11institutetext: Department of Electrical Engineering,
Indian Institute of Science, Bangalore, India.
11email: {jayatejak, krohit<EMAIL_ADDRESS>
# TACLE: Task and Class-aware Exemplar-free Semi-supervised Class Incremental
Learning

Jayateja Kalla∗ Rohit Kumar∗ Soma Biswas

###### Abstract

We propose a novel TACLE (TAsk and CLass-awarE) framework to address the
relatively unexplored and challenging problem of exemplar-free semi-supervised
class incremental learning. In this scenario, at each new task, the model has
to learn new classes from both (few) labeled and unlabeled data without access
to exemplars from previous classes. In addition to leveraging the capabilities
of pre-trained models, TACLE proposes a novel task-adaptive threshold, thereby
maximizing the utilization of the available unlabeled data as incremental
learning progresses. Additionally, to enhance the performance of the under-
represented classes within each task, we propose a class-aware weighted cross-
entropy loss. We also exploit the unlabeled data for classifier alignment,
which further enhances the model performance. Extensive experiments on
benchmark datasets, namely CIFAR10, CIFAR100, and ImageNet-Subset100
demonstrate the effectiveness of the proposed TACLE framework. We further
showcase its effectiveness when the unlabeled data is imbalanced and also for
the extreme case of one labeled example per class.

###### Keywords:

semi-supervised class incremental learning task-adaptive threshold class-aware
weighted cross-entropy loss

$\ast$$\ast$footnotetext: contributed equally to this work

##  1 Introduction

Recently, incremental or continual learning [36, 42] has emerged as an
important research direction due to its wide applicability, especially in
real-time scenarios where models need to adapt to new data continuously [21,
22]. It addresses the practical limitations of collecting all data at once
[33] and potential privacy concerns [9] where only the model is accessible but
not the training data. But the major challenge faced by neural network models
when dealing with continuous data stream is catastrophic forgetting [23],
where previously learned knowledge is overwritten as the model adapts to new
information. Among various settings in continual learning [50], Class
Incremental Learning (CIL) [42, 8] has gained popularity due to its wide
applicability, where the model is initially trained on a set of base classes
and is subsequently updated when new sets of classes becomes available
(referred to as a task). Most of the existing CIL works assume that
significant amounts of labeled data is available at each task, which is quite
restrictive. It is only recently that researchers have started to address the
more challenging and realistic Semi-Supervised Class-Incremental Learning (SS-
CIL) [52, 6, 31, 29], where the model has access to a few labeled samples per
task, while most of remaining training data is unlabeled.

Figure 1: Difference between Class Incremental Learning (CIL), Semi-Supervised
CIL (SS-CIL), and Exemplar-Free Semi-Supervised CIL (EFSS-CIL) settings.

In this work, we propose a novel framework termed TACLE (TAsk and CLass awarE)
for this challenging SS-CIL task, in a completely exemplar-free setting. Here,
we do not need access to any examples of the previous classes, thereby
complying to privacy concerns or requiring additional storage. Fig. 1 shows
the difference between CIL, SS-CIL and exemplar-free SS-CIL settings. Inspired
by the success of pre-trained models for many applications which also includes
continual learning [27, 19, 38, 62], we propose to leverage their
generalization capacity for the challenging EFSS-CIL task. Specifically
inspired by Slow Learner [62], our approach is also a two-stage method. In the
first stage, it learns robust feature representations, and in the second
stage, it utilizes the mean and variance estimated from these features to
adjust classifiers. For these two stages, we propose three novel modules: (i)
a task-wise adaptive threshold to effectively utilize unlabeled data across
tasks; (ii) a class-aware weighted cross-entropy loss to enhance the
performance of under-represented classes by addressing the imbalance in the
unlabeled data that surpasses the threshold, in the first stage; and (iii)
exploiting the unlabeled data for better classifier alignment in the second
stage, which further enhances the EFSS-CIL. Extensive experiments conducted on
various datasets, including CIFAR-10, CIFAR-100, and ImageNet-Subset100,
demonstrate the effectiveness of the proposed modules in handling the EFSS-CIL
task. To this end, our contributions are as follows:

  1. 1.

To the best of our knowledge, TACLE is the first work to address the
challenging EFSS-CIL setting.

  2. 2.

We leverage pre-trained models to address EFSS-CIL, proposing three novel
components: task adaptive threshold, class-aware weighted cross-entropy, and
exploiting unlabeled data for classifier alignment.

  3. 3.

Extensive experiments on various datasets designed for EFSS-CIL demonstrate
the effectiveness of the proposed approach.

  4. 4.

Furthermore, experiments on extreme cases such as 1-shot EFSS-CIL and
imbalanced scenarios further validate the efficacy of our framework.

The rest of the paper is organized as follows: Section 2 briefly overviews
related works, Section 3 introduces the notations, while Section 4 discusses
the proposed methodology, and Section 5 provides the experimental results. The
paper concludes with an ablation study and analysis of the proposed
components.

##  2 Related Works

In this section, we briefly discuss about the related works in literature.
1\. Class Incremental Learning (CIL): aims to progressively incorporate new
classes into the model and multiple works have been proposed in literature to
address the issues in CIL. These works can be broadly classified into three
categories: (i) Data-centric approaches: These approaches [37, 11, 10, 28, 12,
7, 41] mainly concentrate on adding exemplars to the model to alleviate
catastrophic forgetting. However, their performance may degrade if no storage
buffer is available for exemplars. Thus, many approaches [63, 64, 40, 62] have
started addressing the more realistic exemplar-free CIL setting, without
access to exemplars from previous tasks. Recently, there is a growing trend in
leveraging pre-trained models for CIL [27, 19, 38, 62, 54, 55]. Our work is
inspired from the recent SLCA [62] framework, which achieves impressive
performance for exemplar-free CIL task. (ii) Model-centric approaches: These
approaches [58, 57, 46, 55, 54, 47] rely on dynamic expansion of the model to
enhance their representation ability to mitigate catastrophic forgetting.
Another line of approaches [10, 60, 1, 32] estimate the importance of weights
in the model and apply regularization to those weights. (iii) Algorithm-
centric approaches: focus on designing training strategies, such as knowledge
distillation [24], to mitigate catastrophic forgetting. Knowledge distillation
is used for transferring knowledge from old tasks to new tasks and different
variants have been proposed: logits distillation [42, 36, 25, 56], feature
distillation [26, 16, 30, 18], relation distillation [20, 59], etc.

2\. Semi-Supervised Learning (SSL): The SSL paradigm aims to train models
effectively using a combination of labeled and unlabeled data. One of the
successful and commonly used SSL frameworks involves consistency
regularization and leveraging pseudo-labels for the unlabeled samples.
FixMatch [48] is a popular SSL technique that assigns pseudo-labels based on a
predefined confidence threshold. Few other successful SSL approaches are [4,
3, 35], which align the unlabeled data feature distributions and [61, 53, 13,
15], which uses different pseudo-labeling strategies.

