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

\begin{figure}[t!]
\centering
	\includegraphics[width=0.97\linewidth]{compare_archv2.pdf}
	\vspace{-.1in}
	\caption{Illustration of the major difference of pipeline between previous WILSS work and {FMWISS}{}. Given a model pre-trained on old classes with pixel-level labels ($\mathcal{Y}^{t-1}$), previous work~\cite{cermelli2022wilson} learn new classes ({\itshape e.g.}, \textit{horse}) via image-level labels ($\mathcal{C}^t$), while {FMWISS}{} improves and effectively utilizes the supervision from complementary foundation models.}
	\label{fig:compare_arch}
    \vspace{-.2in}
\end{figure}

Semantic segmentation is a fundamental task in computer vision and has witnessed great progress using deep learning in the past few years. It aims at assigning each pixel a category label.
Modern supervised semantic segmentation methods~\cite{chen2017deeplab,chen2018encoder} are usually based on published large-scale segmentation datasets with pixel annotations. Despite the promising results, one model pre-trained on one dataset is prone to easily forget learned knowledge when being retrained on another dataset with new classes.
This phenomenon is known as catastrophic forgetting~\cite{mccloskey1989catastrophic}, which is caused by large changes of model parameters to model new samples with novel categories without accessing old samples.

A promising approach to solve such catastrophic forgetting problem is called incremental learning. Many methods have been proposed to solve image classification task~\cite{kirkpatrick2017overcoming,chaudhry2018riemannian,zenke2017continual,li2017learning,dhar2019learning,rebuffi2017icarl,castro2018end,shin2017continual,hou2019learning,wu2018memory,ostapenko2019learning}.
Recently, a few methods have been presented to address incremental learning for semantic segmentation (ILSS) task, where only new classes of training samples of the current step are labeled with pixel annotations and old classes of the previous step are labeled as background.
Modern ILSS methods can be classified into two categories: regularization-based and replay-based.
Regularization-based methods~\cite{cermelli2020mib,douillard2021plop,michieli2021sdr} focus on distilling knowledge, {\itshape e.g.}, output probability, intermedia features, from pre-trained model of previous step.
Replay-based methods~\cite{maracani2021recall} propose to store the information of previous old classes or web-crawled images and replay for new training steps.
However, a key barrier to further develop these methods is the requirement for pixel-level annotations for new classes.
Very recently, WILSON~\cite{cermelli2022wilson} first proposes a new task, weakly incremental learning for semantic segmentation (WILSS), to incrementally update the model from image-level labels for new classes. Despite the comparable results, the image-level labels can not provide details to accurately locate each segment, which limits the performance and development of WILSS.

In this work, we explore to improve and more effectively utilize the supervision of new classes given image-level labels while preserving the knowledge of old ones. We propose a \underline{\textbf{F}}oundation \underline{\textbf{M}}odel drives \underline{\textbf{W}}eakly \underline{\textbf{I}}ncremental learning for \underline{\textbf{S}}emantic \underline{\textbf{S}}egmentation framework, dubbed FMWISS.

Firstly, as shown in Figure~\ref{fig:compare_arch}, we are the first attempt to leverage pre-trained foundation models to improve the supervision given image-level labels for WILSS in a training-free manner.
To be specific, we propose pre-training based co-segmentation to distill the knowledge of vision-language pre-training models ({\itshape e.g.}, CLIP~\cite{radford2021clip}) and self-supervised pre-training models ({\itshape e.g.}, iBOT~\cite{zhou2021ibot}), which can be complementary to each other. However, it is not trivial to apply the pre-trained models.
We first adapt CLIP for category-aware dense mask generation. Based on the initial mask for each new class, we then propose to extract compact category-agnostic attention maps with seeds guidance using self-supervised models. We finally refine the pseudo masks via mask fusion.
We further propose to optimize the still noisy pseudo masks with a teacher-student architecture, where the plug-in teacher is optimized with the proposed dense contrastive loss. Thus we can more effectively utilize the pseudo dense supervision.
Finally, we present memory-based copy-paste augmentation to remedy the forgetting problem of old classes and can further improve the performance.

The contributions of this paper are as follows:
\begin{itemize}
\itemsep -0.1cm
\item We present a novel and data-efficient WILSS framework, called FMWISS, which is the first attempt to utilize complementary foundation models to improve and more effectively use the supervision given only image-level labels.

\item We propose pre-training based co-segmentation to generate dense masks by distilling both category-aware and category-agnostic knowledge from pre-trained foundation models, which provides dense supervision against original image labels.

\item To effectively utilize pseudo labels, we use a teacher-student architecture with a proposed dense contrastive loss to dynamically optimize the noisy pseudo labels.

\item We further introduce memory-based copy-paste augmentation to remedy the forgetting problem of old classes and can also improve performance.

\item Extensive experiments on Pascal VOC and COCO datasets demonstrate the significant efficacy of our {FMWISS}{} framework.
\end{itemize}

\section{Related Work}

\noindent
\textbf{Incremental Learning for Semantic Segmentation.} In addition to an exhaustive exploration of incremental learning for image classification~\cite{kirkpatrick2017overcoming,chaudhry2018riemannian,zenke2017continual,li2017learning,dhar2019learning,rebuffi2017icarl,castro2018end,shin2017continual,hou2019learning,wu2018memory,ostapenko2019learning}, a relatively few methods~\cite{cermelli2020mib,douillard2021plop,klingner2020cil,maracani2021recall,michieli2019ilt,michieli2021sdr} have been proposed to tackle the incremental learning for semantic segmentation task, which can be classified into regularization-based and replay-based methods.
Regularization-based methods~\cite{cermelli2020mib,douillard2021plop,michieli2021sdr} focus on preserving knowledge from previous training steps. For instance,
MiB~\cite{cermelli2020mib} proposes a modified version of traditional cross-entropy and knowledge distillation loss terms to regularize the probability of old classes and distill previous knowledge respectively, so as to remedy the background shift problem.
PLOP~\cite{douillard2021plop} proposes a multi-scale pooling technique to preserve long and short-range spatial relationships at the feature level.
SDR~\cite{michieli2021sdr} proposes to optimize the class-conditional features by minimizing feature discrepancy of the same class.
In addition, as a replay-based method, RECALL~\cite{maracani2021recall} uses web-crawled images with pseudo labels to remedy the forgetting problem.
Pixel-by-pixel labeling for semantic segmentation is time-consuming and labor-intensive. Recently, some literature proposes to attain segmentations from cheaper and more available supervisions, {\itshape e.g.}, sparse point~\cite{bearman2016s}, and image-level label~\cite{huang2018weakly,lee2019ficklenet,sun2020mining}, which has been attracting more and more attention these years. Most image-based weakly supervised semantic segmentation methods~\cite{araslanov2020ss,lee2021eps,wang2020seam} leverage image-level labels to optimize the class activation map (CAM) and then extract pseudo dense annotations.
However, the image-level label is rarely explored in incremental learning for semantic segmentation.

Very recently, WILSON~\cite{cermelli2022wilson} first proposes a novel weakly incremental learning for semantic segmentation (WILSS) task, which extends a pre-trained segmentation model using only image-level labels and achieves comparable results.
In this work, inspired by WILSON~\cite{cermelli2022wilson}, we present a {FMWISS}{} framework to improve and effectively utilize the image-level labels by distilling the knowledge of the complementary foundation models.

\begin{figure*}[t!]
	\begin{center}
	\includegraphics[width=0.9\textwidth]{arch.pdf}
	\end{center}
    \vspace{-.2in}
	\caption{Illustration of the proposed {FMWISS}{} framework. The plug-in teacher module (ASPP~\cite{chen2014deeplabv2}) is to learn the segments of both old and new classes during training, which is eliminated during inference. The model at step \textit{t} is optimized using the outputs of the pre-trained model at step \textit{t}-1 and the learned logits of the online teacher module.}
	\label{fig:framework}
	\vspace{-.1in}
\end{figure*}

\noindent
\textbf{Visual Foundation Models.} We mainly focus on two kinds of foundation models in computer vision, including the vision-language pre-training (VLP) models and the self-supervised pre-training models.
VLP~\cite{radford2021clip,jia2021scalingalign} plays an important role in multimodal research, {\itshape e.g.}, VQA~\cite{antol2015vqa}, text-to-image generation~\cite{ramesh2022hierarchicaldalle2}, zero-shot classification~\cite{zhou2021coop,zhou2022cocoop}. A representative VLP work is CLIP~\cite{radford2021clip}, which jointly trains the image and text encoders on 400 million image-text pairs collected from the web and demonstrates promising results on zero-shot image classification tasks. Recently, MaskCLIP~\cite{zhou2021maskclip} adapts CLIP to zero-shot semantic segmentation in a training-free manner, which illustrates the potential of CLIP in category-aware dense prediction.
Self-supervised visual pre-training can be classified into three categories: contrastive learning based~\cite{oord2018infonce,chen2020simple,he2020momentum}, distillation based~\cite{grill2020bootstrap,caron2021dino}, and masked image modeling based~\cite{he2022mae,zhou2021ibot}. Among these methods, iBOT~\cite{zhou2021ibot} and DINO~\cite{caron2021dino} are two representative approaches to automatically perform class-agnostic dense features modeling.
These two kinds of foundation models can be complementary to each other.

