\section{Evaluation on Small-Scale Datasets}













\section{Comparison with M$^3$L with C-NP as Source Domain}
\label{sec:sota-c-np}
To ensure a comprehensive comparison with ~\cite{M3L}, we present additional experimental results using the new protocol of CUHK03~\cite{CUHK03}, C-NP, as a source domain, which were omitted from the main section due to space constraints. Table \ref{tab:src-tgt-dataset-setup-c-np} summarizes each new experiment, detailing the source domains used, target domain and ID/image counts for each.
\begin{table}[ht]
\centering
    \begin{tabular}{l|l|c|c|c}
        \hline
        Sources & Target & Combined-Src-IDs & Combined-Src-Images & Target-Images \\
        \hline\hline
       
       
       
       
        C-NP+D+MS & M & 2,510 & 56,508 & 19,281 \\
        C-NP+M+MS & D & 2,559 & 52,922 & 19,889 \\
        C-NP+D+M & MS & 2,220 & 36,823 & 93,820 \\
        \hline
    \end{tabular}
    \caption{Details for experiments involving C-NP in Sources.}
    \label{tab:src-tgt-dataset-setup-c-np}
\end{table}

\noindent Table \ref{tab:soa-c-np} compares our DEX{} with~\cite{M3L}. Under this different experimental setting, our method continues to surpass leading state-of-the-art methods by significant margins.

\begin{table}[h]
\centering
\begin{tabular}{c|l|cc}
\hline
\multirow{2}{*}{Sources}   & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{Market-1501} \\ 
\cline{3-4} & 
\multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\
\hline
\multirow{5}{*}{C-NP+D+MS} & 
DualNorm$_{50}$ & \multicolumn{1}{c|}{76.5} & 48.5 \\
& QAConv$_{50}$ & \multicolumn{1}{c|}{68.6} & 39.5 \\
& M$^3$L (ResNet-50) & \multicolumn{1}{c|}{76.5} & 51.1 \\
& M$^3$L (IBN-Net50) & \multicolumn{1}{c|}{78.3} & 52.5 \\ \cline{2-4} & 
DEX (Ours) & \multicolumn{1}{c|}{ \textbf{79.7}  } & \textbf{53.3}  \\
\hline\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{DukeMTMC-reID} \\ 
\cline{3-4} & 
\multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\
\hline
\multirow{5}{*}{C-NP+M+MS} &
DualNorm$_{50}$ & \multicolumn{1}{c|}{66.1} & 48.8 \\
& QAConv$_{50}$ & \multicolumn{1}{c|}{64.9} & 43.4 \\
& M$^3$L (ResNet-50) & \multicolumn{1}{c|}{67.1} & 48.2 \\
& M$^3$L (IBN-Net50) & \multicolumn{1}{c|}{67.2} & 48.8 \\ \cline{2-4} & 
DEX (Ours) & \multicolumn{1}{c|}{ \textbf{72.1} } & \textbf{53.5} \\
\hline\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{MSMT17\_V2} \\
\cline{3-4} & 
\multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\
\hline
\multirow{5}{*}{C-NP+D+M} &
DualNorm$_{50}$ & \multicolumn{1}{c|}{34.4} & 13.5 \\
& QAConv$_{50}$ & \multicolumn{1}{c|}{29.9} & 10.0 \\
& M$^3$L (ResNet-50) & \multicolumn{1}{c|}{32.0} & 13.1 \\
& M$^3$L (IBN-Net50) & \multicolumn{1}{c|}{37.1} & 15.4 \\ \cline{2-4} & 
DEX (Ours) & \multicolumn{1}{c|}{ \textbf{42.7} } & \textbf{17.9} \\ 
\hline
\end{tabular}
\caption{Comparison of our DEX{} against the most recent state-of-the-art DG Person ReID, for the experiments that use CUHK-NP in Sources.}
\label{tab:soa-c-np}
\end{table}

\section{Detailed Differences between DEX{} and ISDA}
\label{sec:diff-datasets-isda-reid}

Our method is inspired by ISDA~\cite{ISDA}, a recent work on deep feature augmentation. Still, it is significantly different as we found it impractical to apply it, originally proposed for image classification tasks, directly to multi-source domain generalization for Person ReID (DG-ReID). In the original formulation, a different covariance matrix is stored and updated for each class corresponding to person identities in ReID. However, in DG-ReID the number of classes grows large when multiple source datasets are merged for training, imposing a strong memory overhead as each matrix takes up $O(n^2)$ space with feature dimension $n=2048$ in our case. In our case, the experiment with the lowest number of training classes is already close to 2,500, making direct application of~\cite{ISDA} infeasible. 

For problems with a large number of classes such as ImageNet~\cite{ImageNet}, ISDA approximated the class-conditional covariance by storing just the matrix diagonals, reducing the per-class memory overhead to $O(n)$ while still reaping the benefits. However, even with this approximation, using a class-conditional approach could not consistently outperform our baseline model. Looking deeper, we believe this is because DG-ReID datasets have far fewer samples per class compared to those used in the original work, making estimation of per-class covariance matrices unstable. Datasets used in~\cite{ISDA} have 500 samples per class in the case of CIFAR-100 and 5000 samples per class in CIFAR-10~\cite{CIFAR}. In ImageNet~\cite{ImageNet}, a majority of the classes have 1300 samples each, with the lowest being 732. In stark contrast, the median samples-per-identity is between 10 and 25 for ReID, \emph{over an order of magnitude smaller}. Table \ref{tab:sup-samples-per-pid} shows a detailed comparison between the dataset statistics of their datasets and our ReID datasets. Such drastically different distributions indicate that class-conditional covariances may not be the most stable solution. 


\begin{table}[ht]
\centering
    \begin{tabular}{l|c|c|c|c}
        \hline
        Dataset(s) & Mean & Median & Min & Max \\
        \hline \hline
        CIFAR-10 & 5000 & 5000 & 5000 & 5000 \\
        CIFAR-100 & 500 & 500 & 500 & 500 \\
        ImageNet~\cite{ImageNet} & 1281.2 & 1300 & 732 & 1300 \\
        \hline \hline
        Market-1501 (M) & 17.2 & 15 & 2 & 72 \\
        DukeMTMC-reID (D) & 23.5 & 20 & 6 & 426 \\
        CUHK03 (C) & 9.6 & 10 & 6 & 10 \\
        MSMT17\_V2 (MS) & 30.8 & 25 & 6 & 392 \\
        \hline \hline
        C+D+MS & 20.0 & 13 & 6 & 426 \\
        C+D+M  & 15.1 & 10 & 2 & 426 \\
        C+M+MS & 18.6 & 10 & 2 & 392 \\
        D+M+MS & 24.9 & 20 & 2 & 426 \\
        \hline \hline
    \end{tabular}
    \caption{Comparison of samples per class between the datasets used in previous work on deep feature augmentation~\cite{ISDA} and those from Person ReID. ReID datasets have far fewer samples per class, making estimation of class-conditional covariance matrices unstable.}
    \label{tab:sup-samples-per-pid}
\end{table}

\section{Model Training Details}
\label{sec:baseline-training-details}

In this section we describe the full details of our training method.

