AnaCP: Toward Upper-Bound Continual Learning via Analytic Contrastive Projection
Authors: Saleh Momeni
Changnan Xiao
Bing Liu
Venue: NeurIPS 2025 spotlight ()
Keywords: Continual Learning
Class-Incremental Learning
Contrastive Learning
Extreme Learning Machines
Primary area: general_machine_learning

Abstract: This paper studies the problem of class-incremental learning (CIL), a core setting within continual learning where a model learns a sequence of tasks, each containing a distinct set of classes. Traditional CIL methods, which do not leverage pre-trained models (PTMs), suffer from catastrophic forgetting (CF) due to the need to incrementally learn both feature representations and the classifier. The integration of PTMs into CIL has recently led to efficient approaches that treat the PTM as a fixed feature extractor combined with analytic classifiers, achieving state-of-the-art performance. However, they still face a major limitation: the inability to continually adapt feature representations to best suit the CIL tasks, leading to suboptimal performance. To address this, we propose AnaCP (Analytic Contrastive Projection), a novel method that preserves the efficiency of analytic classifiers while enabling incremental feature adaptation without gradient-based training, thereby eliminating the CF caused by gradient updates. Our experiments show that AnaCP not only outperforms existing baselines but also achieves the accuracy level of joint training, which is regarded as the upper bound of CIL.

AnaCP: Toward Upper-Bound Continual Learning via Analytic Contrastive Projection
Saleh Momeni', Changnan Xiao², Bing Liu'
Department of Computer Science, University of Illinois Chicago
ChangnXX.gittubbl.. {smomen3, liub]&uic. edu changuanziaodgmail.
Abstract
This paper studies the problem of class-incremental learning (CIL), core setting within continual learning where a model learns a sequence of tasks, each containing a distinct set of classes. Traditional CIL methods, which do not leverage pre- trained models (PTMs), suffer from catastrophic forgetting (CF) due to the need to incrementally learn both feature representations and the classifier. The integration PTMs into CIL has recently led to efficient approaches that treat the PTM as fixed feature extractor combined with analytic classifiers, achieving state-of- the-art performance. However, they still face a major limitation: the inability to continually adapt feature representations to best suit the CIL tasks, leading suboptimal performance. To address this, we propose AnaCP (Analytic Contrastive Projection), novel method that preserves the efficiency of analytic classifiers while enabling incremental feature adaptation without gradient-bass training, thereby eliminating the CF caused by gradient updates. Our experiments show that AnaCP not only outperforms existing baselines but also achieves the accuracy level of joint training, which is regarded the upper bound of CIL.
Introduction
Continual learning (CL) learns sequence of tasks incrementally, where each task introduces set of new classes [1]. The key challenge in CL is catastrophic forgetting (CF) [2], a phenomenon previously learned ones. Among CL settings, class-incremental learning (CIL.) [3] is particularly challenging as it needs to build a unified classifier recognize all encountered classes, without task-id information test time. This paper focuses on the CIL setting. Early CIL approaches typically trained models from scratch using regularization, experience replay, or architectural modifications to mitigate CF [4, 5J. However, they fall significantly short of joint training accuracy, which trains model with the data from all tasks simultancously. representing the upper bound for CIL performance [6].
where learning new tasks degrades the performance
Recent CIL methods increasingly exploit are-trained models (PTMs) to improve accuracy by lever- aging their strong feature representations [7. 8. 9]. Existing PTM-based approaches for CIL can be broadly divided into three main categories: (i) fine-tuning the PTM, either fully or through lightweight adapter [10], (ii) optimizing learnable prompts while keeping the PTM parameters frozen [11], and (iii) using the PTM as a fixed feature extractor paired with an analytic classifier, such as the nearest class mean (NCM) method or more advanced variants [12, 13, 14]. We use the term analytic to describe methods with a closed-form solution that requires no gradient-bases training. The first two groups require task-specific training, which slow and prone CF. The third group is highly efficient and immune to CF because it avoids gradient-baad based updates.
Analytic approaches often achieve state-of-the-ee performance in CIL, outperforming methods that fine-tune the PTM or learn prompts [15, 14J. However, a major limitation of the analytic methods
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

is their inability to adapt the PTM features to suit the downstream tasks, leading to suboptimal performance. Prior works have proposed to fine-tune the PTM on the first task, called first session adaptation (FSA) [16, 13]. However, the PTM must remain frozen afterward to maintain the integrity of analytic learning; otherwise, their closed-fome formmmffommmooo solutions will not work.
This paper introduces AnaCP (Analytic Contrastive Projection), a novel method that enables analytic approaches to also perform feature adaptation. Our analytic method is related to extreme learning machines (ELMs) [17, 18). as outlined in Section 3. AnaCP adapts features using a contrastive projection layer, inspired by contrastive learning [19, 20], which draws samples from the same class closer while pushing different classes apart to enhance separation. However, unlike standard contrastive learning, which requires gradient- craseeettbbsed training for each task and suffers from CF, AnaCP achieves a similar effect analytically. With the adapted features, an NCM classifier can be easily constructed (see Section 4.3). However, we found that building another ELM classifier by sampling feature representations from distributions of previous tasks yields better performance, while remaining fully analytic. To summarize, this work makes the following contributions:
1. We propose novel analytic approach that enables continual adaptation of feature represen- tations across tasks, addressing the long-standing limitation of fixed representations in prior analytic methods.
2. Our method avoids CF entirely, as it requires gradient-based training and instead relies on closed-form updates.
3. This approach is highly efficient, requiring no trainable parameters and incurring negligible computational overhead.
4. Through extensive experiments, we show that when paired with a strong PTM, our method achieves accuracy comparable to the joint training upper bound. This is particularly notable, as the inability to match joint training remains a key barrier to the practical adoption of CL.
2 Related work
Many CIL approaches have been proposed deal with CF. These methods can be categorized into three main groups: (i) Regularization methods, which mitigate CF by penalizing updates to parameters that are important for old tasks [21, 22, 23, 24], or by aligning the current model with those of earlier ones using knowledge distillation [25, 26]. (ii) Experience replay methods, which retain a subset of past task samples in a buffer and use them in the new task training [27, 28, 29, 30, 31].A variation of this is pseudo-replay
where synthetic samples or feature representations are generated to simulate past data [32, 33, 34, 35J. Our method also replays feature representations in its final step, but they are sampled from each class's 'ss distribution represented by its mean and a shared covariance. (iii) vrchitecture-busee methods, which expand the network for each task [36, 37, 38), or isolate parameters through learning task-specific sub- networks via masking or orthogonal projections [39, 40, 41, 42, 43], and then use a task-id prediction method at test time [6, 44, 45, 46].
Early approaches to CIL learned both feature representations and classification parameters for each new task without using PTMs, suffering from serious CF. Recent methods address this limitation by leveraging PTMs, which substantially improve CIL performance [7, 12, 47, 13, 6, 14], primarily following three strategies: (i) fine-tuning the PTM, either by directly updating its parameters (e.g.. SLCA [10]) or by adding adapters [6, 48, 49]. (ii) learning prompts, where the PTM remains frozen and trainable prompts are introduced to condition its representations (e.g., L.2P [11], DualPrompt [47]. CODA-Promph [50], as well as other variants [51, 52, 53)). (iii) treating the PTM as frozen feature extractor with an analytic classifier [13, 54, 14].
Our method aligns with the third strategy, which relies on closed-form solutions. The simplest method is NCM [55, 56], which computes a mean vector for each class and assigns each test sample to the class with the nearest mean. Another method is SLDA [57]. which takes advantage of linear discriminant analysis (LDA) [58]. KLDA [14] applies an RBF kernel to expand the feature space before using LDA for classification. The regularized least squares used in ACIL [12] and GACL [54] also within this paradigm. Analytic CIL methods can be enhanced by adopting the FSA strategy, where the PTM is fine-tuned on the first task and then kept frozen for subsequent tasks. APER [56] adopts this strategy with an NCM classifier. RanPac [13] has a similar approach but applies random projection [18] to the feature space, improving class separation. LoRanPAC [59] enables RanPAC

---

to use a much higher dimensional random projection. FeCAM [15] uses a Mahalanobis distance classifier with normalized covariance matrices.
We follow the analytic CII. paradigm by using PTMs as frozen feature extractors. However, unlike previous methods, introduce contrastive projection layer adapt the features for each task, which enables AnaCP to improve the accuracy while preserving the computational efficiency.
Background
Incremmnreeettlll Learning: CIL seeks to sequentially learn a series of tasks, each introducing a new set of classes, while prohibiting access to data from previously encountered tasks. Specifically, each task defined by training dataset D. {(x)) (6) ( > where .1(") E X, represents M1
an input sample, and y/
(4) E V4+ is its class label. The class sets 3/ are mutually exclusive, and = - }i, defines the complete set of classes encountered far. The core objective of CIL is to
learn single classifier f X' + y capable of predicting the class label of any test instance without the knowledge of the task it belongs to.
Ridge regression a closed-form method for training a linear classifier on fixed features using one-hot encoded targets [60]. Given feature matrix X RNxd from the PTM and a one-hot label matrix Y E RNNC", the objective is to minimize the squared error with L regularization:
Ridge Regression:
min W
XW Y11 + W/I,
(1)
where Ả controls the strength of the regularization. This objective penalizes deviations from the target labels while encouraging smaller weights to prevent overfitting. The solution is obtained by setting the gradient for W to zero, yielding the closed-fon optimal weights:
W = X
x + X
(2)
often called a ridge classifier or regularized least squares. Here, X X called the Gram matrix (G) and X Y is the cross matrix (H). This closed-form solution is attractive because it forgoes iterative training and directly computes a global optimum.
When tasks arrive sequentially, we can compute the ridge regression solution without revisiting past data [17, 12]. Let (X,, Y.) denote the data from task Rather than storing all data, we can incrementally update the Gram and cross matrices as follows:
Analytic CIL:
G = G X, H. = H Y.,
where G, and H, are the gram and cross matrices after task respectively. Here, we slightly abuse the notation for H, by allowing the number of classes to increase over time. To maintain dimensional consistency, both H,-1 and the one-hot labels in Y, must be padd-padddd This allows us compute the updated solution:
W, (G, + -H,
Random Projection and Extreme Learning Machines: To improve the feature representations, the original d-dimensional features can be projected into higher-dimensional space of dimension D before learning the analytic classifier in the projected space. [18] proposes to project the features via a random nonlinear layer:
Z = (XR).
(5)
where R. RddxD is fixed matrix with random values and o(-) is nonlinear activation, for which we use a GELU function. The classifier is learned analytically via ridge regression:
W = (z _ AI) - ZT
(6)
This solution can be updated incrementally as before (Eqs. and 4). The random projection acts like a kernel function, expanding the feature space and introducing nonlinear interactions among input features, which enhances class separability.
3