\section{Method}

\subsection{Problem Definition and Notation}
Let $\mathcal{X}$ be the input image space and each image $x \in \mathcal{X}$ consists of a set of pixels $\mathcal{I}$ with $|\mathcal{I}| = H \times W$. Let $\mathcal{Y}$ be the label space.
In the incremental learning for semantic segmentation setting~\cite{cermelli2020mib}, the training procedure is arranged into multiple steps, and each learning step $t$ will involve novel classes $\mathcal{C}^t$ with pixel annotations, constructing a new label set $\mathcal{Y}^t = \mathcal{Y}^{t-1} \cup \mathcal{C}^t$.
However, different from the original incremental setting, in the novel weakly incremental learning for semantic segmentation (WILSS) setting, recently proposed by WILSON~\cite{cermelli2022wilson}, the pixel annotations are only provided for the initial step, {\itshape i.e.}, $t=0$. For the following steps, we can only access to training sets with image-level annotations for new classes, and can not access to the training samples of previous training steps anymore. The goal is to learn and update a model to perform segmentation on new classes without forgetting old classes.

\subsection{Pre-training Based Co-segmentation}

It is still challenging to use only image-level labels to supervise the dense prediction tasks, {\itshape e.g.}, semantic segmentation, since image-level labels can not provide detailed information to accurately locate each segment. This limitation inspires us to investigate the following question:  \textit{how to improve the supervision of new classes from image-level labels?}
To tackle this question, we propose a pre-training based co-segmentation method to utilize the knowledge of foundation models in a training-free manner. We distill the complementary knowledge of two kinds of foundation models, including the vision-language pre-training models, {\itshape e.g.}, CLIP~\cite{radford2021clip}, and the self-supervised pre-training models, {\itshape e.g.}, iBOT~\cite{zhou2021ibot}, DINO~\cite{caron2021dino}.

\noindent
\textbf{Initial Mask.}
We believe that the pre-trained vision-language model, {\itshape e.g.}, CLIP, has encoded rich semantic information in its features as it learns to associate image with language caption from 400 million image-text pairs. To get dense prediction of a new class image, we apply the pre-trained CLIP model to extract category-aware pixel annotations given image-level labels.
As shown in Figure~\ref{fig:framework}, to be specific, given an image $x$ of step $t$ with image-level labels $\mathcal{C}^t$, we first extract dense image features $F$ from the CLIP image encoder $f_I$. Then, project  $F$ via the final linear projection layer $f_{proj}$ of $f_I$.
\begin{equation}
\overline{F} = | f_{proj}(F) |_{2}, ~~ \overline{F} \in \mathbb{R}^{h \times w \times d},
\end{equation}
where $|\cdot|_{2}$ denotes L2 normalization along the channel dimension, $d$ is the feature dimension of the joint space.
We then compute the text embeddings by taking as input the prompt with target classes $\mathcal{C}^t$ of step $t$:
\begin{equation}
\overline{T} = | f_T({\tt prompt} (\mathcal{C}^t)) |_2, ~~ \overline{T} \in \mathbb{R}^{\mathcal{C}^t \times d},
\end{equation}
where $f_T$ is the CLIP text encoder, ${\tt prompt}(\cdot)$ denotes prompt engineering, which ensembles multiple prompt templates as in~\cite{radford2021clip}.

We then compute the pixel-text score maps using the language-compatible image feature embeddings $\overline{F}$ and the text embeddings $\overline{T}$ by:
\begin{equation}
\mathcal{M}_{init} = \overline{F} \cdot \overline{T}^{\top}, ~\mathcal{M}_{init} \in \mathbb{R}^{h \times w \times \mathcal{C}^t},
\end{equation}
which indicates that each pixel will be assign a score for each class in $\mathcal{C}^t$, and $\mathcal{M}_{init}$ can be viewed as the initial segmentation results with category information.

\noindent
\textbf{Refine Mask via Seeds Guidance.} The pseudo mask $\mathcal{M}_{init}$ generated by CLIP~\cite{radford2021clip} can provide rich category-aware pixel annotations, but the mask is noisy since the training paradigm of CLIP based on image-text pairs doomed to be good at instance-level classification rather than segmentation.
To improve the mask quality, we propose to distill the knowledge of another kind of foundation models, {\itshape i.e.}, self-supervised pre-training models, which have shown promising performance in local feature modeling~\cite{caron2021dino,zhou2021ibot}. These models can produce compact category-agnostic attention maps. However, \textit{how to extract segmentations for a target class given an image that may contain multiple objects?}
To address this issue, we propose to refine the initial mask via category-specific seeds guidance.
Specifically, we randomly select $N=\{(i_p, j_p)\}^{N}_{p=1}$ seed points from initial mask $\mathcal{M}_{init} \in \mathbb{R}^{h \times w \times \mathcal{C}^t}$ for each target class $c \in \mathcal{C}^t$, and extract the corresponding attention maps from the pre-trained self-supervised model.
Let $S$ denotes the image encoder of the self-supervised model, $S(x) \in \mathbb{R}^{h \times w \times n}$ denotes the output attention maps of the last self-attention block. We extract the category-aware attention map with the guidance of seeds as follows. For simplicity, we only show the calculation on one class $c \in \mathcal{C}^t$:
\begin{equation}
\mathcal{M}^{c}_{seeds} = \big [\frac{1}{N} \sum^{N}_{p=1}  \frac{1}{n} \sum^{n} S(x) \big ]_{\tt binary},
\label{eq:m_seeds}
\end{equation}
where $n$ denotes the number of attention heads. The $N$ seed points are randomly sampled from the foreground of binarized $\mathcal{M}_{init}$ for each new class and training step.
$[\cdot]_{\tt binary}$ is a binarization operation that sets all the values greater than the threshold $\mathcal{T}$ to 1, otherwise 0. $\mathcal{T}$ is dynamically updated to keep the top $\mathcal{K}$\% ($\mathcal{K}=70$ by default) locations from the averaged attention map.
As shown in Figure~\ref{fig:seeds}, we visualize extracted attention maps of two classes (\textit{horse, dog}), nine seeds ($N=9$) can already show good clustering performance.

Finally, we get the refined mask via simple mask fusion for better performance:
\begin{equation}
\mathcal{M}_{refine} = \mathcal{M}_{init} \cup \mathcal{M}_{seeds}, ~~\mathcal{M}_{refine} \in \mathbb{R}^{h \times w \times \mathcal{C}^t},
\label{eq:fusion}
\end{equation}
where $\cup$ represents mask fusion operation, which is the union operation in our experiments by default.

\subsection{Pseudo Label Optimization}

\begin{figure}[t!]
\centering
	\includegraphics[width=0.95\linewidth]{contrast.pdf}
    \vspace{-.1in}
	\caption{Illustration of the dense contrastive loss calculation process. The colorful points represent pixels with different categories.}
	\label{fig:contrast}
	\vspace{-.1in}
\end{figure}

Previous WILSS literature~\cite{cermelli2022wilson} use learned CAM to supervise the segmentation learning of new classes, and CAM is optimized with a binary cross-entropy (BCE) loss against one-hot image-level labels.
Now, we have the generated pseudo pixel labels that can provide more information than image-level labels, a natural question is: \textit{how to effectively utilize such supervision?}

We propose to use a teacher-student architecture to further optimize the still noisy pseudo mask. To be specific, by taking the segmentation model as student model, we introduce a plug-in teacher module (ASPP network in Figure~\ref{fig:framework}) to dynamically learn better pseudo masks during training.
To learn the teacher module, we first propose to use the pixel-wise binary cross-entropy loss $\mathcal{L}^{new}_{\text{BCE}}$ to supervise the predictions of the new classes at step $t$ as follows, and we leave the old classes optimization in the next section.
\begin{equation}
\begin{split}
\mathcal{L}^{new}_{\text{BCE}} = - \frac{1}{|\mathcal{C}^{t}| |\mathcal{I}|} \sum_{i \in \mathcal{I}} \sum_{c \in \mathcal{C}^t} \mathcal{M}^{c, i}_{refine}\log(p^{c, i}) \\
+ (1 - \mathcal{M}^{c, i})\log(1 - p^{c, i}),
 \end{split}
 \label{eq:pixelbce}
\end{equation}
where $p^{c, i}$ denotes the predicted probability on new class $c$ of pixel $i$.
However, the pixel-wise BCE loss mainly focus on the optimization of the target foreground class $c$ of current input image and treat all other classes as background, which ignores the correlation among pixels. To better utilize the multi-class predictions and corresponding pixel-wise pseudo labels among the entire dataset, inspired by the InfoNCE~\cite{oord2018infonce} loss in unsupervised representation learning, we propose to perform dense contrastive learning.

Specifically, as depicted in Figure~\ref{fig:contrast}, for a pixel $i$ of a new class image and its corresponding pseudo annotation, we collect all the pixels with the same class label as $i$ to compose positive samples $\mathbf{P}_i$, and collect the points of other classes to compose negative samples $\mathbf{N}_i$. Formally, our dense contrastive loss $\mathcal{L}^{new}_{\text{DCL}}$ can be calculated as follows. For simplicity, we only show the loss on pixel $i$:
\begin{equation}
\begin{aligned}
& \mathcal{L}^{new}_{\text{DCL}} \\
& = \frac{1}{|\mathbf{P}_i|} \sum_{q_{+} \in \mathbf{P}_i}-\log \frac{\text{exp}(i \cdot q_{+}/\tau)} {\text{exp}(i \cdot q_{+}/\tau) + \sum\limits_{q_{-} \in \mathbf{N}_i} \text{exp}(i \cdot q_{-}/\tau)},
\end{aligned}
\label{eq:dcl}
\end{equation}
where $\tau$ is a temperature term (0.1 by default). For training efficiency, we randomly sample only ten points for each contained class of the current mini-batch.

The pixel-wise BCE loss in Eq.~(\ref{eq:pixelbce}) and the dense contrastive loss in Eq.~(\ref{eq:dcl}) can be complementary to each other, which help the teacher module to learn discriminative pixel features as well as regularize the pixel feature space by intra-class and inter-class pixel feature modeling.

