Video Classification

A Non-Local Operation is a component for capturing long-range dependencies with deep neural networks. It is a generalization of the classical non-local mean operation in computer vision. Intuitively a non-local operation computes the response at a position as a weighted sum of the features at all positions in the input feature maps. The set of positions can be in space, time, or spacetime, implying that these operations are applicable for image, sequence, and video problems. Following the non-local mean operation, a generic non-local operation for deep neural networks is defined as: $$ \mathbb{y}\_{i} = \frac{1}{\mathcal{C}\left(\mathbb{x}\right)}\sum\_{\forall{j}}f\left(\mathbb{x}\_{i}, \mathbb{x}\_{j}\right)g\left(\mathbb{x}\_{j}\right) $$ Here $i$ is the index of an output position (in space, time, or spacetime) whose response is to be computed and $j$ is the index that enumerates all possible positions. x is the input signal (image, sequence, video; often their features) and $y$ is the output signal of the same size as $x$. A pairwise function $f$ computes a scalar (representing relationship such as affinity) between $i$ and all $j$. The unary function $g$ computes a representation of the input signal at the position $j$. The response is normalized by a factor $C\left(x\right)$. The non-local behavior is due to the fact that all positions ($\forall{j}$) are considered in the operation. As a comparison, a convolutional operation sums up the weighted input in a local neighborhood (e.g., $i − 1 \leq j \leq i + 1$ in a 1D case with kernel size 3), and a recurrent operation at time $i$ is often based only on the current and the latest time steps (e.g., $j = i$ or $i − 1$). The non-local operation is also different from a fully-connected (fc) layer. The equation above computes responses based on relationships between different locations, whereas fc uses learned weights. In other words, the relationship between $x\_{j}$ and $x\_{i}$ is not a function of the input data in fc, unlike in nonlocal layers. Furthermore, the formulation in the equation above supports inputs of variable sizes, and maintains the corresponding size in the output. On the contrary, an fc layer requires a fixed-size input/output and loses positional correspondence (e.g., that from $x\_{i}$ to $y\_{i}$ at the position $i$). A non-local operation is a flexible building block and can be easily used together with convolutional/recurrent layers. It can be added into the earlier part of deep neural networks, unlike fc layers that are often used in the end. This allows us to build a richer hierarchy that combines both non-local and local information. In terms of parameterisation, we usually parameterise $g$ as a linear embedding of the form $g\left(x\_{j}\right) = W\_{g}\mathbb{x}\_{j}$ , where $W\_{g}$ is a weight matrix to be learned. This is implemented as, e.g., 1×1 convolution in space or 1×1×1 convolution in spacetime. For $f$ we use an affinity function, a list of which can be found here.

A Non-Local Block is an image block module used in neural networks that wraps a non-local operation. We can define a non-local block as: $$ \mathbb{z}\_{i} = W\_{z}\mathbb{y\_{i}} + \mathbb{x}\_{i} $$ where $y\_{i}$ is the output from the non-local operation and $+ \mathbb{x}\_{i}$ is a residual connection.

Group Normalization is a normalization layer that divides channels into groups and normalizes the features within each group. GN does not exploit the batch dimension, and its computation is independent of batch sizes. In the case where the group size is 1, it is equivalent to Instance Normalization. As motivation for the method, many classical features like SIFT and HOG had group-wise features and involved group-wise normalization. For example, a HOG vector is the outcome of several spatial cells where each cell is represented by a normalized orientation histogram. Formally, Group Normalization is defined as: $$ \mu\_{i} = \frac{1}{m}\sum\_{k\in\mathcal{S}\_{i}}x\_{k} $$ $$ \sigma^{2}\_{i} = \frac{1}{m}\sum\_{k\in\mathcal{S}\_{i}}\left(x\_{k}-\mu\_{i}\right)^{2} $$ $$ \hat{x}\_{i} = \frac{x\_{i} - \mu\_{i}}{\sqrt{\sigma^{2}\_{i}+\epsilon}} $$ Here $x$ is the feature computed by a layer, and $i$ is an index. Formally, a Group Norm layer computes $\mu$ and $\sigma$ in a set $\mathcal{S}\_{i}$ defined as: $\mathcal{S}\_{i} = ${$k \mid k\_{N} = i\_{N} ,\lfloor\frac{k\_{C}}{C/G}\rfloor = \lfloor\frac{I\_{C}}{C/G}\rfloor $}. Here $G$ is the number of groups, which is a pre-defined hyper-parameter ($G = 32$ by default). $C/G$ is the number of channels per group. $\lfloor$ is the floor operation, and the final term means that the indexes $i$ and $k$ are in the same group of channels, assuming each group of channels are stored in a sequential order along the $C$ axis.