\subsection{Backbone model} We use an ImageNet~\cite{ImageNet} pre-trained ResNet-50~\cite{ResNet} with instance normalization applied on the first three out of four Bottleneck blocks, as prescribed in DualNorm~\cite{DualNorm}. The final layer stride is reduced to 1 (originally 2). A batch normalization layer with no bias is applied to the final layer features~\cite{DualNorm}.

\subsection{Loss functions} 
For regularization, the softmax loss $\mathcal{L}_{soft}$ applies label smoothing with $\epsilon=0.1$.
The triplet loss is defined as such: \[\mathcal{L}_{tri} = \sum_{a,p,n} [\delta(\mathbf{x_a},\mathbf{x_n}) - \delta(\mathbf{x_a},\mathbf{x_p}) + \gamma]_{+} \]where $[\cdot]_{+} = max(\cdot, 0)$, ($\mathbf{x_a},\mathbf{x_p},\mathbf{x_n}$) refer to the triplets (anchor, positive, negative) that are found in the batch, $\gamma=0.3$ is the triplet margin, and $\delta$ is a metric; in our case, we use Euclidean distance. Our batch sampling scheme follows~\cite{StrongBaseline}, selecting $k=4$ samples per PID in the batch to ensure sufficient triplets for training. The center loss is defined as such: \[ \mathcal{L}_{cen} = \sum_{i=1}^{m} \lVert \mathbf{x_i} - \mathbf{c_{y_i}} \rVert^2 \]where $i$ indexes a batch size of $m$, $y_i$ is the class label for $x_i$ and $c$ are the class centroids, updated dynamically during training. To recap, the overall loss function for training a baseline model without DEX{} is: \[ \mathcal{L}_{base} = \beta_{soft} \mathcal{L}_{soft} + \beta_{tri} \mathcal{L}_{tri} + \beta_{cen} \mathcal{L}_{cen} \]with $\beta_{soft}=1,\beta_{tri}=1,\beta_{cen}=5\times10^{-4}$. Applying DEX{} or DEXLite{}, the overall loss then changes to: \[\mathcal{L}_{overall}(t) = \mathcal{L}_{DEX{}/DEXLite{}}(\lambda_{t}) + \beta_{tri} \mathcal{L}_{tri} + \beta_{cen} \mathcal{L}_{cen}\]with the strength of augmentation tempered by epoch $t$ as described in the main paper.

\subsection{Input pre-processing}

We resized the input to [384,128], pad it 10 pixels around with zeros and crop out [384,128]. We then apply a horizontal flip to the image with probability $p=0.5$ and random-erasing (RE) augmentation with a probability $p=0.1$.

\subsection{Other training details} 
We train for 60 epochs ($T=60$) with a batch size of 32 using the Adam optimizer, linearly warming up the learning rate $\eta$ from 0 to $1.75 \times 10^{-4}$ in 10 epochs. Afterwards, $\eta$ is reduced by a factor of 0.1 at epochs 30 and 55.


\section{Introduction}
\label{sec:intro}


Person Re-identification (Person ReID) has achieved impressive performance on academic benchmarks in recent years. However, generalization issues prevent its transition into the applied world. For example, a model trained on one Person ReID domain using standard techniques can achieve high accuracy when independently tested within the same domain, but its performance degrades drastically when tested on a unseen domain. This reveals a lack of generalization ability in single-dataset supervised models and suggests that the features learned by these models over-fit the training domain instead of capturing the general features relevant for person discrimination. In recent years, much of Person ReID research has focused on unsupervised domain adaptation (DA)~\cite{MMFA,TJ-AIDL,UMDL,SPGAN}, which uses unlabeled data collected from the target domain to alleviate the domain over-fitting problem. However, in many real-world applications, access to the data from the target domain beforehand may not be a valid assumption to make. Therefore, domain generalization (DG) is a more practical strategy for that problem. DG methods leverage the different distributions of multiple datasets to reduce domain bias.

Current DG Person ReID methods involve complex frameworks such as meta-learning, hyper-networks and memory banks~\cite{DIMN,QAConv,M3L} supported by custom loss functions and normalizations. In this paper, we tackle the DG problem of Person ReID from a novel perspective using deep feature augmentation. We propose \textbf{D}omain \textbf{E}mbedding E\textbf{x}pansion (DEX{}), a deep feature augmentation module that leverages person and domain labels to fill the domain gap between deep features during training. Many Generative Adversarial Network (GAN)~\cite{Goodfellow2014GenerativeNets} based methods also transfer style information from one domain to another while preserving person identity features. However, such methods are computationally expensive and require a  nontrivial GAN-training stage. Our proposed DEX{} implicitly projects extracted deep features across domain manifolds during the training process, as shown in Figure \ref{fig:overall-method}. Applying DEX{} on our baseline (DualNorm~\cite{DualNorm} + BagTricks~\cite{StrongBaseline} over a ResNet-50~\cite{ResNet} backbone) allows us to outperform state-of-the-art methods on all large-scale benchmarks by a wide margin. Integrating DEX{} on other popular Person ReID architectures such as Multi-Granularity Network (MGN)~\cite{MGN} and Part-Based Convolutional Baseline (PCB)~\cite{PCB}, demonstrates consistent improvement in model generalization. When utilizing multiple Person ReID datasets for training, the increase in unique person-identities (PIDs) could lead to a huge demand for GPU memory. We also developed a memory-light version of DEX{} (DEXLite{}) that applies negative sampling to reduce computation, memory consumption, and training time. DEXLite{} supports datasets with large numbers of PIDs, larger batch sizes, and multi-branch model architectures.

To summarize, our contributions are as follows:

\begin{itemize} [noitemsep,nolistsep]
  \item We propose DEX{}, a deep feature data augmentation method tailored for the multi-domain generalization Person ReID problem that leverages domain labels to implicitly project deep features over domain manifolds.
  \item With DEX{} and Instance Normalization (IN), a simple ResNet50 backbone can outperform state-of-the-art performance on all large scale Person ReID DG benchmarks (Market-1501, DukeMTMC-reID, CUHK03 and MSMT17) by a wide margin. 
  \item For memory-limited machines, we developed DEXLite{}, a memory-light version of DEX{}, that uses negative sampling to reduce memory use during training, enabling the use of this technique on a broader range of problems. We apply DEXLite{} on two multi-branch architectures, MGN and PCB, to demonstrate significant improvements. 
  \item DEXLite{} also outperforms state-of-the-art methods in most of the small-dataset DG benchmark metrics and closely matches the top performers for the remaining metrics.
  \item Our proposed method is straightforward and does not require complex frameworks or specialized neural network architectures.
\end{itemize}