\subsection{Memory-based Copy-Paste Augmentation}

\begin{figure}[t!]
\centering
	\includegraphics[width=0.8\linewidth]{copypaste.pdf}
    \vspace{-.1in}
	\caption{Illustration of the memory-based copy-paste augmentation. Notably, we will not use the ground-truth labels of new classes of augmented labels.}
	\label{fig:copypaste}
	\vspace{-.1in}
\end{figure}

In addition to improving and effectively leveraging the supervision of new classes for WILSS, we propose a memory-based copy-paste augmentation strategy to stabilize the learning of old classes and can further improve the performance of the segmentation model.
As shown in Figure~\ref{fig:copypaste}, we first construct a memory bank for each old class, and each class archive will store $\mathcal{B}$ foreground instances and segmentation labels during the base model training. Then, in step $t$, we randomly pick one pair of foreground images and labels from a randomly selected old class archive, and randomly paste them to the new class image.
Now, the training samples contain new class images at step $t$ as well as old class images and pixel labels at step $t$-1. We thus optimize the old class learning of the teacher module as:
\begin{equation}
\begin{split}
\mathcal{L}^{old}_{\text{BCE}} = - \frac{1}{|\mathcal{Y}^{t-1}| |\mathcal{I}|} \sum_{i \in \mathcal{I}} \sum_{c \in \mathcal{Y}^{t-1}} g(f^{t-1}_{\theta}(\hat{x}))^{c,i}\log(p^{c, i}) \\
 + (1 - g(f^{t-1}_{\theta}(\hat{x}))^{c,i})\log(1 - p^{c, i}),
 \end{split}
\end{equation}
\begin{equation}
g(f^{t-1}_{\theta}(\hat{x}))^{c,i} =
\begin{cases}
1, & \hat{x}^{c,i}~\text{augmented}, \\
g(f^{t-1}_{\theta}(\hat{x}))^{c,i}, & \text{otherwise},
\end{cases}
\end{equation}
where $g(\cdot)$ is the logistic function, $f^{t-1}_{\theta}$ is the trained model at step $t$-1, $p^{c, i}$ is the predicted probability on old class $c$ of pixel $i$, $\hat{x}$ denotes the augmented image.

\subsection{Overall Optimization}
We optimize the segmentation model $f_{\theta}^{t}$ at step $t$ by distilling the knowledge of the trained model $f^{t-1}_{\theta}$ and the dynamically updated teacher module $T^{t}$.
Since $T^{t}$ is optimized mainly through the binary cross-entropy loss, we use the BCE loss to distill the prediction of $T^{t}$ to model $f_{\theta}^{t}$.
Considering that the learned pseudo mask is not perfect, we use the soft pixel labels as the final supervision for new classes $\mathcal{C}^t$, and use the weighted average value of the old model and teacher module outputs as the supervision for old classes:
\begin{equation}
q^{c,i} =
\begin{cases}
\alpha |T^{t}(x)|_{\text{hard}} + (1-\alpha) g(T^{t}(x))  , & \text{if}~ c \in \mathcal{C}^{t}, \\
\beta g(f_{\theta}^{t-1}(x)) + (1-\beta) g(T^{t}(x)), & \text{otherwise},
\end{cases}
\label{eq:qci}
\end{equation}
where $|\cdot|_{\text{hard}}$ denotes one-hot operation to set one to the class with the maximum score for each pixel and zero to others. $\alpha$ and $\beta$ are trade-off parameters and we set $\alpha=0.5, \beta=0.9$ by default. Then, the BCE loss for $f_{\theta}^{t}$ is:
\begin{equation}
\begin{split}
\mathcal{L}^{all}_{\text{BCE}} = - \frac{1}{|\mathcal{Y}^{t}||\mathcal{I}|} \sum_{i \in \mathcal{I}} \sum_{c \in \mathcal{Y}^{t}} q^{c,i}\log(p^{c, i}) \\
+ (1 - q^{c,i})\log(1 - p^{c, i}),
\end{split}
\end{equation}
where $\mathcal{Y}^{t}$ is the set of all seen classes and $p=f_{\theta}^{t}(x)$ represents the output of segmentation model at step $t$.

The overall learning objective is as follows:
\begin{equation}
\mathcal{L}_{overall} =  \mathcal{L}^{new}_{\text{BCE}} + \lambda \mathcal{L}^{new}_{\text{DCL}} + \mathcal{L}^{old}_{\text{BCE}} + \mathcal{L}^{all}_{\text{BCE}},
\end{equation}
where $\lambda$ is the loss weight of $\mathcal{L}^{new}_{\text{DCL}}$.

\section{Experiments}

\subsection{Datasets and Protocols}
To ensure a fair comparison, we follow the experimental settings of the state-of-the-art (SoTA) WILSS method WILSON~\cite{cermelli2022wilson} for datasets and protocols. Different from~\cite{cermelli2020mib,maracani2021recall} rely on pixel-wise annotation on new classes, we only use image-level labels for novel classes as WILSON.

\noindent
\textbf{Datasets:} we consider two standard evaluation benchmarks including Pascal VOC 2012~\cite{everingham2010pascalvoc} and COCO~\cite{lin2014coco}. COCO consists of 118,287 and 5,000 images for training and validation with 80 annotated object classes. Pascal VOC is composed of 1,464 training and 1,449 validation images with 20 labeled object classes. We follow the standard method~\cite{ahn2018learning,kolesnikov2016seed,cermelli2022wilson} to augment the VOC dataset with images from~\cite{hariharan2011semantic}, building up 10,582 and 1,449 images for training and validation, respectively.
We also follow the practice of~\cite{cermelli2022wilson} to use the train split and the annotation of COCO-Stuff~\cite{caesar2018cocostuff} that addresses the annotation overlapping problem of COCO~\cite{lin2014coco}.

\noindent
\textbf{Protocols:} previous works~\cite{cermelli2020mib} introduce two different incremental learning protocols: \textit{disjoint} and \textit{overlap}.
In \textit{disjoint}, images of each training step only contain pixels of previous seen and current classes.
In \textit{overlap}, each training step contains all the images, where pixels can belong to any class. Thus, the overlap protocol is more realistic and challenging compared to the disjoint. In our experiments, we follow the previous WILSS work~\cite{cermelli2022wilson} to apply these two protocols on the VOC dataset, including \textbf{15-5 VOC}, where 15 base classes are learned in the first training step and 5 new classes are continuously learned in the second step; \textbf{10-10 VOC}, where 10 base classes are learned in the first step and another 10 new classes are added in the second step.
In addition, we also verify our method on the \textbf{COCO-to-VOC} protocol, which is a new incremental learning scenario proposed in~\cite{cermelli2022wilson}. To be specific, in the first step, we learn the 60 classes of COCO that do not appear in the VOC dataset. Then, we continuously learn the 20 classes of VOC. Following common practice~\cite{cermelli2020mib,maracani2021recall,cermelli2022wilson}, we report the standard mean Intersection over Union (mIoU) results on the validation sets.

\subsection{Implementation Details}
As in WILSON~\cite{cermelli2022wilson}, we use a Deeplab V3~\cite{chen2017deeplabv3} with a ResNet-101~\cite{he2016deep} backbone for VOC and a Wide-ResNet-38 for COCO, both pre-trained on ImageNet~\cite{deng2009imagenet}.
We train all the models for 40 epochs with a batch size of 24 and the SGD optimizer with a learning rate of 1$e^{-3}$, momentum of 0.9, weight decay of 1$e^{-4}$. Before training the segmentation model, we first warm up the teacher module for five epochs. We set $\lambda=0.1$, $\alpha=0.5$, and $\beta=0.9$.
As for foundation models, in terms of the VLP model, we find that MaskCLIP~\cite{zhou2021maskclip} is an alternative solution to adapt CLIP for better dense prediction, and we use its mechanism based on the pre-trained CLIP with ViT-B architecture.
In terms of the self-supervised model, we use pre-trained iBOT~\cite{zhou2021ibot} with ViT-L architecture by default.

\subsection{Baselines}
Since weakly incremental learning for semantic segmentation (WILSS) is a novel setting proposed by WILSON~\cite{cermelli2022wilson}, we also compare our framework with both supervised incremental learning and weakly supervised semantic segmentation methods as in~\cite{cermelli2022wilson}.
For supervised incremental learning methods using dense pixel-wise annotations, we compare with eight representative state-of-the-art works, including LWF~\cite{li2017lwf}, LWF-MC~\cite{rebuffi2017lwfmc}, ILT~\cite{michieli2019ilt}, MiB~\cite{cermelli2020mib}, PLOP~\cite{douillard2021plop}, CIL~\cite{klingner2020cil}, SDR~\cite{michieli2021sdr}, and RECALL~\cite{maracani2021recall}.
As for the weakly supervised semantic segmentation methods adopted to the incremental learning scenario, we compare with the reported results with the pseudo labels generated from class activation maps (CAM), SEAM~\cite{wang2020seam}, SS~\cite{araslanov2020ss}, and EPS~\cite{lee2021eps} as in~\cite{cermelli2022wilson}.

\subsection{Results.}
\subsubsection{Performance on 15-5 VOC}
In this setting, for a fair comparison, we also introduce 5 classes in the incremental step as in~\cite{cermelli2022wilson}: \textit{plant, sheep, sofa, train, tv monitor.}
As shown in Table~\ref{tbl:voc15-5}, our {FMWISS}{} achieves the new state-of-the-art results in all the settings (disjoint and overlap) compared to all the pixel label based and image label based methods.
To be more specific, compared to pixel label based methods, our WILSS method {FMWISS}{} even outperforms the best method by 3.5\% and 3.2\% in the two settings, respectively.
Compared to image label based methods, {FMWISS}{} improves the overall performance by \textbf{3.4\%} and \textbf{6.1\%} in the two settings against previous SoTA WILSON~\cite{cermelli2022wilson}.
Notably, {FMWISS}{} significantly improves the performance on new classes (16-20) by \textbf{7.0\%} and \textbf{12.8\%} in the disjoint and overlap settings, respectively.

