lawyer, so please be aware the below observations should not be interpreted as legal advice, but I'm going to do my very best to spell out a number of the major GDPR issues facing Ecwid consumers under.
With the introduction of That the EU's new GDPR laws, there are several legal steps that website owners now should take to ensure that they are adequately protecting EU customers' and visitors' privacy. There are serious financial penalties for not doing this (to the point where it is typically a great idea to consult a lawyer on what to do); and even when your business isn't based in the EU, then you still will need to comply with the regulations where any website visits in the EU are concerned.
There doesn't seem to be Anything that stops you meeting the first three requirements easily enough with Ecwid, although you will have to devote time and possibly money creating adequate notices and crafting information capture forms so they are GDPR compliant.
So for example, if you Use a Facebook Advertising cookie in conjunction with your Ecwid store, you will be breaking up GDPR laws unless you've got a banner in place which does all of the above.
Nowout of the box at There is not a means to take care of the cookie approval issue with Ecwid. Nor is there a decent program available from the Ecwid app store (the only alternative on this front that I can locate, the'EU cookie banner', doesn't seem to supply the essential performance — despite costing $1.99 per month to utilize ).
It Appears to me that the only option available to Ecwid users would be to use a professional product like CookiePro, which will provide all the necessary performance to make cookie approval fully GDPR compliant. Despite being a powerful product nonetheless, Cookiepro does need quite a great deal of configuration and you'll want to set quite a great deal of time aside to set this up.
I really enjoy The fact that you're able to run a web site without paying anything. This makes the setup process that much simpler, because you simply have to punch in your email and make a password to proceed straight to the backend interface.
The machine has Wizards for each platform you want to place your shop on. If you've got a WordPress site, simply walk through three steps to get up and running. You could also click on options like Facebook and Joomla, depending on the place you would like to sell.
The backend Design is perfect, since it walks you through every website creation and integration measure with a few nice photos and text. As soon as you get your shop implemented on a website or social page it looks fairly slick.
The design Depends somewhat on the subject you've got on your website, however as you can see below, it displays photos well and appears clean and simple to navigate. I especially enjoy the Shopping Bag place, which is prominent and easy to find for customers when they wish to checkout.
Though many Sites will be cellular friendly, its nice knowing that Ecwid includes a native shopping application for both iOS and Android. Merchants now receive a native shopping application for iOS and Android.
The closing Design item that makes sense to mention is your language instrument. Since running an online store generally requires you to attain out to individuals from throughout the planet, you're bound to stumble upon a few customers who would like to read product webpages and other content in their native tongue. Ecwid supports 45 languages, so if a user would like to translate from English into Spanish, that is no problem in any respect.
Ecwid is a Third-party remedy to your present site, so you'd normally need to implement additional SEO and marketing tools to truly get out the word. That said, Ecwid supplies quality SEO features to help merchants increase their visibility in Google searches.
Each step is Clear and concise, so that you can just go in there and sort in a product name, price and image then save the merchandise for afterwards. Obviously you could always open the Powerful Options, but they different these for when you are ready to start ramping up your store.
It's not always Easy to locate an ecommerce platform which does not charge fees, but that's just what you get with Ecwid. They never control any kind of transaction fee with any of those programs they offer, making it desirable for any store that's trying to keep down costs and to improve margins.
Remember that Ecwid is not a payment processor, so you've got to set up something like PayPal or Stripe to process all the trades that come through your site. It is pretty easy to implement these systems, because Ecwid integrates with over 40 international payment options. However, each of those processors have their own trade fees so you need to prepare for them.
· The'starter site' option is a good stopgap measure for merchants who want a shop quickly, but have yet to create a complete site to add the Ecwid widget to.
Ecwid comes With four plans, one of which is totally free. They market the free plan like crazy, and mention that a number of different platforms drag you into a free trial, where you will finally need to pay.
The Free plan Allows you to sell 10 products, whereas the Venture plan ups that depend to 100 products and you get things like an iPhone direction app. The company program goes up to 2500 products for a wonderful price and you get live chat support. Priority support comes alongside the Unlimited program and you can also market an unlimited number of merchandise.
Ecwid is one of The most economical solutions available on the marketplace. You can see that it is actually cheaper than many of the other platforms we've reviewed previously, so if you're searching for value, this could be the perfect plugin for you.


Heads-up! First Win8 Critical Security Updates A'Comin!