---

Analylic
Contrastive Projection
PTM
Classifier
Random Featurest
Ernanced Fieaturcs
Input Layer
Contrastive
Projection
Random
Projection
Layer
The random projection layer uses fixed, randomly assigned weights, while the contrastive projection layer weights computed analytically. Compared to the ELM architecture, AnaCP introduces an additional contrastive projection layer that adapts the feature representations. (Right) I-SNE visualization of the input features (first five classes of ImageNet-R) and their enhancement after contrastive projection using DINO-v2 as the PTM. Random features are generally separable than input features due their higher dimensionality, even though this is not easily observable in the 2D I-SNE map.
Figure 1: (Left) Architecture of AnaCP:
Methodology
Existing analytic CIL methods operate fixed feature representations, allowing the classifier be updated analytically without revisiting prior data. Freezing the PTM is essential because modifying it during training would alter the feature representations, undermining previous analytic updates and leading to CF. However, this rigid strategy also limits the capability to adapt feature representations suit the downstream CIL tasks.
To overcome this limitation, we propose a novel analytic approach that also adapts feature represen- tations for the continual learning tasks. The pipeline of approach, illustrated in Figure (left), begins with the PTM generating feature representations, termed the input layer. These features are transformed via random projection (RP) layer into higher-dimensional space [18) and then passed through the contrastive projection (CP) layer, which enhances the class separability. The CP layer draws inspiration from contrastive learning, where the samples from the same class (positives) are drawn closer, while samples from different classes (negatives) are pushed apart, typically using contrastive loss. However, applying this directly CIL would lead CF due to iterative gradient updates. We achieve similar effects via an analytic CP layer that can be incrementally updated as new tasks arrive. The impact of this CP layer on feature distribution is depicted in Figure (right). Finally, classifier layer makes the final predictions based on these adapted features.
4.1 Positive Alignment via Prototype Regression
We begin with the ELM formulation, where ridge regression is employed to map the features from the RP layer the target vectors, previously defined:
W = (Z Z TT,
where Z E ND represents the random feature obtained from the RP layer, and T contains target vectors for inputs. When T is one-hot encoded for classification, the cross matrix T reduces to a matrix where each column is the sum of random features belonging to given class. This can be factorized as:
= ZT MN
Here, M E DxC contains the class prototypes m., defined as the means of the random features of class and N diag(ni,..... ric)) holds the number of samples per class. Both M and N can be computed incrementally as each task arrives.
This formulation can be extended to arbitrary targets. Instead of using one-hot vectors, we can assign each class target prototype, representing its ideal position in the projected space. These target prototypes can have any dimensionality: however, to preserve the geometric structure of the representations, we set their dimension to match that of the input layer, d. Let C'd denote the target prototype matrix, where each Pe specifies the desired projection for class c. For instance,

---

Pe can be set as the original class mean of the input layer, pulling the feature representations of class c toward their respective mean, In this case, the cross matrix becomes:
H = -= Σ
Σ
2 P = Σ m.n.P. = MNP iEc
(9)
This decomposition enables efficient incremental updates by maintaining class protolypes M com- puted based on the features from the random projection layer, sample counts N, and target prototypes P. The learned projection W maps samples toward their corresponding target prototypes, effectively pulling intra-class samples together and enhancing positive alignment.
4.2 Negative Repulsion via Target-Prototype Separation
Aligning input samples to their respective class means (using class means target prototypes) improves intra-class compactness but does not guarantee adequate inter-class separation. In particular, some class means may lie close each other in the feature space, making them hard to distinguish. To address this, we refine the target prototypes by shifting the class means to enhance the separation between classes.
Let C = (HI..... (C)) E R denote the matrix of class means at the input layer. We normalize these means by whitening them with respect to the feature covariance matrix E (shared by all classes). This adjustment is essential because a large variance in some dimensions can give a false impression of class separability. For example, in low-variance dimension even a small separation is meaningful, whereas in high-variance dimensions, a much larger separation is needed to achieve the same effect. Whitening corrects for this imbalance by accounting for the variance of each feature dimension. The covariance is computed incrementally as [15]:
Σ,
N₂-
E, E.-1 No
ΣΣ
EExx (x;
(x) Mc)
(10)
N
eEC, iEc
where N₂ is the total number samples seen up to task t and C, is the set of classes introduced at task t. We can then transform the class means as:
C= 1/2C
(11)
yielding whitened means with unit variance in all directions. We then perform singular value decomposition (SVD) on the whitened class means:
Č USV
(12)
where U E RdxC is an orthonormal basis of the imput space, V RCC defines the class means subspace, and S e CCCC is a diagonal matrix containing the singular values.
Our objective is to enhance the separation between class means, quantified by the sum of their pairwise cosine similarities. In principle, maximum separation would be achieved if the means arranged uniformly on the surface of hypersphere. However, this strict configuration would significantly alter the original data geometry, distorting the feature representations. To maintain the structure while increasing class separation, we introduce adjustment the singular values in S, which perturbs the class means in directions that reduce their pairwise cosine similarities:
$ S + oDiaggor..... oc).
(13)
where a is scaling factor, and 8, is defined in the following Lemma. Lemma 4.1. Denote Wi...., WC EC as arbitrary vectors, and ec RC as a set of
orthogonal bases of RC. Denote (x, = x y as the inner product and 0(z, v) = | lill as the cosine similarity. There exist and
r y
1
1, if
[22 1 (mm,)))20)) (ei, wyy || (ei, wi) (ww,, wyyl] < 0.
[wyl]
jti
8,
1
0, if
[22 1 (m)001120)) (ei, myy) || (ex, wz) 1w5,, wyYl] 0.
||w!||
1, else,
5

---

S.F.
ΣE 10(w; + adje, wj + ed, - j#
Σ
E J
(w,, myy]
(14)
See the proof in Appendix A. In Eq. 12, we denote SV (W1,... WC) and V = (ei,...,,cc)
Each w; in the subspace SV is perturbed by ad,e, effectively shifting it in an orthogonal direction with magnitude a, By Lemma 4.1, there exist coefficients .1..... &g and a scalar a > 0 such that Eq. 14 holds. The sign of each 5; determines whether the shift occurs in the direction of e or its opposite. This condition arises from the proof of Lemma 4. where we analyze the derivative the function fa()), defined as the sum of cosine similarities involving class i. By selecting 6; accordingly, we ensure that the slope of f.(a) at a 0 is negative, which guarantees that a small positive a decreases the cosine similarity. The choice of is also important: if a is too small, the shift becomes negligible, whereas if it is too large, the reduction in cosine similarity may no longer be valid. In practice, we set a 1 in experiments.
Defining Diag 61. ......... ..)............... the lemma guarantees that the average cosine similarity among the columns of (S + a is smaller than that of SVT Since the columns of U R form an orthogonal basis in Rd the transformations preserve inner products and norms:
(Uws; Uwy) (we,, wy), ||ura] orral || = ||w/l|, ||Uwy|| || = ||wey||
(15)
Thus, the cosine similarity between transformed vectors remains the same, i.c., (Uw, Uwy) = Ow;; wj). Therefore, the average cosine similarity among the columns of U(S + VA) is also reduced compared to the original matrix C = USVT.
Note that separability measured as the sum of cosine similarities, but the class means are whitened. This procedure is closely related to Mahalanobis distance, which has been shown to outperform cosine similarity related contexts [15]. By whitening, we effectively assess separation using Mahalanobis distance; after increasing the separation, we de-whiten the features to restore their original scale:
Č USV. Č=
(16)
The separated class means are then used as target prototypes for the CP layer by setting P in Eq. 9 to C, aligning samples with their respective classes while enhancing the separation between classes.
4.3 Classifier
The CP layer is an analytic module that adapts feature representations across tasks without modifying the underlying PTM. To increase its capacity, we extend it with multiple random projections. Since each RP is initialized independently, we learn a corresponding CP for each RP, all sharing the same set of target prototypes. Specifically, the random features to the same target prototype space. Given an input x, each head produces a projection and the output is obtained by averaging across heads:
define H such heads, where each CP head (h) maps
u (h) ((xR("))
(1) W(h,,
(h)
(17)
H
This aggregated representation u is then classified using NCM, which assigns it to the nearest target prototype in P. As shown Table (row 3), AnaCP with an NCM classifier already outperforms all baselines. However, NCM is often surpassed by more expressive classifiers. To further improve performance, we place an ELM classifier after the averaged CP representation.
Unlike PTM features and their random projections, which remain fixed, the CP outputs evolve as new tasks are introduced due to the incremental computation of the CP layer. Directly updating the ELM classifier incrementally (Eq. 3) may therefore lead to CF. To mitigate this, we employ pseudo- replay strategy. We model the PTM features (input layer) as a multivariate Gaussian distribution parameterized by the class means and a shared covariance matrix, from which we generate pseudo- replay samples for training. This approach resembles that of [10], which also trains the classifier on generated features. However, whereas [10] maintains separate covariance matrix per class (leading to memory cost that grows with the number of classes), we use a single shared covariance matrix across all classes. This design significantly reduces memory usage while yielding comparable