\def{P}{{P}}
\def{I}{{I}}
\begin{table}[t!]
\centering
\resizebox{\linewidth}{!}{%
\begin{tabular}{rc|lll|lll}
\toprule
\multirow{2}{*}{Method} & \multirow{2}{*}{Sup}      & \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
                        &                           & 1-15    & 16-20    & All     & 1-15    & 16-20    & All    \\
\midrule
Joint$^{\ast}$                      				& {P}{}         & 75.5    & 73.5     & 75.4    & 75.5    & 73.5     & 75.4   \\ \hline
FT$^{\ast}$                         				& {P}{}         & 8.4     & 33.5     & 14.4    & 12.5    & 36.9     & 18.3  \\
LWF$^{\ast}$~\cite{li2017lwf}       			& {P}{}         & 39.7    & 33.3     & 38.2    & 67.0    & 41.8     & 61.0   \\
LWF-MC$^{\ast}$~\cite{rebuffi2017lwfmc}  	& {P}{}    	   & 41.5    & 25.4     & 37.6    & 59.8    & 22.6     & 51.0   \\
ILT$^{\ast}$~\cite{michieli2019ilt}      			& {P}{}       & 31.5    & 25.1     & 30.0    & 69.0    & 46.4     & 63.6   \\
CIL$^{\ast}$~\cite{klingner2020cil}      		& {P}{}       & 42.6    & 35.0     & 40.8    & 14.9    & 37.3     & 20.2   \\
MIB$^{\ast}$~\cite{cermelli2020mib}      		& {P}{}        & 71.8    & 43.3     & 64.7    & 75.5    & 49.4     & 69.0   \\
PLOP~\cite{douillard2021plop}            		& {P}{}       & 71.0    & 42.8     & 64.3    & \underline{75.7}    & 51.7     & \underline{70.1}   \\
SDR$^{\ast}$~\cite{michieli2021sdr}     		& {P}{}        & \underline{73.5}    & 47.3     & \underline{67.2}    & 75.4    & 52.6     & 69.9   \\
RECALL$^{\ast}$~\cite{maracani2021recall}  	& {P}{}       & 69.2    & \underline{52.9}     & 66.3    & 67.7    & \underline{54.3}     & 65.6   \\
\midrule
CAM$^{\dagger}$                     						& {I}{}   & 69.3    & 26.1     & 59.4    & 69.9    & 25.6     & 59.7   \\
SEAM$^{\dagger}$~\cite{wang2020seam}        			& {I}{}    & 71.0    & 33.1     & 62.7    & 68.3    & 31.8     & 60.4   \\
SS$^{\dagger}$~\cite{araslanov2020ss}       				& {I}{}   & 71.6    & 26.0     & 61.5    & 72.2    & 27.5     & 62.1   \\
EPS$^{\dagger}$~\cite{lee2021eps}           				& {I}{}    & 72.4    & 38.5     & 65.2    & 69.4    & 34.5     & 62.1   \\
WILSON$^{\dagger}$~\cite{cermelli2022wilson}  			& {I}{}    & 73.6    & 43.8     & 67.3    & 74.2    & 41.7     & 67.2   \\
{FMWISS}{} (Ours)                              & {I}{}    & \textbf{75.9 (+2.3)}  & \textbf{50.8 (+7.0)}  & \textbf{70.7 (+3.4)}  & \textbf{78.4 (+4.2)}  & \textbf{54.5 (+12.8)} & \textbf{73.3 (+6.1)} \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Results on the 15-5 setting of Pascal VOC. $^{\ast}$ denotes the results are from~\cite{maracani2021recall}, $^{\dagger}$ denotes the results are from~\cite{cermelli2022wilson}. `P' and `I' indicate pixel-level and image-level labels, respectively. The best methods of using image-level labels and using pixel-level labels as supervision are \textbf{bold} and \underline{underlined}, respectively.}
\label{tbl:voc15-5}
\vspace{-.1in}
\end{table}

\subsubsection{Performance on 10-10 VOC}
In this setting, for a fair comparison, we also introduce 10 classes in the incremental step as in~\cite{cermelli2022wilson}: \textit{dining table, dog, horse, motorbike, person, plant, sheep, sofa, train, tv monitor.}
As reported in Table~\ref{tbl:voc10-10}, our {FMWISS}{} achieves the new state-of-the-art performance against the image label based methods and achieves \textit{on par} or even better performance than the pixel label based methods.
Specifically, compared to pixel label based methods, we achieve an overall performance of 64.6\% on disjoint protocol, which is very close to ILT's 64.7\%. On overlap protocol, we achieve an overall performance of 69.1\%, which is even 1.8\% higher than SDR's 67.4\%.
Compared to image label based methods, our {FMWISS}{} achieves the best results on all the protocols, and we achieve overall performance improvements of \textbf{3.8\%} and \textbf{4.1\%} in both settings compared to WILSON~\cite{cermelli2022wilson}.

\begin{table}[t!]
\centering
\resizebox{\linewidth}{!}{%
\begin{tabular}{rc|lll|lll}
\toprule
\multirow{2}{*}{Method} & \multirow{2}{*}{Sup} & \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
                        &                      & 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
Joint$^{\ast}$                   					& {P}{}                & 76.6    & 74.0     & 75.4    & 76.6    & 74.0     & 75.4   \\ \hline
FT$^{\ast}$                        				& {P}{}                & 7.7     & 60.8     & 33.0    & 7.8     & 58.9     & 32.1  \\
LWF$^{\ast}$~\cite{li2017lwf}                     	& {P}{}                & 63.1    & 61.1     & 62.2    & \underline{70.7}    & 63.4     & 67.2   \\
LWF-MC$^{\ast}$~\cite{rebuffi2017lwfmc}         & {P}{}                & 52.4    & 42.5     & 47.7    & 53.9    & 43.0     & 48.7   \\
ILT$^{\ast}$~\cite{michieli2019ilt}                       & {P}{}                & \underline{67.7}    & \underline{61.3}     & \underline{64.7}    & 70.3    & 61.9     & 66.3   \\
CIL$^{\ast}$~\cite{klingner2020cil}                     & {P}{}                & 37.4    & 60.6     & 48.8    & 38.4    & 60.0     & 48.7   \\
MIB$^{\ast}$~\cite{cermelli2020mib}                  & {P}{}                & 66.9    & 57.5     & 62.4    & 70.4    & 63.7     & 67.2   \\
PLOP~\cite{douillard2021plop}                        	& {P}{}                & 63.7    & 60.2     & 63.4    & 69.6    & 62.2     & 67.1   \\
SDR$^{\ast}$~\cite{michieli2021sdr}     		& {P}{}                & 67.5    & 57.9     & 62.9    & 70.5    & \underline{63.9}     & \underline{67.4}   \\
RECALL$^{\ast}$~\cite{maracani2021recall}     & {P}{}                & 64.1    & 56.9     & 61.9    & 66.0    & 58.8     & 63.7   \\
\midrule
CAM$^{\dagger}$                     & {I}{}                			& 65.4    & 41.3     & 54.5    & 70.8    & 44.2     & 58.5   \\
SEAM$^{\dagger}$~\cite{wang2020seam}                    		& {I}{}                & 65.1    & 53.5     & 60.6    & 67.5    & 55.4     & 62.7   \\
SS$^{\dagger}$~\cite{araslanov2020ss}                      		& {I}{}                & 60.7    & 25.7     & 45.0    & 69.6    & 32.8     & 52.5   \\
EPS$^{\dagger}$~\cite{lee2021eps}                     			& {I}{}                & 64.2    & 54.1     & 60.6    & 69.0    & 57.0     & 64.3   \\
WILSON$^{\dagger}$~\cite{cermelli2022wilson}                  	& {I}{}                & 64.5    	& 54.3     		& 60.8    	& 70.4    	& 57.1     & 65.0   \\
{FMWISS}{} (Ours)                  					& {I}{}                &  \textbf{68.5 (+4.0)}       &  \textbf{58.2 (+3.9)}        	& \textbf{64.6 (+3.8)}     & \textbf{73.8 (+3.4)}    & \textbf{62.3 (+5.2)}   & \textbf{69.1 (+4.1)} 	\\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Results on the 10-10 setting of Pascal VOC. $^{\ast}$ denotes the results are from~\cite{maracani2021recall}, $^{\dagger}$ denotes the results are from~\cite{cermelli2022wilson}.}
\label{tbl:voc10-10}
\end{table}

\subsubsection{Performance on COCO-to-VOC}
This is a more challenging setting. First, the base model is trained on 60 classes of the COCO dataset, which are not overlapped with VOC. Then we train the additional 20 classes from VOC dataset with image-level labels in the second step.
The results are reported in Table~\ref{tbl:coco2voc}, {FMWISS}{} also achieves the new
state-of-the-art performance against the WILSS methods.