\section{Related Work}
\label{sec:related-work}

\noindent \textbf{Person Re-identification.} 
Deep learning based Person ReID approaches developed in recent years, such as PCB~\cite{PCB}, BagTricks~\cite{StrongBaseline}, and MGN \cite{MGN} have achieved impressive accuracy in Person ReID. These methods are usually trained and evaluated within the same dataset. However, due to the difficulty of data collection and limited numbers of cameras and pedestrians, existing datasets suffer from limited variability in location, weather, pedestrian clothing, illumination, and camera color settings. Such limitations induce a strong domain bias during training and significantly degrade model performance when testing on other domains. Hence, many domain adaptation (DA) methods such as UMDL~\cite{UMDL}, SPGAN~\cite{SPGAN}, TJ-AIDL~\cite{TJ-AIDL}, MMFA~\cite{MMFA} were proposed to bridge the gap between domains for the Person ReID problem. DA methods utilize unlabeled data from the target domain to generate pseudo-labels or transfer the target domain image style to the source domain. Although many DA approaches yield good performance improvements when dealing with the cross-domain problem, these methods still require a large amount of data from the target domain, hence limiting their application to real-world Person ReID problems. Domain generalization (DG) methods, on the other hand, operate under a more challenging scenario, assuming no access to any target domain data. The common objective among DG methods is to learn a general universal feature representation that is robust to domain shift. DualNorm \cite{DualNorm} first introduced instance normalization (IN) in the early stages of the network to normalize the style and content variations of the datasets. On the other hand, MMFA-AAE~\cite{MMFA-AAE} used a domain adversarial learning approach to remove domain-specific features. Latest DG methods such as DIMN~\cite{DIMN}, QAConv~\cite{QAConv} and M$^3$L~\cite{M3L} used hyper-networks or meta-learning coupled with a memory bank strategy. These meta-learning approaches require complicated training procedures, which makes model optimization difficult. Different from all existing methods, DEX{} addresses the domain generalization issue from a novel deep feature domain augmentation perspective. Our method uses widely available tools, a ResNet-50 backbone, and does not require complex frameworks or training procedures.

\noindent\textbf{Augmentation.} Most of the proposed augmentation solutions in Person ReID use GANs ~\cite{Goodfellow2014GenerativeNets} to transfer target domain image styles to source domain images. LSRO~\cite{DukeMTMC-reID} and DG-Net~\cite{DG-Net} first used GANs as an augmentation for better representation learning in Person ReID. SPGAN~\cite{SPGAN} and PTGAN~\cite{MSMT17} then expanded this to cross dataset scenarios. However, these GAN-based approaches mainly transfer image-style differences across different domains without considering other semantic differences such as clothing styles, weather, etc. Furthermore, training such generative models is difficult and computationally expensive, with the final outputs exhibiting noticeable artifacts. Our method focuses on a new augmentation direction for Person ReID, which directly performs semantic transformations in the deep feature space. Many works~\cite{DFI,DeepAugment,ISDA} discovered that it was possible to meaningfully alter the semantics of image samples (\emph{e.g}\bmvaOneDot{} changing the color of an object) by perturbing their corresponding deep features in specific directions. DeepAugment~\cite{DeepAugment} proposed to pass images through a pretrained image-to-image model while altering the features via stochastic operations in the model, producing multiple diverse yet semantically consistent images for training. However, training good image generation models is challenging and time-consuming, and the increase in data leads to increased memory use and training time. ISDA~\cite{ISDA} proposed to project deep features by sampling semantic directions from class-conditional covariance matrices, implicitly performing the projections and reducing memory footprint by optimizing a surrogate robust upper-bound loss. Our proposed DEX{} is tailored for the multi-domain generalization Person ReID problem. It expands feature samples in meaningful domain-semantic directions while preserving person identity information.

\section{Method}
\label{sec:method}
\begin{figure}[t]
\includegraphics[width=12.6cm]{images/DEX_Architecture.pdf}
\caption{Our proposed solution illustrated. Our baseline is enhanced by reducing the probability of RE and applying IN at early layers of a deep feature extractor. In feature space, our deep augmentation method DEX{} improves domain manifold coverage by implicitly projecting the feature points in directions of the domain distribution. Best viewed in color. }
\label{fig:overall-method}
\end{figure}
\vspace{-1em}
\subsection{Domain Embedding Expansion (DEX{})} 

To improve feature representation learning and close domain gaps, we propose DEX{}, a deep feature augmentation technique specially adapted for multi-domain generalization problems. Building on previous deep feature augmentation methods~\cite{DFI,DeepAugment,ISDA}, we perturb deep features generated by the model as a form of augmentation. Each deep feature is projected along directions sampled from a zero-mean normal distribution with covariance matrix estimated from the feature's domain; this is so that features from different domains are projected in directions that correspond to semantic transformations meaningful to their domain. The covariance matrices are estimated online during training. Similar to ISDA~\cite{ISDA}, the data samples are not explicitly perturbed. Instead, we optimize a proxy loss function that upper-bounds the expected cross-entropy loss of perturbed data samples. Figure \ref{fig:our-method} presents an overview of our method.

\noindent\textbf{Formulation} DEX{} is a modification to the classification branch of the model. The regular softmax loss $\mathcal{L}_{soft}$ is computed from the feature output of the model and the weights of its fully connected layer as such: 
\begin{equation} 
\mathcal{L}_{soft}=\frac{1}{N} \sum_{i=1}^{N} -\log \left( \frac{\exp(\mathbf{w}_{y_i}^{\intercal} \mathbf{a_i} )}{\sum_{j=1}^{C} \exp(\mathbf{w}_{j}^{\intercal} \mathbf{a_i})} \right),
\label{eqn:softmax}
\end{equation}
where $N$ is the batch size indexed by $i$, $C$ is the number of unique PIDs indexed by $j$, $\mathbf{a_i}$ are deep features output by the model and $\mathbf{w}$ are weight vectors of the model's fully connected layer; biases are omitted in our classifier layer. The design rationale behind DEX{} is derived from \cite{ISDA}. First we consider the \emph{expected} softmax loss if the deep features were projected along domain-conditional covariance directions $\Sigma_{d_i}$: 
\begin{equation} 
\begin{split}
\mathcal{L}_{\infty} & = \frac{1}{N} \sum_{i=1}^{N} \mathbb{E}_{ \mathbf{\Tilde{a}_i}  } \left[ -\log \left( \frac{\exp(\mathbf{w}_{y_i}^{\intercal} \mathbf{ \Tilde{a}_i } )}{\sum_{j=1}^{C} \exp(\mathbf{w}_{j}^{\intercal} \mathbf{ \Tilde{a}_i  })} \right) \right] \\
& = \frac{1}{N} \sum_{i=1}^{N} \mathbb{E}_{ \mathbf{\Tilde{a}_i}  } \left[ \log \left(  
\sum_{j=1}^{C} \exp( (\mathbf{w}_{j}^{\intercal} - \mathbf{w}_{y_i}^{\intercal}) \mathbf{ \Tilde{a}_i  }) \right) \right],
\end{split}
\label{eqn:loss-infinity}
\end{equation}
\noindent where $ \mathbf{ \Tilde{a}_i } \sim \mathcal{N}( \mathbf{a_i} , \lambda \Sigma_{d_i}) $ are the augmented features assumed to be normally distributed around $\mathbf{a_i}$ with domain-conditional covariance $\Sigma_{d_i}$, and $\lambda \ge 0$ controls the strength of the augmentation. Applying Jensen's Inequality, $\mathbb{E}[\log (X)] \le \log (\mathbb{E} [X])$, we can move the $\log$ out of the expectation to get:

\begin{equation} 
\mathcal{L}_{\infty} \le \frac{1}{N} \sum_{i=1}^{N} \log \left( \sum_{j=1}^{C} \mathbb{E}_{ \mathbf{\Tilde{a}_i}  } [ \exp( (\mathbf{w}_{j}^{\intercal} - \mathbf{w}_{y_i}^{\intercal}) \mathbf{ \Tilde{a}_i  })  ] \right)
\label{eqn:loss-jensen}
\end{equation}