Next Tuesday, November 13, will be the first Patch Tuesday since the official Windows 8 release occurred on October 26. Thus, it's entirely fitting that Windows 8 will receive its first-ever "Critical" updates on that day. I puzzled over an article from Lance Whitney at CNET a few minutes ago because it was entitled "Windows 8, RT to get first critical security patches next Tuesday," until it finally dawned on me that he wasn't saying "first security patches" in general, but rather "first security patches with a Critical designation." Because MS explains this as a "vulnerability whose exploitation could allow code execution without user interaction," this is pretty serious stuff indeed.
Three items make the critical grade for immanent Windows 8 security patches.
Of the three items that apply to Windows 8 with critical designations (Bulletins 2, 4, and 5) all are labeled with remote code execution, and at least two of them will require a restart (1 and 5) and 4 may also require a restart as well. It should be interesting to see exactly what these bulletins cover, and how well Windows 8 slips into the regular Patch Tuesday cycle going forward. So far, we've seen two Windows Updates for the Flash Player, an important GA cumulative update (KB2756872), protected content playback (KB2768703), and logo images in All Apps view (KB2751352). But other than the usual Flash folderol there's been nothing designed to fend off potential system takeovers. Maybe next Tuesday will change things?


text:
EEOC Announces $77,500 Settlement in Equal Pay Discrimination Lawsuit
On April 1, 2019, the U.S. Equal Employment Opportunity Commission (EEOC) – the agency that enforces federal laws prohibiting employment discrimination – announced that a manufacturer of diesel engines, Cummins, Inc., will pay $77,500 to settle an EEOC equal pay discrimination lawsuit for allegedly paying a female employee less than a male performing the same work, according to an EEOC press release.
EEOC Equal Pay Discrimination Lawsuit
"Employers should provide men and women in the same workplace with equal pay for equal work," Faye Williams, regional attorney for the EEOC's Memphis District Office, stated in the press release. "Not only is it fair, it's the law. As the fight against unequal pay in the workplace continues, the Commission remains committed to challenging pay disparity until we realize the goal of wage equality."
The EEOC filed the lawsuit to obtain relief for a former female employee who worked for Cummins at its Business Services facility in Nashville, Tennessee. The EEOC charged that Cummins paid her less than a male employee even though they performed the same job duties in violation of The Equal Pay Act (EPA) of 1963 and Title VII of the Civil Rights Act of 1964 which prohibit wage discrimination based on sex.
Along with the monetary relief, Cummins – which denied any liability or wrongdoing in the lawsuit – entered into a two-and-a-half-year consent decree requiring the company to train its employees and management on the requirements of the EPA and Title VII. Cummins also agreed to report complaints of pay discrimination to the EEOC and permit the EEOC to monitor the firm's compliance with the decree.
The announcement from the EEOC about the settlement in the equal pay discrimination lawsuit came one day before Equal Pay Day – the symbolic day dedicated to raising awareness about the gender pay gap in the United States – which was held on April 2, 2019, to symbolize how far into the year women must work to earn what men earned in the previous year. The exact date differs from year to year.
Equal Pay Day was originated by the National Committee on Pay Equity (NCPE) in 1996 as a public awareness event to illustrate the gap between men's and women's wages. Since the latest wage figures are not available until late August or September, the NCPE decided to select a Tuesday in April as Equal Pay Day. For more information about Equal Pay Day, see the NCPE's Equal Pay Day Kit or contact the NCPE.
According to the NCPE, the gender wage gap has narrowed by less than one-half a penny per year in the United States since Congress passed the EPA while statistics from the U.S. Census Bureau revealed that women earned 80 percent of what men earned in 2015. As a result, laws prohibiting employers from asking applicants about salary history will increase in the U.S. as the equal pay movement spreads.
Bans on employers asking about salary history have passed in cities such as Atlanta, Chicago, Cincinnati, Kansas City, Louisville, New Orleans, New York City, Philadelphia, Pittsburgh, and San Francisco. Salary history bans have also passed in the states of California, Connecticut, Delaware, Hawaii, Illinois, Massachusetts, Michigan, New Jersey, New York, Oregon, Pennsylvania, Vermont, and Wisconsin.
"If new pay is based on previous pay, then gender pay gaps are perpetuated. The goal of equal pay laws is to base compensation on the work performed and not rely on previous pay that may reflect gender discrimination," explained Attorney Lester Rosen, the founder and Chief Executive Officer (CEO) of Employment Screening Resources® (ESR) and the author of 'The Safe Hiring Manual.'