\begin{table}[t!]
\centering
\resizebox{0.85\linewidth}{!}{%
\begin{tabular}{rc|lll|l}
\toprule
\multirow{2}{*}{Method} & \multirow{2}{*}{Sup}      & \multicolumn{3}{c|}{COCO} &  VOC \\
                        &                           & 1-60    & 61-80    & All     & 61-80        \\
\midrule
FT$^{\dagger}$                         			& {P}{}	& 1.9     	& 41.7     & 12.7	& \underline{75.0}     \\
LWF$^{\dagger}$~\cite{li2017lwf}       		& {P}{}      & 36.7	& \underline{49.0}     & \underline{40.3}    	& 73.6       \\
ILT$^{\dagger}$~\cite{michieli2019ilt}      		& {P}{}    	& \underline{37.0}    	& 43.9     & 39.3    	& 68.7      \\
MIB$^{\dagger}$~\cite{cermelli2020mib}    	& {P}{}    	& 34.9    	& 47.8     & 38.7    	& 73.2       \\
PLOP$^{\dagger}$~\cite{douillard2021plop}            	& {P}{}    	& 35.1    	& 39.4     & 36.8    	& 64.7      \\
\midrule
CAM$^{\dagger}$                     					& {I}{}   & 30.7    	& 20.3     & 28.1    	& 39.1     \\
SEAM$^{\dagger}$~\cite{wang2020seam}        		& {I}{}   & 31.2    	& 28.2     & 30.5    	& 48.0       \\
SS$^{\dagger}$~\cite{araslanov2020ss}       			& {I}{}   & 35.1    	& 36.9     & 35.5    	& 52.4      \\
EPS$^{\dagger}$~\cite{lee2021eps}           			& {I}{}   & 34.9    	& 38.4     & 35.8    	& 55.3      \\
WILSON$^{\dagger}$~\cite{cermelli2022wilson}  		& {I}{}   & 39.8    	& 41.0     & 40.6    	& 55.7      \\
{FMWISS}{} (Ours)                  		& {I}{}   & \textbf{39.9 (+0.1)}   & \textbf{44.7 (+3.7)} & \textbf{41.6 (+1.0)}    & \textbf{63.6 (+7.9)}      \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Results on the COCO-to-VOC setting. $^{\dagger}$ denotes the results are from~\cite{cermelli2022wilson}.}
\label{tbl:coco2voc}
\vspace{-.1in}
\end{table}

\subsection{Ablation Studies}
Unless otherwise specified, we perform the ablation experiments with iBOT~\cite{zhou2021ibot} as the self-supervised model with ViT-B architecture based on the 10-10 VOC setting.
We provide more ablation details, {\itshape e.g.}, ablations of $\alpha, \beta, \mathcal{K}$, in our ${\tt supplementary}$ materials.

\subsubsection{Effect of Number of Seeds}
As depicted in Figure~\ref{fig:seeds}, we visualize the impact of number of seeds when calculating $\mathcal{M}_{seeds}$. Based on the category-aware $\mathcal{M}_{init}$ of two classes (\textit{horse, dog}), more random seeds guidance leads to more compact attention maps and nine seeds are enough to get good clustering results for training efficiency.
Moreover, the category-agnostic $\mathcal{M}_{seeds}$ can be complementary to the initial $\mathcal{M}_{init}$, which is indicated by red boxes.

\begin{figure}[t!]
\centering
	\includegraphics[width=0.94\linewidth]{seedsv2.pdf}
    \vspace{-.1in}
	\caption{Effect of the number of randomly selected seeds.}
	\label{fig:seeds}
	\vspace{-.1in}
\end{figure}

\subsubsection{Analysis of Mask Fusion}
In this section, we verify the effect of mask fusion operation in Eq.~(\ref{eq:fusion}). As shown in Table~\ref{tbl:mask_fusion}, we compare the results of two fusion operations and the result without fusion (``None''). Performing co-segmentation with ``Union'' can significantly improve performance, especially on new classes (53.25\% $\rightarrow$ 55.45\%, 56.39\% $\rightarrow$ 60.54\%).
The results indicate that the proposed pre-training based co-segmentation does improve the supervision and performance for WILSS against original image-level labels.

\begin{table}[t!]
\centering
\resizebox{0.8\linewidth}{!}{%
\begin{tabular}{c|ccc|ccc}
\toprule
 Fusion 		& \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
Operation    & 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
None           &  67.83           &  53.25        &  61.96       &  73.25      & 56.39        & 66.45  \\
Intersection	       &  66.85           & 51.17         &  60.40       &  74.12      & 54.02        & 64.95  \\
Union                      &  67.23           &  55.45        &  \textbf{62.74}       &  73.12      & 60.54        & \textbf{67.94}  \\

\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Performance comparison of the mask fusion operation. ``None'' denotes using only the $\mathcal{M}_{init}$ from CLIP.}
\label{tbl:mask_fusion}
\end{table}

\subsubsection{Effect of Dense Contrastive Objective}
We further analyze the effect of the proposed dense contrastive loss in Table~\ref{tbl:contrast}. Compared to the result without using $\mathcal{L}^{new}_{\text{DCL}}$ ($\lambda=0.0$), introducing our proposed dense contrastive loss with a loss weight of 0.1 further improves the performance on new classes by 1.77\% and 0.38\% in the two settings, respectively. We thus set $\lambda=0.1$ in our experiments by default.
The results show that the plug-in teacher module equipped with the proposed $\mathcal{L}^{new}_{\text{DCL}}$ can more effectively optimize and leverage the dense supervision for WILSS.

\begin{table}[t!]
\centering
\resizebox{0.8\linewidth}{!}{%
\begin{tabular}{c|ccc|ccc}
\toprule
\multirow{2}{*}{$\lambda$ of $\mathcal{L}^{new}_{\text{DCL}}$} 		& \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
                                                                & 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
0.0     & 67.23         &   55.45      &  62.74         & 73.12        & 60.54        & 67.95    \\
0.1     & 67.94         &   57.22      &  \textbf{63.91}        &  73.44        &  60.92       & \textbf{68.28}   \\
1.0     & 67.15         &   57.94      &  63.87         & 72.08        &  61.05       &  68.17 \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Ablation experiments on the dense contrastive objective $\mathcal{L}^{new}_{\text{DCL}}$. $\lambda=0.0$ represents eliminating the dense contrastive loss.}
\label{tbl:contrast}
\end{table}

\subsubsection{Effect of Memory-based Copy-paste Augmentation}
As reported in Table~\ref{tbl:copypaste}, we analyze the effect of the proposed memory-based copy-paste augmentation. Without further tuning, we fix the augmentation probability as 0.5.
Compared with the results without augmentation, applying the copy-paste augmentation with $\mathcal{B}=50$ can already improve the performance of old classes (67.94\% $\rightarrow$ 68.64\% in disjoint, 73.44\% $\rightarrow$ 73.71\% in overlap) for saving memory consumption.

\begin{table}[t!]
\centering
\resizebox{0.8\linewidth}{!}{%
\begin{tabular}{cc|ccc|ccc}
\toprule
\multirow{2}{*}{Rand.}		& Memory-bank 		& \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
                            & $\mathcal{B}$   	& 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
\multirow{5}{*}{0.5}  	  &  0      & 67.94         	&   57.22      	&  63.91       &   73.44       &  60.92       & 68.28   \\
					   &  10       & 68.85            	&   57.14       	&  64.29       &    73.11      &  61.50       & 68.40  \\
						 &  50       & 68.64           	& 57.90         	&  \textbf{64.56}       &    73.71     	&  62.06       & \textbf{68.95}	  \\
						 & 100     & 68.41   		& 58.09       	&  64.55       &    73.26     	&  61.78       & 68.60   \\
						 &  500     & 68.73           	& 58.29        	&  64.80       &    73.50      &  62.28       & 68.97   \\

\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Ablation experiments on the memory-based copy-paste augmentation. $\mathcal{B}=0$ denotes removing augmentation.}
\label{tbl:copypaste}
\vspace{-.1in}
\end{table}

\subsubsection{Effect of Different Self-supervised Models}
We experiment with two representative self-supervised models~\cite{zhou2021ibot,caron2021dino} based on different ViT architectures.
As shown in Table~\ref{tbl:selfup_model}, both bring promising results and we use iBOT with ViT-L for better and stable performance

\begin{table}[t!]
\centering
\resizebox{0.85\linewidth}{!}{%
\begin{tabular}{cc|ccc|ccc}
\toprule
Self-supervised		& \multirow{2}{*}{Arch.}  & \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
Model				& 			     		  & 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
\multirow{2}{*}{iBOT~\cite{zhou2021ibot}}  	  &  ViT-B  & 68.64  & 57.90  &  64.56  & 73.71 &  62.06 & 68.95	  \\
						                   &  ViT-L  & 68.51  & 58.20  &  \textbf{64.64} &  73.79 & 62.26  & \textbf{69.09} \\
						                     \cmidrule{2-8}
\multirow{2}{*}{DINO~\cite{caron2021dino}} 	  &  ViT-B  & 68.01  & 59.14  &  64.86  & 73.11 &  60.98 & 68.14  \\
						                     &  ViT-S  & 66.86  & 58.85	&  64.17  & 70.97 &	 59.57 & 66.43  \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Performance comparison by using different self-supervised pre-training models.}
\label{tbl:selfup_model}
\end{table}

\subsubsection{Factor-by-factor Experiments}
We conduct a factor-by-factor experiment on the proposed pre-training based co-segmentation, dense contrastive loss, and memory-based copy-paste augmentation.
As shown in Tabel~\ref{tbl:factorbyfactor}, each design has a positive effect, and all designs are combined to obtain the best performance.