We apply the moment generating function $\mathbb{E}[\exp(tX)]=\exp(t \mu + \frac{1}{2} \sigma^2 t^2)$, $X \sim \mathcal{N}(\mu,\sigma^2)$, substituting $t$ with $(\mathbf{w}_{j}^{\intercal} - \mathbf{w}_{y_i}^{\intercal})$ and $X \sim \mathcal{N}(\mu, \sigma^2)$ with $\mathbf{ \Tilde{a}_i } \sim \mathcal{N}( \mathbf{a_i} , \lambda \Sigma_{d_i})$, to derive our loss: 
\begin{equation}
\mathcal{L}_{DEX{}}(\lambda) =\frac{1}{N} \sum_{i=1}^{N} -\log \left( \frac{\exp(\mathbf{w}_{y_i}^{\intercal} \mathbf{a_i} )}{\sum\limits_{j=1}^{C} \exp(\mathbf{w}_{j}^{\intercal} \mathbf{a_i} + \frac{\lambda}{2}(\mathbf{w}_{j}^{\intercal}-\mathbf{w}_{y_i}^{\intercal})\Sigma_{d_i} (\mathbf{w}_{j}-\mathbf{w}_{y_i}) )} \right) \ge \mathcal{L}_{\infty}
\label{eqn:isda-dom}
\end{equation}
Thus, $\mathcal{L}_{DEX{}}$ upper bounds the \emph{expected} softmax loss of projecting deep features $\mathbf{ a_i }$ over directions encoded in $\Sigma_{d_i}$, and we can directly optimize $\mathcal{L}_{DEX{}}$ to reap the benefits of augmentation while avoiding the extra computation of explicitly projecting features.

Different from \cite{ISDA} that performs implicit augmentation in class-semantic directions, DEX{} explores meaningful \emph{domain-semantic directions} in the deep manifold space for different Person ReID datasets. ISDA was proposed in the context of image classification problems and is impractical for multi-domain Person ReID problems where thousands of per-class covariance matrices collectively impose a prohibitive memory overhead. Approximations have been proposed by \cite{ISDA} to overcome this memory issue, but even so, our experiments show that applying ISDA naively fails to improve the baseline for all benchmarks. Our analysis reveals that Person ReID datasets have very few samples-per-class (10-25 on average) which makes covariance estimation unreliable, compared to the datasets used in ISDA which have 500-5,000 on average. DEX{} is a superior design for two reasons. Firstly, there are much fewer domains than classes so we need not rely on approximations to reduce memory use. Secondly, since the number of samples-per-domain is very large (numbering in the 10,000s), the domain-conditional covariance estimates are stable. The wide domain gaps observed in DG Person ReID show that \emph{deep features invariably encode domain semantics}; consequently, their estimated domain-conditional covariance matrices would contain meaningful domain-semantic directions. Experimentally, DEX{} significantly improves performance for every benchmark. Ablation studies comparing ISDA with our method are presented in Section \ref{sec:experiments}, and a detailed study of the differences between Person ReID datasets and those studied in ISDA are presented in Supplemental Material.

\subsection{Domain Embedding Expansion Lite (DEXLite{})}
DEX{} requires additional memory during training. During each back-propagation step, intermediate tensors require {\em extra} space on the order of $O(B_{CE} (Df^2 + CN))$. $B_{CE}$ is the number of cross-entropy loss branches that apply DEX{}, $D$ is the number of domains, $f$ is the feature dimension, $C$ is the number of PIDs in the training set with batch size $N$. By using approximations~\cite{ISDA}, we can reduce the complexity to $O(B_{CE} (Df + CN))$. However, there are many reasonable scenarios where $B_{CE}$ and $C$ can dominate the complexity. If there are multiple classification loss branches as in the case of PCB~\cite{PCB} and MGN~\cite{MGN}, or if the number of PIDs explodes as a result of merging more source domains, memory overhead grows infeasible. For these use cases, we developed a lightweight version of DEX{} (DEXLite{}) that applies negative sampling to alleviate this issue. Negative sampling is most popularly used in classification problems with a large number of classes, most notably in training language models to speed up softmax loss computation over a large vocabulary~\cite{Word2Vec}. Computing the full denominator of Equation \ref{eqn:isda-dom} is memory intensive and wasteful since most classes are negatives; in our sampling strategy, a batch size of $B$ only has $\frac{B}{4}$ unique identities, meaning that if we train on a dataset with 10,000 PIDs, a batch size of 32 contains 8 unique positive IDs that account for only 0.08\% of all identities. We propose to sample only a subset of negatives to reduce the total number of classes considered during DEX{} augmentation. The loss function of Equation \ref{eqn:isda-dom} then changes to:
\begin{equation}
\mathcal{L}_{DEXLite{}}(\lambda)=\frac{1}{N} \sum_{i=1}^{N} -\log \left( \frac{\exp(\mathbf{w}_{y_i}^{\intercal} \mathbf{a_i} )}{\sum_{j \in P_s} \exp(\mathbf{w}_{j}^{\intercal} \mathbf{a_i} + \frac{\lambda}{2}(\mathbf{w}_{j}^{\intercal}-\mathbf{w}_{y_i}^{\intercal})\Sigma_{d_i} (\mathbf{w}_{j}-\mathbf{w}_{y_i}) )} \right),
\label{eqn:isda-dom-lite-full}
\end{equation}
where $P_s$ is the set of sampled PIDs, including positives; the space complexity is reduced to $O(B_{CE} (Df + |P_{s}|N))$, with $|P_{s}| \ll C$. The development of DEXLite{} enables us to apply this augmentation onto a wider range of models and datasets with many PIDs. As an added bonus, it also speeds up training. To demonstrate its capability, we implement DEXLite{} on MGN and PCB and report significant improvements in Section \ref{sec:experiments}.
\begin{figure}[t]
\centering
\includegraphics[width=12.4cm]{images/DEX_DEXLite.pdf}
\caption{DEX{}: (a) This illustrates how DEX{} is applied to a single classifier branch; (b) Given a model with multiple classifier branches, such as PCB shown above, we store and update a separate set of covariance matrices for each branch and also compute a per-branch DEXLite{} loss. For illustration only, we reduced the PCB network to 3 stripes. }
\label{fig:our-method}
\end{figure}