3\. Semi-Supervised Class Incremental Learning (SS-CIL): Online Replay with
Discriminator Consistency (ORDisCo) [52] is a pioneering work addressing SS-
CIL, focusing on interdependently learning a classifier with a conditional
Generative Adversarial Network (GAN). This approach involves the continual
transmission of the learned data distributions to the classifier. However, the
method incurs prohibitive costs when applied to higher-resolution images like
ImageNet-100. Boschinia et al. [6] introduced Contrastive Continual
Interpolation Consistency (CCIC) for this task, combining the advantages of
rehearsal based methods with consistency regularization and distance-based
constraints. In ESPN [29], outliers are introduced in the unlabeled data to
enhance the realism of the problem. More recently, NNCSL [31] proposed a soft
nearest-neighbor framework to learn powerful and stable representations. In
contrast, the proposed TACLE framework leverages pre-trained models to enhance
representations, thereby eliminating the need for exemplars.

##  3 Problem Formulation

We now formally define the problem of Semi-Supervised Class Incremental
Learning (SS-CIL) and introduce relevant notations used throughout the paper.
In CIL, the model is trained on total $\mathcal{T}$ sequential data streams
(or tasks) denoted by
$\\{\mathcal{D}^{(1)},\mathcal{D}^{(2)},\ldots,\mathcal{D}^{(\mathcal{T})}\\}$,
each with its corresponding class label set is denoted by
$\\{\mathcal{C}^{(1)},\mathcal{C}^{(2)},\ldots,\mathcal{C}^{(\mathcal{T})}\\}$.
Throughout this training process, the number of parameters in the feature
extractor $\\{\Theta\\}$ remains unchanged. However, new classifiers
$\\{\psi^{(1)},\psi^{(2)},\ldots,\psi^{(\mathcal{T})}\\}$ are incrementally
added after training each task. In traditional CIL, at task $t$, the model
have access to large amount of labeled data $\mathcal{D}^{(t)}$, where
$t=1,\ldots,\mathcal{T}$ along with old task exemplars.

In contrast, in SS-CIL, the data for the present task $t$ consists of both
labeled and unlabeled samples i.e
$\mathcal{D}^{(t)}\in\\{\mathcal{D}_{l}^{(t)}\cup\mathcal{D}_{ul}^{(t)}\\}$.
Here, it is assumed that both labeled and unlabeled samples come from the same
task classes $\mathcal{C}^{(t)}$, and the number of labeled samples is
significantly smaller compared to that of unlabeled data i.e.,
$|\mathcal{D}_{l}^{(t)}|<<|\mathcal{D}_{ul}^{(t)}|$. Once the model
$\\{\Theta,\psi^{(1:t)}\\}$ has learnt from the current task data
$\mathcal{D}^{(t)}$, it has to perform well on all the classes seen so far i.e
$\\{C^{(1:t)}\\}$. Throughout SS-CIL, the model learns one base task and a
total of $\mathcal{T}-1$ tasks in an incremental fashion, with no overlap in
the label space between the different tasks, i.e. $C^{(i)}\cap C^{(j)}=\phi$
for ($i\neq j$). In the SS-CIL protocol, an exemplar bank $\mathcal{E}$ will
be updated after each task to alleviate the catastrophic forgetting. However,
in EFSS-CIL, there are no exemplars saved for future tasks (because of privacy
or storage costs), which makes the problem more challenging and realistic.

##  4 Proposed Method

Now, we describe in detail, our proposed TACLE (TAsk and CLass-awarE)
framework, designed specifically for EFSS-CIL. As discussed earlier, we have
access to both labeled data
$\mathcal{D}_{l}^{(t)}=\\{\mathbf{x}_{i}^{l},y_{i}^{l}\\}_{i=1}^{N_{l}^{(t)}}$
and unlabeled data
$\mathcal{D}_{ul}^{(t)}=\\{\mathbf{x}_{i}^{ul}\\}_{i=1}^{N_{ul}^{(t)}}$, for
task $t$. Here, $N_{l}^{(t)},N_{ul}^{(t)}$ are the number of labeled and
unlabeled samples, respectively. The TACLE framework adopts a two-stage
training strategy for each task, namely (i) stage 1: Feature Representation
Learning: This stage leverages both labeled and unlabeled data to learn robust
feature representations and (ii) stage 2: Classifier Alignment: This stage
focuses on aligning the classifiers with the learned features from both
labeled and unlabeled data. At task $t$, the model is trained by utilizing
labeled data $\mathcal{D}_{l}^{(t)}$ through standard supervised loss:

$\mathcal{L}_{s}(\mathbf{x}_{i}^{l},y_{i}^{l})=\mathcal{H}(p_{i}^{l},y_{i}^{l})$
(1)

where $\mathbf{x}_{i}^{l}$ is the labeled sample and
$p_{i}^{l}=\psi^{(t)}(\Theta(\mathbf{x}_{i}^{l}))$ is the predicted
probability distribution given by the model for task $t$; $\mathcal{H}$
represents the standard cross-entropy loss. Now, we describe the different
proposed modules to effectively utilize the available unlabeled data at
current task.

###  4.1 Stage 1: Learning Feature Representations

Task-wise adaptive threshold: To leverage information from unlabeled data, we
draw inspiration from SSL framework FixMatch [48], where, unlabeled data
contributes to the learning process if the model’s confidence surpasses the
predefined threshold $\gamma$ (typically set to 0.95). In the EFSS-CIL
setting, a fixed threshold across tasks may not be effective, since the number
of classes increases with each task, thereby impacting the confidence scores
of the unlabeled data.

12345$0.6$$0.7$$0.8$$0.9$$1$TasksACSa.)
CIFAR10246810$0.6$$0.7$$0.8$$0.9$$1$TasksACSb.) CIFAR100 Figure 2: Illustrates
the Average Confidence Score (ACS) for unlabeled data across tasks. The ACS
calculated by taking average of maximum probability confidence scores from all
the unlabeled data, at the end of training. The observed decaying trend
indicates that using a fixed high threshold in SS-CIL may not be suitable for
effective utilization of unlabeled data in feature learning. Due to the fixed
threshold, the amount of unlabeled data utilized for training is significantly
reduced as tasks progresses.

To analyze this confidence scores across tasks, we plot the Average Confidence
Score (ACS) of the unlabeled data for CIFAR10 and CIFAR100 datasets after each
task in Fig. 2. The exact task splits are discussed in the experimental
section. For ACS calculation, after training each task, we pass the respective
task’s unlabeled data through the model and calculate the average of their
confidence scores, which provides insight into the average maximum confidence
of the unlabeled data. Empirically, we observe that the ACS value reduces as
the tasks progresses. As the number of classes increase with more tasks, it
induces more confusion in the model predictions, thereby reducing the
confidence value on the unlabeled data. To address this issue, we propose a
task-wise adaptive threshold instead of a fixed threshold to effectively
leverage the unlabeled data available at task $t$.