\begin{table}[t!]
\centering
\resizebox{\linewidth}{!}{%
\begin{tabular}{ccc|ccc|ccc}
\toprule
Pre-training         & \multirow{2}{*}{$\mathcal{L}^{new}_{\text{DCL}}$}  & Copy-paste	    & \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
based Co-seg.        &                                             & Aug.           & 1-10  & 11-20  & All   & 1-10  & 11-20 & All  \\
\midrule
                     &                                             &                & 67.83 & 53.25  & 61.96  & 73.25 & 56.39 & 66.45 \\
\checkmark           &                                             &                & 67.23 & 55.45  & 62.74  & 73.12 & 60.54 & 67.94 \\
\checkmark           &  \checkmark                                 &                & 67.94 & 57.22  & 63.91  & 73.44 & 60.92 & 68.28 \\
\checkmark           &  \checkmark                                 & \checkmark     & 68.64 & 57.90  & 64.56  & 73.71 & 62.06 & 68.95 \\
\checkmark           &  \checkmark                                 & \checkmark     & 68.51 & 58.20  & \textbf{64.64}  & 73.79 & 62.26 & \textbf{69.09} \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Effect of each design proposed in this work. The last row indicates the result of using ViT-L architecture.}
\label{tbl:factorbyfactor}
\end{table}

\begin{table}[t!]
\centering
\resizebox{0.8\linewidth}{!}{%
\begin{tabular}{rc|ccc|ccc}
\toprule
\multirow{2}{*}{Method}		        & \multirow{2}{*}{Sup} 		 & \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
                                    &    	                     & 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
WILSON~\cite{cermelli2022wilson}    & I                          & 64.5 & 54.3 & 60.8 & 70.4 & 57.1 & 65.0 \\
WILSON~\cite{cermelli2022wilson}    & P                          & 69.5 & 56.4 & 64.2 & 73.6 & 57.6 & 66.7 \\
\midrule
{FMWISS}{} (Ours)  	                &  I                         & 68.5 & 58.2 & \textbf{64.6} & 73.8 & 62.3 & \textbf{69.1}  \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Comparison with previous WILSS SoTA~\cite{cermelli2022wilson} trained with direct dense annotations.}
\label{tbl:com_dense}
\end{table}

\begin{table}[t!]
\centering
\resizebox{0.8\linewidth}{!}{%
\begin{tabular}{rc|ccc|ccc}
\toprule
\multirow{2}{*}{Method}             & Train  		 & \multicolumn{3}{c|}{Disjoint} & \multicolumn{3}{c}{Overlap} \\
                                    & Data    	     & 1-10    & 11-20    & All     & 1-10    & 11-20    & All    \\
\midrule
WILSON~\cite{cermelli2022wilson}    & 100\%          & 64.5    & 54.3  & 60.8  & 70.4  & 57.1  & 65.0   \\
\midrule
\multirow{3}{*}{{FMWISS}{} (Ours)}            & 100\%          & 68.5    & 58.2  & 64.6  & 73.8  & 62.3  & 69.1	\\

                                    & 50\%           & 66.7    & 56.0  & 62.7  & 72.1  & 60.5  & 67.4 \\
                                    & 30\%           & 68.5    & 51.5  & 61.5  & 75.7  & 55.7  & 66.8 \\
\bottomrule
\end{tabular}%
}
\vspace{-.1in}
\caption{Performance comparison with fewer training data.}
\vspace{-.1in}
\label{tbl:datasize}
\end{table}

\subsubsection{Data Efficiency Experiment}
We first compare with WILSON~\cite{cermelli2022wilson} trained with direct dense pixel-level labels (P) for all classes in Table~\ref{tbl:com_dense}. It is worth noting that {FMWISS}{} based on only image-level labels (I) still outperforms it, especially in the challenging overlap setting.
We further evaluate {FMWISS}{} with fewer training data in Table~\ref{tbl:datasize}. It is notable that {FMWISS}{} trained with only 30\% data still outperforms WILSON trained with 100\% data.
Combining Table~\ref{tbl:com_dense}, Table~\ref{tbl:datasize}, and the fast convergence result (Sec.~4) in {\tt supplementary} materials, we can conclude that {FMWISS}{} is a significantly data-efficient WILSS framework.

\subsubsection{Visualization}

We report qualitative results indicating the superiority of our {FMWISS}{} framework on both old ({\itshape e.g.}, \textit{bottle}) and new ({\itshape e.g.}, \textit{person, horse, dog, sofa}) classes in Figure~\ref{fig:visualize}.

\begin{figure}[t!]
\centering
	\includegraphics[width=0.91\linewidth]{vis.pdf}
    \vspace{-.1in}
	\caption{Qualitative comparison between previous WILSS SoTA~\cite{cermelli2022wilson} and our {FMWISS}{} on the 10-10 VOC setting. From left to right: image, WILSON~\cite{cermelli2022wilson}, {FMWISS}{} and the ground-truth.}
	\label{fig:visualize}
	\vspace{-.1in}
\end{figure}

\section{Limitations}
Like WILSON~\cite{cermelli2022wilson}, the {FMWISS}{} framework is not designed for single-class incremental learning steps, the proposed dense contrastive objective needs some other classes as negative samples.

\section{Conclusion}

In this paper, we present a novel and data-efficient {FMWISS}{} framework for weakly incremental learning for semantic segmentation. {FMWISS}{} is the first attempt to exploit knowledge of pre-trained foundation models for WILSS.
We propose pre-training based co-segmentation to generate dense supervision based on image-level labels.
We further use a teacher-student architecture with a proposed dense contrastive loss to more effectively utilize the pseudo labels.
Besides, we introduce memory-based copy-paste augmentation to improve the forgetting problem of old classes.
Extensive experiments demonstrate the superior results of {FMWISS}{}.

{\small
\bibliographystyle{ieee_fullname}

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We found MFPEasy online and when we made an enquiry we were contacted within a day or two. The person who contacted us was really nice and informative. Even though we weren't ready to build at the time, the person who initially made contact kept checking up on us to see how we were going with everything, which we thought was nice. We felt that the communication was very thorough and we felt involved and knew what was going on throughout the whole process. One of the things that stood out on the job site was the politeness of the tradesmen, they were very well mannered and they did not swear or anything. The installation was very smooth, we had no problems at all. We would absolutely recommend MFPEasy.
We had some friends who had their pool done around the corner. We liked how the product was installed and how it came out. The ease of process stood out, everything flowed really well. Every occasion I rang wanting something resolved to a question, it was done on the spot. If not, they always promptly returned my call. With regards to the installation, everything was very professional and tidy. What we were told we were paying for was what we paid for. We have already recommended MFPeasy to our friends. Very easy people to work with, when you are handing over a lot of money, you have peace of mind, knowing you're working with professionals. Polite service, the best experience we've had.
They had ownership in the way they spoke to me. It wasn't just a job, but a passion. Everything was at a high level. The communication was good. If we had any queries they always got back to us promptly. I felt that we had ownership of the process as it was happening, and were kept in the loop. I have already recommended them.
I found their prices were a lot cheaper than their competitors. It's the first pool I have ever had. I liked the fact that I could do some of the work myself. They installed the pool shell and I did all the landscaping myself. The communication was good, if I had any queries they answered them through phone calls and emails. No complaints with the installation process. Everything went smoothly and was easy.
The process took longer than I was expecting, because we had considerably bad weather so that did make it a bit difficult. The day the pool was meant to go in it poured down with rain! So it didn't start very well but towards the end it came together nicely. Once Michael got onto the Job everything ran really smoothly. I can't fault his communication his professionalism. Whatever he said he was going to do, he made sure it was completed. He always followed up and delivered. Everyone was great in their communication always getting back to me. Especially warren, even though he was very busy he would always make sure to call back if he missed a call. I am very happy with how involved I was and I felt like my decisions were heard and followed through on. Once Michael was on the scene I felt confident that everything would get done exactly the way it should. I did have a problem with how the water feature was placed but as soon as I spoke to Warren about it he organised to get it re-done which was fantastic! We are very happy with the overall result. We were able to swim as soon as the pool went in, but for safety we couldn't have others over until everything was completed. Overall the pool looks great and it will be getting lots of use in the coming Summer Holidays!
My experience with MFPE was very good. When I called Warren for the quote he just seemed really good and honest and the price was very competitive, so that's why I went with them. In fact everyone I dealt with on the team was really good. They would all call me with any little issues and fix them straight away. If they missed my call, which was very rare, they would get back to me straight away so communication was super easy. I was made to feel very involved in the process, and any concerns that I had were always discussed and resolved quickly. Everyone was happy to work as a team, myself included so there were no dramas whatsoever. We did have a tree that was in the way of the pool that we had to remove, but that wasn't anyone's fault. Apart from that everything worked out well. We are so happy with it and excited for summer when we can move in!
We got a few quotes for pools from different companies but they were all too expensive, we were on a very tight budget. So we decided to look for pool kits. When we came across MFPE the price was too good to refuse! It was perfect and we had the option to do it ourselves which I really liked. We still got a quality pool that was exactly the same as the other ones we were looking at, but it was $1000 cheaper! That wasn't a special deal either, just the normal price! I was very impressed. Michael and Warren were really helpful during the installation. They gave me tips on how to get the angles and the levels right, and the best way to install the pool, which I thought was great customer service. Even after the sale, they were still interested; wanting to make sure everything went well for me. If I needed to call them for advice they were ready to answer my questions, and they always got back to me straight away. I really am happy with all that they have done, and if I had to do it again, I'd definitely go with MFPE.
Dealing with MFPE was a really good experience. It was simple and easy. They forwarded me the plans and I told them what I wanted to do. There were no instructions on the plans regarding where to lay certain plumbing and valves for hot water (maybe they could include this in the future?) etc, but it was easy enough to get a hold of Michael and he talked me through the whole process and I had no problems. I'm very happy with the quality of the pool and my experience with MFPE. Supply Date: 01/06/2015.
MFPE's communication was above and beyond what we expected.
Sometimes I would send an email on a Saturday, hoping for a Monday close of business reply but received a reply as soon as Saturday night. It was simple enough to understand, and detailed enough to give us confidence. When the pool was going in, Warren made a few very good suggestions and we went with them. For example, he suggested putting in the provisions for heating so that at some point in the future, if we want to, it will be very simple to switch it over. We did not find MFPE pushy at all. Instead, they listened to what we wanted and made sure it was achievable. They involved us at a level that we were comfortable with which was great. The actual install of the pool was far more exciting than it was nerve racking! It's not every day that you can get a crane come to your place to lift a pool shell down the side of your house. Several of our neighbours came to see what all the fuss was about and the kids loved watching it too. We didn't price other pavers so we couldn't say for sure how competitive the 3D pricing was, but what we can say is that it certainly was very convenient! The display pavers were in the back of the 3D truck which made it simple and easy to choose what we wanted, from our driveway!. We really felt that the tradespeople were much tidier than some other tradespeople that have worked in our backyard. There was some damage to our grass, but it was nothing we weren't already expecting, so that was no problem. End Result? Brilliant. Great. As an addition to the backyard from an aesthetic point of view, we are thrilled. The kids get so much fun out of it and it has certainly added value to our property. When we made the decision to do it, we were really pleased and we have not been disappointed at all. We had a few other quotes… but we chose to go with MFPE because Warren was friendly but also extremely professional and was able to tell us when each step would happen (which it did!). Whenever we asked a question, his extensive knowledge of the industry and our specific job meant that he could answer us on the spot. It has quite definitely met our expectations and was much less stressful that we had envisaged. Definitely, definitely, definitely, definitely EASY! We have already recommended MFPE to our friends because it was exactly that, EASY! Warren told us it would take three days and we hesitantly accepted that, but when the dig started on a Wednesday and we were swimming on Friday night, we couldn't have been happier! Communication 5/5 Involvement 5/5 Install Process 5/5 Overall Result 5/5 Installed: 12/01/2015.
After hearing a number of "no, we can't"s from other pool companies, it was great to hear Warren explain how it was possible to achieve our dream pool. As we had a difficult site, all potential problems were discussed up front so we could have back up plans in place. His ideas about where to put the pump and the layout etc were really effective. We chose our pavers online with 3D and then discussed it with the team over the phone. They were helpful and gave us great service. We knew exactly what was going on the whole time and whenever we needed to get in touch with the boys to ask a question, everything was fully explained and they were always easy to contact. When it came time for the install, we had total confidence. Due to our location, everything had to be scheduled very tightly. On the day, everything turned up as the boys said it would and the install ran smoothly and seamlessly. The team cleaned up after themselves and left our property looking great. The whole process with MFPE was most definitely that – easy. We love our pool. Absolutely love it. The brilliant black colour makes the water just gorgeous. The coping and paving looks wonderful. Working in the construction industry, we understand that problems can happen. Whenever we had a slight concern, Warren dealt with our query himself immediately or put us in touch with someone who could help out straight away. We couldn't be happier! Communication 5/5 Involvement 4.5/5 Install Process 4/5 Overall Result 5/5 Installed: 24/11/2014.


