CI-CBM: Class-Incremental Concept Bottleneck Model for Interpretable Continual Learning
Authors: Amirhosein Javadi
Tuomas Oikarinen
Tara Javidi
Tsui-Wei Weng
Venue: Accepted by TMLR ()

Abstract: Catastrophic forgetting remains a fundamental challenge in continual learning, in which models often forget previous knowledge when fine-tuned on a new task. This issue is especially pronounced in class incremental learning (CIL), which is the most challenging setting in continual learning. Existing methods to address catastrophic forgetting often sacrifice either model interpretability or accuracy. To address this challenge, we introduce Class-Incremental Concept Bottleneck Model (CI-CBM), which leverage effective techniques, including concept regularization and pseudo-concept generation to maintain interpretable decision processes throughout incremental learning phases. Through extensive evaluation on seven datasets, CI-CBM achieves comparable performance to black-box models and outperforms previous interpretable approaches in CIL, with an average 36\% accuracy gain. CI-CBM provides interpretable decisions on individual inputs and understandable global decision rules, as shown in our experiments, thereby demonstrating that human-understandable concepts can be maintained during incremental learning without compromising model performance. Our approach is effective in both pretrained and non-pretrained scenarios; in the latter, the backbone is trained from scratch during the first learning phase.

Tara Javidi Published in Transactions on Machine Learning Research (04/2026)
CI-CBM: Class-Incremental Concept Bottleneck Model for Interpretable Continual Learning
Amirhosein Javadi
amjovadi edu
Deportment of Electrical and Computer Engineering, University of California San Diego
Tuomas Oikarinen
toikarinen edu
Department of Computer Science and Engineering, University of California San Diego
tjavidi edu
Department of Electrical and Computer Engineering, University of California San Diego
Tsui- Wei Weng
buengrusdd edu
Hakeroghu Data Science Institate, University of California San Diego
Reviewed on OpenReview: https: openeevie......... net/ forun? id- Wf60pLgj24
Abstract
Catastrophic forgetting remains a fundamental challenge in continual learning, which models often forget previous knowledge when fine-tuned on a new task. This issue is espe- cially pronounced in class incremental learning (CIL), which is the most challenging setting in continual learning. Existing methods to address catastrophic forgetting often sacrifice either model interpretability or accuracy. To address this challenge, we introduce Class- Incremental Concept Bottleneck Model (CI-CBM), which leverage elfective techniques, including concept regularization and pseudo- concept generation to maintain interpretable decision processes throughout incremental lcarning phases. Through extensive evaluation on seven datasets, CI-CBM achieves comparable performance to black-box models and out- performs previous interpretable approaches in CIT, with an average 36% accuracy gain. CI- CBM provides interpretable decisions individual inputs and understandable global deci- sion rules, as shown in our experiments, thereby demonstrating that uuman-understandee concepts can be maintained during incremental learning without compromising model per- formance. Our approach is effective both pretrained and non-pretrained scenarios; in the latter, the backbone trained from scratch during the first learning phase. Code is publicly available at github.com/impportAAiy CL-CBM
1 Introduction
Deep learning models have demonstrated exceptional performance when trained on large-scale, stationary datasets all at once, as evidenced by breakthroughs computer vision (He et al. 2016). healthcare (Ron- neberger et al. 2015 Zhang et al. 2024), and robotics (Mnih 2013). However, their performance deteriorates substantially when data arrives sequentially over time (De Lange et al. 2021). Contimuously retraining mod- els from scratch each time new data arrives is computationally expensive, time-consuning,, and impractical. These limitations have spurred growing interest in continual learning, different learning paradigm that seeks to enable models to learn from evolving data streams without forgetting previously acquired knowledge.
Continual learning (Parisi et al. 2019) enables models to incrementally update their knowledge and adapt to new data over time. In this work, we focus on the class incremental learning (CIL) setting (Van de Ven & Tolias 2019), which is widely regarded as the most challenging form of continual learning. In CIL, each phase introduces a new set of classes disjoint from previously seen ones, and inference time, a single model must classify test samples from all observed classes without access to phase identifiers. A central difficulty

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Concepts
Class
Concepts
Class
Concepts
Class
blue boad
small, forked tail
a blue head
small, focked tail
blue head
small. forked tail
white wing bars
Tree
white wing bars
Tree
small, blue body
Tree Swallow
small, blue body
Swallow
small, blue body
Swallow
NOT orange feet
NOT browwshhbroown body
NOT reddish-brown body
NOT yellow or orange plumage
NOT yellow or orange plumage
NOT orange foet
NOT reddisl-brewn body
NOT orange-ycllow logs
NOT yellow orange plumage
NOT bright orange breast
NOT a bright orange breast
NOT black cap on the female
NOT orange feet
NOT a yellow eye
large, hooked
Phase 2
Phase 3
Phase 4
Figure 1: Visualization of the final layer weights with absolute values greater than 0.2 for the Tree Swallow class in the CUB dataset under a four-phase scenario. Concepts with negative weights are labeled as 'NOT" concepts. Positive and negative concepts in phase 2 are shown in blue and red, respectively, while concepts added in phases 3 and 4 are shown in orange and purple. As new phases arrive, CI-CBM can preserve the positive concepts while learning more discriminative negative features. The thickness of each edge corresponds to the absolute value of the weight. Additional visualizations are provided in Section A16
2013), where learning new tasks often interferes with previously acquired knowledge, leading to substantial accuracy degradation on earlier tasks.
in this setting is calastrophic forgelling (Goodfellow al.,
To address catastrophic forgetting in CIL, conventional methods utilize a bounded buffer to store subset of exemplars (Rebulli et al., 2017 Hou el al. 2019 Wu et. al.) 2019) from previous phases. The model is then fine-tuned jointly on both the current phase data and the stored data. However, this approach raises concerns regarding privacy and storage limitations. Rocently, the Excmplar-Free CIL (EFCIL.) approach has
gained increasing attention (Zhu al.) 2021b] 2022 Petit et al. 2023 The main challenge in this approach is to classify between old and new classes without access to old data. Some approaches (Zhu et al., 2021b; 2022) propose fine-tuning the model on new classes while employing knowledge distillation to preserve the learned knowledge from old classes. Others (Petit et al. 2023 Panos et al. (202)) freeze the feature extractor after the first phase and focus on incrementally learning the classifier in the next phases. Other hods
(Wang et al. 2022c by Smith et al., 2023 employ a backbone model that has been pretrained on large-scale datasets. However, these models depend heavily on strong pretraining and exhibit a significant performance drop when the backbone trained on first-phase data instead of a large-scale dataset (Tang et al., 2023).
Although recent advancements in CIL offer promising solutions to catastrophic forgetting, the decision- making mechanisms of these models are often difficult to understand and are regarded as black-boxr processes. Interpretability is crucial for uncovering the information a model uses when classifying inputs, which is critical for identifying biases. Researchers have developed methods to interpret black-box deep neural networks (DNNs) in continual learning (Patra & Noble 2020). However, most mothods focus on examining the DNN model after training is complete, with only a Tew approaches, such as ICICLE (Rymarezyk et al. 2023). IN2 (Yang et al., (024),, CONCIL (Lai et al.) 2025), and CLG-CBM (Yu et al.) 2025), focusing on learning models that are interpretable by design. Despite being pioneering work in this dircction, ICICLE is restricted to specific architectures and fine-graines datasets, while IN2's suboptimal concept expansion compromises efficiency, and CONCIL relies on per-sample concept annotations. CL.G-CBM and the other mentioned interpretable CIL methods rely on pretrained backbones, which can blur the CIL objective of learning beyond what is already encoded in pretraining. To our knowledge, our proposed method is the first interpretable CIL model to demonstrate robust in both pretrained and non-pretrained settings. Moreover, the performance gap between current interpretable models and unrestricted ones in CIL further diminishes the incentive to adopt interpretable approaches, as their reduced accuracy makes the models less practical for worldw use. These limitations motivate our work to develop more generalizable and inherently interpretable approach to class incremental learning, suitable for both pretrained and non-pretrained model scenarios.
In this paper, we propose a new an effective framework called the Class Incremental Concept Bottleneck Model (CI-CBM) to extend the Concept Bottleneck Model (CBM) for the challenging Exemplar- Free CIL (EFCIL) setting. In the EFCIL setting, due to the absence of samples from previous classes, the learned functionality of each concept and its contribution to those classes must be preserved while allowing the model to continually learn new concepts and adjust their contributions across all classes. To address these
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problems, CI-CBM
employs effective mechanism to prevent concept drift and mitigate classifier bias (see Figure 1 and G Our contributions are summarized below:
We introduce a new approach to learn inherently interpretable neural models for class incremental learning with much better performance and utility. Unlike previous interpretable approaches in CTL, our approach CI-CBM achieves 25-43% higher accuracy across multiple benchmarks while maintaining scalability and adaptability across various datasets and architectures, demonstrating strong performance both with pretrained backbone models and when trained from scratch.
We propose new techniques including concept regularization to prevent the learned concepts from losing their functionality while learning new concepts. Additionally, utilize pseudl-concepts for previous class data in conjunction with actual concepts for new class data to incrementally train the sparse classifier across different phases.
We evaluate approach by conducting comprehensive EFCIL evaluation scenarios and performing ablation studies to assess the impact of different components of the proposed method. The results demonstrate the superiority of our method over other interpretable models in CIL, achieving an average accuracy gain of 36%.
2 Related work
2.1 Class Incremental Learning
Class Incremental Learning (CIL) aims to extend the capabilities of doep lcarning models to continuously learn from new data and adapt new classes over time while retaining previously acquired knowledge. The goal is to develop a model that can classify all previously which requires balance between plasticity, the flexibility to learn new features, and stability, the resistance to forgetting old information. The phenomenon of catastrophic forgetting (Goodfellow et al. 2013) illustrates a fundamental trade-off in CIL, where the effort to incorporate new information can result in the loss of valuable knowledge from previous phases, leading to a sharp drop in performance on previous classes.
classes effectively at any stage of training,
To address catastrophic forgetting, several approaches have been proposed: (I) Regularization-basee meth- ods: These approaches (Kirkpatrick et al., 2017 Wang et al., 2021 mitigate forgetting by constraining changes in critical parameters across phasos. However, these methods lack reliable metrics for paramcter importance and perform poorly in CIL (Van de Ven & Tolias 2019 (II) Architectuue-baseed methods:
These approaches expand network capacity dynamically when a new phase arrives (Rusu et al. 2016 Yan
et al. 2021). However, a key challenge is the increasing memory and computational costs as the architecture grows, making it crucial to manage the rate of expansion with each phasc. (III) Rehearsal- mothods: These approaches utilize various sampling strategies, such as herding (Rebulli et al. (017), diieerity--aware
sampling (Bang et al. 2021), reservoir sampling (Buzzega et al. (020)), and greedy sampling (Prabhu al.
2020), to store samples in bounded memory. These samples then used for knowledge distillation (Li &
Hoiem 2017 Rebuffi et al. 2017 Dhar et al. 2019 bias correction (Hou et al. 2019 Wu et al. 2019),
gradient regularization (Lopez-Pax & Ranzato, 2017 Chaudhry et al. 2018). Despite their effectivence in addressing catastrophic forgetting, rehearsal-based methods pose privacy risks, as storing data from previous phases may expose confidential information. Generative models can be trained to produce samples from pre-
vious classes (Wu al. 2018 Gao & Liu 2023 but they are prone to catastrophic forgetting (Thanh- Tung & Tran 2020) and are vulnerable model inver-invvrsion attacks (Zhang al.] 2020).
Class Incremental Learning (EFCIL) approaches have gained popularity. These methods often focus on learning high-quality feature representations in the first phase, which usually covers around half of the total classes. For instance, FeTrIL (Petit et al.) 2023) freezes the feature extractor after this initial phase and generates pseudo-featuues using basic geometric transformations based on the class mean. The aim of such methods is to maximize the utility of the representations learned in the first phase for the subsequent phascs. FcTTIL+++ (Hogca et al. (2224) extends FeTrIL by additionally storing the per- class diagonal covariance alongside each class centroid, and by applying a lightweight optimization align the variance of pseudo-features with that of the original features.
Recently, Exemplar-Fre
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Recent advancements have introduced methods that leverage ImageNet-pretranne ViT models. Among these, some approaches (Wang et al. 2022c Tang et. al. 2023) introduce lightweight prompts that are concatenated with input patches and processed alongside them, enabling task-specific adaptation without modifying backbone weights. These methods maintain a pool of prompts, selecting or generating instance- specific ones through key-query matching (Wang el al. 2022c), clustering (Wang et al. 2022a), or attention- based combinations (Smith et al., 2023). However, these methods require strong pretrained backbone and tend to experience performance degradation when the data from the first phase is used for pretraining the backbone (Tang et al. 2023). In addition, the core idea of CIL is to enable system to acquire knowledge that was previously unavailable (Zhou et al. 2024b). The use of large pretraining datasets like ImageNet raises the question of whether these models encounter truly novel information. However, our approach reduces dependence on extensive pretraining, making it applicable to both pretrained and non- con-pretrained scenarios.