"When an employer has a background screening firm perform past employment verifications, it is critical that firm knows which cities, counties, and states prohibit such questions, as well as software that facilitates compliance with equal pay laws, or else that employer could be fined," said Rosen, noting that this trend was chosen by ESR as one of the "ESR Top Ten Background Check Trends" for 2019.
ESR Employment Verifications Comply with Equal Pay Laws
Employment Screening Resources® (ESR) – a leading global background check provider – offers employers flexible and customizable employment verifications that provide the salary history of applicants only if permitted by state and local equal pay laws. To learn more about employment verifications from ESR, visit www.esrcheck.com/Background-Checks/Verifications-References/.
Categories icon 2019, Equal Pay
Tags icon discrimination, EEOC, Equal Pay, pay equity, salary history, SHM 4, wage equity
Pennsylvania Public Utility Commission Releases Report on Uber Driver Background Check Process
March 2019 Jobs Report Reveals U.S. Economy Added 196,000 Jobs in Month


Dr. William J. Mitsch is a Professor of Natural Resources and Environmental Science at The Ohio State University in Columbus, Ohio. He completed his Ph.D. under the ecologist H.T Odum, and has become a leading expert on biogeochemical cycles in wetlands and computer simulation models of wetland ecosystems. Mitsch has been a pioneer in ecological engineering and a tireless advocate for wetland preservation, creation, and restoration.
Mitsch co-authored Wetlands, the most widely used textbook and reference on wetlands in the United States. He has written or edited seven other books and has published more than 150 scholarly research articles. Not only has he broken new ground in wetland theory, but Mitsch has continued to use his knowledge in practical problem-solving projects. He was one of the designers and researchers on the Des Plains River Reconstruction project, and he currently manages his own constructed wetland research site, the Olentangy River Wetland Research Park, located at The Ohio State University.
In 1992, Mitsch organized and chaired the IV International INTECOL Wetlands Conference in Columbus, the largest wetland conference ever held. He serves as President of the Society of Wetland Scientists and is founder and Editor-In-Chief of the journal Ecological Engineering. In the past three years, Mitsch has given approximately 60 invited scholarly presentations and keynote speeches across the globe. He is a frequent advisor to state and federal governments on wetlands and has often served as a consultant on both natural and created wetland projects. Mitsch has presented testimony to the U.S. Congress on Clean Water Act wetland issues and served on the National Academy of Sciences' wetland characterization panel.


India ranks among the top five sovereign debt issuers from the emerging economies after China, said Moody's Investors Service.
India ranks among the top five sovereign debt issuers from the emerging economies after China, said Moody's Investors Service.
"The top five largest sovereign EM (emerging market) debt issuers, as of end-2014, were China (with USD 3.5 trillion total sovereign debt outstanding), India (USD 1.3 trillion), Brazil (USD 1.2 trillion), Mexico (USD 387.5 billion) and Turkey (USD 265.5 billion)," it said in a report.
Compared to debt volumes as of end-2000, China has overtaken India and Brazil as the largest debt issuer in 2014, it said.
EM sovereign debt outstanding has grown almost five times between 2000 and 2014.
The report further said that the vast majority of new issuance by emerging market governments or central banks has been directed to debt denominated in local currencies.
"…while EM foreign currency denominated debt grew one and a half times (from USD 0.9 trillion in 2000 to USD 1.2 trillion in 2014), EM local currency debt grew more than six-fold (from USD 1.4 trillion in 2000 to USD 8.7 trillion in 2014)," it said.
India and Brazil also represented a significant share of total local currency government debt, at 14.7 per cent and 13.3 per cent respectively each holding a larger share individually than the share of LatAm (ex-Brazil) and Asia (ex-China and India).
The report said local currency sovereign debt outstanding has grown dramatically over the 2000-14 period, on average by 14.4 per cent per year and far outpacing the annual average of 2.3 per cent growth rate of foreign currency sovereign debt.
By 2014, 88 per cent of total EM debt was in local currency.
Overall, the report said the deepening of local sovereign bond markets has allowed governments to shift a growing portion of their funding to local currency instruments.
The associated decline of currency (and maturity) mismatches reduces the vulnerability of these countries to economic shocks and increases the effectiveness of monetary and fiscal policy.
This argues for lower crisis susceptibility compared to previous decades and should also contribute to the development of private domestic financial markets, it added.