\subsection{Overall Loss Function}
Our proposed method is based on simple ResNet-50 backbone and trained with three losses: softmax loss over PIDs $\mathcal{L}_{soft}$, triplet loss $\mathcal{L}_{tri}$~\cite{TriNet} and center loss $\mathcal{L}_{cen}$~\cite{Wen2016ARecognition}. $\mathcal{L}_{soft}$ is defined in Equation \ref{eqn:softmax} and definitions of $\mathcal{L}_{tri}$ and $\mathcal{L}_{cen}$ are provided in Supplemental Material. We train the baseline with combined loss $\mathcal{L}_{base}$ with $\beta_{soft}=1.0$, $\beta_{tri}=1.0$, and $\beta_{cen}=5\times10^{-4}$:

\begin{equation}
\mathcal{L}_{base} = \beta_{soft} \mathcal{L}_{soft} + \beta_{tri} \mathcal{L}_{tri} + \beta_{cen} \mathcal{L}_{cen}
\end{equation}

The overall loss $\mathcal{L}_{overall}(t)$ is parameterized by current epoch $t$ which controls the strength of the implicit augmentation. $\mathcal{L}_{DEX{}}$ and $\mathcal{L}_{DEXLite{}}$ are defined in Equation \ref{eqn:isda-dom} and Equation \ref{eqn:isda-dom-lite-full}. At epoch $t$, $\lambda_{t}=\frac{t-1}{T-1}\lambda$ with $\lambda=7.5$; we gradually increase $\lambda_{t}$ to pay more attention to later model features as they become more informative over time. For baseline and DEX{} we train for 60 epochs ($T=60$) with a batch size of 32 using the Adam~\cite{Kingma2015Adam:Optimization} optimizer with a learning rate schedule similar to ~\cite{StrongBaseline}. Full details are available in Supplemental Material.
\begin{equation}
\mathcal{L}_{overall}(t) = \mathcal{L}_{DEX{}/DEXLite{}}(\lambda_{t}) + \beta_{tri} \mathcal{L}_{tri} + \beta_{cen} \mathcal{L}_{cen}
\end{equation}

\section{Experiments}
\label{sec:experiments}
\subsection{Datasets and Settings}
We model our experiments after the most recent state-of-the-art method M$^3$L \cite{M3L} in DG Person ReID in four large-scale benchmarks: Market-1501 \cite{Market-1501}, DukeMTMC-reID \cite{DukeMTMC-reID}, CUHK03 \cite{CUHK03} (or its new partition CUHK03-NP \cite{Re-ranking}) and MSMT17\_V2 \cite{MSMT17}. Table \ref{tab:datasets} breaks down the number of IDs and images in each of the training, query and gallery splits for each dataset. For simplicity and clarity, we denote Market-1501, MSMT17, DukeMTMC-reID, CUHK03, and CUHK03-NP as M, MS, D, C, and C-NP.
\begin{table}[h]
\centering
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{l|c|c|c|c|c|c|c}
\hline
Dataset       & Abbreviation & Train-IDs & Train-Images & Query-IDs & Query-Images & Gallery-IDs & Gallery-Images \\ \hline
Market-1501~\cite{Market-1501}   & M            & 751       & 12,936       & 750       & 3,368        & 750         & 15,913         \\
MSMT17\_V2~\cite{MSMT17}    & MS           & 1,041     & 32,621       & 3,060     & 11,659       & 3,060       & 82,161         \\
DukeMTMC-reID~\cite{DukeMTMC-reID} & D            & 702       & 16,522       & 702       & 2,228        & 1,110       & 17,661         \\
CUHK03-NP~\cite{Re-ranking}     & C-NP         & 767       & 7,365        & 700       & 1,400        & 700         & 5,332          \\
CUHK03~\cite{CUHK03}        & C            & 1,367     & 26,263       & -         & -            & -           & -              \\ \hline
\end{tabular}
\end{adjustbox}
\caption{Dataset details. For testing we always use the query/gallery split of C-NP. We follow ~\cite{M3L} to select either C or C-NP as source domain. C is never used for testing.}
\label{tab:datasets}
\end{table}
\vspace{-1em}



\subsection{Comparison with State-of-the-art Methods under New Evaluation}
Following the new evaluation methodology proposed in \cite{M3L}, we use the detected test subset of the CUHK03 new protocol, CUHK-NP (detected), for testing and CUHK03 as one of the source domains for training. The training splits of any three datasets are combined into a training set and the query/gallery split of the remaining dataset is used for testing.

\begin{table}[h]
\centering
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{c|l|c|c|c|l|cc}
\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c|}{Market-1501} & \multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{DukeMTMC-reID} \\ 
\cline{3-4} \cline{7-8} & 
\multicolumn{1}{c|}{} & Rank-1 & mAP & & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\ 
\hline
\multirow{5}{*}{C+D+MS}  & 
DualNorm$_{50}$ & \underline{78.9} & \underline{52.3} & 
\multirow{5}{*}{C+M+MS}  & 
DualNorm$_{50}$ & \multicolumn{1}{c|}{68.5} & \underline{51.7} \\
& QAConv$_{50}$ & 65.7 & 35.6 & & 
QAConv$_{50}$ & \multicolumn{1}{c|}{66.1} & 47.1   \\
& M$^3$L (ResNet-50) & 74.5 & 48.1 & & 
M$^3$L (ResNet-50) & \multicolumn{1}{c|}{ \underline{69.4} } & 50.5   \\
& M$^3$L (IBN-Net50) & 75.9 & 50.2 & & 
M$^3$L (IBN-Net50) & \multicolumn{1}{c|}{69.2} & 51.1   \\ \cline{2-4} \cline{6-8} 
& DEX (Ours) & \textbf{81.5} & \textbf{55.2} & & 
DEX (Ours) & \multicolumn{1}{c|}{\textbf{73.7}} & \textbf{55.0}   \\ 
\hline\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c|}{MSMT17\_V2}  & \multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{CUHK-NP}       \\ 
\cline{3-4} \cline{7-8} & 
\multicolumn{1}{c|}{} & Rank-1 & mAP & & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\ 
\hline
\multirow{5}{*}{C+D+M} & 
DualNorm$_{50}$ & \underline{37.9} & \underline{15.4} & 
\multirow{5}{*}{D+M+MS} & 
DualNorm$_{50}$ & \multicolumn{1}{c|}{28.0} & 27.6 \\
& QAConv$_{50}$ & 24.3 & 7.5 & & 
QAConv$_{50}$ & \multicolumn{1}{c|}{23.5} & 21.0 \\
& M$^3$L (ResNet-50) & 33.0 & 12.9 & & 
M$^3$L (ResNet-50) & \multicolumn{1}{c|}{30.7} & 29.9 \\
& M$^3$L (IBN-Net50) & 36.9 & 14.7 & & 
M$^3$L (IBN-Net50) & \multicolumn{1}{c|}{ \underline{33.1} } & \underline{32.1} \\ \cline{2-4} \cline{6-8} 
& DEX (Ours) & \textbf{43.5} & \textbf{18.7} & & 
DEX (Ours) & \multicolumn{1}{c|}{ \textbf{36.7} } & \textbf{33.8} \\ 
\hline
\end{tabular}
    \end{adjustbox}
\caption{Comparison with state-of-the-art for DG Person ReID. Bold numbers denote highest scores, while underlined numbers denote second-highest. With DEX{} augmentation, our model surpasses the state-of-the-art in all benchmarks.}
\label{tab:soa}
\end{table}
Table \ref{tab:soa} compares our proposed solution \textbf{DEX{}} against several recent state-of-the-art (SOTA) methods such as DualNorm~\cite{DualNorm}, QAConv~\cite{QAConv} and M$^3$L~\cite{M3L}. All experiments are evaluated on the new large scale DG Person ReID benchmarks. For clarity of presentation and alignment with subsequent ablation studies, extra experiments using CUHK-NP as one of the source domains (which were added later in \cite{M3L}) are presented in Supplemental Material. Nevertheless, our proposed solution surpasses the most recent state-of-the-art method~\cite{M3L} in \emph{all} experimental settings by a significant margin.