2.2 Interpretability
Despite advancements in CIL methods, there remains a gap in understanding how these black-box models function. Interpretability frameworks aim to make the decision-making process of models more transparent. Rather than relying on post-hoc explanations for black-box models, it is more effective to design models that are inherently interpretable, reducing the risk of misleading interpretations (Rudin 2019
The Concept Bottleneck Model (CBM) (Koh et al. 2020 incorporates an intermediate concept bottleneck layer, where each neuron corresponds a human- uniraannnnndettadaabll.e concept. This allows the model's final prediction to be expressed as linear combination of interpretable concepts, significantly improving our in- sight into how decisions are made. CBM requires dense concept annotations in the training data to learn the bottleneck layer, limiting its scalability and applicability. LF-CBM (Oikarinen et al. 2023) addresses this issue by automating the CBM training process, thus reducing reliance on human experts. LF-CBM leverages Large Language Models, such as GPT-3, to gather relevant concepts for each task and aligns image- concept activations using lasion-language models like CLIP (Radford et al. 2021). CBMs have demonstrated signif- icant potential across domains, including medical applications (Yuksekgomul et al., 2022), deep generative
models [Ismail et al. 2023 Kulkarni et al. 2025), and large language models (Sun et al. 2025
Although interpretability is well-established in classical machine learning, it remains underexplored in the context of CIL. ICICLE (Rymarczyk et al. 2023) introduced interpretability in class incremental learning through prototypical parts. However, their work is limited to specific model architectures and fino-grained datasets. IN2 (Yang et al. (2024) extended the CBM by freezing learned concepts and regularizing the predic- tion layer. However, the expansion of the concept set in their approach is not optimal, and its performance is much weaker than that of unrestricted models. CONCIL (Lai et al.] 2025) employed handom-featur expansion and performed continual concept prediction and classification via closed-form ridge-regression up- dates; however, it relies on a pretrained backbone and per-sample concept annotations, limiting practicality in many continual learning settings. Most similar to our approach is CLG-CBM (Yu et al.) 2022), which leverages a frozen, large-scale pretrained CLIP backbone and synthesizes pseudo-featee features for prior classes via prototype- based based augmentation. However, this reliance on strong pretrained backbone may weaken the con- tinual learning premisc of acquiring genuincly new knowledge beyond what alrcady encoded in pretraining.
Generally, there is trade-off between interpretability and accuracy. Previous works, such PCBM Yuk- sekgonul et al.] 2022) (their Tables 1 and 2) demonstrate that interpretable models generally suffer from lower accuracy compared to their black-box counterparts in classical machine learning. LF-CBM (Oikarinen et al. 2023) (their Table 2) alleviates this trade-off by improving accuracy in standard image classification tasks. We found that the gap is more pronounced the context of CIL. As the performance gap between interpretable and unrestricted models widens, the motivation to use interpretable models diminishes. In contrast, our proposed method bridges this gap by providing interpretability with minimal accuracy gap.
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Bowl
Sand
G-1
Notation: R(x) = f(x) p(sa) p(cp))
Feeture vector (1:3)
Pseudo-faature voctor ((x))
Step 1: Unique concept
set expansion
Garden
Helmet
p(ex) = xy 2,_1 f(Xe.)
Pseudo concept vector (,
Cencept vector 0.00)
f,00) w fix)
Bicycle
Wave
4,00 w lox)
New concegt unit for task
Sea
Blue
GPT
Class in task
Mouse
Tail
Step 3: CBL (WE) learning
Classes in task
Concept Set (C2)
Step & Sparse FC layer (Wi) learning with actual and pseudo-concepts
f(x,) f(xx))
(,0%,) fglks,)
CBL (W()
Backbone
Camel
(X1 !
Sparse Prediction
Orchid
Step Embedding
Layer (W)
Bloycle
calculation based on X
Sea
Step 4: Pseudo-
feature and pseudo-
((xgg)
[(x))) concept generation
(d(ks)
Figure 2: Overview of our pipeline for Class Incremental Concept Bottleneck Model (CI-CBM). Color-coded
text matches the corresponding stages in the figure.
3 Methods
To make this work self con-acontaieed, we begin by reviewing the Label-free Concept Bottleneck Models (LF- CBM) framework and then explain how adapt it for the EFCIL scenario.
3.1
Label-free Concept Bottleneck Models (LF-CBM)
Concept Set Creation and Filtering. The concept refers the group of concepts included in the interpretable concept bottlencck layer. These concepts represent features that both important to the problem and easy for humans to understand, such as key features, common surrounding items, and superclasses. These concepts are generated automatically by prompting GPT-3 to identify concepts related to each class in the dataset. The concepts for all classes are then combined to form an initial concept set. This set is further refined by filtering out concepts that are too lengthy, those that closcly resemble the class names, and concepts that are similar to each other.
Learning the Concept Bottleneck Layer. The next step involves learning the projection weights Wc, which map the frozen backbone model's feature space onto space where the axes correspond to interpretable concepts. Let C' (t.....,t ,t)] represent the concept set, and D {I1,... ..ii....,,,. ENN the training dataset. The concept activation matrix P is calculated and stored, where P., = (x,)) (tz),, with E, and Er denoting the CLIP image and text encoders, respectively. The weights We are optimized to maximize the similarity between the neuron's activation patterns and the target concepts. The similarity measured using the differentiable cosine-cubed function, defined as:
Ps
L(Wo) Σ sim(t,, 9i) = Σ
(1)
Here, di denotes the activation of the i-th neuron in the projection layer, and q represents q normalized have mean and standard deviation
Learning the Sparse Final Layer. The final step involves learning sparse prodictor, WP,br), using the GLM-SAGA WWng et al.) 2021 solver with elastic net objective.
min Wr.br
Σ
Lee (WFFf(a))) + br. v.) + (R.(WP)
(2)
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Algorithm CI-CBM Training in Exemplar-Free Class-Incremenia Learning
Require: Phase datasets {D, (X,, X=) backbone f: initial concept set C₁; distillation weight B.
Initialize phase 1 concept C via LLM prompts and filtering.
Compute P1 using vision-language model: Pi (x,)
(ax)) Er (cz) for X1, Ct.
3: Learn W by minimizing concept alignment loss (Eq. 1
4: Train sparse predictor (W F. bb)) on concept features fc(æ) = (ff(2 (Eq. 2
5: Store class centroids ju(c) for all classes seen in phase 1 in backbone feature space.
6: for t= 2 to do
7: (Module I) Concept set expansion:
Generate candidate concepts for new classes in Y, using LLM prompts.
Using cosine similarity in text-embedding space, remove candidates that are too similar to any seen class name or near-duplicates of existing concepts in C--1; remove lengthy concepts.
10:
Update concept set C2 - Ct-1 (filtered new concepts].
11:
Compute pt on current data: ji - Er(x;) Er(c)) for I; Xt, C..EE.. Cr. (Module II) Concept bottleneck learning with distillation:
12:
13:
Cache previous outputs on current data for old concepts: (x) - Wt f(x) for x Xt.
Expand W with new neurons to match [Cr].
14:
15:
Learn W by minimizing alignment distillation loss (Eq. 3 with weight B.
16:
(Module III) Pseudo-feature and pseudo-concept generation:
17:
Compute and store new class centroids p(c) for classes in Y,.
18:
for each past class Cp do
19:
Find nearest new class ca by cosine similarity between centroids. Generate pseudo-features: f(c,) - f(c)) p(ca) + u(cp)
20:
(Eq. 4 (Eq. 5
21:
Project to pseudo-concepte felep) - W&f(ep)
22:
end for
23:
Train (Wz, b'z) using real concepts for new classes and pseudo-concepts for past classes (Eq.
24:
end for
where R. (Wp) = -- [|r] + Wrll, with |-|| representing the Frobenius norm and |- the element- wise matrix norm, and fe(x) = Wcf(z) denotes the projection of backbone features into the concept space.
3.2 Class Incremental Concept Bottleneck Model (CI-CBM)
To adapt LF-CBM for the class incremental learning setting, we introduce three main modules, as illustrated in Figure (I) curated concept set expansion (Step 1), (IT) knowledge-press prrugggigreeriingggggg concept learning (Step 3), and (III) dynamic adaptation in the sparse prediction layer (Step 4-5). Let D (D1, D2...., Dr} denote the sequence of datascts from the first to the last phase, where cach dataset D, (X,, Y.) { Vo.j 1 consists of N₂ labeled samples received by the model at phase t. The classes across different phases are disjoint, and the phase boundaries remain unknown. When the first batch of data, D1, arrives, the model is trained following the LF-CBM approach, as outlined in Section 3.1 After completing the learning process for phase t 1-,, the model has a concept set Ct-1, containing M,-1 concepts related to the previously seen classes [U-=] Yi,, along with a concept. bottleneck layer Wt and a unified sparse prediction layer (Wz 17pp",b; (b
Module (I): Incremental Concept Set Expansion. When a new phase begins, concepts for the new classes are generated using GPT-3, filtered, and added to the concept set. To avoid adding redundant concepts during expansion, embed each candidate concept, each existing concept, and each class name of seen classes using a text encoder (Sentence-Transfrmmec Transformer and the CLIP text encoder) and compute cosine similarity. We discard a candidate if its similarity exceeds 0.9 to any existing concept or exceeds 0.85 to any class name. Full generation/filtenn filtering pipeline details are provided Appendix A1l As result, the updated concept set C, contains M, unique concepts. Next, the concopt activation matrix pf R.N M, is computed using a multinodal model based on the new training dataset D, and the combined concept set C.- In experiments, we used SigL.P Zhai al. 2023 instead of CLIP RRadford et al.] 2021 as the

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multimodal model for computing Pt. SigLIP is recent model that focuses image-text pairs and employs sigmoid loss function, in contrast to the softmax-based contrastive learning approach used in CLIPP
Module (II): Preventing Concept Drift in the Concept Bottleneck Layer with Distillation. As the concept set expands, the learned W adjusted to accommodate new neurons for the added concepts, resulting We which must be learned. Naively fine-tuning W on D, risks shifting the functionality of previously learned concepts to the new data, leading to catastrophic forgetting of past knowledge. Conversely, freezing the learned concepts to prevent updates limits the model's adaptability. Before expanding W to accommodate new concepts, the scores for the current concepts the dataset from the new phase are calculated and saved. During the training of the concept bottleneck layer, an additional distillation loss is introduced to regularize the loss function, aiming to prevent the output of the current model (W2) from drifting too far from the saved output of the previous model 1W) The loss function is defined as:
M. L(W')
P
M
3
Σ
(3)
2
1=1
12l19
where B 3 O is a scalar hyperparameter that weights the distillation regularizer.
Phase 1 Feature
Phase 2 Feature
Pseudo Feature
Original Features
Koh Dal
for
-10
-10
-10
-10
-10
-10
-10
-10
5
Figure 3: Illustration of the pseudo-feature generation procedure with a loy example. In Phase 1, the model distinguishes between red and blue classes using actual features. In Phase 2, learns to discriminate among all seen classes (red, blue, orange, green) without access past-class data. For each past class, the closest new class is identified by cosine similarity between centroids (marked by the symbol). Pseudo-features for past classes are generated by shifting the feature distribution from the closest new class to the target past class. The model then distinguishes all seen classes using actual features for new classes and pseudo-feature for past classes. The rightmost subfigure visualizes the actual features for all classes at the end of Phase 2.
Dynamic Adaptation of Prediction Layer and Pscudo-Concopi Generation. The prediction layer, Wi, and its bias, bi, must be expanded to accommodate both new concepts and class labels, while preserving the learned associations between previous classes and concepts stored in W and bf Following Petit et al. (2023). we generate pseudo-fcatures for past classes by shifting the data distribution of the nearest new class from the new class mean to the target past class mean, as shown in Figure 3 The centroids of each class in the backbone's feature space are computed and stored as the class is introduced. For each past class, its nearest new class is identified by calculating the cosine similarity between their centroids. Let Cp denote cach past class, G₂ the closest new class Cp. and μl(p)) and p(c,)) the mean features of classes Gp and Cn, respectively, as extracted by the frozen backbone model Pseudo-features for past classes are generated by the following shift:
Module (III):
f(cp) f(en) u(en) + u(cp)
(4)
The pscudo-features are then projected into the concept space using the learned concept bottleneck at phase t, Wi. to generate pseudo-concepts:
felc,) (())
(5)
These pseudo-concee concepts for past classes, along with the actual concepts for new classes, used to train the sparse predictor W
min W (E.
Σ
Lee (WHf(((s))) + bp..))) + Σ Lee (Wbf((())))))) by, v.) XR, (W+)
(6)
(D..
This allows us to train the model with eseudo-concepts for previous classes, without storing any information except for each class mean. See Algorithm for the full sequence of steps across phases.
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3.3 Controlled Geometric Perspective
Original Features Su
Pasudo Peatures (c. with Original
62 MTG, 1) 1.111
C ANjC, 11 5.90
FJ MTE 00 18
MIO.