We denote a given unlabeled sample and its augmentation as
$\mathbf{x}_{i}^{ul},\mathbf{\hat{x}}_{i}^{ul}$, and their respective
prediction probabilities as $p_{i}^{ul},\hat{p}_{i}^{ul}$. The unsupervised
loss, that incorporates a task-wise adaptive threshold is calculated as

$\mathcal{L}_{us}(\mathbf{x}_{i}^{ul})=\mathbbm{I}(\max(p_{i}^{ul})>\gamma_{a}^{(t)})\cdot\mathcal{H}(\hat{p}_{i}^{ul},\operatorname*{argmax}(p_{i}^{ul}))$
(2)

Here, $\mathbb{I}$ is an indicator function which is 1 if the maximum value of
model output probability $p_{i}^{ul}$ surpasses this adaptive threshold
$\gamma_{a}^{(t)}$, otherwise, the loss is 0. The task-wise adaptive
threshold, $\gamma_{a}^{(t)}$ is inspired from the inverse sigmoid function
[39, 17], and here we adapted it for the EFSS-CIL task as follows:

$\gamma_{a}^{(t)}=\frac{\alpha}{1+e^{\alpha t}}+\beta,$ (3)

Figure 3: The proposed TACLE introduce two components in stage 1 training at
task $t$: C1. Task-wise adaptive threshold ($\gamma_{a}^{(t)}$) is employed in
the computation of the unsupervised loss $\mathcal{L}_{us}$. C2. Class-aware
weights are utilized in the computation of both supervised and unsupervised
losses, where the weights are determined based on the class-wise distribution
of pseudo-unlabeled data.

We observe that the dynamic threshold computed using the above equation
decreases as the task index $t$ increases, which aligns with the inverse
sigmoid behavior. The hyper-parameters $\alpha$ and $\beta$ provide
flexibility in controlling the rate of threshold reduction. This dynamic
adjustment ensures an effective utilization of unlabeled data in the feature
learning process, allowing the model to better adapt to different tasks. In
all our experiments, across all datasets, we use $\alpha=0.5,\>\beta=0.65$.
Further analyses of these choices and dynamic threshold behavior plots across
tasks are provided in the Appendix.

Class-aware weighted loss: While the task-wise adaptive threshold helps to
learn better feature representations from unlabeled data across tasks, even
within a task, there is significant class imbalance among samples surpassing
the task-wise adaptive threshold. This imbalance can bias the model training
towards classes with more pseudo-labels, hindering the performance on under-
represented classes. To mitigate this, inspired from the SSL [61, 15] works,
we propose a very simple, yet effective class-aware weighted cross-entropy
loss.

At task $t$, after each epoch during stage 1, we calculate the normalized
histogram of confident unlabeled samples across different classes. This
histogram, represented as a vector $\zeta\in\mathbb{R}^{|\mathcal{C}^{(t)}|}$,
serves as the basis for the class-aware weighted distribution $\bar{\zeta}$
used in the weighted cross-entropy loss calculation. The class-aware weighted
distribution $\bar{\zeta}$ is calculated as $\bar{\zeta}=2-\zeta$, which
ensures that the class having maximum number of confident unlabeled samples in
histogram $\zeta$ has $\bar{\zeta}=1$, and class with least confident
unlabeled samples has $\bar{\zeta}=2$ ($1\leq\bar{\zeta}\leq 2$). Essentially,
this class-aware weighted distribution assigns higher weights to under-
represented classes and lower weights to well-represented ones. Using this
distribution $\bar{\zeta}$, we assign the weight
$w_{i}^{l}=\bar{\zeta}_{y_{i}^{l}}$ for a labeled sample pair
$(\mathbf{x}_{i}^{l},y_{i}^{l})$. Similarly, for an unlabeled sample
$\mathbf{x}_{i}^{ul}$, we set
$w_{i}^{ul}=\bar{\zeta}_{\operatorname*{argmax}(p_{i}^{ul})}$ ($w_{i}^{ul}$ is
determined based on the pseudo-label i.e.,
$\operatorname*{argmax}(p_{i}^{ul})$). The total stage1 training loss
incorporating these class-aware information calculated as

$\mathcal{L}_{stage1}=\mathcal{L}_{s}(\mathbf{x}_{i}^{l},y_{i}^{l})\cdot
w_{i}^{l}+\mathcal{L}_{us}(\mathbf{x}_{i}^{ul})\cdot w_{i}^{ul}$ (4)

Fig. 3 illustrates the complete stage 1 training of TACLE, which utilizes the
task-wise adaptive threshold and class-aware weighted loss to train the model
for EFSS-CIL.

Figure 4: After stage 1 training, we filter out under-confident samples and
create the expanded label set
$\tilde{\mathcal{D}}^{(t)}=\mathcal{D}_{l}^{(t)}\cup\tilde{\mathcal{D}}_{ul}^{(t)}$.
We estimate class statistics for task $t$ using this expanded label set.
Utilizing class-wise statistics for all encountered classes, we fine-tune all
classifiers with the classifier alignment loss $\mathcal{L}_{ca}$, defined in
Eq. 5. This comprehensive strategy which effectively utilizes the unlabeled
data, constitutes our third component (C3) in the proposed approach.

###  4.2 Stage 2: Classifier alignment using unlabeled data

In pre-trained models, aligning classifiers with the underlying class
distributions plays a critical role in achieving optimal performance. In the
SLCA method, classifier alignment involves utilizing class means and
variances, denoted as
$\\{\mu_{k}^{(t)},\Sigma_{k}^{(t)}\\}_{k=1}^{|\mathcal{C}^{(t)}|}$, calculated
in feature space of dimension $d$, where $|\mathcal{C}^{(t)}|$ represents the
number of classes in task $t$. These class distribution parameters
$\mu_{k}^{(t)}\in\mathbb{R}^{d}$ and $\Sigma_{k}^{(t)}\in\mathbb{R}^{d\times
d}$ are estimated from the available labeled data $\mathcal{D}_{l}^{(t)}$ and
stored, along with the old task classes distributions
(${\mu_{k}^{(1:t-1)},\Sigma_{k}^{(1:t-1)}}$). In stage 2 classifier alignment
process, all the class distributions (${\mu_{k}^{(1:t)},\Sigma_{k}^{(1:t)}}$)
from task 1 to $t$ are utilized to align all the classifiers in the model. For
this purpose, a class-wise distribution is approximated by as a multi-
dimensional Gaussian $\mathcal{N}(\mu_{k}^{(1:t)},\Sigma_{k}^{(1:t)})$
function, from which features are sampled to align the classifiers of both the
current task and all the previous tasks’. The classifier alignment loss is
given by
$\mathcal{L}_{ca}(\mu_{k}^{(1:t)},\Sigma_{k}^{(1:t)})=\mathcal{H}(\psi^{(1:t)}(z),k)$,
where $z\sim\mathcal{N}(\mu_{k}^{(1:t)},\Sigma_{k}^{(1:t)})$ are samples in
feature space from all the classes seen so far.