\subsection{Comparison with State-of-the-art Methods under Old Evaluation}

While the preceding sections focused on new evaluation benchmarks set by M$^3$L \cite{M3L}, we appreciate that much of previous work on DG Person ReID based their evaluations on the old small-scale datasets VIPeR~\cite{VIPeR}, PRID~\cite{PRID}, QMUL-GRID~\cite{GRID}, and i-LIDS~\cite{i-LIDS}. For completeness, we present our evaluation of DEX{} on these small-scale benchmarks.  Table \ref{tab:old-eval-sota} compares our DEX{} under this small-dataset evaluation scheme against other current state-of-the-art DG Person ReID methods. Following standard evaluation methodology, we trained on multiple large-scale benchmark datasets CUHK02~\cite{CUHK02}, CUHK03~\cite{CUHK03}, CUHK-SYSU~\cite{CUHK-SYSU}, Market-1501~\cite{Market-1501} and DukeMTMC-reID~\cite{DukeMTMC-reID} and compared against other state-of-the-art methods trained under the same setting. Combining all source datasets resulted in a total of 121,765 images with 18,530 unique PIDs. Because the large number of PIDs takes up a significant GPU memory overhead for DEX{}, we trained our model using DEXLite{} instead, sampling 2,000 PIDs to reduce memory use and speed up training.

\begin{table}[ht]
\centering
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{l|cccc|cccc|cccc|cccc}
\hline
\multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{4}{c|}{VIPeR (V)} & \multicolumn{4}{c|}{PRID (P)} & \multicolumn{4}{c|}{GRID (G)} & \multicolumn{4}{c}{i-LIDS (L)} \\ \cline{2-17} 
\multicolumn{1}{c|}{} & R-1    & R-5   & R-10  & mAP   & R-1   & R-5   & R-10  & mAP   & R-1   & R-5   & R-10  & mAP   & R-1    & R-5   & R-10  & mAP   \\ \hline \hline
AugMining~\cite{AugMining} & 49.8   & \underline{70.8}  & 77.0  & - & 34.3  & 56.2  & 65.7  & -     & 46.6  & \underline{67.5}  & \underline{76.1}  & - & 76.3 & \underline{93.0}  & \underline{95.3}  & - \\
DDAN~\cite{DDAN} & 56.5   & 65.6  & 76.3  & 60.8  & 62.9  & 74.2  & 85.3  & 67.5  & 46.2  & 55.4  & 68.0  & 50.9  & 78.0 & 85.7  & 93.2  & 81.2  \\
DIMN~\cite{DIMN} & 51.2 & 70.2  & 76.0  & 60.1  & 39.2  & 67.0  & 76.7 & 52.0 & 29.3  & 53.3  & 65.8  & 41.1  & 70.2 & 89.7  & 94.5  & 78.4  \\
DIR-ReID~\cite{DIR-ReID} & 58.3 & 66.9 & \underline{77.3}  & 62.9  & \textbf{71.1}  & \underline{82.4}  & \underline{88.6}  & \underline{75.6}  & 47.8  & 51.1  & 70.5  & \underline{52.1}  & 74.4   & 83.1  & 90.2  & 78.6  \\
DualNorm$_{resnet}$~\cite{DualNorm} & 59.4   & -  & -  & -  & 69.6  & -  & -  & -  & 43.7  & -  & -  & - & 78.2 & -  & -  & -  \\
MMFA-AAE~\cite{MMFA-AAE} & 58.4   & -  & -  & -  & 57.2  & -  & -  & -  & 47.4  & -  & -  & - & 84.8 & -  & -  & -  \\
RaMoE~\cite{RaMoE} & 56.6   & -  & -  & \underline{64.6}  & 57.7  & -  & -  & 67.3  & 46.8  & -  & -  & 54.2 & \underline{85.0} & -  & -  & \underline{90.2}  \\
SNR~\cite{SNR} & 52.9   & -  & -  & 61.3  & 52.1  & -  & -  & 66.5  & 40.2  & -  & -  & 47.7 & 84.1 & -  & -  & 89.9  \\
BCaR~\cite{BCaR} & \textbf{65.8} & -  & -  & -  & 70.2  & -  & -  & -  & \underline{52.8}  & -  & -  & - & 81.3 & -  & -  & -  \\
\textbf{DEXLite{} (Ours)} & \underline{65.5} & \textbf{79.2} & \textbf{83.6} & \textbf{72.0} & \underline{71.0} & \textbf{87.8}  & \textbf{92.5}  & \textbf{78.5} & \textbf{53.3} & \textbf{69.4} & \textbf{79.0} & \textbf{61.7} & \textbf{86.3} & \textbf{95.2} & \textbf{97.3} & \textbf{90.7} \\ \hline
\end{tabular}
\end{adjustbox}
\caption{Evaluation on small-scale benchmarks VIPeR, GRID, PRID and i-LIDS.}
\label{tab:old-eval-sota}
\end{table}

DEXLite{} demonstrates good all-round performance, surpassing the state-of-the-art methods in GRID and i-LIDS for all measures and coming in first for Rank-5, Rank-10 and mAP for all benchmarks. For VIPeR and PRID, our method is second place for Rank-1, closely matching the top performers. It is interesting to note that our Rank-5, Rank-10 and mAP scores surpass other methods by a significant margin even without re-ranking. This indicates that application of DEX{} improves feature generalization such that \textbf{all positives} in the gallery obtain a better ranking, and attests to the effectiveness of DEX{} as a plug-and-play method.