3..20
Ca: 3,22
C2
Figure 4: Visualization of decision boundaries in the feature space. Black lines indicate Bayes-optimal boundarics, and colored regions denote predicted class assignments. Dashed circles represent one standard deviation from each class mean. Left: original class feature distributions, where differences in variance lead curved boundaries between old and new classes. Right: pseudo-feature distributions generated by our method, where matched variances lead to linear boundaries that closely follow the true Bayes boundaries.
To further motivate the design of our method, we provide controlled analysis based on class distributions in the feature space. Consider toy example with two learning phases, each introducing two new classes. We model each class's feature distribution as a multivariate Gaussian ((us of where E IRd. The Bayes optimal decision boundary between classes and j is where log px() = log Pz()):
log])(z)
()T() -
20 x- - 1xll?
2
1
1
logı((z) (xg
=
1 -1112 + d log 0,²
|| 12y12 + dl dolog of
jj
( #
2
[
d log o
This boundary is generally quadratic but becomes approximately linear when class variances are similar. Our method shifts new class distributions toward old class centroids, forming pseudo-feature distributions with original means and nearby new class variances e.g., class 1 becomes ((H1, enabling linear boundary with class 3 due to matched variance. The boundary between real and pscudo-feature distributions closcly matches the true boundary, especially when their variances are similar. Figure ! illustrates this effect. The left panel shows the Bayes-optimal decision regions induced by the original class distributions, where differences in class variances lead to curved boundaries. In contrast, the right panel depicts the pseudo- feature distributions introduced by our method, where the resulting boundaries become linear while still closely approximating the true Bayes decision surfaces. Subsequently, all features (actual features for new classes and pseudo-features for old classes) projected into the concept space, where concept funetionality is preserved via our drift mitigation, enabling concept-basee classification.
This controlled analysis assumees that class-conditional features are reasonably concentrated around their centroids, so that mean shifts preserve much of the relevant geometry. This requires a well-trained feature extractor, which may not always be available realistic CIL settings. To bridge this controlled picture to realistic high-dimensional representations and to assess sensitivity to pretrained vs. non-pretrained feature extractors, we provide empirical validation in Supplementary Section A15
4 Evaluation
Datasets and Implementation Details. To evaluate the performance of our proposed method, we perform comprehensive experiments on several CIL datasets: CIFAR-10, CIFAR-100 KKriheessy et al. 2009), CUB /aa et al. 2011), TinyImageNet (Le Yang, 2015), ImageNet-Subsot, ImageNet (Deng et al. 2009 and Places365 (Zhou et al. 2017). We employ ResNet-18 (He et al.) 2016). DeiT [Tovrron et al, modified to match ResNet-18's parameter count by adjusting the embedding dimension and number
2021
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CIEAR-10
CIEAR 100
CUB
Taylinggeee
Placesassi
ImsggeNet
T-3
Tw5
7-10
7-20
T-4
T--0
T-20
2-5 7-10
7-20
T-5
T-10
7-20
T-6
J-10
2--21
ICICLE Rymarcark al 2005
35.0
18.5
9.0
IN2
Yani ir 4
325
64.9
41.9
27.5
173
5055
20.1
13.0
30.9
21.6
14.5
CO Lant
3025
61.3
CI-CBM (mirs
80.4
68.8
68.8
07.8
02.2
65.3
06.1
48.6
48.7
48.5
48.3
49.3
49.0
31.7
32.1
31.5
Full nitausa
70.9
67.7
50.0
50.7
01.6
30.3
34.1
Table 1: Experiment I Comparisons of the Average Incremental Accuracy of CI-CBM with other inter- pretable models in CIL. The same pretrained backbone was used to reproduce IN2 ( (Yang et al. 2024) results for a fair comparison. The results for ICICLE (Rymarczyk ot al., 2023) and CONCIL (Lai ct al. 2025) are as reported in their original paper. Cells marked with *-" indicate that results were unavailable. The full rehearsal approach retains all previous training data across phases, providing an upper bound for evaluating CI-CBM's performance.
of heads, and ViT ViT-Base/16 (Dosovitskiy et al. 2020 as backbone models. The subsequent parameters follow the setup from LF-CBM (Oikarinen et al. 2023). The regularization parameter À is selected to ensure that cach class has 35 to 55 non-zero weights, leading to sparsity levels ranging from 1% to 5% across different datasets. To ensure a fair comparison, we use the same random seed 1993 as the compared methods (Zhul et al.) 2021b 2022; Petit et al. 2023 Rymarczyk et al.) 2023) to shuffle the classes and split them into phases. Each configuration is evaluated three times, and the average results are reported.
Evaluation Metric. We report the average incremental accuracy as the mean of the average accuracy across all incremental phases, including the first phase. Additionally, offer average accuracy for each phase to provide an understanding of the accuracy progression throughout the continual learning process. Further, we report the average incremental forgetting in the Appendix.
Comparison to Interpretable Methods. We compare our interpretable model against ICICLE, IN2, CONCIL, and CLG-CBM which, to the best of our knowledge, are the only existing interpretable methods designed for the CIL setting. We also evaluate full rehearsal strategy, where the training data from all previous phases is stored in memory and accessible for each new phase, though this is highly impractical in real-world settings. However, this approach helps us understand how closely our method reaches the best. possible performance. Our backbone model for the CIFAR-10/100, CUB, and Places365 datasets is ResNet-18 pretrained on ImageNet, and for the Meee and ImageNet datasets, it is pretrained on Places365. For cach datasct, we distribute the classes evenly across T phases.
Table | (Experiment I) demonstrates that our approach significantly outperforms all the compared inter- pretable methods. CI-CBM achieves an average improvement of 35.50%, 39.57%, and 26.40% on CIFAR-10, CIFAR-100, and Tiny Inngee,,,et,, respectively. On CUB, CI-CBM improves over prior interpretable basclines (ICICLEF/I22) by 43.13% on average across T e [4, 10, 2 and additionally outperforms CONCIL at their reported setting (T = 10) by 4.0%. Our performance on the Places365 and ImageNet datasets demonstrates that our proposed approach is capable of incremental classification on challenging large-scale datasets. As the total number of phases increases, our method remains robust and maintains its average incremental accuracy, while the other compared methods fail to do so. By comparing CI-CBM with the impractical full rehcarsal scenario, we find that our approach shows only small 2.6% decrcase on average, demonstrating its effectiveness in maintaining learned knowledge without retaining any samples from previous phases.
Comparison to Non-Pretrained and Non-Interpretable Methods. Motivated by the results observed in interpretable models and the investigation of the effect of the pretrained backbone model on our metric
scores, we exlend our analysis to unrestricted models. We follow Tell (Petit et al. 2023 and APG (Tang
3CLG-CBM uses a pretrained ViT backbone; therefore, we report the comparison to CLC-CBM under the same pretrained Table focuses comparisons under a Res.Net backbone for fair evaluation among ResNet-basodd
VII setting in Table Interpretable methods.
"ICICLE used a KesNet-31 backbone pre-trained on ImageNet. We use ResNet-18 for compatibiltyy with most CIL models. results are 62.9. 65.9, and 66.4 for T 4, 10, and 20 phases, respectively. We note that on CUB the average incremental accuracy slightly increases the number phases grows. This because Imnetrnet-retrainee backbone yields well-structured feature space, allowing fcature preserve past knowledge effectively. Since all classes in CUB are birds, the concepts introduced in each phase remain broadly relevant and discriminatvee, which can further improve average incremental performance as phases become finer-grained.
With ResNet-34,

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Published in Transactions on Machine Learning Research (04/2026)
CIFAR-100
ThnyInageNet
ImtgeeNot-Sunng SutubbetttStt
Method
Interpretability
7=5
T=10
7=
7=5
7=10
T=
7=5
7=10
T=20
EWC
Kirkpatrick
2017
24.5
21.2
15.9
18.8
15.8
12.4
20.4
LWF3
2017
17.4
23.5
iCaRL-
Rebull
2017
51.0
48.3
11.6
31.7
31.0
27.8
50.5
LUCIR
Hou
51.2
25.2
28.1
18.9
56.8
41.4
28.5
MUC!
ct
2020
49.4
30.2
21.3
32.6
26.6
21.9
35.1
SDCT
Yu
2220
56.5
57.0
58.9
61.2
PASSI
Zhu
2021b
63.5
61.8
58.1
49.6
17.3
6444
61.8
51.3
SSRE
Ahu et
122
65.9
65.0
61.7
50.4
48.9
48.2
67.7
RTTiL
Petit
2023
66.3
65.2
61.5
54.8
53.1
52..2
72.2
71.2
EFC
Magistri
sl.
20224
X
08.2
65.9
57.5
56.5
75.4
71.6
SOPE*
Zhu al.
2023
X
66.6
65.8
61.8
53.7
52.9
51.9
69.2
FCS
et al. 2024
X
02.1
60.3
58.3
46,0
41.9
42.5
G1.7
DCM
Ott ot al.
2024
67.9
66.8
64.0
54.8
53.9
52.5
70.5
70.0
65.5
TASS
Liu
2724
X
68.7
67.4
62.7
55.1
54.2
52.7
74.3
72.6
68.7
CI-CBM (ours)
61.9
60.5
60.2
49.2
48.3
47.3
67.6
66.2
66.9
Full rehearsal
V
03.7
63.5
62.1
50.5
50.4
50.2
71.7
71.7
09.6
Table 2: Experiment II Comparisons of the average incremental accuracy of CI-CBM with EFCI, unrestricted ResNet- based methods non-pretrained scenario. Models marked with a represent reported results from (Petit al., 2023), while those marked with an ý indicate reported findings from (Zhu et al. 2021b), and models marked with a * denote results reported in their paper. Cells marked with "_' indicate that results unavailable. The full rehearsal approach retains all previous training data across phases, providing upper bound for evaluating CI-CBM's performance.
Cifar-100 10 phases
TinylmagNet 10 phases
ImagNet-Subseet 10 phases
Average accuracy
80
60
IGHRLONN
ICaRL
40
PABB
SSRE
20
20
FHTHIL
(GUMS
10
2
Incremental Phases
Incremental Phases
Incremental Phases
Figure 5: Experiment III Average accuracy curves for CIFAR-100, TinylmageNet, and ImageNet-Subset
over 10 learning phases, comparing C1-CBM with other unrestricted ResNet-based methods.
et al. 2023 to train ResNet-18 and Deil', respectively, from scratch in the initial phase, Afterward, we
froeze them as the backbone for CI-CBM and incrementally learn the classes. We conduct a comparative
analysis of our method against classical approaches (Kirkpatrick
al. 2017
Li Hoiem
2017 Rebulli
let al. 2017 Hou al.] 2019), SOTA ResNet-based models (Zhu et 2021b a 2022
Petit al. 2023
and SOTA prompt-based methods (Wang et al. 2022c Tang et al.] 2023
We follow the setup described in (Petit et al. 2023 Tang et al. 2023), evaluating CIFAR-100 and TmageNet-
Subset under the following configurations: (i) an initial set of 50 classes with 5 phases, each introducing 10 classes, (ii) 50 initial classes followed by 10 phases of 5 classes each, (iii) 40 initial classes with 20 phases, tested with 100 initial classes, with the remaining classes distributed as follows: (i) phases of classos, (ii) 10 phases of classes, (fii) phases of classes.
each introducing 3 classes. Additionally, TinyImageNer
Table 2 Exxpermmen II) illustrates that our interpretable model demonstrates superior performance compared to many unrestricted ResNet-based models, with minimal 7.5% difference in accuracy compared to the SOTA models. Figure 5 [Experiment III) presents the average accuracy curve for CIFAR-100, TinyImageNet, and ImageNet-Subset across 10 phases. Although CI-CBM starts with the lowest accuracy in the initial phase due to interpretability constraints, effectively learns to distinguish new classes while preserving performance on previously learned classes, ultimately achieving a high average accuracy by the final phase.
Table (Experiment IV) compares the performance of CI-CBM with prompt-based models using a DeiT backbone trained from scratch in the first phase. Without needing any additional prompts, CI-CBM outper-
10

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Published in Transactions on Machine Learning Research (04/2026)
Phase Pred: Sturgeon
Phase 2 Pred: Sturgeon
Phase 3 Pred: Sturgeon
GT: Sturgeon
barbel on the chin
barbel on the chin dam
barbel on the chin
a fish
trigger
pointed teeth
pointed
large tail
fishing mountains
box
lake
bexy shape
perch
balt
soldier
fishing rod
NOT
Sum of 552 other features
Sum of 652 other features
Sum 748 other features
Contnbutton
Contribution
Contribution Value
Figure 6: Visualization of model reasoning and concept contributions for an image the Sturgeon class, introduced the first phase of the ImageNet- image using actual features. In the second and third phases, CI-CBM continues accurately distinguish it among larger set of classes by generating pscudo-concepts. Additional visualizations are provided in Supplement Section A16
In the first phase, CI-CBM correctly classifies the
forms L2P (Wang al. 2022ch and DualPrompt (Wang et al. 2022b), two methods that fail to generalize when trained from scratch in the initial phase. CI-CBM achieves performance comparable to APG (Tang et al. 2023), despite the latter's use of prompt generatons, which involve cross-allention layers, groups of learnable parameters, and linear layers, leading to a more parameter-intensin model. Results with more incremental phases are reported in the Appendix.