However, relying solely on labeled data might not accurately capture the true
class distributions due to the inherent scarcity of labeled data in EFSS-CIL
settings, specially if we have as few as a single labeled sample per class.
Towards this goal, we propose to incorporate the confident unlabeled samples
to better estimate of the class distributions parameters. We show that this
can further aid the classifier alignment process.

We achieve this by constructing an expanded label set, denoted by
$\tilde{\mathcal{D}}^{(t)}=\mathcal{D}_{l}^{(t)}\cup\tilde{\mathcal{D}}_{ul}^{(t)}$.
This combines the original labeled data with pseudo-labeled data derived from
confident unlabeled samples defined as
$\tilde{\mathcal{D}}_{ul}^{(t)}=\\{\\{\mathbf{x}_{i}^{ul},\operatorname*{argmax}{(p_{i}^{ul})}\\}\mid\mathbf{x}_{i}^{ul}\in\mathcal{D}_{ul}^{(t)},\max{(p_{i}^{ul})}>\gamma_{a}^{(t)},i=1\ldots
N_{ul}^{(t)}$}. The improved statistics are calculated using
$\tilde{\mathcal{D}}^{(t)}$ is denoted as
$\\{\tilde{\mu}_{k}^{(t)},\tilde{\Sigma}_{k}^{(t)}\\}$ which are then utilized
for classifier alignment in the stage 2 training loss function:

$\mathcal{L}_{stage2}=\mathcal{L}_{ca}(\tilde{\mu}_{k}^{(1:t)},\tilde{\Sigma}_{k}^{(1:t)})$
(5)

Fig. 4 illustrates the stage 2 training process. These two stages are the same
for each incremental task and these final aligned classifiers are used for
classification during inference. Algorithm 1 summarizes the TACLE training
strategy for EFSS-CIL paradigm.

Input: $\\{\Theta,\psi\\}\leftarrow$ Model;
$\\{\mathcal{D}^{(1)},\mathcal{D}^{(2)},\ldots,\mathcal{D}^{(\mathcal{T})}\\}\leftarrow$
Data stream;

$E_{s1}\leftarrow$ No. of epochs for stage 1; $E_{s2}\leftarrow$ No. of epochs
for stage 2;

for  _$t\leftarrow 1$ to $\mathcal{T}$_ do

$\mathcal{D}_{l}^{(t)}=\\{\mathbf{x}_{i}^{l},y_{i}^{l}\\}_{i=1}^{N_{l}^{(t)}};\mathcal{D}_{ul}^{(t)}=\\{\mathbf{x}_{i}^{ul}\\}_{i=1}^{N_{ul}^{(t)}};$

$\zeta\leftarrow\text{Uniform distribution across all classes}$

$//$ $\\#Stage$ 1: Feature Representation Learning $//$

for  _$e_{s1}\leftarrow 1$ to $E_{s1}$_ do

$\mathcal{B}_{l}=\text{SampleMiniBatch}(\mathcal{D}_{l}^{(t)})$;
$\mathcal{B}_{ul}=\text{SampleMiniBatch}(\mathcal{D}_{ul}^{(t)})$;

$\hat{\mathcal{B}}_{ul}=\text{ImageAugmentations}(\mathcal{B}_{ul})$;

$\mathcal{O}_{l},\mathcal{O}_{ul},\hat{\mathcal{O}}_{ul}=\Theta(\psi^{(t)}(\mathcal{B}_{l},\mathcal{B}_{ul},\hat{\mathcal{B}}_{ul}));$

$w^{l}\leftarrow\text{Assigning class-aware weights for labeled data
}\mathcal{B}_{l}\text{ using }\bar{\zeta};$

$w^{ul}\leftarrow\text{Assigning class-aware weights for unlabeled data
}\mathcal{B}_{ul}\text{ using }\bar{\zeta};$

$\mathcal{L}_{stage1}\leftarrow\mathcal{L}_{s}(\mathcal{B}_{l})\cdot
w^{l}+\mathcal{L}_{us}(\hat{\mathcal{B}}_{ul})\cdot w^{ul};\>$ // Total loss
for stage1 (Eq. 4)

$\zeta\leftarrow\text{Update the histogram distribution using
}\mathcal{D}_{ul}^{(t)},\gamma_{a}^{(t)};$

$\bar{\zeta}\leftarrow(2-\zeta);$ // Normalization

$\\{\Theta,\psi^{(t)}\\}\leftarrow\text{Update model parameters using
}\mathcal{L}_{stage1};$

$//$$\\#Stage$ 2: Classifier Alignment$//$

$\tilde{\mathcal{D}}^{(t)}\leftarrow\text{Expanded labelled data set using
}\mathcal{D}_{l}^{(t)},\mathcal{D}_{ul}^{(t)},\gamma_{a}^{(t)};$

$\tilde{\mu}_{k}^{(t)},\tilde{\Sigma}_{k}^{(t)}\leftarrow\text{Estimate mean
and variance using }\tilde{\mathcal{D}}^{(t)};$ // $\text{where
}k\in{1,2,.,|\mathcal{C}^{(t)}|}$

for  _$e_{s2}\leftarrow 1$ to $E_{s2}$_ do

$\mathcal{L}_{stage2}\leftarrow\mathcal{L}_{ca}(\tilde{\mu}_{k}^{(1:t)},\tilde{\Sigma}_{k}^{(1:t)});$
// Alignment loss for classifiers (Eq. 5)

$\psi^{(1:t)}\leftarrow\text{Update classifier parameters using
}\mathcal{L}_{stage2}$;

Algorithm 1 TACLE for semi-supervised class incremental learning

##  5 Experiments

Here, we discuss the datasets used, implementation details and experimental
results of the proposed methodology.

###  5.1 Datasets

We evaluate our approach on three widely used SS-CIL datasets, which we
briefly describe below.
(i) CIFAR10 [34]: This dataset comprises $32\times 32$ images, with a total of
50,000 training images and 10,000 validation images distributed across 10
classes. Following the SS-CIL protocol, we structured the learning into 5
tasks, each involving the incremental learning of 2 classes (2-2-…-2) per
task. In each task, the model has access to both labeled and unlabeled data.
(ii) CIFAR100 [34]: With a total of 100 classes, each consisting of $32\times
32$ images, CIFAR100 presents 500 training and 100 validation images for each
class. The SS-CIL protocol here spans 10 tasks, introducing 10 new classes in
each task (10-10-…-10). In both CIFAR10 and CIFAR100 images are resized to
$224\times 224$ for compatibility with the pre-trained models.
(iii) ImageNet-Subset100 [49]: This dataset is a subset of ImageNet-1k [45],
containing 100 classes. All images were resized to $256\times 256$ pixels and
randomly cropped to $224\times 224$ pixels during training. For each of the
100 classes, there are 1,300 training images and 50 testing images. For the
SS-CIL protocol, it is structured into 20 tasks, introducing 5 new classes in
each task (5-5-…-5).
Supervision levels: We evaluated our approach under different levels of
supervision for labeled data proposed in NNCSL [31]. The percentage of labeled
data used per task is set to $0.8\%,5\%,\text{and }25\%$ for CIFAR10 and
CIFAR100. For ImageNet-Subset100, we use supervision levels of
$1\%,5\%,\text{and }25\%$.