\subsection{Ablation Study on the Effects of each Technique}
Table \ref{tab:ablation-baseline} studies the effects of instance normalization (IN), reducing probability of random erasing (RE), ISDA~\cite{ISDA}, and DEX{} to the BagTricks~\cite{StrongBaseline} baseline. Adding IN yields the most significant benefit. Reducing the probability of RE or applying DEX{} also yield significant generalization benefits. Combined with IN, we tested two configurations of RE, in the first removing the augmentation entirely (NoRE), and in the other reducing the probability of applying RE on a sample from 0.5 to 0.1 (RE(0.1)). A small probability of RE seems to improve model generalization slightly. Using just IN and RE(0.1) can yield very competitive performance in all benchmarks except for CUHK-NP. Adding ISDA does not always improve the baseline. With DEX{}, performance gains are more consistent and are especially significant in the case of CUHK-NP with a \textbf{7.7\%} improvement in Rank-1 and \textbf{5\%} increase in mAP that outperforms the current state-of-the-art by a large margin.
\begin{table}[h]
\centering
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{c|l|c|c|c|l|cc}
\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c|}{Market-1501} & \multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{DukeMTMC-reID} \\ \cline{3-4} \cline{7-8} & 
\multicolumn{1}{c|}{} & Rank-1 & mAP & & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\ 
\hline
\multirow{8}{*}{C+D+MS}  & 
BagTricks & 71.6 & 43.3 & 
\multirow{8}{*}{C+M+MS}  & 
BagTricks & \multicolumn{1}{c|}{58.2} & 40.8   \\
& +IN (=DualNorm) & 78.9 & 52.3 & & 
+IN (=DualNorm) & \multicolumn{1}{c|}{68.5} & 51.7   \\
& +RE(0.1) & 74.0 & 45.6 & & 
+RE(0.1) & \multicolumn{1}{c|}{63.1} & 44.6   \\
& +DEX & 71.9 & 45.4 & & 
+DEX & \multicolumn{1}{c|}{66.1} & 48.1   \\
& +IN+NoRE & 80.8 & 54.0 & & 
+IN+NoRE & \multicolumn{1}{c|}{70.4} & 52.8   \\
& +IN+RE(0.1) & 81.0 & 54.3 & & 
+IN+RE(0.1) & 
\multicolumn{1}{c|}{71.0} & 53.4   \\
& +IN+RE(0.1)+ISDA & 79.6 & 53.9 & & 
+IN+RE(0.1)+ISDA & 
\multicolumn{1}{c|}{72.3} & 54.5   \\
& +IN+RE(0.1)+DEX (\textbf{Ours}) & \textbf{81.5} & \textbf{55.2} & & 
+IN+RE(0.1)+DEX \textbf{(Ours}) & 
\multicolumn{1}{c|}{\textbf{73.7}} & \textbf{55.0}   \\ 
\hline\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c|}{MSMT17\_V2}  & \multirow{2}{*}{Sources} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{CUHK-NP}       \\ \cline{3-4} \cline{7-8} & 
\multicolumn{1}{c|}{} & Rank-1 & mAP & & \multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\ 
\hline
\multirow{8}{*}{C+D+M}   & 
BagTricks & 19.4 & 6.9 & 
\multirow{8}{*}{D+M+MS}  & 
BagTricks & \multicolumn{1}{c|}{20.1} & 19.6   \\
& +IN (=DualNorm) & 37.9 & 15.4 & & 
+IN (=DualNorm) & \multicolumn{1}{c|}{28.0} & 27.6   \\
& +RE(0.1) & 23.5 & 8.5 & & 
+RE(0.1) & \multicolumn{1}{c|}{23.9} & 23.5   \\
& +DEX & 22.9 & 8.7 & & 
+DEX & \multicolumn{1}{c|}{25.9} & 25.1   \\
& +IN+NoRE & 42.0 & 17.1 & & 
+IN+NoRE & \multicolumn{1}{c|}{28.0} & 28.2   \\
& +IN+RE(0.1) & 42.4 & 17.5 & & 
+IN+RE(0.1) & \multicolumn{1}{c|}{29.0}      & 28.8   \\
& +IN+RE(0.1)+ISDA & 41.8 & 17.7 & & 
+IN+RE(0.1)+ISDA & \multicolumn{1}{c|}{32.6} & 32.4   \\
& +IN+RE(0.1)+DEX (\textbf{Ours}) & \textbf{43.5} & \textbf{18.7}& & 
+IN+RE(0.1)+DEX (\textbf{Ours}) & \multicolumn{1}{c|}{\textbf{36.7}} & \textbf{33.8}  \\ \hline
\end{tabular}
\end{adjustbox}
\caption{Ablation study comparing the effects of applying IN, reducing RE probability, applying ISDA; and applying DEX{} on a strong baseline ResNet-50 model from BagTricks~\cite{DualNorm}}
\label{tab:ablation-baseline}
\end{table}
\vspace{-1em}

\subsection{Applying DEXLite{} to Multi-branch Architectures}
We demonstrate general applicability of DEX{} by applying it on multi-branch architectures that incur a large increase in memory use. For these architectures, we can limit the sample size to apply DEXLite{} effectively. We selected two well-known multi-branch models in supervised Person ReID: PCB~\cite{PCB}, and MGN~\cite{MGN}. PCB divides the final feature tensor into six horizontal stripes, each of which becomes a local PID prediction branch. We apply DEXLite{} each of these local branches in PCB. MGN consists of eight PID prediction branches, with three global-level features and five part-level features. We apply DEXLite{} to the three global-level prediction branches to contrast PCB's part-level design.
\begin{table}[h]
\centering
    \begin{adjustbox}{width=\textwidth}
\begin{tabular}{c|c|l|c|c|c|c|l|cc}
\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{l|}{\multirow{2}{*}{Model}} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c|}{Market-1501} & \multirow{2}{*}{Sources} & \multicolumn{1}{l|}{\multirow{2}{*}{Model}} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{DukeMTMC-reID} \\ \cline{4-5} \cline{9-10} & 
\multicolumn{1}{l|}{} & 
\multicolumn{1}{c|}{} & Rank-1 & mAP & & \multicolumn{1}{l|}{} & 
\multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\ 
\hline
\multirow{4}{*}{C+D+MS} 
& \multirow{2}{*}{MGN~\cite{MGN}} & 
+IN+RE(0.1) & 62.9 & 29.7 & 
\multirow{4}{*}{C+M+MS} &
\multirow{2}{*}{MGN~\cite{MGN}} & 
+IN+RE(0.1) & \multicolumn{1}{c|}{62.2} & 40.8 \\
& & +IN+RE(0.1)+DEXLite{} & \textbf{63.7} & \textbf{32.8} & & &
+IN+RE(0.1)+DEXLite{} & \multicolumn{1}{c|}{\textbf{64.3}} & \textbf{44.4} \\ \cline{2-5} \cline{7-10} & 
\multirow{2}{*}{PCB~\cite{PCB}} & 
+IN+RE(0.1) & 71.2 & 42.4 & & 
\multirow{2}{*}{PCB~\cite{PCB}} & 
+IN+RE(0.1) & \multicolumn{1}{c|}{65.5} & 45.1 \\
& & +IN+RE(0.1)+DEXLite{} & \textbf{73.1} & \textbf{45.1} & & & 
+IN+RE(0.1)+DEXLite{} & \multicolumn{1}{c|}{\textbf{66.5}} & \textbf{46.8} \\ \hline\hline
\multirow{2}{*}{Sources} & \multicolumn{1}{l|}{\multirow{2}{*}{Model}} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c|}{MSMT17\_V2}  & \multirow{2}{*}{Sources} & \multicolumn{1}{l|}{\multirow{2}{*}{Model}} & \multicolumn{1}{c|}{\multirow{2}{*}{Method}} & \multicolumn{2}{c}{CUHK-NP} \\ 
\cline{4-5} \cline{9-10} & 
\multicolumn{1}{l|}{} & 
\multicolumn{1}{c|}{} & Rank-1 & mAP & & 
\multicolumn{1}{l|}{} & 
\multicolumn{1}{c|}{} & 
\multicolumn{1}{c|}{Rank-1} & mAP \\ 
\hline
\multirow{4}{*}{C+D+M}   & 
\multirow{2}{*}{MGN~\cite{MGN}} & 
+IN+RE(0.1) & 23.1 & 8.3 & 
\multirow{4}{*}{D+M+MS}  & 
\multirow{2}{*}{MGN~\cite{MGN}} & 
+IN+RE(0.1) & \multicolumn{1}{c|}{18.1} & 15.5 \\
& & +IN+RE(0.1)+DEXLite{} & \textbf{25.9} & \textbf{9.6} & & &
+IN+RE(0.1)+DEXLite{} & \multicolumn{1}{c|}{\textbf{22.9}} & \textbf{21.0} \\ 
\cline{2-5} \cline{7-10} & 
\multirow{2}{*}{PCB~\cite{PCB}} & 
+IN+RE(0.1) & 36.4 & 14.6 & & 
\multirow{2}{*}{PCB~\cite{PCB}} & 
+IN+RE(0.1) & \multicolumn{1}{c|}{25.2} & 25.2 \\
& & +IN+RE(0.1)+DEXLite{} & \textbf{37.3} & \textbf{15.2} & & &
+IN+RE(0.1)+DEXLite{} & 
\multicolumn{1}{c|}{\textbf{28.4}} & \textbf{27.2} \\ \hline
\end{tabular} 
\end{adjustbox}
\caption{Applying DEXLite{} to multi-branch architecture models such MGN~\cite{MGN} and PCB~\cite{PCB} similarly yield performance improvements}
\label{tab:ablation-mgnpcb}
\end{table}