Comparison to Pretrained ViT-Based Methods. Following prior works, we use ViT-Base/ model pretrained on ImageNet-21k, utilizing the final [CLS] token as the backbone feature. For each dataset, we distribute the classes evenly across T phases. Table (Experiment V) shows that CI-CBM achieves competitive accuracy, only 7% lower CIFAR-100 and 3.1% lower on CUB compared to SOTA models, demonstraating that CI-CBM provides interpretability with minimal performance trade-off. Moreover, CT- CBM outperforms the interpretable baseline CLG-CBM by 1.1% on CIFAR-100 and 2.6% on CUB.
Interpretability and Insights on Model Reasoning. To provide a comprehensive understanding of our model's interpretability, Figure [ presents a Sankey diagram that offers global insights into the concept-to- class relationships. the diagram, line widths are proportional absolute weights, displaying only concepts with absolute weights greater than 0.2. Concepts with negative weights are labeled as "NOT" concepts. The findings reveal that the model consistently relied the same positive concepts across different phases without needing to impose constraints like freezing weights. Additionally, as new classes were introduced, more discriminative negative concepts were incorporated, enabling the model to better differentiate between similar classes. Figure B illustrates the local explanations for individual decisions made by the model using a randomly chosen image from the Sturgeon class the first phase of the ImageNet-Subest dataset. The contribution of concept j to the output for input my. in phase is given by Contrib(aRR: i.j) = WpLi.5 [)] This figure illustrates how the model's salient concepts evolve across phases: semantically related classes (c.g., eel, coho) are introduced, generic concepts (o.g., "a fish") become less discriminative and diminish in contribution, while more class-specific concepts (e.g., "barbel on the chin") remain dominant, allowing the model to classify the image correctly in later phases.
CIFAR-100
Image:NetSSubee
Method
Interpretability
T==00
T-=00
T'=10
7==14
T.2P (Wang al.
2022c
36.5
18.8
25.1
29.9
DualPrompt Wang et al.
2022b
X
26.8
11.8
35.8
30.3
APG Tang et al.
2023
X
66.6
62.4
75.5
69.8
CI-CBM (ours)
59.5
59.7
54.6
55.6
Full rehearsal
62.7
63.4
58.9
60.4
Table 3: Experiment IV Comparison of the average incremental accuracy between CI-CBM and EFCIL unrestricted prompt-based methods in a non-pretrained scenario. The DeiT backbone model is trained using data from the first phase. Results for the compared methods are reported from [Tang et al. 2023
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Published in Transactions on Machine Learning Research (04/2026)
Method
Interpretability CIFAR-100 (T-10)
CUB (T=10)
L2Pt
[Wang et al.
2022c
84.6
65.2
DualPromph
Wang et
2022b
81.3
68.5
CODA-Promp
Smith of al.
2023
86.3
79.5
APG
Tang al. 2023
89.3
LAE
Gso et
2023
89.9
ESN
Wang et a..
2023
86.3
Simple CIL
Zhou el al.
2024a
87.6
87.1
ConvPrompl
Roy
2024
88.8
80.2
EASE Zhou al. 2024c
87.8
86.8
SAFE Zhaa ct al.
2024
92.8
91.1
CLG-CBM Yu
2025
84.5
85.4
CI-CBM (ours)
85.6
88.0
Full rehearsal
87.8
88.7
Table 4: Experiment V Average incremental accuracy of CI-CBM and EFCIL with pretrained ViT-
Base/ 16 backbone. indicates results reported by Zhao et al. 2024 indicates results taken from the corresponding papers; = denotes unavailable results.
CIFAR-100
FinyImageNet
Concept reg
Pseudo-Conee Concept
T=5
T=10
T=20
7=5
T-10
T-=20
x
X
38.0
26.2
16.9
29.1
20.9
14.4
X
38.0
26.3
16.9
29.2
21.0
14.3
X
/
68.4
68.2
67.6
48.2
48.3
48.2
68.8
68.8
67.8
48.6
48.7
48.5
Table 5: Experiment VI (Ablation Study) Performance impact of different components of CI-CBM
Ablation Study. To assess the effect of each component in C1-CBM, we conduct an ablation study on CIFAR-100 and TinyImageNet datasets, analyzing the average incremental accuracy. Table 5 (Experiment VI) highlights the contributions of concept regularization and pseudo-concepl generation. The results are follows: (i) Skipping pseudo-concept generation leads to weights with zero and negative biases in previous class weights, causing their accuracy to drop to zero and significantly lowering overall performance, (ii) Con- cept regularization alone cannot prevent this, as it only preserves concepts within the Concept Bottleneck Layer but does not stop the weights for previous classes from being pushed to zero. (iii) Pseudo-concepts improve performance by helping the model distinguish between new and old classes. (iv) Combining pseudo- concept generation with concept regularization provides further performance gains. In the Appendix, we include broader set of ablations covering concept generation and filtering choices, predictor sparsity and concept-set size, robustness to noisy concept activations, and an alternative strategy for learning the pre- diction layer. We further study sensitivity to the distillation weight 3 (both accuracy and concept-fidelity metrics), the effect of swapping CLIP with SigLIP when computing the concept-activation matrix P (accu- racy and fidelity), the unique-concept expansion mechanism and its impact on model het/iiteerretabilityy. and pscudo-fcature reliability under Irrernet-pretrained vs. 1-trainod backbones.
5 Conclusion
In this work, we propose CI-CBM, interpretable model for Exemplar-Free Class Incremental Learning (EFCIL). CI-CBM extends the Concept Bottleneck Model with concept regularization and psoudo-concopt generation to incrementally learn the concept bottleneck layer and sparse prediction layer. Our approach outperforms other interpretable models designed for EFCIL, achieving an average accuracy gain 36% and approaching SOTA black-box performance, demonstrating effectiveness both pretrained and non- pretrained settings. We further illustrate how CI-CBM's maaiiign-makinggg adapts with new phases, providing global and local insights, and present ablation studies to assess the impact of various model components.
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Published in Transactions on Machine Learning Research (04/2026)
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A1 Appendix Overview
In this section, we provide a brief overview of the Appendix contents. The Appendix is primarily focused on (i) defining precise evaluation metrics for the CIL setting, (fi) presenting extended experiments and ablation studies that analyze the behavior of CI-CBM across different backbones and regimes, and (iii) showcasing additional qualitative visualizations that illustrate model reasoning and weight structure.
First, in Section A2 we discuss the main limitations of our method. Section A3 defines the metrics used throughout our CIL evaluations and reports extended results on average incremental forgetting across three backbones and datascts (Experiments VII-IX). Sections A4 presenntt scries of ablation studics examining concept generation, sparsily, concept-set size, robustness to noisy concept activations, and an alternative strategy for learning the prediction layer (Experiments X- X-XIV). In Section A9 we analyze our unique- concept expansion mechanism and its effect on model size and interpretability (Experiment XVT). Section A10 evaluates the challenging one-class- incremene regime (Experiment XV). Section A11 details the full concept- generation pipeline, including prompts, few-shot examples, and filtering steps. Section A12 studies the effect of the distillation regularizer weight on daassincreemenal accuracy (Experiment XVII; Table [A10), while Section analyzes how distillation impacts the interpretabilityy and semantic fidelity of the learned concept bottleneck using CL.P-bbaeed concept-fidelity metrics. We further ablate the choice of vision-language model used to compute the concept-activation matrix P by swapping CLIP with SigLIP, and report its effect both incremental accuracy (Experiment XIX; Table and concept fidelity (Experiment XX; Table A13 classifier under two backbone regimes
Section A analyzes pseudo-featury reliability using a (ImageNet-pretrained vs. trained only on the first phase), highlighting the effect of pretraining on feature separability and accuracy, and showing that our full method improves test accuracy in both regimes. Finally, Section A16 provides additional qualitative visualizations of model weights and per-image concept attributions that complement the figures in the main paper.
A2 Limitation
The main limitations of our research point to future directions. First,, the model sometimes forms incorrect correlations between specific concepts and classes, warranting further investigation to see if this stems from the training process or vasion-language model misalignments. Second, our pscudo-concept generation relies on basic geometric translations and projections. A more refined approach to generating realistic pseudo- concepts could reduce overlap between old and new classes, improving model performance.
A3 Metrics for the CIL Setting and Further Experiments
Let as.j denote the model's accuracy on the j-th task after learning the i-th task, where >> j. The following standard metries are used to evaluate continual learning performance, assuming each phase contains an equal amount of data:
Average Phase Accuracy:
A
a+
(A1)
t
Average Phase Forgetting:
F t-1
1
Σ
(as at.j)
(A2)
e (1....1-1]
Average Incremental Accuracy:
1
A =
A
(A3)
T
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Average Incremental Forgetting:
T
Fr
(A4)
For scenarios with unbalanced phases, such as when the first phase contains a larger number classes for backbone protraining, a weighted version of average phase accuracy and forgetting should be calculated, where the weights are proportional the size of each phase.
CIFAR-100
Tiny ImageNe
ImageNeetSubset
Method
T-5
T-10
T-20
T-60
T-5
T-10
T-20
T-100
T=5
T-10
T-20
T-60
CI-CBM
11.4
13.0
17.1
8.4
9.5
10.9
14.6
11.9
13.6
16.9
19.5
Full rehearsal
8.8
8.7
11.0
11.7
7.0
7.2
7.4
7.8
7.0
7.1
8.1
8.6
Table Al: Experiment VII - Average incremental forgetting of CI-CBM the non-pretrained scenario with the ResNet-18 backbone, trained on first-phase data from CIFAR-100, TinylmageNet, and ImageNet- Subset, and evaluated under 5, 10, 20, and 60 incremental phase settings. The full rehearsal approach retains all previous training data across phases, providing upper bound for evaluating CI-CBM's performance. (Complementary to the results in Table
CIFAR- 100
ImageNet Sut-Su
Method
T
F
A
CIFAR-100
CUB
Method
T
CI-CBM (ouss
60.1
8.5
56.2
6.6
Á
Á
59.5
8.5
54.6
59.7
10.2
54.4
10.8
CI-CBM (ours)
5
85.6
6.5
87.6
4.9
60
58.5
11.7
52.3
13.4
10
85.6
7.9
88.0
4.5
Full rehearsal
62.5
4.4
38.6
20
85.3
9.0
88.2
4.6
58.9
Full rehearsal
5
87.0
3.3
88.5
4.0
20
63.4
5.1
59.6
5.5
10
87.8
3.4
88.7
3.5
60
63.4
6.0
59.0
6.4
20
88.2
3.8
88.7
4.2
Table A2: Experiment VIII Average incremen- tal accuracy (A) and forgetting (F)) of C1-CBM in the non-pretrained scenario with the DeiT back- bone, Irained on first-phase data from CIFAR-100 and ImageNet-Subset, and evaluated under 5, 10, 20, and incremental phase settings. The full re- hearsal approach retains all previous training data across phases, providing upper bound for evaluat- ing CL-CBM's performance. (Complementary to Ta- ble
Table A3: Experiment IX Average incremen- tal accuracy (A) and forgetting (F) of CI-CBM in the pretrained scenario with the
VIT-B/16 backbone, evaluated under 5, 10, and 20 in- cremental phase settings. The full rehearsal approach retains all previous training data across phases, pro- viding upper bound for evaluating C1-CBM's per- formance. (Complementaryy to Table 4
Tables A1 Experiment VII) and A2 (Experiment VIII) present the average incremental forgetting in the
raieee scenario with the ResNet-18 and DeiT backbones, respectively. Table A3
(Experiment IX)
presents the average incremental forgetting in the pretrained scenario with the ViT-B 16 IN11K backbone.
A4 Alternative Concept Generation Methods
We conduct an experiment to evaluate the importance of using GPT-3 for our model's performance by comparing it against generating the initial concept sets with ConceptNet (Speer & Havasi
2013). Note that
ConceptNet is not a language model but rather a knowledge graph. The results Table A4 [Experiment X) show that our proposod pipcline, when using the concopt sets generated from ConceptNet, still performs well on CIFAR-100 100 and TinylmageNet. However, there is a slight decrease in accuracy (approximately a 2% drop) compared to using GPT-3-generated concepts. Furthermore, we observe that ConceptNet completely
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fails on CUB, whereas GPT-3-generated concepts achieve strong results. This highlights the effectiveness of GPT-3 in generating concepts for fine-grained datasets where ConceptNet struggles.