---

performance. Specifically, we reuse the class means and shared covariance matrix from Eq. 10 for feature generation. The generated samples are then processed by the RP and CP layers to form the classifier input, upon which the ELM is trained using Eq. 6.
5 Experiments
5.1 Experimental Setup
Datasets: We conduct experiments on five publicly available datasets: CIFAR100 (100 classes) [61], ImageNet-R (200 classes) [62], CUB (200 classes) [63], Tiny ImageNet (200 classes) [64], and Cars (196 classes) [65]. For all datasets, we use the official train and test splits. Each dataset is split into 10 disjoint tasks by shuffling classes, and experiments are repeated with three different random seeds to account for variability in class-task assignments.
We compare AnaCP with range of baselines, including prompt-learning methods (I.2P [11]. DualPrompt [47], and CODA- -roompt [50]). fine-tuning method (SLCA [10]), and analytic methods that treat the PTM as a frozen feature extractor. The analytic baselines include SimpleCIL [55], SLDA [57], KLDA [14], GACL [54], APER [56], FeCAM [15]. and RanPac [13], with some incorporating FSA. For complete performance perspective, we also include results from joint linear probe, where linear softmax classifier is trained on the PTM features using gradient descent with all tasks' data, and joint fine-tuning which directly fine-tunes the PTM on the entire dataset and serves as the upper bound for CIL performance.
Baselines:
Implementation Details:
For the PTMs, we use DINO-v2 [66] and MoCo-v3 [67], both of which are self-supervised PTMs. This choice helps prevent information leakage, as supervised PTMs are exposed to class labels during training, some of which may reappear in CIL, leading to unintended information leakage. MoCo-v3 is pre-trained on ImageNet- - a commonly used but relatively small dataset for pre-training in prior studies. However, because ImageNet- Ik (or even ImageNet-21k) is considered limited for real-world applications, we also utilize DINO-v2, a more powerful model pre-trained on the substantially larger LVD-142M dataset. For joint fine-tuning, we employ LoRA adapters [68] instead of full fine-tuning. as we found this approach to be more accurate.
The prompt learning baselines taken from the [50] repository, while SLCA, FeCAM, and RanPac are evaluated using their original implementations. All remaining analytic baselines are incorporated into unified experimental setup, following their official implementations ensure fair comparison. We also adopt FSA following [56] before applying AnaCP to the frozen PTM as it helps improve accuracy. We use RP dimension D 5000, number of CP heads H 3. and number of generated feature representations per class for the classifier R = 100 as the default configuration; ablations on other variants are included. The regularization parameter À in Eq. 6 for ELM is set 102, and the coefficient a for class mean repulsion is set to 1. These values were optimized on a validation set derived from the CIFAR100 training set and are consistently used across all datasets and both PTMs. All experiments are conducted on single NVIDIA A 100 GPU with 80GB VRAM.
Evaluation Metric: We evaluate model performance using two primary metrics: Last Accuracy (ALas)), the accuracy after completing all tasks, and Average Incremental Accuracy (Awwg), calculated as A + Σラ= A,, where A, denotes the accuracy at the end of task t. Additionally, we measure running time and memory efficiency to assess the practicality of the methods. We also define relative error reduction as Ad. x 100, where Ag is the bascline accuracy and A, is the improved accuracy. To
5.2 Comparison with Baselines
Table 1 presents the main results of our experiments, with all methods using DINO-v2 as the PTM. AnaCP consistently outperforms all baselines across the evaluated datasets, achieving an absolute improvement in last accuracy ranging from 1.03% to 3.17% across different datasets, corresponding to a relative error reduction between 4.8% and 31.4%. We can observe that using replay features with shared covariance (AnaCP) achieves similar results to class class-specific covariances (AnaCP- Σ,) while significantly reducing the number of parameters. AnaCP also surpasses the joint linear probe all datasets and achieves comparable accuracy to joint fine-tuning, which represents the 'The code of AnaCP is available at https::/gittuu..oom//// http://ghttbbb.oosslaaammmmmaaaa
7

---

Method
CIFARI00
ImageNNttRR
CTR
Tiny Imaggeet
Cars
Joint linear probi
80 20
82.49-aam
80 35gn
85.43
86. 20
fixe-uning
88.
80.87awca
1.3P
88. 50
81. 50
84.77
70.57
62, 62.08.1
72.8520
80 g0.30gm
51.45
54 10:70-00
10 83,
DualPonne
33.13
46
84.50
79
22.
29.00.0ca
84.64.0
03.31 A6
CODA Prompe
90,87
85 20.0
88 44
82 39
83.1 2.07
78.88
50.58 D0.T7
50.50
58. 1s3.49.2.00
42 153 23.77
SLCA
50. 2032
88
53
86
58.07
$9.38
85,31
80.77 00.70..0 A4
85.
SimpleCTI.
98.18
20
80.04 gm
75
91 30 59
86.5 20
87. 80.0000
83. 17 2m
06. 26.78 10
96
SLDDA
90.25 p0.28
87.57
83
77 25
95.05
89.51
87. 77.80...m
52.69_a.u
89.97
87 20
KLDA
92.9700
g5. 10
82 23
77.75 m
50.54 10:33
20:20-00 20
22.91 os
91.30 91,30) oe
GACL
50.85400
90 1010...0
S1.91
81.74
90.2
50.3
90.09
96.70
89, 89,76_g
84.02 44.02
APER
45
.8.1
86 66.32
80.61 .0.04
a1.18
88.85,0.2
.9.26,n.c
64.50.o 21
65. 65.10
FeCAM
50,27
29.08
S1.61
70. 73.27.9.30
91,59.9.72
87.632035
89.47 29.4
84.75.a
90.64..006
85. 72..72
RanPAC
0000 m9
67.90
86.41-9.3
92.57-0.04
84.67-1
01.45 115--.. 1et
57 +
AmsCP-7 byy
96.452022
92 12a01
90.38 20.0
80 a0u6
55. 22.88
50.6120035
91.8 21.8
57.71
54:79
910 57..5.
AnsCPP
40
86
90.67
91.67
87.36 AM
94-16
00.06-
Rel. Fioor
22.5% 1
20.7 1
16.25
11.995
0.195
9.8% 1
9.4%
4.8%5L
$1.438
25.355
Table 1: Comparison of AnaCP with baselines using DINO-v2 as the PTM. All methods are replay-free. AnaCP employs a shared covariance matrix for pseudo-replay feature generation, while AnaCP-2i, uses separate covariance matrix for each class; the latter is reported only as an ablation since it requires more parameters. The best result (excluding AnaCP-Li,) is shown in bold, and the second-best is underlined. Rel. Error indicates the reduction in error rate achieved by AnaCP compared to the best baseline for the column.
Method
CIFARIOO
ImageNet-RR
CUB
Imageeet
Cars
Auu
Joint lncar probe
83.8
50. 16
Gd.I9ancc
$1.12,a
41.36
fize
87.45
79.242m023
$2.54_9x
H1
SLCA
28.54an.a
69 69.54
60.06
9..6
70.42.0.11
70.88
68.98.0.5
63.5
65.47 86
68.00
SimpleCIL
79:2710.47
45.83
27.0
36.35.9.01
45.88
77.01
71.01.0.0
28.99.0
19.
SLDA
36. 20
14
65:37 01 1M
58. 22:
20.6 61
81. 10.00 20:75
75:30 mm
18:33 X22
60. 20.72
KI DA
85.97 10.2
81. 15
63.64.0.7
58 00
78. 49 0.227
71.39
82.46.0.0
75.67
77:53..
60.1
GACT
55.99 1..3
10.00...0
64.02 1M
56. 9..49
$4.72 10.54
78.78
72.48 4b
APER
s0.51.135
T1.36
64.79_g
72
6334-0
S0.0
7284_
45,00
122
FeCAM
a4.73
27.20
61:61 m0
55. 25.0
73.61
.0.5
$1.28
24.49_1.. 04
24.55
RanPMC
86 16.99
79.57
70.6M 20.17
62,50
72.69
82.9
78.25
80.20
72.61
AnaCP: Ey
90.10
83.57 20.12
07.91
28.3
79.05,0cc
$3.88,014
80002 20
53,08_.0 04
79.24
AmcCP
80.00 80.91,0.0
83. 70
74 11.60.0.
67. g0.4s
84.21
78.61
85.45
85.43.0.0
79:32 ...1
84 78
78. 70
Rel.
8.98C
22.356
21.67
4.6%
2.545 1
22,356
22.2%
Table 2: Comparison of AnaCP with baselines using MoCo-v3 as the PTM. The prompt learning baselines are excluded here due to their much lower accuracy, which is also the case in Table 1.
upper bound for CIL. Notably, on two datasets, AnaCP even exceeds this upper bound, while on the remaining datasets, the largest accuracy gap is only around 2%. These results highlight that AnaCP's feature adaptation is highly effective, even without directly training the PTM on each task.
We also evaluate AnaCP using MoCo-v3 as the PTM, as presented in Table 2. AnaCP outperforms the baselines by a larger margin with MoCo-v3 than with DINO-v2, as the weaker features of MoCo-v3 make the CP layer more impactful. In this case, the gap to joint fine-tuning increases to 6%, which is expected since MoCo-v3 a weaker PTM and benefits more from full fine-tuning. However, given that both PTMs have the same architecture (number of layers and hidden size), there is no reason to prefer a weaker PTM in real-world applications.
5.3 Analysis of Catastrophic Forgetting
The CP layer in our method is inherently immune to CF, as it operates on frozen PTM and updates its statistics (prototypes and the Gram matrix) incrementally without overwriting prior information. In contrast, the final ELM classifier relics pseudo-replay, which in principle could introduce some forgetting. In practice, however, we found this effect to be minimal. To verify this, we evaluate under the musk-incremental learning (TIL) setting, where the task identity is provided at inference time. Specifically, we present the accuracy matrix Aft][t where each entry denotes the accuracy on task i after training the first t tasks of CIFAR- 100 (10-task split) using DINO-v2 as the backbone.
We adopt the TIL setting for this analysis because offers a clearer view of forgetting. In CIL, accuracy inevitably decreases as more tasks are introduced, not necessarily due to forgetting, but because the classification problem becomes harder with a growing number of classes. By contrast, TIL keeps the classification difficulty fixed, since each task has constant number of classes and the
8