###  5.2 Implementation details and Evaluation Protocol

Inspired by SLCA [62], we adopted a pre-trained ViT-B/16 backbone model for
all our experiments. To test the approach’s effectiveness for different pre-
trained models, we have experimented with a supervised pre-trained model
(trained on ImageNet-21k [43]) and also a self-supervised pre-trained model
(trained on MoCo v3 [14]). Results on both CIFAR10 and CIFAR100 are reported
for these pre-trained models, while for ImageNet-Subset100, we use the MoCo v3
pre-trained model (since the other model cannot be used due to data overlap).
In stage 1 of training, which focuses on feature representation learning, the
model is trained for 10 epochs for CIFAR-10 and CIFAR-100 and for 5 epochs for
ImageNet-Subset100. We used an SGD optimizer with learning rate $0.005$,
momentum 0.9 and weight decay of $5e^{-3}$ for all the experiments across all
datasets. Batch sizes are set to 128 for CIFAR10 and CIFAR100 and 64 for
ImageNet-Subset100. During stage 2 of training, the classifier alignment is
performed for 5 epochs for all datasets. All the experiments are conducted on
a system equipped with two NVIDIA RTX A5000 GPUs, each with 24GB of memory. We
use the PyTorch deep learning library for our implementation.
Evaluation protocol: For fair comparison, our approach is evaluated using the
same data splits and evaluation protocol proposed in NNCSL [31]. The
evaluation considered both top-1 cumulative and average accuracy to assess the
models. These metrics are calculated as follows, let $t$ represent the task
ID, where $t\in{1,...,\mathcal{T}}$. Then $Acc_{1:t}^{t}$ denotes the model’s
accuracy on the test data of all tasks from $1$ to $t$ after learning task
$t$. Consequently, upon completion of task $\mathcal{T}$, the average
incremental accuracy is computed as
$\frac{1}{\mathcal{T}}\sum_{t=1}^{\mathcal{T}}Acc_{1:t}^{t}$ and
top1-cumulative accuracy is reported as $Acc_{1:\mathcal{T}}^{\mathcal{T}}$.

Table 1: Average incremental accuracy on CIFAR10 after 5 tasks and CIFAR100
after 10 tasks for SS-CIL. The number in brackets indicates the number of
exemplars; our approach does not use any exemplars. Here, $\star$: models
trained from scratch, ${\dagger}$: models initialized with MoCo v3 pretrained
weights, and ${\ddagger}$: models initialized with ImageNet pretrained
weights; RN18: ResNet18 architecture, FT: fixed threshold.

Method Model CIFAR 100 CIFAR 10 $0.8\%$ $5\%$ $25\%$ $0.8\%$ $5\%$ $25\%$ Fine
Tuning RN18⋆ 1.8 $\pm$ 0.2 5.0 $\pm$ 0.3 7.8 $\pm$ 0.1 13.6 $\pm$ 2.9 18.2
$\pm$ 0.4 19.2 $\pm$ 2.2 oEWC [32] 1.4 $\pm$ 0.1 4.7 $\pm$ 0.1 7.8 $\pm$ 0.4
13.7 $\pm$ 1.2 17.6 $\pm$ 1.2 19.1 $\pm$ 0.8 ER [44] (500) RN18⋆ 8.2 $\pm$ 0.1
13.7 $\pm$ 0.6 17.1 $\pm$ 0.7 36.3 $\pm$ 1.1 51.9 $\pm$ 4.5 60.9 $\pm$ 5.7
iCaRL [42] (500) 3.6 $\pm$ 0.1 11.3 $\pm$ 0.3 27.6 $\pm$ 0.4 24.7 $\pm$ 2.3
35.8 $\pm$ 3.2 51.4 $\pm$ 8.4 FOSTER [51] (500) 4.7 $\pm$ 0.6 14.1 $\pm$ 0.6
21.7 $\pm$ 0.7 43.3 $\pm$ 0.7 51.9 $\pm$ 1.3 57.1 $\pm$ 2.0 X-DER [5] (500)
8.9 $\pm$ 0.3 18.3 $\pm$ 0.5 23.9 $\pm$ 0.7 33.4 $\pm$ 1.2 48.2 $\pm$ 1.7 58.9
$\pm$ 1.5 PseudoER [31] (500) RN18⋆ 8.7 $\pm$ 0.4 11.4 $\pm$ 0.5 18.3 $\pm$
0.2 50.5 $\pm$ 0.1 56.5 $\pm$ 0.6 57.0 $\pm$ 0.6 CCIC [6] (500) 11.5 $\pm$ 0.7
19.5 $\pm$ 0.2 20.3 $\pm$ 0.3 54.0 $\pm$ 0.2 63.3 $\pm$ 1.9 63.9 $\pm$ 2.6
PAWS [2] (500) 16.1 $\pm$ 0.4 21.2 $\pm$ 0.4 19.2 $\pm$ 0.4 51.8 $\pm$ 1.6
64.6 $\pm$ 0.6 65.9 $\pm$ 0.3 CSL [31] (500) 23.6 $\pm$ 0.3 26.2 $\pm$ 0.5
29.3 $\pm$ 0.3 64.5 $\pm$ 0.7 69.6 $\pm$ 0.5 70.0 $\pm$ 0.4 NNCSL [31] (500)
27.4 $\pm$ 0.5 31.4 $\pm$ 0.4 35.3 $\pm$ 0.3 73.2 $\pm$ 0.1 77.2 $\pm$ 0.2
77.3 $\pm$ 0.1 PseudoER [31] (5120) RN18⋆ 15.1 $\pm$ 0.2 24.9 $\pm$ 0.5 30.1
$\pm$ 0.7 55.4 $\pm$ 0.5 70.0 $\pm$ 0.3 71.5 $\pm$ 0.2 CICC [6] (5120) 12.0
$\pm$ 0.3 29.5 $\pm$ 0.4 44.3 $\pm$ 0.1 55.2 $\pm$ 1.4 74.3 $\pm$ 1.7 84.7
$\pm$ 0.9 ORDisCo [52] (12500) - - - 41.7 $\pm$ 1.2 59.9 $\pm$ 1.4 67.6 $\pm$
1.8 CSL [31] (5120) 23.7 $\pm$ 0.5 41.8 $\pm$ 0.4 50.3 $\pm$ 0.8 64.3 $\pm$
0.7 73.1 $\pm$ 0.3 73.9 $\pm$ 0.1 NNCSL [31] (5120) 27.5 $\pm$ 0.7 46.0 $\pm$
0.2 56.4 $\pm$ 0.5 73.7 $\pm$ 0.4 79.3 $\pm$ 0.3 81.0 $\pm$ 0.2 SLCA [62] (0)
ViTs† 66.43 $\pm$ 0.04 81.86 $\pm$ 0.02 86.95 $\pm$ 0.01 93.55 $\pm$ 0.03
94.45 $\pm$ 0.01 96.19 $\pm$ 0.01 SLCA+FT (0) 71.67 $\pm$ 0.09 83.96 $\pm$
0.06 86.91 $\pm$ 0.02 94.07 $\pm$ 0.07 95.35 $\pm$ 0.05 96.08 $\pm$ 0.02 TACLE
(ours) (0) 79.51 $\pm$ 0.08 85.58 $\pm$ 0.05 87.24 $\pm$ 0.02 94.59 $\pm$ 0.08
95.49 $\pm$ 0.05 96.02 $\pm$ 0.01 SLCA [62] (0) ViTs‡ 63.67 $\pm$ 0.03 91.38
$\pm$ 0.02 93.69 $\pm$ 0.01 91.64 $\pm$ 0.02 97.79 $\pm$ 0.01 98.56 $\pm$ 0.01
SLCA+FT (0) 88.23 $\pm$ 0.04 93.30 $\pm$ 0.03 94.08 $\pm 0.01$ 98.45 $\pm$
0.03 98.26 $\pm$ 0.02 98.89 $\pm$ 0.02 TACLE (ours) (0) 92.35 $\pm$ 0.06 93.59
$\pm$ 0.04 94.10 $\pm$ 0.02 98.61 $\pm$ 0.03 98.44 $\pm$ 0.03 98.86 $\pm$ 0.02