CIFAR-100
CUB
Tiny ImageNet
Method
7=5
7=
T=20
7=
7'=10
T=20
7=
7==10
7=20
CI-CBM (ConceptNeet 66.8
67.1
66.5
27.6
24.3
23.8
48.3
48.4
47.8
CI-CBM (GPT-3 (original))
68.8
68.8
67.8
62.2
65.3
66.1
48.6
48.7
48.5
Table A4: Experiment X (Ablation Study) ConceptNet vs. GPT-3 for initial concept set generation
A5 Impact of Sparsity on Model Performance
Table A5 Experiment XI) presents the effect of sparsity along with the corresponding sparsity levels. Wong et al. (2021) proposed fiuting a sparse linear prediction layer on top of deep feature representations, showing that sparse models are more interpretable while maintaining high accuracy. Our results generally suggest that removing the sparsity constraint neither improves performance nor interpretability. In particular, CI- CBM with dense prediction layer (i.e., setting X 0 in Eq. 2 performs slightly worse than the sparse variant across both CIFAR-100 and TinyImageNet (Table A5 During training, our goal is to optimize the prediction layer to distinguish between pseudo-concepts of past classes and actual concepts of new classes, expecting that the learned layer will classify both old and new classes based on their actual concepts in the test datasets. A dense layer might overly focus on the pseudo-concept distribution, while sparse prediction layer relics on fewer concepts per class, making it more robust and yiclding slightly better performance.
CIFAR-100
TingemtgeNet
Method
T=5
T=10
T=20
T=
T=10
T=20
CI-CBM (dense)
68.4
68.6
68.3
46.5
47.0
47.0
CI-CBM (sparse (original])
68.8
68.8
67.8
48.6
48.7
48.5
Sparsity
4.84%
5.70%
7.02%
2.06%
2.43%
3.30%
Table A5: Experiment XI (Ablation Study) Performance impact of sparsity constraints
Beyond accuracy, we also evaluate interpretability when removing sparsity. Figure A1 repeats the same per-image concept contribution analysis used in Fig. 6 but trains the final predictor without the sparsity regularizer. Although the dense model still classifies this example correctly, the attribution mass is spread across many concepts: the top-ranked concepts each contribute only marginally the predicted class, while the aggregate contribution of the remaining concepts dominates. This makes the explanation less concise and harder to interpret, since there is no small set of core concepts with clearly dominant contributions.
A6 Effect of Concept Set Size on Performance
Table A6 Experiment XII) presents the impact of reducing the number of available concepts during training. We simulate reduced concept availability by randomly masking a portion of the concept set and training the model using only the remaining subset. This setting evaluates the model's robustness incomplete or noisy concept supervision. As shown, performance remains relatively stable even when only 25% of the concept set is used, with less than 3.5% drop in accuracy for CIFAR-100 and 2.1% drop for TinylmageNNet. Beyond predictive performance, we investigate whether reducing the available concept set degrades expla- nation quality. We repeat the qualitative interprelability analyses under a reduced-concepl. setting in which 50% of the concepts are randomly masked. Fig. A2 presents the final-layer weight structure for the Tree Swallow class on CUB across four phases under 50% concept availability, corresponding the full-concopt visualization in Fig. [ Although some class-specific concepts (e.g., blue head and small, forked tail) are un- available under masking, the model selects semantically and visually related alternatives (e.g., blue eyes and
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Phase Pred: Sturgeon
Phase 2 Pred: Sturgeon
Phase 3 Pred: Sturgeon
GT: Sturgeon
barbel on the chin
barbel on the chin
barbel on the chin
mouth
pointed teeth
pointed teeth
mouth
fishing rod
pointed
fishing
fishing
NOT object tool
bait
perch
balt box
Sum of 552 other features
Sum of 652 other features
Sum 748 other features
Contmbutton
Contribution Volue
Contribution Value
Figure A1: Visualization of model reasoning and concopt contributions for the same Sturgeon example as Fig. G but with a dense prediction layer trained by setting the sparsity coellicient. to X Although the prediction is correct, the contribution is dispersed across many concepts: the top-ranked concepts have small individual impact compared to the summed contribution of the remaining concepts, making the explanation less concise and harder to interpret.
Eq. 2
CIFAR-100
Concept Use
100%
75%
50%
25%
100%
75%
50%
25%
Accuracy 68.8
68.4
67.5
65.5
48.6
48.0
47.5
46.5
Table A6: Experiment XII (Ablation Study) Accuracy vs. concept availability.
small, rounded body) and maintains coherent set of discriminative positive concepts while continuing to acquire informative negative (NOT) concepts new phases arrive. Fig. A3 shows concept contributions for the same Sturgeon example as in Fig. G on ImageNet-Subsot under the same 50% concept availability. The dominant contributing concepts remain visually aligned with the input image and follow a similar reasoning pallern to the full-concept. setting.
Overall, even under a substantial reduction concept availability (50% masking), CI-CBM preserves both global interprctability (a stable class-level weight structure across phases) and local interpretability (instance- level concept. attributions aligned with the input image). The main qualitative change is that when fine- grained, class-defining attributes missing from the available concept pool, the explanations shift to closely related, visually grounded alternatives; interpretability is expected to degrade more noticeably only when the concept set becomes so small that such class-defining attributes are systematically unavailable.
A7 Robustness to Noise in Image-Concepe Alignment
To evaluate the sensitivity of our method to noise in concept supervision, inject Gaussian noise into the concept activation matrix P at different signal-to-noise ratio (SNR) levels during training. Table A7 (Experiment XIII) reports accuracy for SNR levels of 10 dB, 5 dB, and 0 dB. We observe that performance degrades only marginally as noise increases, indicating that the model remains robust even under noisy concept activations.
CIFAR-100
IinyImageNet
SNR Level
None
10 dB
5 dB
dB
None
10 dB
5 dB
dB
Accuracy (%)
68.8
68.6
68.1
67.9
48.6
48.3
48.2
47.4
Table A7: Experiment XIII (Ablation Study) Accuracy SNR in image-concept alignment.

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Concepts
Class
Concepts
Class
Concepts
Class
eyes
blue eyes
all-dark plunage
small, rounded body
small, rounded body
bluc eyes
all-cark plumage
all-dark plumage
a small, rounded body
black band across cyes
black band across eyes
Tree
NOT orange
Tree Swallow
NOT on head
NOT a red crest on the head
Swallow
NOT orange feet
NOT yellow orange plunage
NOT streaked breast
a yellowish
NOT yellow or oninge plumage
NOT orange feet
NOT large eyes
large eyes
NOT' large, hawk-like body
NOT yellow orange plumage
NOT a yellowish hill
NOT rusty- brown fenthers
Phase 2
Phase 3
Phase 4
Figure A2: Visualization of the final-layer weights with absolute values greater than 0.2 for the Tree Swallow class in the CUB dataset under a four-phase -hase scenario when training with only 50% of the available concepts (randomly maskod), following the same sctup as Fig. 1 Concepts with negative weights are labeled "NOT" concepts. Positive and negative concepts in phase 2 are shown in blue and red, respectively, while concepts added in phases 3 and 4 are shown in orange and purple. Although some class-specifie concepts (e-g., blue head and small, forked tail) may be missing due to reduced concept availability, C1-CBM compensates by selecting semantically related cues (e.g., blue eyes and small, rounded body) and maintains a coherent set of discriminative positive and negative features across phases. The thickness of each edge corresponds to the absolute value of the weight.
Phase Pred: Sturgeon
Phase 2 Pred: Sturgeon
Phase 3 Pred: Sturgeon
GT: Sturgeon
barbel on the chin a large tail fin
barbel on the chin
barbel on the chin
a seat for the rider
bait box
lake
a balt box
NOT a bexy shape
small mouth tool
a large fin
NOT treat
tool
shooting range
road
hollow interior other features
tool
Sum features
389 features
2.5 Contribution
Contribution Value
Figure A3: Visualization of model reasoning and concept contributions for the same Sturgeon example as Fig. but trained with only 50% of the available concepts (randomly masked). Despite reduced concept availability, CI-CBM still predicts the correct class and assigns highest contribution to concepts that remain visually aligned with the input.
A8 Alternative Approach for Learning the Prediction Layer
In addition to CI-CBM, we evaluate two alternative strategies for learning the prediction layer (Table A8 Experiment XIV). (i) Local Class Discrimination expands the prediction layer to accommodate new classes at each phase while freesing the weights associated with previously learned classes. This strategy prioritizes separating newly introduced classes from earlier ones. It performs well for T'=5, where each phase introduces enough classes to reduce overlap; however, performance drops substantially for T=20,, 20, where fewer classes are added per phase and inter-phase overlap becomes more severe. In contrast, CI-CBM maintains global separability by generating pseudo-concepts, resulting in robust performance across different values of T. (ii) Concept-Space Prototype Generation tests natural variant of our pseudo-sample mechanism: instead of generating pseudo-features in the backbone feature space and projecting them through the cur- rent concept bottleneck, attempt to perform the same translation directly in concept space using class prototypes. Specifically, for each previous class we compute a concept-space centroid using the bottleneck representation before fine-tuning on the current, phase. Since newly introduced concept dimensions did not exist in earlier phases, we set the corresponding entries of previous-class prototypes to zero and then apply prototype translation in concept space. This variant performs poorly across settings (Table A8 supporting our hypothesis that concept-space translation is unreliable under concept expansion and continual bottleneck adaptation: phases progress, the concept bottleneck both expands (introducing concept coordinates)
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and drifts (shifting the representation of previously learned concepts under dligument/distillationn causing old class centroids to become misaligned with the updated concept basis. By contrast, CI-CBM gener-
ates pseudo-samples in a more stable representation space (the backbone feature space) and then maps them through the current bottleneck to obtain pscudo-concepts, yiclding robust performance across different values of? T.
CIFAR-100
Tiny ImageNet
Method
T=5
T=10
7=20
T=5
T=10
T=20
Local Class Discrimination
63.5
55.2
42.6
46.1
41.3
33.2
Concept-Space Prototype Generation
48.2
35.8
27.2
33.4
25.3
18.9
CI-CBM
68.8
68.8
67.8
48.6
48.7
48.5
Table A8: Experiment XIV (Ablation Study) Performance comparison of alternative prediction layer learning strategy.
Method
Interpretability
CIFAR-100 (T=60)
TinylmageNet (T=100)
ImageNet-Subset (6=
ReTT-I.
Pettit et al. 2023
x
59.8
50.2
65.4
DSLDA
Hayes & Kanan 2020
x
60.5
52.6
63.6
CI-CBM
touns)
V
55.9
44.8
60.8
Full rehearsal
62.0
50.1
69.3
Table A9: Experiment XV Comparison of the average incremental accuracy of CI-CBM and FeTrIT.
Petit et al. 2023) and DSLDA (Hayes & Kanan 2020) in a setting where each incremental phase introduces one new class. This sctting represents a special case of Table
A9 Unique Concept Expansion
Our approach also ensures that only unique concepts are added during each new phase of learning. When a new phase arrives, concepts for the newly introduced classes are generated using GPT-3. However, due possible similaritics between some new concepts and cxisting classes, naively adding all generated concepts to the concept set can lead to multiple versions of the same concept in the set. Unlike IN2 (Yang et al., 2024), which incorporates duplicate concepts, we ensure that only truly new concepts are added to prevent this redundancy. Figure A4 (Experiment XVI) illustrates the difference in the number of concepts per seen class when duplication is avoided (Unique Concept Set Expansion) versus when all generated concepts are added (Cumulative Concept Count). As shown, avoiding duplication results nearly half the number of concepts by the final phasc. This Icads much lighter concept bottleneck layer and prodiction layer, en- abling more efficient optinization. Importantly, removing duplicates improves interpretability by preventing attribution fragmentation: if semantically identical (or near- (ceniidett concepts appear multiple times, their contributions can be split across duplicate dimensions, making explanations longer and less concise. By keeping a single instance of each concept, we preserve the same semantic signal while concentrating weight and attribution on one concept. dimension, yielding cleaner and more stable explanations.
A10 One-Clast Increments in EFCIL
Table A9 (Experiment XV) presents results for one-class increments, task that many EFCIL methods struggle with, as they typically require at least two classes per increment to effectively update the model. The table reports results for CIFAR-100 and ImageNet-Subsect with an initial phase of 40 classes and 60 incremental phases, and for ImageNt with an initial phase of 100 classes and 100 incremental phases.
A11 Concept Generation Pipeline
For each new class, we generate candidate concepts using a fixed of language prompts to query GPT-3. Following the design of LF-CBM (Oikarinen al. 2023). we apply the following three prompts:

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CIFAR-100
CUB
Number of Concepts
Number of Concepts
1400
Curulative Concept Count
Concept Expansion
1000
Expansiio Cumulative Concept Count
1200
1000
600
600
400
200
200
20
100
175 Number Seen Classes
50
100 125
150
200
Number of Seen Classes
Places365
ImageNet
Number of Concepts
Number Concepts
Unique Concept Expansion
10000
Unlque Concept Expansiio
4000
Cumulative Concept Count
Cumulative Concept Count
8000
3000
6000
2000
1000
2000
50 100 150 200 250 300 350 Number of Seen Classes
200
400
600
800
1000
Number of Seen Classes
Figure A4: Experiment XVI (Ablation Study) Comparison of the number of concepts used per number of seen classes across different datasets for 20 phases.