---

0.987
0.987
0.981
0.908
0.981
0.979
0.984
Step [t]
0.988
0.975
0.981
0.986
0.984
0.987
0.977
0.978
0.982
0.980
0.985
0.908
0.973
0.978
0.982 0.980
0.984
0.958
0.907
0.976
0.976
0.979
0.979 0.983 0.955 0.986
0.985
0.973
0.977
0.979 0.979 0.983 0.957 0.984
0.951
0.986
0.973 0.977
0.978 0.981 0.983 0.955 0.984
0.947
0.979
Task [i]
Figure 2: Accuracy matrix A|]] on CIFAR-100 with 10 task splits using DINO-v2 as the backbone under the TIL setting. Each entry shows the accuracy on task after training on the first tasks.
task ID known at inference. Under this setup, forgetting would appear as a decline in accuracy on earlier tasks. However, shown in Figure 2, the accuracy for task 1 (first column) remains nearly constant across all steps. The same holds for other tasks, demonstrating that our method effectively preserves knowledge from prior tasks.
CLS NCM
CP
NR
H
D
CIFARI00
ImageNNttRR
CUB
Tiny Imageee
Cars
88. 1a
81.60guus
86.95
83.63
69.51 2005
91.31a
83.29
89.52aa
85.89
86.25
NCM
/
3
5000
91,86a00
86.01gun
89 89888u
87,02awrr
89.18
ELM
5000
91.12
15.14
89.75 is
86.48 in
89. 89.32
amo8
85.73
90,39
86.69.n.5
90.24.n..0
6
ELM
J
5000
100
92.15gmm
86 26.602m0s
90.48
87.71
90.65
ELM
3
5000
20
92, 12.44000
86 26.39
90
87.29...4
90, 90,45
86.47
90,16,0
67.19
90.57
ELM
5000
100
42.15
86.60.mm
90.48
87.71
90.65
10
ELM
5000
100
91. 91.99gmm
85.72
90.36a0
87. 87.12200
90.35
g2.15
86.60
10
87.71
90.65 jnas
12
ELM
5
5000
100
42.20gnoa
86.62.0.
90.51 90.51
87,76.022
90, 90.68
13
ELM
3
1000
100
90.64.u
84.01
89.56
85.48
88.23
g0.35
85.15
89.97,0 1a
86.24.om
89.93
15
ELM
5000
100
42.15
86.60200s
9044840
87.71
90.65
16
ELM
3 10000
100
92.75
86.86.0
90.60 10
90.73.m.16
Table Ablation studies on AnaCP with DINO-v2 as the PTM. All reported values are Aust- CLS indicates the method employed in the classifier (Section 4.3). CP indicates whether the proposed contrastive projection is applied. NR (negative repulsion) shows whether class mean separation improved through Lemma 4.1; when not used, the original class means serve target prototypes. The table also includes variations in the RP dimension (D), the number of heads the CP layer (H), and the number of feature representations generated per class (R).
5.4 Ablation Studies
We conduct series of ablations evaluate the impact of key components, as shown in Table Rows 1-3 examine the effect of the CP layer. Removing CP and directly applying an NCM classifier PTM features results in significant drop in absolute accuracy between 2.93% 19.97% (row vs. row 3). This highlights the importance of CP in enhancing feature representations, as illustrated in Figure The effect of negative repulsion (NR), which increases the separation between class means (Section 4.2) is also evident; disabling NR and relying only on positive alignment with the original class means as target prototypes leads to an accuracy reduction from 0.38% to 3.23% (row row 3). This confirms that NR is critical component for improving class separability.
The role of classifier is explored in Rows 4-6, where NCM replaced by ELM. We find that using an ELM classifier on average improves the performance by 0.66% (row 3 vs. row 6). Although this requires generating feature representations as pseudo-replay for training the ELM classifier, as explained in Section 4.3. An arbitrary number of feature representations can be sampled from the Gaussian distribution with negligible computational overhead, as detailed the running time analysis.
We observe that increasing the number of generated feature representations R improves performance on some datasets (Rows 7-9). The effects of various numbers of CP heads H (Rows 10-12) and dimensions D (Rows 13-16) are also explored. Generally, increasing these values improves accuracy,

---

albeit at the cost of additional parameters. For the main results, we have used D 5000 and H = 3. We note that even with H 1, AnaCP outperforms all baselines.
5.5 Memory and Running Time Elficiency
AnaCP needs to save C' class means, each of size d, and a shared covariance matrix of size d x d for feature whitening and pseudo-replay feature generation the input layer (Figure 1). While a separate covariance matrix can be maintained for each class, this would result in significant increase in memory as the number of classes grows. As shown in Table 1, using shared covariance matrix does not compromise accuracy. Each CP head maintains the following: (1) an RP matrix of size x D, (2) a D x D Gram matrix, (3) class prototypes (or means) in the random feature space, each of size D, and (4) a projection matrix W of size d x D. We have H such heads in total. The target prototypes do not need to be stored, as they can be derived from the class means. The classifier layer also maintains
RP matrix of size d x D and W of size C' x D. Unlike the CP layer, this layer doesn't 't need to store the Gram matrix for incremental updates, as is computed from generated feature representations after cach task.
For a typical configuration with C 200, d 768, D 5000, and stored parameters amounts to approximately 106.6 million. The majority of these parameters belong to the D x D Gram matrices, which does not increase with the number of classes, Also, none of these parameters are trainable, making them suitable for storage in reduced-precision formats such as float8. This would further reduce the total memory usage to approximately 102 MiB.
3, the total number of
While AnaCP may have a higher parameter count compared to some other methods, the design is balanced with exceptional computational efficiency. For example. CIFAR100 with the DINO-v2 PTM requires only 9 minutes and 18 seconds for training. 6 minutes and 5 seconds of this time are dedicated to the FSA, and minutes and seconds are spent passing inputs through the PTM to extract features. The core operations of AnaCP, including updating the CP layer and training the classifier with generated features, collectively take only 5 seconds. Thus, despite the larger parameter count, these operations are extremely fast. For comparison, baseline such CODA-Promp! that requires task-specific training takes hours and 47 minutes to complete training on CIFARI00, and joint fine-tuning requires I hour and 58 minutes.
5.6 Discussion
Our results support the proposition that a strong PTM is the key to CL, and that representation-lewe forgetting is not the primary limitation. Even simple CIL strategies, when paired with fixed PTM, can achieve near-optimal performance. This view aligns with neuroscience evidence that the human brain maintains stable representations, despite minor drift over time [69, 70]. Cortical activity also preserves a stable similarity structure that supports consistent perception and behavior, even as neural responses gradually shift [71, 70]. The human brain can thus be viewed through evolution, which provides a stable foundation for continual adaptation. Similarly, large-scale pre-training in machine learning resembles this biological evolution and development, producing reusable representations that enable CL without any forgetting, For further discussion, see [72].
innate PTM refined
6 Conclusion
CIL poses significant challenge in continual learning. Recent analytic methods with PTMs have shown promise. However, since they cannot learn or adapt features obtained from PTMs to suit specific CII. tasks, their performance is still suboptimal. This paper proposed a novel and principled method, called AnaCP, to adapt features extracted from PTMs analytically, which offers highly efficient and accurate solution for CIL. Empirical evaluations demonstrate that AnaCP outperforms strong baselines, but more importantly, if paired with a strong PTM, its accuracy can be comparable to the joint training upper bound.
Limitations: When using a strong PTM like DINO-v2, AnaCP achieves accuracy on par with the joint fine-tuning upper bound. However, with a weaker PTM such as MoCo-v3, AnaCP cannot match joint fine-tuning accuracy due to the critical role of PTM features played in our method. While strong PTMs are readily available today, improving AnaCP's performance with weaker PTMs remains meaningful goal. Additionally, our work currently focuses CII. We believe AnaCP can extended to TIL and domain inniiinnnneementlll learning (DIL) scenarios with appropriate adaptations.
10

---

Acknowledgments
The work of Salch Momeni and Bing Liu was supported in part by three NSF grants (1IS-2229876, IIS-1910424, and CNS- CNS-2225427), and an NVIDIA's Academia Grant, which provides cloud compute via its Saturn Cloud.
References
[1] Zhiyuan Chen and Bing Liu. Lifelong machine learning. Synthesis Lectures on Artificial Intelligence and Machine Learning, 12(3):1-207, 2018.
[2] Michael McCloskey and Neal J Cohen. Catastrophic interference in connectionist networks: The sequential learning problem. In Psychology of learning and motivation, volume 24, pages 109-165. Elsevier, 1989.
[3] Gido M Van de Ven and Andreas S Toliaa. Three scenarios for continual learning, arXiv preprint UrXiv:/904.077 07734, 2019.
[4] Zixuan Ke and Bing Liu. Continual learning of natural language processing tasks: survey. arXiv preprint arXhv:2211.12711, 2022.
[5] Liyuan Wang, Xingxing Zhang. Hang Su, and Jun Zhu. A comprehensive survey of continual learning: theory, method and application. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024.
[6] Haowei Lin, Yijia Shao, Weinan Qian, Ningxin Pan, Yiduo Guo, and Bing Liu. Class incremental learning via likelihood ratio based task prediction. (CLR-2024, 2024.
[7] Zixuan Ke, Bing Liu, Nianzu Ma, Hu Xu, and Lei Shu. Achieving forgetting prevention and knowledge transfer in continual learning. Advances Neural Information Processing Systems, 34,20. 2021.
[8] Gyuhak Kim, Changnan Xiao, Tatsuya Konishi, and Bing Liu. Learnability and algorithm for continual learning. In International Conference on Machine Learning, pages 16877-16896. PMLR, 2023.
[9] Yutao Yang, Jie Zhou, Xuanwen Ding, Tianyu Huai, Shunyu Liu, Qin Chen, Yuan Xie, and Liang He. Recent advances of foundation language models-basee continual learning: a survey. ACM Computing Surveys, 2024.
[10] Gengwei Zhang, Liyuan Wang, Guoliang Kang, Ling Chen, and Yunchao Wei. Slea: Slow learner with classifier alignment for continual learning on pre-trained model. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 19148-19158, 2023.
[11] Zifeng Wang. Zizhao Zhang, Chen- Yu Lee, Han Zhang, Ruoxi Sun, Xiaoqi Ren, Guolong Su, Vincent Perot, Jennifer Dy, and Tomas Pfister. Learning to prompt for continual learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 139-149, 2022.
[12] Huiping Zhuang, Zhenyu Weng, Hongxin Wei, Renchunzi Xie, Kar-Ann Toh, and Zhiping Lin. Acil: Analytic class innseminccemttalll learning with absolute memorization and privacy protection. Advances in Neural Information Processing Systems, 35:1 35:11602-11614 2022.
[13] Mark D McDonnell, Dong Gong, Amin Parvaneh, Ehsan Abbasnejad, and Anton den Hengel. Ranpac: Random projections and pre-trained models for continual learning. Advances in Neural Information Processing Systems (NeurIP-20233, 36, 2023.
[14] Salch Momeni, Sahisnu Mazumder. and Bing Liu. Continual learning using a kernel-based method over foundation models. In AMAI-2025,, 2025.
[15] Dipam Goswami, Yuyang Liu, Bartlomiej Twardowski, and Joost Van De Weijer. Fecam: Exploiting the heterogeneity of class distributions exemplar- free continual learning. Advances in Neural Information Processing Systems, 36:6582-6595. 2023.