Notes: A popular spot close to Longlands Beck which leaves excellent access onto Longlands Fell and the Uldale Fells via the Cumbrian Way. Due to its popularity it is advised to arrive early if you want to secure a parking places as the spaces can fill up quickly. Parking is free.


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Changes in cotton policy coming in China?
The United States has to pay Brazil millions of dollars each year for failing to eliminate certain cotton subsidies. Meanwhile China runs roughshod over free-market principles, paying its domestic cotton producers $1.25 per pound when the current world price is significantly less than that.
China has spent about $10 billion so far this marketing year on this perplexing policy — hoarding millions of bales of cotton, via imports and purchases from its domestic producers. Joe Nicosia, CEO of Allenberg Cotton Company, believes China was hoping the huge reserve would tighten the market around the rest of the world and drive cotton prices higher.
The idea was that China could then sell cheaper cotton to its domestic textile industry. China was foiled in this attempt, however, because the surplus of cotton outside China was much larger than anticipated. World prices never rose.
WTO enforcers haven't even raised an eyebrow over China's attempt to control cotton prices. Perhaps they know that in China, capitalism is knotted by fear and appeasement.
For example, there is a great deal of political and ethnic unrest in the Xinjiang Province, China's largest cotton-producing area. Keeping everybody happy there drives a lot of cotton price policy, according to Nicosia.
But more often than not, China's policies are all about control. For example, China's ruling elite felt a loss of control after they sold cotton into the rally of 2010-11, according to Nicosia. When they ran out of cotton, they had no government response to prices that continued to move higher. "They lost their ability to have any influence over their domestic market and they didn't like that," Nicosia said.
To get out of the mess, China could take it on the chin and unload its cotton reserve on the rest of the world in one fell swoop. But if they did, it would be an admission that the stock hoarding was bad policy. China doesn't like admitting failure either.
Who knows what they'll do.
The picture could become clearer this fall, as China's party congress selects new leadership to rule the country's 1.4 billion people, hungry for reform. With unrest in Egypt, Syria and Libya as a backdrop, a policy based on keeping people happy may not be the way to go anymore.


By Samuel Renihan. Discovered by Player FM and our community — copyright is owned by the publisher, not Player FM, and audio streamed directly from their servers.
308 episodes available. A new episode about every 2 days averaging 42 mins duration .
A new MP3 sermon from Trinity Reformed Baptist Church is now available on SermonAudio.com with the following details: Title: Resurrection Hope in Hosea Speaker: Dr. Samuel Renihan Broadcaster: Trinity Reformed Baptist Church Event: Sunday - AM Date: 4/21/2019 Bible: Hosea 6:1-6 Length: 44 min.
A new MP3 sermon from Trinity Reformed Baptist Church is now available on SermonAudio.com with the following details: Title: You Need to Repent Subtitle: Jesus and Nicodemus Speaker: Campbell Colledge Broadcaster: Trinity Reformed Baptist Church Event: Sunday Service Date: 4/21/2019 Length: 38 min.
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text:
Teleportation just got easier – but not for you, unfortunately
Ben Buchler, Australian National University – The Conversation
Filed to:Futurism
Thanks to two studies published in Nature last Thursday, the chance of successful teleportation has considerably increased. Which is a good thing, right?
Top image by Photon™ via flickr
Whether or not you've ever been on a long-haul flight, you've probably fantasised about being able to magically disappear from one place and reappear in another. And a natural question for a physicist is whether there is any way to achieve this in practice.
In fact, something known as "quantum teleportation" became a reality in 1997. This first demonstration was for particles of light (photons). Since then, physicists have also applied teleportation to other very small things, for example single atoms.
So when can we expect to just teleport ourselves to our chosen destination? You might want to sit down for this.
The first step to teleporting a person is measuring and recording the position, direction of motion and energy of every particle in the body, which would require more data storage than will ever be available – much, much more.
In fact, a conservative estimate would mean you'd need about 1022 gigabytes (1 followed by 22 zeros) of hard drive space. That's a stack of hard drives about 20 light-years tall.
Proxima Centauri, the nearest star to Earth other than the sun, is around four light-years away.
Worse, we have no method to even make these measurements, let alone reconstruct a person based on the data. So we can forget about teleporting people.
Knowing enough – but not too much
What about something really simple – such as a single particle? How about an atom, or a photon? How can these be teleported?
The problem here was thought to be the Heisenberg uncertainty principle, a cornerstone of quantum mechanics that limits what you can know.
It might sound counter-intuitive, but if you try to measure the position of a single atom you will change its velocity. If you find out exactly how fast it is moving, then you won't know where it is.
The problem is, if you want to teleport a particle, this is precisely the information you want to measure and transmit.
A physicist would call this information the "state" of the particle. If you're not allowed to measure the complete state of the particle, teleportation looks impossible.
Photo Credit: jasoneppink
So the key to teleportation is not knowing too much. As long as the measurements that you make do not reveal the position or velocity, then you have a loophole that allows you to circumvent the uncertainty principle.
What if you could disturb the particle before you measure it, so you never know its state, and then subtract off that disturbance at the other end to recreate the original state of the particle?
This was the breakthrough realisation that American physicist Charles Bennett had in 1993. The key was to disturb the particle you want to teleport in a particular way. You can do this by using a pair of quantum-entangled particles.
These particles are linked to each other so that if you measure the state of one of the entangled pair, you learn about the state of the other half of the pair.
Alice and Bob
In the standard description of teleportation, Alice is teleporting something to Bob. Alice uses one of the entangled particles to measure the state of the input particle. She records what she measures and sends the information to Bob.
Bob can't tell what the state of the particle was, because the entanglement used in the measurement hides the true nature of the state.
What Bob can do, however, is use the information from Alice to modify the state of the other entangled particle. In this way he can recreate the exact state of the particle Alice originally measured.
This is how quantum teleportation works. Most photon experiments teleport over a metre or so inside a lab, although there has recently been a demonstration over 143km in the Canary Islands.
A sense of security
It turns out that quantum teleportation is not just a good party trick. The nature of the communication between Alice and Bob in this system is pretty interesting.
The information that Alice measures and sends to Bob cannot be used to recreate the input state without the other entangled particle. That means Eve the eavesdropper can't spy on Alice's measurement and get the information for herself.
The entangled pair is unique, so only Bob can recreate the original state. Immediately you have a technique for secure communication.
If you encode information in your particles, measure them with one part of an entangled state and then send the information to Bob, you have cryptography that is made strong by quantum physics. You really can't crack it by any means, unless you have the other part of the entangled pair.
A 128-qubit superconducting adiabatic quantum optimisation processor chip. Wikimedia Commons
Teleportation has many other uses in quantum information systems.
These are proposed methods for building computers and communication networks that use quantum mechanics as a core part of their functionality and have enormous potential to provide secure communications and high-speed computing.
The catch is that any time you want to move quantum information from one place to another in one of these systems, you can't just measure the information and send it to the next part of the process, since the measurement will destroy the information. Instead, you can teleport it.
The two papers published together in this week's Nature show something very important.
Until now, teleporting photons of light using the method described above has been probabilistic, because you couldn't synchronise the arrival of the entangled photons with the arrival of the photon to be measured.
On the odd occasion when the photons aligned, the measurement would only work half the time. That means every time you try and teleport your information it will only work very occasionally – much less than 1% of the time.
If you have a lot of back-to-back-teleporting circuits in your quantum computer or quantum network, the chances of them all working together will become vanishingly small.
These two most recent experiments show deterministic quantum teleportation in two different systems so that the process is no longer probabilistic. Instead it can, in principle, work every time a photon is ready to be teleported.
Photo Credit: mercurialn
One of the new studies – by researchers from Japan and Germany – shows how it is possible to teleport photons of light that are in the infrared spectrum, just below the wavelength visible to the human eye.
The other experiment – by researchers in Switzerland and Australia – demonstrates teleportation of microwave photons with a frequencies between 4 and 7 GHz.
Scientists teleport information in an electronic circuit
We're still a far way's off from being able to beam people through space, but in a science first,…
Neither system is production-ready, in the sense that they are both just proof of principle experiments. Although the teleportation is no longer probabilistic, it is still not 100% efficient – a 40% chance of success in the case of the infrared system and 25% in the case of the microwave system.
Still, this is a vast improvement on less than 1% that was previously possible with photons. Long-haul flights will continue for some time yet, but the new experiments represent a milestone on the long road to building a functional quantum information system.
Ben Buchler receives funding from the ARC centre of Excellence for Quantum Computation and Communication technology (CQC2T).
This article was originally published at The Conversation. Read the original article.