"List the most important features for recognizing something as a {class)."
"List the things most commonly seen around a fclass)."
"Give superclasses for the word {class]."
Each prompt is issued twice to increase diversity, and responses are combined to form initial concept pool. To improve consistency, use few-shot prompting with two fixed example classes and their expected outputs. These examples are shared across all datasets and phases.
The raw concept set is then filtered in three stages:
Length filter: Remove concepts longer than 30 characters.
Class similarity filter: Remove concepts with cosine similarity 0.85 to any class name, using Sentence-Transfore Transformer and CLIP text embeddings.
Redundancy filter: Remove near-duplicate concepts with cosine similarity to any earlier concept. the set.
This filtered set is then used to update the concept set. All steps are automated and applied incrementally for each new phase. The full pipeline is implemented in the released codebase.
A12 Impact of Distillation Regularizer Weight on Accuracy.
To quantify the effect the distillation regularizer, 3, Eq. on class-incremental performance, we sweep I (0, 0.25, 0.5, 1, 5) and report the resulting average incremental accuracy. For CIFAR-100 and TinyIma- geNet, we follow the bareannnd--bbbboeeeeeee setting of Experiment I (Table [ for ImageNet-Subsect we follow the non-pretrained setting of Experiment IT (Table 2 Table A10 shows that introducing the distillation

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term (B 0) consistently improves accuracy over the no-distillation baseline (3 0), indicating that dis- tillation effectively mitigates concept drift across phases. Performance typically peaks at moderate value, with B = achieving the best overall accuracy across datasets. We therefore set 3 = in all experiments.
CIFAR-100
TinylmageNe
ImageNet Subset
Concept reg
7-
T=10
7-20
7-4
T=10
7-20
5=
1=10
7=20 20
68.4
68.2
67.6
48.2
48.3
48.2
66.5
64.9
66.1
0.25
68.5
68.6
67.5
48.2
48.7
48.4
67.3
65.5
66.8
3 0.5
68.6
68.7
67.7
48.6
48.8
48.6
67.4
65.8
66.7
3
68.8
68.8
67.8
48.6
48.7
48.5
67.8
66.2
66.9
8 = 2
68.7
68.6
67.8
48.5
48.7
48.7
67.3
66.2
66.4
3
67.8
67.8
67.2
48.4
48.7
48.5
67.2
66.2
66.4
Table A10: Experiment XVII (Ablation) - Effect of distillation weight 8. Average incremental
accuracy (%) when varying the distillation regularizer weight. 3 Eq. CTFAR-100 and Tiny InylmgeeNet use the protrained-backbonn protocol of Experiment I, while ImageNet-Subset uses the non-pretrained protocol of Experiment II. Results are reported for different numbers of incremental phases T.
A13 Impact of the Distillation Regularizer on Concept Fidelity.
To assess the effect of the distillation regularizer in Eq. 3 on interpretability and concept fidelity of the concept bottleneck, analyze the learned concept representations the test set be denoted by Drest [II,...,,NT] and the final concept vocabulary by CT (f1....,tM We first compute and store a CLIP-based concept-activation matrix P E N where each entry measures the alignment. between the i-th test image and the j-th concept text via CLIP embeddings:
the test split of each benchmark. Let
P. Er(x;) ET((G).
(A5)
with Eg and Er denoting the CLIP image and text encoders, respectively. Next, we record the activations of the concept-bottleneck (target) neurons the same test set: for each bottleneck unit is and each image 2i Dreat, compute the scalar activation (z(z)). This yields activation vector for neuron k,
qh [Ax(11) .............. ( ERN.
(A6)
Given neuron k we assign it a concept label by comparing d against the concept-specific response profiles induced by P, selecting the most similar concept im under cosine similarity. Concretely, letting Pm P.m. e RN denote the m-th column of P (the activation profile of concept tm over Dust), we define
m(() = arg max Com( ()(......M))
(A7)
and associate unit k with concept back), indicating which semantic concept the unit responds to most strongly. We follow the same protocol as Experiment XVII: CIFAR-100 and TinylmageNet use a pretrained backbone (Experiment I), while ImageNet-Subset uses the non-pretrained setting (Experiment IT). Table A11 reports two complementary concept-fidelity metrics. First, CLIP cosine similarity measures the cosine similarity between the predicted concept and the ground-truth concept in the CLIP text-embedding space. Second, Top-5 concept accuracy measures whether the ground-truth concept appears among the top-5 most simi- lar concepts ranked by cosine similarity. For reference, the number of candidate concepts is M = 872 for CIFAR100, M = 1700 for TinyImageNer and M = 979 for ImageNet. Subset. As shown, enabling the dis- tillation regularizer consistently improves concept-fidelity measures across datasets, indicating that better preserves semantic alignment of concept units while learning incrementally. This supports our hypothesis that regularizing against drift in previously learned concepts essential for maintaining interpretable and stable concept representations under continual adaptation.
8

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Published in Transactions on Machine Learning Research (04/2026)
CIFAR100
TinylmageNel
ImageNet Subset
Metric
Concept reg
7=5
T=10
T=20
7=5
T=10
T=20
T=5
T=10
T=20
0.916
0.891
0.874
0.876
0.864
0.854
0.840
0.822
0.786
CLIP cosine similarity
0.927
0.929
0.890
0.883
0.886
0.869
0.914
0.887
0.850
84.7
76.5
68.8
70.8
65.0
61.4
54.3
41.6
23.6
Top-5 accuracy
87.7
87.0
71.8
74.7
74.0
66.5
80.6
74.9
57.7
Table All: Experiment XVIII (Ablation Study) Impact of the distillation-based concept regularizer on concept fidelity bottleneck units across continual-learminn phase gramularities T {5, 10, 20). We report CLIP cosine similarity between the predicted and ground-truth concepts in the CLIP text-embedding space, and Top-5 concept accuracy (whether the ground-truth concept appears among the top-5 most similar concepts under cosine similarity). Results are shown for CIFAR100, IinylmageNel, and ImageNet Subset. Enabling concept regularization (V) consistently improves semantic aligmment compared to no regularization (x), indicating reduced drift of learned concept reprosentations during incremental adaptation.
A14 Impact of Vision-Language Model (SigLIP vs. CLIP).
We compute the concept-activation matrix P using vision-language model (VLM) to align concept- bottleneck units with their corresponding concepts. In this ablation, we keep the full training pipeline identical to Experiment (Table D and only swap the VLM used to compute P (CLIP vs. SigL.P). Ta- ble A12 shows that replacing CLIP with SigLIP consistently improves class-incrrmmental accuracy across datasets and phase configurations, suggesting stronger concept alignment in P and, consequently, better downstream performance. Beyond accuracy, also evaluate concept fidelity using the same metrics and
CIFAR-100
CUB
Tiny ImyylmageNet
Method
T=5
T=10
T=20
T=4
T=10
T=20
T=5
T=10
T=20
CI-CBM (CLIP)
68.6
68.7
67.2
60.5
62.4
63.6
47.0
47.2
47.3
CI-CBM (SigLIP)
68.8
68.8
67.8
62.2
65.3
66.1
48.6
48.7
48.5
Table A12:
Experiment XIX (Ablation Study) Incremental accuracy (%) when computing the concept activation matrix P with different VLMs (SigLIP vs. CLIP). This experiment follows the same sctup as Experiment I (Table T and only swaps the VLM used to compute P.
evaluation protocol introduced in Section A13 Table shows that SigLIP improves concept-fidelity mea- sures as well, indicating that the learned concept units are more semantically aligned and interpretable when P is computed with SigLIP.
CIFAR100
CUB
TinyImageNet
Metric
VLM
T=5
T=10
T=20
T=4
T==00
T==20
T=5
T=10
T-=20
CLIP
0.890
0.888
0.890
0.949
0.854
0.830
0.866
0.866
0.845
CLIP cosine similarity
SigLIP
0.927
0.929
0.837
0.961
0.876
0.837
0.883
0.886
0.869
CLIP
73.6
74.9
49.4
72.9
58.5
53.4
66.6
66.5
57.0
Top-5 accuracy
SigLIP
87.7
87.0
71.8
78.9
68.8
49.4
74.7
74.0
66.5
Table A13: Experiment XX (Ablation Study) Concept-fidelity metrics when computing the concept- activation matrix P with different VLMs (CLIP vs. SigLIP), while keeping the training protocol identical Experiment 1 (Table D. We report CLIP cosine similarity and Top-5 concept accuracy using the same evaluation procedure Section A13 SigLIP yields higher concept-fidelity scores in most settings, indicating improved semantic aligument of the learned concept unils.

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Published in Transactions on Machine Learning Research (04/2026)
A15 Pseudo-Features Track Real Feature Geometry Under a Prototype Classifier
The pseudo-feature construction is designed to approximate the feature distribution of previously seen classes using only summary statistics and the current feature space. To assess whether pseudo-features behave similarly to real samples in a realistic, multi-class setting, we perform a controlled analysis using a simple cosine-prototype classifier.
We consider class-incremental protocol with T 10 phases CIFAR100. Given frozen feature extractor, compute centroid (prototype) for each class using its training samples, and classify by assigning each feature to the class with the maximum cosine similarity to its centroid. We report results for two backbone settings: (t) an Imageeet-pretrainee ResNet-18 (corresponding to Experiment I in Table [], and (fi) the same architecture trained on the first-phase data only and then frozen (corresponding to Experiment II in
Table 2p.
Fig. A5 visualizes four phaso-by-phase matrices. For each entry (i,j), we evaluate performance on classes introduced at phase after learning up phase i:
Training (cosine-prototype): accuracy on training samples using the phase-i centroids.
Pseudo-feature (cosine-prololype): for each class introduced at phase j < i, we generate pseudo- features at phase and report the fraction whose nearest centroid (among all phase- centroids) is their own class centroid.
Test (cosine-prototype):: accuracy on held-out real samples using the phase-i cent.
Ours (test): test accuracy of the proposed method (not the cosine-prototype classifier).
Across phases, the pseudo-feature matrix closely matches the corresponding training and test matrices under the cosine-prototype classifier. This indicates that, when evaluated by the same nearest-centroid decision rule, pseudo-features induce similar confusion patterns and decision boundaries to those produced by real data.
We further analyze second setting which the backbone is not ImageNet-pretrainnd but instead trained only on the first-phase data and then kept fixed. In this scenario, we observe a qualitatively similar aligument: pseudo-feature accuracy remains close to the accuracy measured on real training and test samples under the same
classifier. At the same time, the accuracy is noticeably higher for classes introduced in the first phase, while it is consistently lower for classes introduced in later phases across all three matrices (training, pseudo-feature, and (est). A plausible explanation is that, the backbone is trained only using first-phase supervision, which shapes the backbone's feature space to separate the first-phase classes well. As a result, features from early classes tend to cluster more tightly around their class centroids. In contrast, for classes introduced in later phases (which did not participate in backbone training), their features may be less clustered and less centered around single centroid, making nearest-centroid classification less reliable for these classes.
Importantly, this trend should not be altributed to pseudo-features alone. Instead, it rellects a limitation of centroid-based modeling when the backbone feature space is not well clustered for newly introduced classes: in that case, nearest-centroid accuracy drops for both real features and psoudo-fcatures at the same time. This also highlights the role of representation quality: stronger pretrained backbones typically provide better class separation and therefore improve both prototype classification and pseudo- feature reliability. However, relying solely on strong pretraining does not address the core objective of dass-incremental learning, namely acquiring new knowledge beyond what is already encoded in the backbone.
Despite these representation constraints, our full method improves test accuracy in both the pretrained and tett--haseetaiie settings, with particularly pronounced gains in the latter. This suggests that the concept bottleneck layer provides an additional, structured space in which samples become more separable, even when the raw feature space is not well organized for newly introduced classes. In addition to improving incremental generalization, this mechanism also supports concept-based interpretability by grounding predictions in a small set of activated concepts.
A16 Additional Visualization for Model Reasoning
10

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Published in Transactions on Machine Learning Research (04/2026)
Figure A5: Experiment XXI We visualize phase-by-phas accuracy matrices with entry (i.j) evaluating classes introduced at phase j after learning up to phase i. Columns 1-3 use the same protoypp classifier (nearest class centroid in cosine similarity): (1) training accuracy on real training samples, (2) pseudo-feature accuracy (fraction of pseudo-features whose nearest centroid is their own class centroid), and (3) validation accuracy on real held-out samples. (4) reports test accuracy of our method (not the cosinc-prototype classificr). Top row: Imageeeetpretrrineed ResNet-18 backbone. Bottom row: ResNet-18 trained only on first-phase data. Pseudo-feature accuracy closely tracks real-data accuracy under the same cosine-prototype rule, while our method substantially improves incremental test performance in the weaker- backbone setting.
Concepts
Class
Concepts
Class
Concepts
Class
shepherd
mottled gray and white coat
motiled gray and white coat
small medium sized dog
a small to medium-sized dog
mottled gray and white coot
short, smooth cost
grayish color
leenne!