---

[16] Aristeidis Panos, Yuriko Kobe, Daniel Olmeda Reino, Rahaf Aljundi, and Richard E Turner. First session adaptation: strong replay-free free baseline for class inassinncremenal learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 18820-18830, 2023.
[17] Nan- Ying Liang, Guang-Bin Huang, Paramasivan Saratchandran, and Narasimhan Sundararajan. fast and accurate online sequential learning algorithm for feedforward networks. IEEE Transuctions neural networks, 17(6):1411-14) 2006.
[18) Guang- Boiang-Bin Huang, Hongming Zhou, Xiaojian Ding, and Rui Zhang. Extreme learning ma- chine for regression and multiclass classification. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cyberneticcs), 42(2):113-52) 2011.
[19] Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan. Supervised contrastive learning. Advances in neural information processing systems, 33:18661-18673, 2020.
[20] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International conference on machine learning, pages 1597-1607. PmLR, 2020.
[21] James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaune Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Barobkkaaaaiiskk,, et al. Overcoming catastrophic forgetting in neural networks. Proceedings of the national academy of sciences, 1 114(13)3521-3356 2017.
[22] Friedemann Zenke, Ben Poole, and Surya Ganguli. Continual learning through synaptic intelligence. In International Conference on Machine Learning, pages 3987-3995, PMLR, 2017.
[23] Tianlin Liu, Lyle Ungar, and João Sedoc. Continual learning for sentence representations using conceptors. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, NAACL-IILT 2019, Minneapolis, MN, USA, June 2-7, 2019, Volume 1 (Long and Short Papers), 2019.
[24] Dingcheng Li, Zheng Chen, Eunah Cho, Jie Hao, Xiaohu Liu, Fan Xing, Chenlei Guo, and Yang Liu. Overcoming catastrophic forgetting during domain adaptation of seq2seq language generation. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Compulational Linguistics: Human Language Technologies, 2022.
[25] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv: 1503. 02533, 2015.
[26] Pietro Buzzega, Matteo Boschini, Angelo Porrello, Davide Abati, and Simone Calderara. Dark experience for general continual learning: a strong, simple baseline. Advances in neural information processing systems, 13:1002015593, 2020.
[27] Rahaf Aljundi, Eugene Belilovsky, Tinne Tuytelaars, Laurent Charlin, Massimo Caccia, Min Lin. and Lucas Page-Caccia. Online continual learning with maximal interfered retrieval. Advances neural information processing systems, 32, 2019.
[28] Arslan Chaudhry, Naeemullah Khan, Puneet Dokania, and Philip Torr. Continual learning in low- rank orthogonal subspaces. Advances in Neural Information Processing Systems, 33:9900-999 99111, 1, 2020.
[29] Dongsub Shim, Zheda Mai, Jihwan Jeong, Scott Sanner, Hyunwoo Kim, and Jongseong Jang. Online class-incremental continual learning with adversarial shapley value. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 9630-9638, 2021.
[30] Qingbin Liu, Xiaoyan Yu, Shizhu He, Kang Liu, and Jun Zhao. Lifelong intent detection via multi-strategy rebalancing. arXiv preprint arXiv: 20022000.000 04445, 2021.
[31] Yujia Qin, Jiajie Zhang, Yankai Lin, Zhiyuan Liu, Peng Li, Maosong Sun, and Jie Zhou. Elle: Efficient lifelong pre-training for emerging data. In Findings of the Association for Computational Linguistics: ACL 2022, pages 2789-281 10, 2022.
12

---

[32] Xialei Liu, Chenshen Wu, Mikel Menta. Luis Herranz, Bogdan Raducanu, Andrew D Bagdanov. Shangling Jui, and Joost van de Weijer. Generative feature replay for class-incremental learning. In Proceedings of the IEEF/CVF conference on computer vision and pattern recognition workshops, pages 226-227, 2020.
[33] Gido M Van de Ven, Hava T Siegelmann. and Andreas S Tolias. Brain-inspired replay for continual learning with artificial neural networks. Nature communications, (1(1):4069, 2020.
[34] Kai Zhu, Wei Zhai, Yang Cao, Jiebo Luo, and Zheng-Jun Zha. Self-sustainnng representation expansion for non-exemplar fass-incremmnnal learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9296-9305, 2022.
[35] Zheng Gong, Kun Zhou, Wayne Xin Zhao, Jing Sha, Shijin Wang. and Ji-Rong Wen. Continual pre-training of language models for math problem understanding with syntax-aware memory network. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 5923-5933, 2022.
[36] Fu- Yun Wang, Da- Wei Zhou, Liu Liu, Han-Jia Ye, Yatao Bian, De-Chuan Zhan, and Peilin Zhao. Beef: Bi-compatible class-incremental learning via energy-based expansion and fusion. In The Eleventh International Conference Learning Representations, 2022.
[37] Shipeng Yan, Jiangwei Xie, and Xuming He. Der: Dynamically expandable representation for class incremental learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1012-303,220 2021.
[38] Chengwei Qin, Chen Chen, and Shafiq Joty. Lifelong sequence generation with dynamic module expansion and adaptation. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 6701-6714. Association for Computational Linguistics, 2023.
[39] Joan Serra, Didac Suris, Marius Miron, and Alexandros Karatzoglou. Overcoming catastrophic forgetting with hard attention to the task. In International Conference on Machine Learning, pages 4548-4557. PMLR, 2018
[40] Suchin Gururangan, Mike Lewis, Ari Holtzman, Noah A Smith, and Luke Zettlemoyer. Demix layers: Disentangling domains for modular language modeling. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics, pages 5557-5576, 2022.
[41] Binzong Geng, Fajie Yuan, Qiancheng Xu, Ying Shen, Ruifeng Xu, and Min Yang. Continual learning for task-oriented dialogue system with iterative network pruning, expanding and masking. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics (ACI/ICNN.P), 2021.
[42] Mitchell Wortsman, Vivek Ramanujan, Rosanne Liu, Aniruddha Kembhavi, Mohammad Raste- gari, Jason Yosinski, and Ali Farhadi. Supermasks in superposition. Advances in Neural Information Processing Systems, 33: 33:15173-15184 2020.
[43] Junpeng Liu, Kaiyu Huang, Hao Yu, Jiuyi Li, Jinsong Su, and Degen Huang. Continual learning for multilingual neural machine translation via dual importance-based model division. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 12011- 2023.
[44] Gyuhak Kim, Changnan Xiao, Tatsuya Konishi, Zixuan Ke, and Bing Liu. A theoretical study on solving continual learning. Advances in neural information processing systems, 35:5065-5079, 2022.
[45] Mingyang Wang, Heike Adel, Lukas Lange, Jannik Strötgen, and Hinrich Schüizee Rehearsal- free modular and compositional continual learning for language models. In Proceedings of the 2024 Conference of the North Americon Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 2: Short Papers), pages 469-480, 2024.
13

---

[46] Jathushan Rajasegaran. Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Mubarak Shah. itaml: An inremeenal task-agnostic leta-learning approach. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 13588-13597, 2020.
[47] Zifeng Wang, Zizhao Zhang, Sayna Ebrahimi, Ruoxi Sun, Han Zhang, Chen- Yu Lee, Xiaoqi Ren, Guolong Su, Vincent Perot, Jennifer Dy, et al. Dualprompt: Complementary prompting for rehearsal-fie continual learning. In European Conference on Computer Vision, pages 631-648. Springer, 2022.
[48] Yan-Shuo Liang and Wu-Jun Li. Inflora: Interference-free low-rank adaptation for continual learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pages 23638-23647, 2024.
[49]
Hai-Long Sun, Da- Da-Wei Zhou, Hanbin Zhao, Le Gan, De-Chuan Zhan, and Han-Jia Ye. Mos: Model surgery for pre-trained model-based class-incremental learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 20699-20707, 2025.
[50] James Seale Smith, Leonid Karlinsky, Vyshnavi Gutta, Paola Cascante- Bonilla Donghyun Kim, Assaf Arbelle, Rameswar Panda, Rogerio Feris, and Zsolt Kira. Coda-pronne ppooptooppttttmm Continual decomposed attention- prompting for rehearsal-free continual learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11909-11919, 2023.
[51] Liyuan Wang, Jingyi Xie, Xingxing Zhang, Mingyi Huang. Hang Su, and Jun Zhu. Hierarchi- cal decomposition of prompt-based continual learning: Rethinking obscured sub-optimality. Advances in Neural Information Processing Systems, 05x69054-69077 2023.
[52] Dahuin Jung, Dongyoon Han, Jihwan Bang, and Hwanjun Song. Generating instance-level prompts for rehearsal-free continual learning. In Proceedings of the IEEF/CVF International Conference on Computer Vision, pages 11 11847-11877 2022.
[53] Anurag Roy, Riddhiman Moulick, Vinay K Verma, Saptarshi Ghosh, and Abir Das. Con- volutional prompting meets language models for continual learning. In Proceedings of the IEEF/CVF Conference on Computer Vision and Patlern Recognition, pages 2361 6666623626, 2024.
[54] Huiping Zhuang, Yizhu Chen, Di Fang, Run He, Kai Tong, Hongxin Wei, Ziqian Zeng, and Cen Chen. GACL: Exemplar-free generalized analytic continual learning. In Advances in Neural Information Processing Systems. Curran Associates, Inc., 2024.
[55] Paul Janson, Wenxuan Zhang, Rahaf Aljundi, and Mohamed Elhoseiny. A simple baseline that questions the use of pretrained-models in continual learning, arXiv preprint 2rX14:2210.04428. 2022.
[56] Da- Wei Zhou, Han-Jia Ye, De-Chuan Zhan, and Ziwei Liu. Revisiting class-incremental learning with pre-trained models: Generalizability and adaptivity are all you need. International Journal of Computer Vision, 2024.
[57] Tyler L Hayes and Christopher Kanan. Lifelong machine learning with deep streaming linear discriminant analysis. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshops, pages 220-221, 2020.
[58] Shaoning Pang, Seiichi Ozawa, and Nikola Kasabov. Incremental linear discriminant analysis for classification of data streams. IEEE transactions on Systems, Man, and Cybernetics, part (Cybermetics), (5(5):905-914 2005.
[59] Liangzu Peng, Juan Elenter, Joshua Agterberg, Alejandro Ribeiro, and René Vidal. Loranpae: Low-rank random features and pre-trained models for bridging theory and practice continual learning. ICLR, 2025.
[60] AK Md Ehsanes Saleh, Mohammad Arashi, and BM Golam Kibria. Theory of ridge regression estimation with applications. John Wiley & Sons, 2019.
[61] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009.
14