###  5.3 Baselines:

We compare our TACLE framework against both supervised CIL approaches and
exemplar-based SS-CIL approaches. In the realm of traditional approaches, we
included online Elastic Weight Consolidation (oEWC) [32], a method that does
not require replay buffers, making it a relevant comparison point for our
buffer-free approach. For replay-based strategies, we compare with exemplar
replay method [44], iCaRL [42], FOSTER, [51] and XDER [5]. Additionally, we
considere PseudoER [31], a two-stage learning approach that combines
Experience Replay (ER) with semi-supervised learning (PAWS) [2]. Among the SS-
CIL approaches, we selected three major exemplar-based baselines: CCIC [6],
ORDisCo [52], and NNCSL [31]. Each of these approaches requires storing data
from previous tasks in memory buffers. CCIC and NNCSL explicitly define their
memory buffer sizes as either 500 or 5120, while ORDisCo stores all labeled
data, resulting in a buffer size of 12500. In contrast, our proposed approach
operates with a buffer size of 0, making it more realistic compared to these
methods.

Given a pre-trained ViT’s backbone architecture, a direct comparison with
previous approaches that utilized ResNet architectures may not be entirely
fair. To address this, we included SLCA [62], a powerful CIL technique that
uses ViT pre-trained models from labeled data, and SLCA with fixed threhold
$\gamma$ inspired by FixMatch [48], aiming to leverage unlabeled data. Both
these methods serve as a baseline for an equitable comparison using ViT
architectures, and we set the buffer size to 0 for consistency with our TACLE
framework for these approaches.

###  5.4 Experimental Results

This section presents the experimental results achieved by our TACLE
framework. Table 1 summarizes the comprehensive findings on the CIFAR10 and
CIFAR100 datasets, considering different pre-trained models with varying
labeled data percentages. The mean of average incremental accuracy over three
seeds [31] are reported for a comprehensive evaluation. For the CIFAR10
dataset, in the challenging scenario where only $0.8\%$ labeled data is
available, TACLE exhibits notable improvements over the baseline SLCA. In that
context, when leveraging MoCo v3 as the pre-trained model, TACLE achieves a
$1.04\%$ enhancement, while with ImageNet pre-training, it achieves a
substantial $7\%$ improvement. As the percentage of labeled data increases to
$5\%$, TACLE maintains its effectiveness, showcasing a $1.04\%$ improvement
over SLCA with MoCo pre-training and a $0.65\%$ improvement with ImageNet pre-
training.

On CIFAR100 dataset, using the MoCo pre-trained model, TACLE achieves
improvements of $13.08\%$ and $3.72\%$ over SLCA for $0.8\%$ and $5\%$ labeled
data, respectively. The ImageNet pre-trained model also demonstrates
significant gains, with improvements of $28.68\%$ and $2.21\%$ for $0.8\%$ and
$5\%$ labeled data, respectively. As the percentage of labeled data increases,
the contribution of TACLE or fixed threshold becomes less significant. In such
cases, using even a small proportion of incorrectly pseudo-labeled unlabeled
data may lead to a decrease in performance for pre-trained models. This trend
is evident in the results for CIFAR-10 and CIFAR-100 with $25\%$ labeled data.

In ImageNet-Subset100, TACLE outperforms SLCA by $2.52\%$ and $3.13\%$ in the
$1\%$ and $5\%$ labeled data settings, respectively. The improvements are
prominent for the difficult scenarios, when the percentage of labeled data is
less. The complete results are given in Table 2.

Table 2: Comparison of average incremental accuracy on ImageNet-Subset100
after 20 tasks for SS-CIL. The number in brackets: buffer size; $\star$:
models trained from scratch and ${\dagger}$: model initialized with MoCo v3
pretrained weights.

Method Model ImageNet100-Subset $1\%$ $5\%$ $25\%$ Fine-tuning ResNet18⋆ 1.5
$\pm$ 0.2 2.7 $\pm$ 0.1 4.1 $\pm$ 0.2 ER [44] (5120) 12.2 $\pm$ 0.8 26.3 $\pm$
0.7 38.8 $\pm$ 1.0 FOSTER [51] (5120) 14.8 $\pm$ 1.1 32.8 $\pm$ 0.7 42.1 $\pm$
1.5 X-DER [5] (5120) 10.8 $\pm$ 1.1 27.4 $\pm$ 1.6 45.3 $\pm$ 1.0 CCIC [6]
(5120) 13.5 $\pm$ 1.2 19.5 $\pm$ 0.7 25.9 $\pm$ 0.9 CSL [31] (5120) ResNet18⋆
26.8 $\pm$ 0.4 47.9 $\pm$ 0.2 56.3 $\pm$ 0.5 NNCSL [31] (5120) 29.7 $\pm$ 0.4
51.3 $\pm$ 0.1 65.6 $\pm$ 0.3 SLCA [62] (0) ViTs† 78.30 $\pm$ 0.04 79.29 $\pm$
0.02 82.39 $\pm$ 0.01 SLCA+Fixed Threshold (0) 79.72 $\pm$ 0.08 82.21 $\pm$
0.05 83.08 $\pm$ 0.02 TACLE (ours) (0) 80.82 $\pm$ 0.09 82.42 $\pm$ 0.04 83.01
$\pm$ 0.02

##  6 Analysis and Ablation Studies

12345678910$30$$40$$50$$60$$70$$40.19$$61.23$$65.96$TasksCumulative Acc.a).
One Shot (ImageNet pre-trained)SLCASLCA + Fixed ThresholdTACLE
(ours)12345678910$30$$40$$50$$60$$70$$42.07$$47.32$$49.74$TasksCumulative
Acc.b). One Shot (MoCo v3 pre-
trained)12345678910$60$$70$$80$$90$$61.50$$85.74$$88.99$TasksCumulative
Acc.c). Imbalance (ImageNet pre-
trained)12345678910$60$$70$$80$$90$$66.59$$70.75$$74.20$TasksCumulative
Acc.d). Imbalance (MoCo v3 pre-trained) Figure 5: Analysis of one-shot SS-CIL
and imbalance SS-CIL experiments. Experiments were conducted on CIFAR100
($0.8\%$ labeled data for imbalance scenerio) with 10 tasks, reporting top-1
cumulative accuracy at the end of each task and average cumulative accuracy at
the end of each plot. Results are presented for both pre-trained models.