Figure \ref{fig:our-method}(b) illustrates the multi-branch application of our technique using PCB as an example. MGN's loss is averaged among all branches, so we kept $\lambda$ at 7.5, same as our original baseline experiments. However, PCB sums the losses from all branches instead of averaging so we reduced $\lambda$ by a factor of six (the number of stripes in PCB) to 1.25. We set the sample size to 2,000 for DEXLite{} and train for 40 epochs. Table \ref{tab:ablation-mgnpcb} shows the result of our comparison study. Overall, DEX{} demonstrates its effectiveness as an augmentation strategy and ability to improve the generalization results of a range of models.

\subsection{Ablation Study on Negative Sample Sizes for DEXLite{}}
We investigate the effects of different sample sizes when applying negative sampling in DEXLite{}, shown in Table \ref{tab:ablation-negsample}. The performance improves as the sample size increases but starts to plateau beyond a sample size of around 2,000. With 2,000 negative sample sizes for estimation, DEXLite{} can achieve comparable performance on par with the full DEX{} with much faster training speed and memory usage.

\begin{table}[h]
\centering
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{c|c|c|c|c|c|c|c|c|c}
\hline
\multicolumn{1}{l|}{\multirow{2}{*}{Sources}} & \multirow{2}{*}{Type} & \multirow{2}{*}{Samples} & \multicolumn{2}{c|}{Market-1501} & \multicolumn{1}{l|}{\multirow{2}{*}{Sources}} & \multirow{2}{*}{Type} & \multirow{2}{*}{Samples} & \multicolumn{2}{c}{DukeMTMC-reID} \\ \cline{4-5} \cline{9-10} 
\multicolumn{1}{l|}{} &  &  & Rank-1 & mAP & \multicolumn{1}{l|}{} &  &  & Rank-1 & mAP \\ \hline
\multirow{5}{*}{C+D+MS} & \multirow{4}{*}{DEXLite} & 10 & 54.6 & 30.0 & \multirow{5}{*}{C+M+MS} & \multirow{4}{*}{DEXLite} & 10 & 53.2 & 34.2 \\
 &  & 100 & 69.7 & 42.8 &  &  & 100 & 64.8 & 46.0 \\
 &  & 1000 & 77.0 & 51.4 &  &  & 1000 & 70.8 & 52.6 \\
 &  & 2000 & 80.3 & 54.3 &  &  & 2000 & 72.1 & 53.6 \\ \cline{2-5} \cline{7-10} 
 & DEX & Full & 81.5 & 55.2 &  & DEX & Full & 72.7 & 54.2 \\ \hline \hline
\multicolumn{1}{l|}{\multirow{2}{*}{Sources}} & \multirow{2}{*}{Type} & \multirow{2}{*}{Sample} & \multicolumn{2}{c|}{MSMT17\_V2} & \multicolumn{1}{l|}{\multirow{2}{*}{Sources}} & \multirow{2}{*}{Type} & \multirow{2}{*}{Samples} & \multicolumn{2}{c}{CUHK-NP} \\ \cline{4-5} \cline{9-10} 
\multicolumn{1}{l|}{} &  &  & \multicolumn{1}{l|}{Rank-1} & \multicolumn{1}{l|}{mAP} & \multicolumn{1}{l|}{} &  &  & \multicolumn{1}{l|}{Rank-1} & \multicolumn{1}{l}{mAP} \\ \hline
\multirow{5}{*}{D+M+MS} & \multirow{4}{*}{DEXLite} & 10 & 16.8 & 16.8 & \multirow{5}{*}{C+D+M} & \multirow{4}{*}{DEXLite} & 10 & 17.5 & 6.5 \\
 &  & 100 & 27.6 & 27.0 &  &  & 100 & 31.3 & 12.7 \\
 &  & 1000 & 32.8 & 32.1 &  &  & 1000 & 38.6 & 16.4 \\
 &  & 2000 & 34.4 & 33.3 &  &  & 2000 & 41.5 & 17.6 \\ \cline{2-5} \cline{7-10} 
 & DEX & Full & 34.3 & 32.9 &  & DEX & Full & 43.5 & 18.7 \\ \hline
\end{tabular}
\end{adjustbox}
\caption{Effects of sample sizes in DEXLite{} in comparison with DEX{}}
\label{tab:ablation-negsample}
\end{table}


\section{Conclusion}
\label{sec:conclusion}

In this paper, we introduced a fresh perspective and a novel solution to the problem of domain generalization (DG) in Person ReID, leveraging on domain biases inherently encoded in deep features to augment them directly in domain-semantically meaningful directions. DEX{}, our proposed dual-label implicit augmentation method applied in simple ResNet50 network can surpasses the most of recent state-of-the-art Domain Generalization (DG) Person ReID methods in both new large-scale banchmarks and old small-scale benchmarks by a large margins. Reducing the memory use of our method with negative sampling techniques, we also developed DEXLite{} to make our method applicable to a wide range of model architectures and dataset situations. There is still room to grow before DG Person ReID solutions are robust enough for true real-world use, and we believe that our novel approach will seed more developments along this new paradigm and pave the way for faster innovation.\\

\noindent
\textbf{Acknowledgement}: This work was supported by the Defence Science and Technology Agency (DSTA) Postgraduate Scholarship, of which Eugene P.W. Ang is a recipient. It was carried out at the Rapid-Rich Object Search (ROSE) Lab at the Nanyang Technological University, Singapore.