---

[62] Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, et al. The many faces of robustness: critical analysis of out-of-distribution generalization. In Proceedings of ICCV, pages 4340-83499 2021.
[63] Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. caltech-uesd birds-200-2011 dataset. 2011.
The
[64] Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7:7, 2015.
[65] Linjie Yang, Ping Luo, Chen Change Loy, and Xiaoou Tang. A Sarge-scale car dataset for fine-grained categorization and verification. In Proceedings of the IEEE conference computer vision and pattern recognition, pages 3973-3981, 2015.
[66] Maxime Oquab, Timothée Darcet, Théo Moutakanni, Huy V Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel HAZIZA, Francisco Massa, Alaaeldin El-Nouby, al. Dinov2: Learning robust visual features without supervision. Transactions on Machine Learning Research, 2023.
[67] Xinlei Chen, Saining Xie, and Kaiming He. An empirical study of training self-supervised vision transformers. In 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pages 9620-9629. IEEE Computer Society, 2021.
[68] Edward J Hu, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models. In International Conference on Learning Representations, 2021.
[69] Walter G Gonzalez, Hanwen Zhang, Anna Harutyunyan, and Carlos Lois. Persistence of neuronal representations through time and damage the hippocampus. Science, 365(6455):821- 825, 2019.
[70] Zvi N. Roth and Elisha P. Merriam. Representations in human primary visual cortex drift time. Nature Communications, 14(4422), 2023.
[71] David BT McMahon, Adam P Jones, Igor V Bondar, and David A Leopold. Face-selective neurons maintain consistent visual responses across months. Proceedings of the National Academy of Sciences, 1 111(22):8251-822
2014.
[72] Saleh Momeni and Bing Liu. Achieving upper bound accuracy of joint training in continual learning. arXiv preprint arXiv:2502. 2025.
NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
The abstract and introduction match our claims and the paper's 's scope.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize other settings.
is fine to include aspirational goals as motivation as long is clear that these goals not attained by the paper.
15

---

2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: Limitations is discussed in the conclusion.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e-g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested few datasets with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proof's
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: The only novel theoretical formula included in this paper is lemma 4.1, which is proven in the appendix.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
16

---

Answer: [Yes]
Justification: We provided all information needed to reproduce the results and the code in included in the supplementary materials.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution
specific model and empirical evaluation, may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm.
(b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers have some path reproducing verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification:
The code is included in the supplementary materials.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips. cc/ public/ healcc/ggiids//Cooieeee soredddSummsssooooliiiooo
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https: //nips.cc.. wwtpcc/ccppccpccecccccccccceeeee httgguuddee//// http://eeeummmssiiooeeeeeeeeee httpc/ccppwcccggiideceeeeeeee//e
for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
17

---

The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e-g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification:
We use the official data splits, and all the hyperparameters used are reported.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, or as supplemental material.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer:
[Yes]
Justification:
The standard deviation of the accuracies are reported.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should clearly stated (for example, train/test split, initialization, random drawing of some parameter, overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: The computer resources and the execution time of the experiments reported.
18

---

Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compule required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't I make it into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics https: /tara:////uup.....e http://urrissccppulpllpase https/cccpcccc/tciccccccc
ines?
Answer: [Yes]
Justification: The research complies with NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.
The authors should make to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive socictal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: This paper studies standard machine learning problem with direct societal impact.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (c.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility ML).
11. Safeguards
Question: Does the paper describe safeguards that have been put in place for responsible release of data models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
19

---

Answer:
[NA]
Justification:
There is no high risk misuse.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification:
All the datasets and models are properly cited.
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version the asset used and, possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of in the package should be provided. For popular datasets, paperswi thcode. com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's s creators.
New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: Paper does not release assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details the dataset/codeemoodll as part their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
20

---

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification:
The paper does not include human research experiments.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurIPS Code of Ethies, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country or institution) were obtained?
Question:
Answer: [NA]
Justification: The paper does not include human research experiments.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification: LLMs were only used for editing without any impact on the core methodology.
Guidelines:
The answer NA means that the method development in this research does not involve LLMs as any important, original, or non-standard components.
Please refer to our L.MM policy (https: (https://neur)s //terri/////ss///e ce/ oC//onfferencces22222 2202/LLMM) for what should or should be described.
21

---

A Technical Appendices
Lemma A.1 (Lemma 4.1). Denote Wi...., wc E RC as arbitrary vectors, and ei,...,ec IR as
a set of orthogonal bases of RC. Denote (z, u) = x T as the inner product and ( v) = |= as the cosine similarity. There exist > 0 and
x y
1
if
[2 1 (m,,m))20) w))) ||w;|12 (ei, wi) (w, myy)] 0.
|
j+i
8;
1
0,
if
[[2 1 (m0,0,220) we)) ||w1112 we) [w,,, my>س] = 0,
|wy|l
ifi
1, else,
s.t.
ΣΣ
0ww, + adie, wy + adGez)) S ΣΣ
(w,,, wz)l
(18)
8 jf
Proof. Let
Kwy, wi + ad,e))
fi(a)=
Σ
|wرس|| I|,, + ad,ell
jfi
For simplicity, denote
P(z(a) 1ww + adses, wy + adjee)) = (ws, wj) + adi wy)l
and
q:(0) = =1lus + ad,eelll = v (w, + tooees wy + ad(e))
Therefore, we have
fi(a)) = Σ 1 pt,s(a)
|wy|| %((a)
371
Since
d=n dar 2- -2-1220 we have
(a)(()) = (2 l(wo, dilei, wz).
Since (w) + adie; wi + ad,e;) = (wi, wi) + 20,(e: wi) + a we have
1 (e,, wi) + 2xx
1a=0 5,(es, wi) ||w;]]
((a))a=0 = 2 V(wi ad,e, wa + adje))
Therefore, have
Pha (a)))(()-pp)()///)aa
f((a)a-0= =
[wyl
((
(2 12,,0)))000 - 1). 8, (e,, wy) |||,,]1 1(,, wy)) 8e wi)
Σ
|| ||]|w 1|
|
jfi
5,
[2 (1w,,z)200 - 1) (e,, w,) ||w,|12 - (er, wc) 1ew, wy)l]
|ws
1w
which shows that 8,'s 's defined above guarantee f/(a)la=0 S
Let
[w + ad wi + ad.c;)
gf(a; &)) =
Iw + adæezll ||u + â
Since f() is continuous function, we could take sufficiently small à f/(a') has the same sign when a' E [0, a). Then for a' E [0, a], the 6,'s defined above also guarantee Jf (a; a²) a== S 0. Choosing a = a' gives the result.
22