Norwegiau Elkhound
Norwegian Elkhound
a long, thick body
Norwegian Elkhound
grayish color
short, smooth
a thick cost fur
grayish color
a kennel
NOT chickens
small to sizzd dog
NOT cow
NOT long cars
NOT long cars
NOT coop!
meadow
large front teerh
NOT long cans
NOT a
NOT fishing
Phase
Phase
Phase 3
Figure A6: Visualization of the final layer weights with absolute values greater than 0.2 for the Norwegian Elkhound class in the ImageNet-Subset dataset under five-phase scenario. Concepts with negative weights are labeled "NOT" concepts. Positive and negative concepts in phase 1 are shown in blue and red, respectively, while concepts added in phases 2 and 3 are shown in orange and purple. The thickness of each edge corresponds to the absolute value of the weight. (Complementary to Figure T
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Published in Transactions on Machine Learning Research (04/2026)
Concepts
Class
Concepts
Class
Concepts
Class
Spotted far
Spotted fur
Africa
Jungle
Panthera Pardus
Affica
Pauthera Pardus
Spotted
Panthera
Pardus
A white chest
A white chest
Africa
Sharp claws
An oaks tree
A snare
Jungle
NOT a faghom
A large, spotted body- NOT African wild dogs NOT a vacuum cleaner
An cak
A Cage
NOT feghorn
NOT used for hygiene
NOT vibrant blue color
NOT crest on the bead
Phase
Phase
2
Phase
3
Figure A7: Visualization of the final layer weights with absolute values greater than 0.2 for the Panthera Pardus class in the ImageNet-Subset dataset under a five-phase scenario. Concepts with negative weights are labeled as "NOT" concepts. Positive and negative concepts in phase 1 are shown in blue and red, respectively, while concepts added in phases 2 and 3 are shown in orange and purple. The thickness of cach edge corresponds to the absolute value of the weight. (Complementary to Figure T
Concepts
Class
Concepts
Concepts
Class
Markings for lanes
Markings for lanes
Markings for lunes
Way
Street
Way
Pithole
Made of aspholt concrete
Way
Road
A long, straight puth
Road
Pithole
Road
Made of asphalt
Pithole
NOT plug
long, straight path
long, straight path
NOT
NOT hutch
Smooth, straight lines
NOT heavy, metal body
stop sign
NOT a pedal
NOT a bottlc openet
NOT plug-
NOT watering
NOT male
NOT butch
NOT load of hay
NOT long hood
NOT switch
Phase
Phase 2
Phase
Figure A8: Visualization of the final layer weights with absolute values greater than 0.2 for the Road class in the CIFAR- 100 dataset under five- scenario. Concepts with negative weights are labeled as "NOT" concepts. Positive and negative concepts in phase 1 are shown in blue and red, respectively, while concepts added in phases 2 and 3 are shown in orange and purple. The thickness of each edge corresponds to the absolute value of the weight. (Complementary to Figure] I
Concepts
Class
Concepts
Class
Concepts
Class
A seat
A bicycle scat
A handlebar
A handlebar
A hundlebur
bicycle seat
Tires
Podals
Bleycle
Pedals
Blcycle
Podals
Bleycle
Wheels
Large wheels
Large Wheels
NOT sharp claws
NOT lots of smoke
NOT bus driver
NOT smoke
NOT a smoker
NOT socket
NOT sharp claws
NOT napkin
NOT flowers
NOT a bucket
NOT gray or brown fur
Phase
Phase 2
Phase 3
Figure A9: Visualization of the final layer weights with absolute values greater than 0.2 for the Bicycle class in the CIFAR-100 datasct under a fivo-phase scenario. Concopts with nogative weights are laboled as "NOT" concepts. Positive and negative concepts phase 1 are shown blue and red, respectively, while concepts added in phasos and are shown in orange and purple. The thickness of each edge corresponds to the absolute value of the weight. (Complementary to Figure I
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Published in Transactions on Machine Learning Research (04/2026)
Concepts
Class
Concepts
Class
Concepts
Class
Instrumenis
Acoustics
Acoustics
Instruments
Music
Instruments
mixing board
Acoustcs
Music
Music
Music Studio
sound booth
Music
A player
Studio
A sound booth
An instrument
keybourd
Studio
Instrument amplifiers
Instrument Amplifiers
A player
A soundboard
piano
A mixing console
A sound booth
keybourd
piano
NOT pin cushioo
curved shape
NOT a polar bear
NOT life jacket
NOT gauget
NOT a pin cushion
NOT bright, colerful sign
Phase 1
Phase 2
Phase
Figure A10: Visualization of the final layer weights with absolute values greater than 0.2 for the Music Studio class the Places365 dataset under a five-phase scenario. Concepts with negative weights are labeled as 'NOT' concepts. Positive and negative concepts phase are shown in blue and red, respectively, while concepts added in phases and shown in orange and purple. The thickness of each edge corresponds to the absolute value of the weight. (Complementarry to Figure
Concepts
Class
Concepts
Class
Concepts
Class
A sand dune
A sand dune
sand dunc
Sandy dusty lerrain
mimge
Desert Sand
camel
Desert Sand
A cameel
Desert Sand
camel
Sandy dusty terrain
Sandy dusty terrain
Arid climate
A minge
A mimge
Africa
A NOT blue-grecn color
NOT
dry, sandy surfice
NOT
A campfire
large the
NOT
NOT a porcculiis
NOT colorful flowers
NOT rabbit
NOT
Phase 3
Phase
Phase 5
Figure A11: Visualization of the final layer weights with absolute values greater than 0.2 for the Desert (Sand) class in the Places365 dataset under a five-phase scenario. Concepts with negative weights are labeled as 'NOT' concepts. Positive and negative concepts in phase are shown in blue and red, respectively, while concepts added in phases 4 and shown in orange and purple. The thickness of each edge corresponds to the absolute value of the weight. (Complementary to Figure
Phase Pred: Cardinal
Pred: Cardinal
Pred: Cardinal
GT: Cardinal
Scarlet-red body feathers
Scarlet-red body
feathers
red feathers
Scarlet-red body
around
red around
around
red shoulders
on head
red crest head
red eyes
red shoulders
red eyes
red crest the head
red eyes
red shoulders
Sum of 160 other features
Sum 258 other features
Sum of 3f2 other features
Contributon
Contribution Value
Contribution Value
Phase 1
Phase 2
Phase 3
jay
jay
jay
blue eyes
blue eyes
blue eyes
GT: Blue jay
small, blue body
small, blue body
small, blue bedy
and secretive behavior
and secretive behavior
long tail with white bars
long tall with white bars
long tail with white bars
and secretive behavior large size
large size
large size
NOT a red throat pouch
NOT a red throat pouch
a large blue-grey bird
long, thin body
iridescent feathers
NOT rufous (red brown] color Sum of 312 other features
Sum of 160 other features
Sum of 258 other features
5.D Contribution Value
2.5
6.0 Contribution Value
2.5 S.D
6.0
5.0
Contribution Value
Figure A12: Visualization of model reasoning and concept contributions for images of the Cardinal and Blue Jay classes, introduced in the first phase of the CUB dataset. (Complementary to Figure G
13

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Published in Transactions on Machine Learning Research (04/2026)
Phase Pred: Waterfall
Phase Waterfall
Phase Pred: Waterfall
Waterfall
spray of water
spray water
spray of water
large, sheer rockface
gorge
gorge
NOT cell
NOT cell
water flowing from the top
NOT gerbil
crypt
NOT rat
water
NOT spoon
large, sheer rockface
NOT spoon
water
NOT a spoon
à rushing sound
NOT a gerbil
Understary
Sum of 718 other features
Sum 1261 other features
Sum of 1670 other features
Contribution Value
Contribution Value
Contribution Value
Phase
Phase
Phase Pred: Drugstore
Pred: Drugstore
Pred: Drugstore
GT: Drugstore
drugs
drugs
a pharmacy counter
drugs
register
shop
heat
prescription food toiletries
NOT heat
liquor
food
toiletries
sign with the store's name
shop
Sum of 718 other features
Sum of 1261 other fealures
Sum of 1670 other features
Contribution Value
Contribution Value
Contribution Value
Visualization of model reasoning and concept contributions for images of the Waterfall and Drugstore classes, introduced in the first phase the Places365 datasct. (Complementary to Figure
Figure A13:
Phase
Phase Leopard
Phase Leopard
Leopard
GT: Leopard
spotted
spotted
jungle
spotted
Africa
white chest
hollow Interlor
carnivore
an oak tree
magazine
a cow
hollow interior
NOT plate
snare
sharp claws
NOT loud crow
NOT a vacuum cleaner Sum of 552 other features
jungle
white chest
Sum of 652 other features
Sum of 748 other features
Contribution Value
Contribution Value
Contribution Value
Phase
Phase
Phase Pred: Carton
Pred: Carton
Pred: Carton
GT: Carton
packing material
pa packing material
box
package
package
packing material
made of cardboard
box
a package
box
a white chest
rectangular box at the top
a toy box
coarse texture
NOT shiny, brown exterier
thick, insulating material
balt box thick, insulating material Sum 652 other features
location
wires
dustpan
Sum 552 other features
Sum 748 other features
0.0
2.5 5.0 Contribution Value
Contribution Value
Contribution Value
Figure A14: Visualization model reasoning and concept contributions for images of the Leopard and Carton classes, introduced the first phase of the ImageNet-Subsee (Complementary Figure
14


Reviews:
[{"review_id": "BqKC9Fmd0f", "reviewer": "Reviewer_urji", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "CI-CBM is an extension of Concept Bottleneck Models in the exemplar-free class incremental learning setting. The goal is to maintain interpretability but also mitigate catastrophic forgetting. The proposed method incrementally expands a set of human-interpretable concepts generated by LLMs and aligned to visual features via CLIP/SigLIP. CI-CBM incorporates a distillation-based regularization term on the concept bottleneck layer to preserve old concepts as we learn new concepts. Since data from earlier classes is unavailable, the method adopts a pseudo-feature generation strategy (based on feature-space translation from newly observed classes) to construct pseudo-concepts for past classes. Those pseudo concepts are then used together with current data to train a sparse, unified classifier across all phases. The paper provides a geometric intuition for the pseudo feature mechanism and evaluates CI-CBM on several standard class incremental benchmarks under both pre-trained and non-pretrained backbones. The experiments show improvements over prior interpretable CIL methods and similar performance relative to non-interpretable approaches.", "claims_and_evidence_yn": "Yes", "claims_explanation": "I answered \"yes\" because  there is no \"partially\" option. The empirical results are clear and they support the claim that CI-CBM outperforms prior interpretable CIL methods on the given benchmarks and maintains a degree of concept-level interpretability across phases. The ablation studies also provide evidence that key components of the method (such as pseudo-concept generation and concept regularization) really contribute to performance.\n\nHowever several of the broader claims are only weakly supported. Some conclusions are drawn from a specific experimental regime with particular design choices (eg, frozen backbones, centroid-based pseudo-feature translation, CLIP-aligned concepts, sparse linear classifiers). It is unclear to me how robust these findings are beyond these conditions. In addition some claims about general applicability, stability of learned concepts and the ability to “maintain human-understandable concepts” throughout incremental learning rely primarily on visualizations and limited experiments. I would like to see more systematic or task-agnostic measures of interpretability and concept fidelity. In conclusion the paper is less convincing in supporting the stronger, more general claims made about interpretability and continual learning behavior in broader settings.", "audience_yn": "Yes", "audience_explanation": "I have no doubt about this. Researchers interested in interpretable machine learning, concept bottleneck models, and continual or class-incremental learning would find the paper of interest. I am sure that the communities that work on exemplar-free continual learning, interpretability by design, or the integration of language- and vision-based representations will appreciate the paper’s empirical investigation.", "requested_changes": "The following three papers are very relevant in my opinion and should be cited and contrasted with CI-CBM:\n\nFeTrIL++ https://arxiv.org/abs/2403.07406\nCI-CBM’s pseudo-concept generation mechanism is mathematically identical to FeTrIL-style pseudo-feature translation, right? It seems to me that the only difference is that pseudo-features are projected into a concept space. FeTrIL++ provides a much deeper analysis of when centroid-shift-based pseudo-features work or fail.\n\nCONCIL: https://arxiv.org/abs/2411.17471\nthis paper defines the concept and class incremental learning problem for CBMs as a first-class task and proposes a different solution based on analytic (non-gradient) updates with theoretical guarantees of no forgetting. CI-CBM tackles a similar problem but with heuristic, gradient-based mechanisms. The paper should clarify how its goals and scope differ from CONCIL. I suggest that the authors also temper their claims that CI-CBM represents a very principled solution to CBMs under continual learning\n\nLanguage-Guided Concept Bottleneck Models for Interpretable Continual Learning:\nhttps://openaccess.thecvf.com/content/CVPR2025/papers/Yu_Language_Guided_Concept_Bottleneck_Models_for_Interpretable_Continual_Learning_CVPR_2025_paper.pdf\nThis paper already combines LLM-generated concepts, CLIP alignment, semantic consistency losses, and prototype-based pseudo-replay for exemplar-free class-incremental learning. CI-CBM follows a very similar design pattern. The authors should explain more clearly what is genuinely new relative to this paper. I don't really see the major novelty that CI-CBM brings in this line of work.\n\nSome more specific comments:\n\n\nThe distillation-style loss on the concept bottleneck layer is central but its effect is not well isolated. can you show how concept-level accuracy or stability changes when this regularization is removed? (I mean beyond just showing downstream classification accuracy)\n\n\nThe pseudo-feature translation is taken from FeTrIL. Plz discuss: why translating features and then projecting to concepts is preferable to translating concept activations directly. Are the two equivalent under certain assumptions?\n\n\nThe Gaussian toy example assumes matched or near-matched variances to obtain linear decision boundaries. This assumption is strong and mirrors assumptions in FeTrIL++\n\n\nThe comparison between GPT-generated concepts and ConceptNet concepts is useful. However, the failure on CUB suggests that concept quality is a critical bottleneck. This deserves more emphasis in the main paper as it directly affects the robustness of the approach.