TimeSformer is a convolution-free approach to video classification built exclusively on self-attention over space and time. It adapts the standard Transformer architecture to video by enabling spatiotemporal feature learning directly from a sequence of frame-level patches. Specifically, the method adapts the image model [Vision Transformer](https//www.paperswithcode.com/method/vision-transformer) (ViT) to video by extending the self-attention mechanism from the image space to the space-time 3D volume. As in ViT, each patch is linearly mapped into an embedding and augmented with positional information. This makes it possible to interpret the resulting sequence of vector

Embedded Gaussian Affinity is a type of affinity or self-similarity function between two points $\mathbf{x\_{i}}$ and $\mathbf{x\_{j}}$ that uses a Gaussian function in an embedding space: $$ f\left(\mathbf{x\_{i}}, \mathbf{x\_{j}}\right) = e^{\theta\left(\mathbf{x\_{i}}\right)^{T}\phi\left(\mathbf{x\_{j}}\right)} $$ Here $\theta\left(x\_{i}\right) = W\_{θ}x\_{i}$ and $\phi\left(x\_{j}\right) = W\_{φ}x\_{j}$ are two embeddings. Note that the self-attention module used in the original Transformer model is a special case of non-local operations in the embedded Gaussian version. This can be seen from the fact that for a given $i$, $\frac{1}{\mathcal{C}\left(\mathbf{x}\right)}\sum\_{\forall{j}}f\left(\mathbf{x}\_{i}, \mathbf{x}\_{j}\right)g\left(\mathbf{x}\_{j}\right)$ becomes the softmax computation along the dimension $j$. So we have $\mathbf{y} = \text{softmax}\left(\mathbf{x}^{T}W^{T}\_{\theta}W\_{\phi}\mathbf{x}\right)g\left(\mathbf{x}\right)$, which is the self-attention form in the Transformer model. This shows how we can relate this recent self-attention model to the classic computer vision method of non-local means.

GCT first collects global information by computing the l2-norm of each channel. Next, a learnable vector $ \alpha $ is applied to scale the feature. Then a competition mechanism is adopted by channel normalization to interact between channels. Unlike previous methods, GCT first collects global information by computing the $l_{2}$-norm of each channel. Next, a learnable vector $\alpha$ is applied to scale the feature. Then a competition mechanism is adopted by channel normalization to interact between channels. Like other common normalization methods, a learnable scale parameter $\gamma$ and bias $\beta$ are applied to rescale the normalization. However, unlike previous methods, GCT adopts tanh activation to control the attention vector. Finally, it not only multiplies the input by the attention vector but also adds an identity connection. GCT can be written as: \begin{align} s = F_\text{gct}(X, \theta) & = \tanh (\gamma CN(\alpha \text{Norm}(X)) + \beta) \end{align} \begin{align} Y & = s X + X \end{align} where $\alpha$, $\beta$ and $\gamma$ are trainable parameters. $\text{Norm}(\cdot)$ indicates the $L2$-norm of each channel. $CN$ is channel normalization. A GCT block has fewer parameters than an SE block, and as it is lightweight, can be added after each convolutional layer of a CNN.

ResNet-RS is a family of ResNet architectures that are 1.7x faster than EfficientNets on TPUs, while achieving similar accuracies on ImageNet. The authors propose two new scaling strategies: (1) scale model depth in regimes where overfitting can occur (width scaling is preferable otherwise); (2) increase image resolution more slowly than previously recommended. Additional improvements include the use of a cosine learning rate schedule, label smoothing, stochastic depth, RandAugment, decreased weight decay, squeeze-and-excitation and the use of the ResNet-D architecture.

Concatenation Affinity is a type of affinity or self-similarity function between two points $\mathbb{x\_{i}}$ and $\mathbb{x\_{j}}$ that uses a concatenation function: $$ f\left(\mathbb{x\_{i}}, \mathbb{x\_{j}}\right) = \text{ReLU}\left(\mathbb{w}^{T}\_{f}\left[\theta\left(\mathbb{x}\_{i}\right), \phi\left(\mathbb{x}\_{j}\right)\right]\right)$$ Here $\left[·, ·\right]$ denotes concatenation and $\mathbb{w}\_{f}$ is a weight vector that projects the concatenated vector to a scalar.