Reviews:
[{"review_id": "XpPdKByUGA", "reviewer": "Reviewer_Ah55", "summary": "This paper introduces a method for class-incremental learning (CIL), called Analytical Contrastive Projection (ACP), which bridges the gap between the efficiency and stability of analytical methods and the adaptability of feature learning in continual learning settings. ACP leverages a pre-trained model (PTM) as a frozen feature extractor and proposes an analytical, non-gradient-based mechanism for feature adaptation using a Contrastive Projection (CP) layer. The method analytically aligns samples from the same class while increasing inter-class separation via prototype regression and class mean repulsion and integrates an ELM classifier for final prediction. The authors demonstrate through comprehensive experiments on several benchmark datasets that ACP not only outperforms prior analytical CIL methods and rehearsal-free baselines but also reaches or surpasses the performance of joint training in some cases. Ablation studies and efficiency analyses further support the method’s design and scalability.", "questions": "- Could you provide a more intuitive or geometric explanation of Lemma 4.1? A visual illustration showing how the angular separation between class means is improved would significantly enhance accessibility.\n- Could you elaborate on why using a single shared covariance matrix across all classes works well for pseudo-replay? Have you observed any failure cases or dataset-specific limitations when using this approximation?\n- Since the shared covariance is also used during pseudo-sample generation and classification, how are labels assigned to the generated samples, and how robust is this process across tasks?\n- Would you consider updating or expanding Figure 1 to more clearly show how the matrices described in Section 4 are constructed and applied across tasks? For example, depicting the flow of Gram matrices, projection heads, and ELM updates could greatly help clarify the method.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\nThe paper addresses a highly relevant problem in CIL, while maintaining their computational advantages. The proposed ACP method is conceptually elegant and grounded in strong mathematical formulations, using closed-form solutions to approximate contrastive learning effects. The methodology is clearly described and logically structured. The experimental section is thorough, covering multiple datasets, PTMs (DINO-v2 and MoCo-v3), and a wide array of baselines including recent prompt-based and analytical methods. Results consistently show significant improvements in both average and final accuracy, with ACP performing on par with joint fine-tuning in many scenarios. The ablation studies are comprehensive and confirm the contributions of individual components like the CP layer, class mean repulsion, and the ELM classifier.\n\n## Weaknesses\n\nDespite its merits, a few limitations of the paper deserve further clarification. First, the analytical derivation of class mean repulsion using Lemma 4.1 is mathematically dense and lacks an intuitive geometric explanation or visual illustration, which may limit accessibility to a broader audience. Second, while the proposed pseudo-replay strategy is efficient and empirically effective, the justification for using a single shared covariance matrix across all classes is not fully addressed, especially considering that this shared covariance is used to generate pseudo samples. It remains unclear how the method distinguishes between samples from different tasks (e.g., task A vs. task B) during pseudo-replay, or whether such differentiation is even required under the proposed framework. A deeper discussion of why this approximation works and what its potential limitations are would be beneficial. Finally, although the methodology is described in detail, some parts of the pipeline remain difficult to follow without visual aid. In particular, the main figure (Figure 1) could be improved by clearly showing how the various matrices introduced in Section 4 (e.g., Gram matrices, projection matrices, and components of the pseudo-replay mechanism) are constructed and used during learning.", "was_revised": false, "final_justification": "", "rebuttal": "- **Question 1:**  \n  Intuitively, if class means are too close (i.e., having high cosine similarity), they become easily confusable, making the classification problem harder. Lemma 4.1 enables a transformation where class means are repelled from one another. We will consider including a more detailed geometric visualization in the revision. For now, we refer the reviewer to the t-SNE visualization in Figure 1 (right). The black dots represent class means. As shown, the class means of the \"extracted features\" are less separated, whereas after applying ACP, the data distributions and the class means in the \"enhanced features\" are more distinct, which helps classification.\n\n- **Question 2:**  \n  The assumption behind our pseudo-replay mechanism is that each class distribution is characterized by its mean and a covariance matrix, an approach also used in prior work such as SLCA. However, maintaining a separate covariance matrix for each class increases the number of parameters. We instead use a shared covariance matrix across all classes, which drastically reduces the parameter cost while preserving the performance. This essentially implies that feature correlations are consistent across classes, i.e., if two feature dimensions are positively correlated for one class, they are likely to be so for others as well. In other words, the correlation belongs more to the feature extractor than to specific classes.\n\n  We found that this works well across all datasets we tested (see Tables 1 and 2), and did not observe any failure cases. This shared covariance assumption is also used in the classic Mahalanobis distance and linear discriminant analysis (LDA) methods. It has been shown to perform well in various settings.\n\n- **Question 3:**  \n  Our approach does not rely on any task information for classification or pseudo-replay data generation. In CIL, tasks are often used to organize the sequence of class arrivals. We follow this in our experiments, but our method treats each class independently; we can learn a single class at a time. To generate a pseudo-sample for a class, we sample a noise vector from the shared covariance and add it to the corresponding class mean, which is then labeled with that class.\n\n- **Question 4:**  \n  We appreciate the suggestion to enhance Figure 1. In the revised version, we will update the figure to better illustrate the construction and application of each component."}, {"review_id": "SXHcJO9yZE", "reviewer": "Reviewer_iEp4", "summary": "The paper tackles continual class-incremental learning with pretrained models", "questions": "- How to guarantee the covariance in Eq 10 is strictly positive definite? This is important as in Eq 11 (which has a typo), its inverse is needed to be computed.", "limitations": "See above.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths. The paper tackles a relevant problem of interest to the continual learning audience. The manuscript overall is clearly written with good coverage and clear discussion on the literature. The proposed method is clear (though could be better motivated, see below). The experimental results look strong and the paper has a nice set of ablation studies. \n\n\nWeaknesses. My first major concern is about the comparison regarding RanPAC, one of the most relevant approaches. There are a few implementation differences in the provided RanPAC implementation and its original implementation. RanPAC sets ridge parameter by cross validation and sets dimension $D$ to $10,000$, and uses ReLU as its activation. The paper sets smaller dimension $D=5000$, and  sets a fixed number 100 for both RanPAC and the proposed method, and the proposed method instead uses GELU. It would make more sense and make the paper more convincing if their setups are unified with the same activation (with experiments on both ReLU and GELU), and if RanPAC uses its original dimension and original cross validation approach.\n\nThe second major concern is on the technical development. Section 4 reads like a cookbook and the intuition or motivation behind the strategy proposed is often unclear at least to me. More specifically:\n- What is the motivation to regress a target prototype which is defined to be the class means? If regressing the class mean is a good goal, why don't we just output the class mean of that layer? Note that we can compute the class mean directly. We want to regress the one-hot label as there is no explicit map from features to labels, but we do have an explicit map from features to their means.\n- Why are whitening and de-whitening steps essential? I imagine that we can do SVD directly on C and correct its singular values. It is unclear to me why the whitening is applied on the left in Eq 11 and de-whitening is on the right at Eq 16. Could the authors explain this in more detail? \n- I am confused around Eq 13 and Lemma 4.1. What's that intuition behind Eq 13? Namely, why adding a diagonal shift would reduce cosine similarity? Further, how does this condition on $\\delta_i$ arise? How large $\\alpha$ is, and what is the rationale of choosing $\\alpha=1$? Can Lemma 4.1 be proved for $\\alpha=1$? In general I find a detailed explanation of Lemma 4.1 on its significance is lacking.\n\n\n\nFinally, it would be nice if the authors compare the following baselines either in text or in experiments:\n- HidePrompt, which seems to work very well among prompt based methods (https://proceedings.neurips.cc/paper_files/paper/2023/hash/d9f8b5abc8e0926539ecbb492af7b2f1-Abstract-Conference.html). \n- LoRanPAC, which seems to be a stronger alternative of RanPAC (https://openreview.net/forum?id=bqv7M0wc4x)\n- InfLoRA, which is a representative adapter-based method and the paper seems to compare no methods from this category (https://openaccess.thecvf.com/content/CVPR2024/html/Liang_InfLoRA_Interference-Free_Low-Rank_Adaptation_for_Continual_Learning_CVPR_2024_paper.html)", "was_revised": true, "final_justification": "The rebuttal has adequately addressed my concerns.", "rebuttal": "- **Comparison regarding RanPac:**\n\nAs shown in Table 3, increasing the dimension $D$ generally leads to improved performance. We wanted to use the same dimension for all the methods that utilize this technique (KLDA also uses $D=5000$). Therefore, we set $D=5000$ for all methods to allow a fair comparison. Regarding the activation function, we did not observe significant differences between ReLU and GELU in our experiments. We opted for GELU as it seemed more intuitive: since the goal is to expand the feature dimension, ReLU would zero out all negative values, which contradicts the intention of fully utilizing the expanded dimension. Regarding fixed regularization, we aimed to demonstrate that the method performs consistently well across datasets using the same regularization value. Otherwise, it would raise the concern of what would happen if we wanted to learn two datasets that require completely different regularization values at the same time.\n\nTo further alleviate your concern, we re-ran both ACP and RanPAC with DINOv2 as the backbone, using $D=10000$ and ReLU for both methods. For ACP, we retained our fixed regularization. For RanPAC, we report results using both fixed regularization and its original cross-validation approach:\n\n| **Method**           | **CIFAR100 A_avg** | **CIFAR100 A_last** | **ImageNet-R A_avg** | **ImageNet-R A_last** | **CUB A_avg** | **CUB A_last** | **Cars A_avg** | **Cars A_last** | **T-ImageNet A_avg** | **T-ImageNet A_last** |\n|----------------------|:------------------:|:-------------------:|:--------------------:|:---------------------:|:-------------:|:--------------:|:--------------:|:---------------:|:---------------------:|:----------------------:|\n| ACP                  | 95.61              | 92.87               | 90.48                | 86.84                 | 93.48         | 90.66          | 93.52          | 90.51           | 92.13                 | 87.97                  |\n| RanPAC (fixed reg)   | 94.32              | 90.95               | 87.61                | 84.74                 | 91.85         | 88.94          | 91.81          | 87.31           | 89.66                 | 85.10                  |\n| RanPAC (cross-val)   | 94.47              | 91.13               | 88.52                | 84.74                 | 92.10         | 89.27          | 91.99          | 88.20           | 89.38                 | 84.25                  |\n\nThe results show that cross-validation yields slightly better results overall, although it hurts performance on dataset T-ImageNet. We also note that ACP could be extended to use cross-validation if desired. More importantly, ACP continues to outperform RanPAC consistently across all datasets.\n\n- **Motivation to regress a class prototype:**\n\nIf we understand your question correctly, you are asking why we regress the target prototypes instead of directly returning the class means as the output of the contrastive projection (CP) layer. If that is indeed the question, this approach would not work, since, contrary to the suggestion, we do not have an explicit mapping from the samples to the class means during inference, as the labels are not available. Therefore, directly outputting the class mean is not feasible at test time. Also, the target prototypes we regress are not exactly the original class means; the class means are shifted to improve their separation through Lemma 4.1. We are effectively learning a mapping that, without requiring the label during inference, improves the features by pulling samples from the same class together and pushing them away from other classes. Then, the classifier is learned on top of the improved features, as depicted in Figure 1, which is better than learning it directly on top of the original PTM features.\n\n- **Whitening and de-whitening steps:**\n\nOur goal is to improve class separability, which we quantify by the sum of pairwise cosine similarities between class means. It is indeed possible to apply SVD directly to $C$ and modify its singular values to reduce this sum. However, there is a key limitation with cosine similarity that we aim to address: cosine similarity does not take into account the scale or variance of each feature dimension. For example, in a dimension with low variance, even a small separation is significant, whereas in high-variance dimensions, a much larger separation is needed to achieve the same effect.\n\nTo resolve this, we apply whitening transformation, which is a common data processing method. Whitening sets the variance of all feature dimensions to 1, allowing for a more meaningful measure of separation across directions. This process is closely related to Mahalanobis distance, which has been shown to outperform cosine similarity in related contexts (we refer the reviewer to FeCAM). By whitening the features, we essentially assess separation using Mahalanobis distance, and after increasing the separation, we de-whiten the features to restore the original variance. We will clarify this point further in the revision.