\n\n\nThe paper shows that performance degrades gracefully when fewer concepts are available. It would be useful to connect this result to interpretability: does reduced concept availability also reduce explanation quality, or mainly accuracy?\n\n\nThe “unique concept expansion” mechanism is interesting but its impact is mostly discussed in terms of model size. A brief analysis of how duplicate concepts affect interpretability (not just efficiency) would strengthen this section.\n\nResults in the one-class-increment regime are much weaker than full rehearsal. This setting highlights limitations of pseudo-concept generation and deserves more discussion because it is a realistic EF-CIL scenario.", "broader_impact_concerns": "the work does not raise any ethical concerns that would require an extensive Broader Impact discussion.", "additional_comments": "see above", "extra_scores": {}, "extra_text": {}}, {"review_id": "zRhcKbVFTZ", "reviewer": "Reviewer_jiSK", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors proposed CI-CBM, the extended version of Concept Bottleneck Models to exemplar-free class-incremental learning by incrementally expanding a global concept vocabulary while avoiding storage of past data.\nFor each phase, new concepts are generated using an LLM and aligned with images via a frozen vision–language model, and a concept bottleneck layer is trained to map visual features to concept activations.\nTo prevent previously learned concepts from drifting, a concept-level distillation loss enforces consistency of old concept activations across phases using only current data.\nTo mitigate classifier forgetting without access to old samples, the method synthesizes pseudo-features for old classes by shifting new-class features using stored class means and projects them into concept space as pseudo-concepts.\nA sparse linear classifier is then trained jointly on real concepts for new classes and pseudo-concepts for old classes, enabling unified prediction across all seen classes.\nAt inference time, predictions rely on real concept activations, and class–concept weights provide interpretable global and local explanations.\n\n**S1. Exemplar-Free Knowledge Retention through Pseudo-Features and Pseudo-Concepts.**\nThe proposed method constructively addresses the challenge of exemplar-free class-incremental learning by avoiding the need to store raw data from previous tasks. \nBy retaining only lightweight class-level statistics and synthesizing pseudo-features from newly observed data, the model approximates past class representations without violating memory or privacy constraints. \nProjecting these pseudo-features into the concept space further enables the use of pseudo-concepts to retrain a unified classifier across old and new classes. \nThis strategy offers a practical and scalable alternative to exemplar replay, allowing continual adaptation while maintaining a compact memory footprint and supporting concept-based reasoning throughout training.\n\n**S2. Comprehensive and Rigorous Experimental Evaluation.**\nAnother strength of the proposed method lies in its extensive and well-designed experimental evaluation. \nThe authors validate their approach across multiple benchmark datasets and incremental learning settings, comparing against both interpretable and non-interpretable continual learning baselines. \nIn addition to reporting overall accuracy and forgetting metrics, the experiments include ablation studies that isolate the contributions of key components, such as concept distillation and pseudo-feature generation. \nQualitative visualizations further illustrate how concept-based reasoning evolves across incremental phases, providing complementary insights beyond quantitative performance. \nTogether, these results offer a thorough assessment of both the effectiveness and behavior of the method in class-incremental scenarios.\n\n**W1: Strong Assumptions and Backbone Dependence of Pseudo-Features.**\nThe pseudo-feature mechanism relies on several strong implicit assumptions, including that class-conditional feature distributions can be well approximated by their means, that nearby classes share similar covariance structures, and that feature-space proximity reflects semantic compatibility. \nWhile these assumptions are illustrated through a toy example, they are not guaranteed to hold in complex, multimodal, or fine-grained datasets. \nAs a result, the separability of pseudo-features--and consequently the effectiveness of pseudo-concepts--may depend heavily on the representational quality and inductive biases of the underlying backbone. \nIn settings where the backbone does not produce well-structured or linearly separable feature spaces, pseudo-features may overlap or distort class boundaries, potentially limiting robustness in class-incremental learning.\n\n**W2: Insufficient Clarity and Justification of Design Choices.**\nWhile the overall framework is well structured, several key design choices lack sufficient clarification or justification. \nIn particular, the use of SigLIP for image–concept alignment is not clearly motivated, nor is its impact isolated through ablation against more standard alternatives such as CLIP. \nAdditionally, details of the class-incremental continual learning setup--such as phase construction, class ordering, and their interaction with concept expansion--are not always described with enough precision to fully understand or reproduce the experimental setting. \nThese ambiguities do not invalidate the method, but they make it harder to attribute performance gains to specific components and may limit accessibility for readers seeking to adapt or extend the approach.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Overall, the claims made in the submission are supported by convincing, and clear empirical evidence. \nThe authors present thorough experimental results across multiple datasets and class-incremental settings, accompanied by ablation studies and qualitative analyses that help substantiate the effectiveness of the proposed approach. \nThe reported improvements over prior interpretable and exemplar-free continual learning methods are consistent and well documented, lending credibility to the main performance-related claims.\n\nAt the same time, some aspects of the evidence would benefit from additional clarification or validation. \nIn particular, certain design choices--such as the use of SigLIP for concept alignment and the assumptions underlying pseudo-feature generation--are not fully justified or isolated through targeted ablations. \nMoreover, while the qualitative concept visualizations are informative, further analysis of the faithfulness and robustness of pseudo-concept–based reasoning would strengthen the interpretability claims. \nAddressing these points would improve the clarity and completeness of the evidence, but they do not fundamentally undermine the validity of the submission’s core claims.", "audience_yn": "Yes", "audience_explanation": "At least a portion of TMLR’s audience would be interested in the findings of this paper, as interpretable continual learning is an active and growing area of research at the intersection of representation learning, explainable AI, and lifelong learning. \nThe work addresses a timely problem--how to retain interpretability while performing exemplar-free class-incremental learning--which is relevant to researchers concerned with transparency, robustness, and deployment constraints such as memory and privacy. \nBy combining concept bottleneck models with continual learning mechanisms, the paper speaks to audiences working on interpretability, concept-based models, and practical continual learning systems. \nAs such, its methodological contributions and empirical insights are likely to be of interest to readers seeking interpretable alternatives to black-box continual learning approaches.", "requested_changes": "**Related to W1.**\nTo strengthen the robustness and interpretability claims of the proposed method, the authors are encouraged to more explicitly analyze the limitations of the pseudo-feature and pseudo-concept mechanism.\n\nFirst, introducing failure cases would substantially improve the empirical analysis. \nWhile Fig. 3 provides an intuitive toy example where pseudo-features remain well separated, it is unclear how often this assumption holds in more complex or fine-grained settings. \nVisualizing or quantifying cases where pseudo-features overlap with other classes, or where pseudo-concepts poorly approximate real concept distributions, would help delineate the practical boundaries of the method.\n\nSecond, the qualitative example in Fig. 6 could be strengthened. \nIn its current form, many of the highlighted concepts in later phases do not appear to correspond intuitively to the class \"Sturgeon\", making it difficult to interpret the figure as evidence of meaningful concept-based reasoning. \nProviding additional examples--ideally where the majority of contributing concepts are semantically aligned with the target class--or explicitly contrasting successful and failure cases would improve the clarity and credibility of the interpretability demonstration.\n\n**Related to W2.**\nFirst, the motivation for using SigLIP in the concept alignment module should be made more explicit. \nClarifying why SigLIP was preferred over more commonly used alternatives such as CLIP--particularly in the context of class-incremental learning and concept bottleneck models--would help readers better understand this design decision. \nIncluding a simple ablation or comparison (e.g., SigLIP vs. CLIP under the same pipeline) would further strengthen attribution of performance gains and improve methodological transparency.\n\nSecond, the description of the class-incremental continual learning setup would benefit from greater precision. \nDetails such as how classes are partitioned into phases, how class ordering is determined, and how concept expansion interacts with phase boundaries are sometimes implicit rather than explicit. \nProviding a clearer, step-by-step description of the incremental protocol--possibly with a concise table or schematic--would make the experimental setup easier to follow and reproduce.", "broader_impact_concerns": "I do not identify significant broader impact concerns associated with this work. \nThe proposed method focuses on improving exemplar-free class-incremental learning with an emphasis on interpretability and memory efficiency, which are generally aligned with responsible and trustworthy AI development. \nBy avoiding storage of past data and providing concept-based explanations, the approach may even help mitigate privacy risks and improve transparency in deployed systems. \nOverall, the work is methodological in nature and does not appear to introduce ethical, societal, or safety concerns beyond those commonly encountered in machine learning research.", "additional_comments": "NA", "extra_scores": {}, "extra_text": {}}, {"review_id": "L4A4GAffDd", "reviewer": "Reviewer_oTPr", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this paper, the authors study the problem of interpretable class-incremental learning (CIL). To be specific, they are interested in designing a new concept-bottleneck-layer which can incrementally acquire new concepts to guide CIL. The authors introduce three modules: Concept set expansion, Concept bottleneck layer distillation, Dynamic adaptation of the prediction layer. The proposed method is compared against interpretable CIL methods as well as non-interpretable CIL methods. Significant improvements over interpretable CIL methods are reported.\n\nStrengths:\n\n+ Designing interpretable CIL approaches is an important problem in ML.\n+ Novel approach, bringing together existing ideas and tricks from the literature.\n+ Significant gains are reported.\n+ Overall, well-written and easy-to-follow text.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The paper includes comparisons with the alternative approaches and reports significant improvements.", "audience_yn": "Yes", "audience_explanation": "Interpretable class-incremental learning is of interest to the machine learning community.", "requested_changes": "Weaknesses:\n\n1. Some design choices or steps have not been justified:\n\n1.1. Module 1: \n\n1.1.1. \"If concepts related to the new classes already exist due to their similarity to previous classes, they are not added again.\" => Please describe how you calculate similarity between concepts.\n\n1.1.2. \"In our experiments, we used SigLIP (Zhai et al., 2023) instead of CLIP (Radford et al., 2021), which is used in LF-CBM (Oikarinen et al., 2023), as the multimodal model for computing Pt. SigLIP is a recent model that focuses on image-text pairs and employs a sigmoid loss function, in contrast to the softmax-based contrastive learning approach used in CLIP.\" => Please provide justification for why you used SigLIP instead of CLIP.\n\n1.1.3. Please add here a short explanation for why P_{t-1} is not used while calculating P_t.\n\n1.2. Module 2:\n\n1.2.1. Please include an ablation on the contribution of distillation loss, by introducing a weight.\n\n1.3. Theoretical Perspective => This is a toy-example / controlled-analysis rather than a theoretical analysis.\n\n1.4. It would be helpful to add an algorithm to describe all steps of the algorithm.\n\n2. Experiments:\n\n2.1. Table 1: The proposed method's performance on the CUB dataset increases significantly with the increasing number of tasks. It would be helpful to explain this counter-intuitive result.\n\n2.2. Figure 6: Such visualizations are very helpful. However, the plot clearly shows that some positive concepts (e.g., a large tail fin) disappear and some positive concepts (e.g., \"a fish\") diminish in the new phases. The remaining concepts turned out to be sufficient in such a case but this example shows that the proposed method is not able to preserve important concepts through phases.\n\n2.3. The proposed method is only compared to the other interpretable methods (ICICLE, IN2) in Table 1. Not sure why the remaining experiments (e.g., Experiment 3) do not include results by ICICLE and IN2.\n\n\nMinor comments:\n- \"Cos cubed\" => \"cosine-cubed\"?\n- The following guide can be helpful in writing equations:\n https://wp.optics.arizona.edu/kupinski/wp-content/uploads/sites/91/2023/05/MerminEquations.pdf\n- Eq 1: Please also explain what L and q denote.\n- \"the first to the last phase T,\" => \"the first to the last phase $T$,\"\n- \"prediction layer W_F^{t-1}\" => Either include b_F here as well or modify Eq 2 to absorb the bias in W_F.\n- \"Following (Petit et al., 2023),\" => \"Following Petit et al. (2023),\"\n- \"(Zhao et al.),\" => Year is missing.", "broader_impact_concerns": "N/A.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)