####  6.0.1 TACLE in Challenging Scenarios

To evaluate the efficacy of the proposed TACLE framework in extreme scenarios,
we conducted experiments under two challenging SS-CIL scenarios: one-shot
EFSS-CIL and imbalanced EFSS-CIL.
(i). One-shot EFSS-CIL: In this scenario, each class has only one labeled
sample, while the remaining data remains unlabeled. Experiments are carried
out on CIFAR100 data with a 10-task configuration for one-shot EFSS-CIL. Fig.
5a illustrates the task-wise cumulative accuracy and average incremental
accuracy for one-shot EFSS-CIL with ImageNet as the pre-trained model, and
Fig. 5b shows the results with the MoCo pre-trained model. In both scenarios,
the TACLE framework demonstrates significant improvements of $25.77\%$
(ImageNet pre-trained) and $7.67\%$ (MoCo v3 pre-trained) over the baseline
SLCA. Table 6.0.2 shows the one-shot EFSS-CIL results on ImageNet-Subset100.
(ii). Imbalance SS-CIL: In this setup, the distribution of unlabeled data is
imbalanced, deviating from traditional SS-CIL where unlabeled data is
balanced. We introduced standard imbalance in unlabeled data with an imbalance
ratio between minimum to maximum number of samples is 0.01 (This results in
the minority class having 5 samples and the majority class having 500
samples). We considered $0.8\%$ labeled data on CIFAR100 data with a 10-task
learning setup. Figure 5c and Figure 5d present the experimental results in
these imbalance SS-CIL settings. These outcomes showcase the effectiveness of
the TACLE framework in handling extreme EFSS-CIL scenarios.

####  6.0.2 Ablation Study

In this section, we provide a detailed study of the proposed components in the
TACLE framework. Table 3 presents the detailed experimental results on the
CIFAR100 dataset with $0.8\%$ labeled data using different pre-trained models.
The baseline SLCA [62] utilizes only labeled data for stage 1 and stage 2
classifier alignment. SLCA + Fixed Threshold utilizes unlabeled data for
training. Table 3 shows that incorporating each proposed component of TACLE
has indeed improved the performance. Table 6.0.2 shows the impact of hyper-
parameters ($\alpha,\>\beta$) in task-wise adaptive threshold (Eq. 3). We
observe that the results vary gracefully with change in these parameters.
Discussion on limitations and future work: While TACLE excels in leveraging
unlabeled data from the current task, it inherently assumes (as in the SS-CIL
protocol) that the unlabeled data comes solely from the current task, whereas
real-world scenarios may involve mixed data sources, including samples from
previous tasks or outliers. Exploring these challenging and more realistic
settings will be one of our future directions. Additionally, this framework
can be extended to other tasks like object detection or segmentation.

Table 3: Ablation study on CIFAR100 dataset with ${0.8\%}$ labeled data. The
average incremental accuracy is reported at the end of 10 tasks. The proposed
components are denoted as C1: task-wise dynamic threshold (Eq. 2), C2: class-
aware CE loss (Eq. 4), C3: exploiting unlabeled data in stage 2 (Eq. 5).

Method Data Components Pre-trained Labelled Unlabeled C1 C2 C3 ImageNet MoCo
v3 SLCA ✓ ✗ ✗ ✗ ✗ 63.37 66.43 SLCA + Fixed Threshold ✓ ✓ ✗ ✗ ✗ 88.23 71.67 ✓ ✓
✓ ✗ ✗ 89.10 75.29 TACLE (ours) ✓ ✓ ✓ ✓ ✗ 91.32 77.19 ✓ ✓ ✓ ✓ ✓ 92.35 79.51

Table 4: One-shot SS-CIL on ImageNet-Subset100 for 20 tasks

Method | Avg. inc. acc.
---|---
SLCA |  $59.48$
SLCA + Fixed Threshold |  $61.32$
TACLE (ours) |  67.72

Table 5: Impact of threshold hyper-parameters $\alpha$ and $\beta$ on CIFAR100
dataset.

$\alpha\downarrow$ $\beta$ $\rightarrow$ |  $0.6$ | $0.65$ | $0.7$
---|---|---|---
$0.45$ |  $92.12$ | $91.78$ | $92.07$
$0.50$ |  $91.96$ | 92.35 | $91.01$
$0.55$ |  $91.86$ | $91.01$ | $90.52$

##  7 Conclusion

This paper introduces the framework TACLE, an exemplar-free approach for SS-
CIL. TACLE achieves state-of-the-art results on several benchmark datasets
designed for SS-CIL by leveraging pre-trained models without exemplars. The
proposed approach incorporates three key components to effectively utilize
unlabeled data: (i) Task-wise adaptive threshold: facilitating effective
utilization of unlabeled data, (ii) Class-aware weighted loss: improving
performance on under-represented classes. (iii) Exploiting unlabeled data for
classifier alignment. TACLE demonstrates its effectiveness not only under
standard EFSS-CIL settings but also in extreme scenarios like one-shot EFSS-
CIL and imbalanced EFSS-CIL. A comprehensive analysis conducted on various
datasets underscores the significant improvements achieved by TACLE.

## Appendix

###  0.A.1 Effect of hyper-parameters $\alpha\text{ and }\beta$ on task-wise
threshold

$0$$2$$4$$6$$8$$10$$0.6$$0.8$$1$$Tasks$$\gamma_{d}$(a) changing $\alpha$, for
fixed $\beta=0.7$$\alpha$
Values$0.45$$0.50$$0.55$$0$$2$$4$$6$$8$$10$$0.6$$0.8$$1$$Tasks$$\gamma_{d}$(b).
changing $\beta$, for fixed $\alpha=0.5$$\beta$ Values$0.60$$0.65$$0.70$
Figure 6: Task-wise adaptive threshold output values by changing hyper-
paraneters ($\alpha,\beta$).

This section analyzes the impact of hyper-parameters $\alpha\text{ and }\beta$
on the task-wise adaptive threshold defined by the equation:

$\gamma_{a}^{(t)}=\frac{\alpha}{1+e^{\alpha t}}+\beta,$ (6)

Figure 6 illustrates the behavior of the task-wise adaptive threshold as we
vary $\alpha\text{ and }\beta$ . Table 6 shows the average incremental
accuracy achieved on the CIFAR-100 dataset with $0.8\%$ labeled data per class
across 10 incremental tasks.