redpajama_set_name: RedPajamaCommonCrawl


text:
Why One of Trump's Biggest Legal Threats Is New York's Attorney General
Jan. 17, 2019 , at 8:00 AM
By Amelia Thomson-DeVeaux
Filed under Trump Docket
PHOTO ILLUSTRATION BY FIVETHIRTYEIGHT / GETTY IMAGES
This is the Trump Docket, where we track some of the most important legal cases of the Trump presidency and how their results could shape presidential power. Questions, comments, or thoughts about cases to cover? Email us here.
After two years of legal wrangling, the Trump Foundation will soon be no more. Last month, in the midst of a dramatic month for cases that stem from President Trump's pre-presidency life, a judge signed off on a plan to shutter Trump's much-criticized personal foundation. Under the new agreement, the foundation will be dissolved under court supervision.
In effect, the deal implies that the foundation cannot be trusted to disburse its remaining $1.7 million to legitimate nonprofits. But even though the foundation is dissolving, the lawsuit against the foundation will continue, with the New York attorney general seeking damages for the foundation's alleged "extensive and persistent violations of state and federal law," including the illegal use of foundation money to pay off legal settlements, buy portraits of Trump, and promote Trump's 2016 campaign.
The December settlement is an important reminder of the risk that the state of New York poses for Trump. In particular, New York is uniquely well-positioned to go after Trump where it could hurt him most — through his businesses. In fact, New York has been one of the most significant and I'd argue most underrated legal hazards for Trump since he began his campaign for president. Here are three reasons why.
New York has jurisdiction over Trump's family businesses
Pursuing legal challenges against Trump has become something of a sport among Democratic attorneys general over the past two years, but most of these fights focus on actions taken by Trump's administration rather than matters that implicate him personally. But because Trump's businesses and his presidential campaign are registered in New York, state officials have the authority to investigate and potentially prosecute him for violations of state law.
Trump's attorneys have argued in a separate case that involves a former "Apprentice" contestant who's suing Trump for defamation in New York that as president, he should be immune to lawsuits in state courts. It's an open constitutional question, but two judges have already come down against Trump, saying that when unofficial conduct is involved, there's no reason to exempt the president from state lawsuits. The case is still being appealed, but even if it's decided in Trump's favor, legal actions could still be brought against his businesses or children.
Worse still for Trump, state prosecutions are pardon-proof, since the president's power to grant clemency extends only to federal crimes. This means that while Trump could pardon an associate or family member implicated in, for example, the Mueller investigation (or even try to pardon himself), his get-out-of-jail-free card won't work in New York. There's even been a push to amend New York's double jeopardy laws to make it possible for someone convicted (and, hypothetically, pardoned) under federal law to be prosecuted for corresponding violations of state law.
State prosecutors are especially tough on financial misconduct
Then there's the fact that the offenses where Trump has the greatest potential liability in New York — for example, tax or other kinds of corporate fraud — are ones the New York attorney general's office is particularly adept at handling. Over the past 15 years, New York has steadily stepped up its prosecutions of financial crimes. "Fraud cases are the linchpin of what most attorneys general do, and the laws are particularly strong in New York," said Paul Nolette, a political science professor at Marquette University who studies state attorneys general.
Trump knows this firsthand, because of a previous tangle with former attorney general Eric Schneiderman. The state sued Trump University for defrauding customers in a case that was settled for $25 million. And because Trump ran for office, opening his businesses to a whole new level of national scrutiny, the Trump Foundation lawsuit may have only been the beginning. Before he resigned last year, Schneiderman was reportedly cooperating with special counsel Robert Mueller on matters related to Mueller's investigation of Russian interference in the 2016 election, and state tax officials said they're looking into potential massive tax fraud by the Trump family after reporting from The New York Times last fall. Meanwhile, New York's new attorney general, Letitia James campaigned on a promise to hold the president accountable across a wide range of issues, including his businesses and finances.
"The Mueller investigation is the shiny object everyone is watching," Berit Berger, a former federal prosecutor and the executive director of Columbia Law School's Center for the Advancement of Public Integrity, told me. "But under everyone's nose are what look like much more straightforward violations of state law, including some pretty flagrant tax fraud. Depending on what happens with Mueller, that could be what actually sinks the big ship."
New York prosecutors may have the clearest shot at indicting Trump while he's president
Finally, legal experts told me that if New York officials have sufficient evidence against Trump and the appetite for a protracted legal battle, they may have the best chance at testing a high-stakes constitutional unknown: Is it possible to issue a criminal indictment against a sitting president?
Unlike their federal counterparts, state prosecutors are not bound by a Department of Justice policy that says that a sitting president is immune from indictment (a former president is fair game). "I think it would be hard for a judge to tell New York that it can't pursue charges for criminal violations of its own state law by Donald Trump that occurred before he was president," said Andy Wright, former associate counsel to President Obama.
Not everyone I spoke with agreed with this view, however. Andrew Coan, a law professor at the University of Arizona and the author of a new book about special prosecutors, said there might even be a stronger argument against allowing state attorneys general to indict a president. "The attorney general of New York only speaks for her state's voters, not the country as a whole," he said. "So it seems strange to let that person do something that would significantly impair the president's ability to serve."
But even without an indictment — which would unleash an epic constitutional showdown — New York could still threaten Trump's business empire through civil suits or prosecutions of his family members and inflict a significant amount of political damage on the president in the process.
None of this, of course, answers one key question: If New York is such a danger to Trump, why haven't prosecutors or the attorney general filed charges or a lawsuit against the president or his businesses?
The Trump Foundation case is actually a good example of why one shouldn't read too much into the state's relative inaction. Reports that the foundation was being used for Trump's personal benefit began while he was still running for office, but the lawsuit wasn't filed until 18 months after Trump took office. (There is currently one other case in New York involving Trump — the lawsuit from the former "Apprentice" contestant — that we're tracking as part of the Trump Docket.) But New York officials could be waiting until after Mueller's probe is concluded to take further legal action — or they might be investigating other instances of potential corporate fraud that we aren't yet aware of.
Pre-presidency Trump
Attorneys for Paul Manafort, the former Trump campaign chair who was recently accused of violating his plea agreement with special counsel Robert Mueller, failed to fully redact sensitive details from a recent legal filing in the case. As a result, we learned that Manafort was accused of sharing presidential campaign data with a business associate who has links to Russian intelligence, and that during the campaign he discussed a plan for peace in Ukraine — which Russia and its allies were advocating as a path to lifting Ukraine-related sanctions on Russia. On Tuesday, a subsequent, correctly redacted filing from Mueller spelled out a few more details, including a confirmation that Konstantin Kilimnik, a former Manafort aide with alleged ties to Russian intelligence, is still a focus of the investigation.
Sentencing may be postponed for Rick Gates, a former Trump campaign aide and business partner of Manafort, who has been cooperating with Mueller's investigation. Prosecutors requested a two-month delay in his sentencing because Gates is still assisting with "several ongoing investigations."
Although the case is paused until the partial government shutdown ends, the 4th Circuit Court of Appeals scheduled oral arguments in the District of Columbia and Maryland's emoluments lawsuit against Trump for the court's March 19-21 session.
The D.C. Circuit Court of Appeals reversed the lower court's injunction in a case involving Trump's ban on transgender military service members, concluding that the previous judge had incorrectly concluded that the policy was a "blanket ban on transgender service." The decision had no immediate impact, though, because three other lower courts still have an injunction against it.
A second trial over the addition of a citizenship question to the 2020 Census concluded in California on Friday. During the trial, an expert testified that the question would deter Latinos and noncitizens from responding to the Census.
A trial also ended last week in a case involving the Trump administration's decision to revoke temporary protected status for Haitian immigrants. During the proceedings, Trump's use of the word "shithole" to describe Haiti and other countries came up repeatedly. Attorneys for the Haitians are arguing that the decision to end the policy was spurred by racial bias.
The Supreme Court rejected an unusual challenge to Matthew Whitaker's appointment as acting attorney general last November. In a case involving separate issues related to gun rights, the plaintiff and his lawyers asked the Supreme Court to remove Whitaker's name from the case — arguing that his appointment was illegal — and instead name Deputy Attorney General Rod Rosenstein as a party in the case. Without spelling out their reasons, the justices denied the request on Monday.
A district court judge in New York struck down the Trump administration's decision to add a citizenship question to the 2020 Census, saying Commerce Secretary Wilbur Ross illegally violated federal law when he added the question. Notably, the judge said that while Ross wasn't honest about why he added the citizenship question, the plaintiffs hadn't proved that his aim was discriminatory. The Trump administration is expected to appeal the decision to the U.S. 2nd Circuit Court of Appeals, and ultimately, the case could end up before the Supreme Court.
Amelia Thomson-DeVeaux is a senior writer for FiveThirtyEight. @ameliatd
New York (102 posts) Trump Docket (10) Attorney General (7) Trump Foundation (1)


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