As shown in Figure 6, the threshold value generally decreases with increasing
task number (t). This aligns with the desired behavior of incorporating more
unlabeled data as the number of labeled samples grows. The experiment results
in Table 6 suggest that the choice of $\alpha\text{ and }\beta$ impacts
performance on incremental learning. For example, the configuration with
$\alpha=0.55\text{ and }\beta=0.7$ leads to a lower average accuracy. This is
likely due to a high threshold, which hinders the effective utilization of
unlabeled data. We opted for this decaying threshold function inspired by the
inverse sigmoid due to its simplicity and control over the initial and final
threshold values. This allows for a smooth decrease in the threshold as tasks
progress, enabling the model to leverage more unlabeled data effectively over
time.

Table 6: Impact of threshold hyper-parameters $\alpha$ and $\beta$ on CIFAR100 dataset. $\alpha\downarrow$ $\beta$ $\rightarrow$ |  $0.60$ | $0.65$ | $0.70$
---|---|---|---
$0.45$ |  $92.12$ | $91.78$ | $92.07$
$0.50$ |  $91.96$ | 92.35 | $91.01$
$0.55$ |  $91.86$ | $91.01$ | $90.52$

###  0.A.2 Task-wise cumulative accuracy results

12345678910$50$$60$$70$$80$$90$$100$$63.67$$88.23$$92.35$TasksCumulative
Acc.a). 0.8% labeled (ImageNet pre-trained)SLCASLCA + Fixed ThresholdTACLE
(ours)12345678910$50$$60$$70$$80$$90$$100$$66.43$$71.67$$79.51$TasksCumulative
Acc.b). 0.8% labeled (MoCo v3 pre-
trained)12345678910$85$$90$$95$$100$$91.38$$93.30$$93.59$TasksCumulative
Acc.c). 5% footnote (ImageNet pre-
trained)12345678910$70$$80$$90$$100$$81.86$$83.96$$85.58$TasksCumulative
Acc.d). 5% labeled (MoCo v3 pre-trained) Figure 7:  Analysis for CIFAR100
datasets for different methods. Experiments were conducted for 0.8% and 5%
labeled data with 10 tasks, reporting top-1 cumulative accuracy at the end of
each task and average cumulative accuracy at the end of each plot. Results are
presented for both pre-trained models.

In this section, we report the task-wise cumulative accuracy results for the
proposed approach TACLE, SLCA, and SLCA+Fixed threshold. Figure 7 presents the
results for CIFAR100 with $0.8\%$ and $5\%$ labeled data settings for the
EFSS-CIL protocol. We also report the average incremental accuracy at the end
of the task for both cases where two different pre-trained models are used for
model weight initialization. The proposed TACLE outperforms the baselines by a
significant margin in the both the scenarios.

##  Appendix 0.B Visualization of features: SLCA vs TACLE (task 1,5,9)

Figure 8:  t-SNE visualization of SLCA vs TACLE for given task id 1, 5, and
10. Each point represents image feature vector of dimension 768 (using
ImageNet as pre-trained model).

To visualize the clustering of unlabeled and labeled data, we employ t-SNE
dimensionality reduction on the image features extracted from the model
feature extractor ($\Theta$), which shares parameters across all tasks. We
consider 4 labeled data points from each class, one class prototype for each,
and all the task’s unlabeled data (this is the data samples in CIFAR100 with
$0.8\%$ at every task). Figures 8 and 9 depict t-SNE plots for both the SLCA
approach (which utilizes only labeled data) and our TACLE framework after
tasks 1, 5, and 10. These plots consider two pre-trained models for initial
model weight initialization: ImageNet and MoCo v3. We observe that, by
leveraging unlabeled data, proposed TACLE achieves better clustering and
learns superior feature representations, thereby enhancing the overall
performance of EFSS-CIL.

Figure 9:  t-SNE visualization of SLCA vs TACLE for given task id 1, 5, and
10. Each point represents image feature vector of dimension 768 (using moco V3
as pre-trained model).

###  0.B.1 Challenging Scenarios

####  0.B.1.1 One-shot EFSS-CIL

Fig. 10 depicts the performance of different methods in the one-shot EF-SSCIL
setting for the ImageNet-Subset100 dataset. In this setting, each class has
only one labeled data point along with unlabeled data, hence it is referred to
as the one-shot EF-SSCIL protocol. MoCo v3 pre-trained ViT is used for weight
initialization in these experiments. The ImageNet-Subset 100 dataset is
divided into 20 tasks, with each task containing 5 classes. Therefore, the
number of labeled and unlabeled samples per task is 5 and 6500, respectively.
Our method (TACLE) achieves a $8.75\%$ higher accuracy compared to the SLCA
method on this challenging setting.

1234567891011121314151617181920$50$$60$$70$$80$$59.48$$61.23$$67.73$TasksCumulative
Acc.One Shot (ImageNet pre-trained)SLCASLCA + Fixed ThresholdTACLE (ours)
Figure 10: Evaluation of One-Shot Performance on ImageNet-100 with MoCo v3
Initialization. The experiment uses 1 labeled sample and 1300 unlabeled
samples per class. The 100 classes divided into 20 tasks with 5 classes per
task.

####  0.B.1.2 Imbalance EFSS-CIL

$1$$2$$3$$4$$5$$6$$7$$8$$9$$10$0.820305075100ClassesPercentage of datalabeled
dataUnlabeled data (a) Balalnced data distribution

$1$$2$$3$$4$$5$$6$$7$$8$$9$$10$0.820305075100ClassesPercentage of data (b)
Imbalalnced data distribution

Figure 11: The bar graph illustrates the data distribution for the balanced
and imbalanced unlabeled data per class-wise in the CIFAR100 dataset with
$0.8\%$ labeled data.

Fig. 11(a) illustrates the data distribution in the standard SS-CIL setting,
where the unlabeled data from every class is balanced, meaning the number of
samples from all classes is equal in the unlabeled data (in the standard
setting, they have access to exemplars also but we are not showing for
simplicity). Conversely, Fig. 11(b) shows the data distribution for the
imbalance EFSS-CIL proposed in the paper. In this scenario, we have a highly
skewed distribution for the unlabeled data, with an imbalance ratio of 0.01,
indicating that the ratio between the class with fewer samples and the class
with more samples is 0.01. At every task, unlabeled data follows this
imbalance (head-tail) distribution.

###  0.B.2 Training optimization details

During training, stage 1 for each task is trained for $10$ epochs. A learning
rate schedule is employed, reducing the learning rate by a factor of $10$
after the $8^{th}$ epoch. To facilitate stable initial convergence, the
network is first warmed up for a few iterations using only labeled data loss.
Subsequently, unlabeled data losses are incorporated and added to the total
loss function. The standard SGD optimizer with a batch size of 128 is employed
for both CIFAR-10 and CIFAR-100 experiments. Due to GPU memory limitations, a
reduced batch size of 64 is used for the ImageNet-subset100 experiments.

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