\n\n- **Lemma 4.1 explanation:**\n\nThe intuition behind Eq. 13 is that the diagonal shift is intended to perturb the class means in directions that reduce their pairwise cosine similarity. Specifically, each $w_i$ in the subspace $SV_T$ is perturbed by $\\alpha \\delta_i e_i$, where $\\{e_i\\}$ vectors form an orthonormal basis. This means each $w_i$ is shifted in an orthogonal direction by a magnitude of $\\alpha$. The sign of $\\delta_i$ determines whether the shift is in the direction of $e_i$ or the opposite. This condition arises from the proof of Lemma 4.1, where we take the derivative of the function $f_i(\\alpha)$, representing the sum of cosine similarities for class $i$. By choosing $\\delta_i$ in this way, we ensure that the slope of $f_i(\\alpha)$ at $\\alpha = 0$ is negative, guaranteeing that a small positive $\\alpha$ will reduce cosine similarity.\n\nRegarding the choice of $\\alpha$, if it is too small, the shift becomes negligible; if it is too large, the reduction in cosine similarity may not hold. While it is again possible to optimize $\\alpha$ via cross-validation on each dataset, our goal was to show that a single value works across all datasets. We empirically selected $\\alpha = 1$ by validating on CIFAR100 training data, searching over the range $[0.1, 1, 2, 5, 10]$. This value was then used consistently across all datasets without tuning.\n\nWe agree that a more detailed explanation of Lemma 4.1 and its implications could enhance clarity, and we will include an expanded discussion in the revision.\n\n- **Suggested papers:**\n\nThank you for the helpful suggestions. We will ensure that the recommended papers are cited and discussed in the revised manuscript, as well as incorporated into the experiments.\n\n   InfLoRA and HidePrompt are different approaches from ours. LoRanPac, which is more related to our work, projects the PTM features into a very high-dimensional space (e.g., 100,000) and solves the over-parameterized least-squares problem by truncating the singular value decomposition of the projected features. Their improvement over RanPAC seems to stem from the use of very high-dimensional projections. We note that this technique may also be used in our system to solve the extreme learning machine objective using 100,000 projection dimensions instead of our default of 5,000. Our contribution is entirely different: we propose an analytical contrastive layer that pulls samples of a class toward their mean and pushes class means away from one another, which improves class separation and consequently classification accuracy.\n\n- **Question 1:**\n\nAs for Eq. 11, we clarify that $\\Sigma^{-1/2}$ represents the whitening transformation, i.e., the inverse square root of the covariance matrix. For this to exist, $\\Sigma$ must be positive-definite, which requires at least $n \\geq d$ linearly independent data points. If this condition is not met (e.g., due to a small data size), we add a small regularization term $\\epsilon I$ to the covariance to ensure it becomes invertible. In our implementation, we used $10^{-4} I$."}, {"review_id": "81OMLhIzZj", "reviewer": "Reviewer_yx87", "summary": "This paper focuses on the class-incremental learning (CIL) and proposes ACP (Analytical Contrastive Projection) to enable incremental feature adaptation while maintaining computational efficiency through analytical classifiers. ACP is implemented in a gradient-free method and achieves strong performance on various CIL benchmarks.", "questions": "N/A", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n1.\tThis paper is well-written, and the motivation is clear.\n2.\tThis paper proposes a new way to improve the performance of analytical classifier methods, which are limited by the fixed pre-trained model and linear classifier.\n3.\tExperiments have demonstrated the effectiveness of the proposed ACP on various datasets and settings.\n\nWeakness\n1. Positive Alignment\n- Improvement in Method Description Clarity: While the mathematical formulation of the proposed method appears rigorous, the current presentation significantly increases the cost of understanding for readers. Additionally, redefining the left-hand side of Eq. 9 as $ H = Z^\\top P$ may improve clarity (only suggestion, depending on the authors).\n- Dependence on Pretrained Model: The strategy enhances the RP features by class means of the input layer, aiming to enhance the discriminative power of the analytical classifier. However, this approach is inherently dependent on the quality of the pretrained model (PTM), especially when dealing with cross-domain or fine-grained data. As shown in the experiments, the method primarily benefits from strong self-supervised models such as DINO-v2 and MoCo-v3. Briefly, this strategy does not fundamentally improve the separability of features but rather leverages already well-structured representations.\n\n2. Negative Repulsion\n- Lack of Intuitive Explanation for Lemma 4.1: The construction of $\\delta_i$ is not clearly explained. What specific information or property does this diagonal matrix encode?.\n- Need for Discussion on Relationship with Neural Collapse: It would also be valuable to discuss how the proposed negative repulsion mechanism relates to or differs from the phenomenon of *neural collapse*, which describes the tendency of features within each class to collapse to a fixed simplex structure during training.\n\nMinor:\nPlease carefully check the language and grammar. For example, in Line 3, “Traditional CIL methods does not use” should be “Traditional CIL methods do not use”.", "was_revised": true, "final_justification": "Thanks for the authors' reply. All my concerns have been addressed, and I will keep my score unchanged.", "rebuttal": "- We appreciate the suggestion regarding the presentation of the mathematical formulation. We will improve the readability in the revised paper.\n\n- We acknowledge that our method relies on PTMs for well-learned representations, which was also mentioned in the limitation section in the paper. However, this is a common characteristic of most modern CIL approaches using PTMs such as prototype-based methods, prompt learning, and even fine-tuning, which similarly require access to high-quality representations from PTMs. Additionally, we believe this dependence is not restrictive, as PTMs are increasingly accessible across different domains and modalities, and their quality is also getting better.\n\n- The motivation behind Lemma 4.1 is to move the class means in directions that reduce their pairwise cosine similarity. Specifically, each $w_i$ in the subspace $SV_T$ is perturbed by $\\alpha \\delta_i e_i$, where $e$ vectors form an orthonormal basis. This means each $w_i$ is shifted in an orthogonal direction by a magnitude of $\\alpha$. The sign of $\\delta_i$ determines whether the shift is in the direction of $e_i$ or the opposite. This condition arises from the proof of Lemma 4.1, where we take the derivative of the function $f_i(\\alpha)$, representing the sum of cosine similarities for class $i$. By choosing $\\delta_i$ in this way, we ensure that the slope of $f_i(\\alpha)$ at $\\alpha = 0$ is negative, guaranteeing that a small positive $\\alpha$ will reduce cosine similarity, i.e., shift the class means away from one another.\n\n\n- We agree that drawing connections to neural collapse provides a valuable perspective, and we will address this in the revision. Indeed, our contrastive projection shares important similarities with this phenomenon. In neural collapse, all samples within a class collapse to their class mean, which aligns with our method, where we explicitly map all samples from a class to their respective class means. Neural collapse also leads to class means forming a simplex equiangular tight frame, i.e., every pair of class means is equally separated. However, unlike neural collapse, our goal is not to enforce equidistant class means. Instead, we seek to preserve the underlying geometry of the features while pushing the class means away from one another, inspired by contrastive learning. Also, neural collapse occurs in the terminal phase of training (TFT) when the loss approaches zero, which makes it difficult to achieve in continual learning due to incremental learning and catastrophic forgetting. Our method minimizes inter-class variation and enhances class separability analytically without fine-tuning the PTM.\n\n- We will also carefully review the manuscript for grammar and language clarity."}, {"review_id": "Vjv5Sr2zGq", "reviewer": "Reviewer_fcMA", "summary": "Analytical Contrastive Projection (ACP) tackles class-incremental continual learning by using a frozen pre-trained model (PTM) with an entirely closed-form feature-adaptation pipeline. It first projects PTM features into a higher-dimensional random space, then applies an analytical contrastive projection that pulls same-class embeddings together and pushes different-class embeddings apart in the closed form solutions type, without any gradient-based training of the PTM.", "questions": "I will be happy to update the scores if the authors can effectively address the following questions. \n1.\tWhy are exemplars required despite the strong generalization capabilities of the pre-trained models?\n2.\tCan you compare the performance with and without random projections in the ablation studies?\n3.\tHow is negative repulsions different from the underlying mechanism of contrastive learning containing both positive and negative data? (SimCLR[1] for example)\n4.\tWhy isn’t forgetting performance compared? This gives better insight into the performance numbers, helping understand the stability-plasticity tradeoff. \n\n[1] A Simple Framework for Contrastive Learning of Visual Representations", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths – \n1. Contrastive projection layer that is trainable in a non-iterative closed loop form.\n2. Pseudo replay features to train final ELM classifier, requiring synthetic replay but only through closed-form updates.\n3. Extensive experiments conducted with different PTM backbones and datasets.\n\nWeakness – \n1. Through the strong generalization capabilities of PTM, why do they still require replay of samples.\n2. Banking heavily on a prior work RANPAC[1] and adding the ACP layer on top of the well performing RANPAC. \n3. Ablation studies should take into consideration of removing random projections and then comparing the performance. \n4. It is unclear how contrastive projections is different from negative-repulsion.\n[1] RanPAC: Random Projections and Pre-trained Models for Continual Learning (Mark McDonnell, Dong Gong, Amin Parvaneh, Ehsan Abbasnejad, Anton van den Hengel)", "was_revised": true, "final_justification": "Authors has addressed major concerns raised by the reviewer, which is reflected in the final rating.", "rebuttal": "We acknowledge the similarity of our method to RanPAC; however, RanPAC directly uses features from the frozen PTM without adapting them to downstream task data. Our motivation was to address this limitation by introducing the contrastive projection, which enhances feature quality before classification.\n\n- **Question 1:**  \n  Our method has a contrastive projection (CP) layer that improves the features by pulling together samples from the same class and repelling class means from one another. This projection is learned analytically based on the class means and the Gram matrix of the PTM features, and does not require any exemplars or replay data.  \n  \n  However, the prediction is performed by an ELM classifier built on the output of the CP layer. In principle, we could also learn the ELM classifier analytically (similar to the CP layer), but this would require storing the class means and Gram matrix of the projected features. Unfortunately, the CP layer changes with each new task — each time a task is added, the projection is updated — so unlike the PTM, the output space of the CP layer is not fixed. Therefore, to compute these statistics in the new space, we rely on generated pseudo-replay data.  \n  \n  Note that if we remove the ELM classifier and use an NCM classifier directly with the target prototypes, we no longer need the pseudo-replay data. The results of the NCM classifier are slightly worse than those of ELM, but still outperform the baselines, as shown in row 3 of Table 3.\n\n- **Question 2:**  \n  Thank you for the suggestion. We have included a comparison without the random projections. The results below show final accuracy using the DINOv2 backbone:\n\n  | proj\\_dim     | CIFAR-100 | ImageNet-R | CUB   | T-ImageNet | Cars  |\n  | ------------- | --------- | ---------- | ----- | ---------- | ----- |\n  | no projection | 90.35     | 83.29      | 89.34 | 85.30      | 87.29 |\n  | 1000          | 90.64     | 84.01      | 89.56 | 85.48      | 88.23 |\n  | 2000          | 91.35     | 85.15      | 89.97 | 86.24      | 89.93 |\n  | 5000          | 92.15     | 86.60      | 90.48 | 87.71      | 90.65 |\n  | 10000         | 92.75     | 86.86      | 90.60 | 88.11      | 90.73 |\n\n  We observe that using no projection performs slightly worse than setting \"proj_dim=1000\". As the projection dimension increases, accuracy also improves. Note that the original feature dimension is \"d=768\".\n\n- **Question 3:**  \n  Conceptually, our approach follows a similar idea as SimCLR and other contrastive learning methods: pulling same-class samples together and pushing different classes apart. The key difference lies in how these objectives are achieved. SimCLR and similar methods rely on gradient-based optimization to learn embeddings using a contrastive loss, which is not well-suited for continual learning due to the incremental nature of learning and catastrophic forgetting from backpropagation. Our motivation is to achieve the same contrastive effects analytically, so we can support incremental updates while avoiding forgetting (also see the forgetting results below).\n\n- **Question 4:**  \n  We did not initially report forgetting metrics because our method, like most prototype-based methods, is inherently immune to catastrophic forgetting. This is because we operate on a frozen PTM, and all statistics (class means and Gram matrix) can be incrementally updated without overwriting previous information. Note that even if we had access to all data simultaneously, we would end up with the same class means and Gram matrix, indicating that our approach does not suffer from the traditional forgetting.\n\n  Although this might not hold for the final ELM classifier, which is trained using pseudo-replay, we found its effect to be minimal in practice. This also explains why our method can achieve accuracy on par with joint training. To empirically support this, we have included additional results under the task-incremental learning (TIL) setting, where the task ID is known at inference time. We present the matrix A[t][i], whose elements represent the accuracy on task *i* after learning the first *t* tasks on CIFAR-100 with 10 task splits, using DINOv2 as the backbone.\n\n  The matrix A[t][i] is shown below:\n\n      0.987   -       -       -       -       -       -       -       -       -    \n      0.987   0.981   -       -       -       -       -       -       -       -    \n      0.989   0.978   0.980   -       -       -       -       -       -       -    \n      0.988   0.981   0.979   0.984   -       -       -       -       -       -    \n      0.988   0.975   0.981   0.986   0.984   -       -       -       -       -    \n      0.987   0.977   0.978   0.982   0.980   0.985   -       -       -       -    \n      0.988   0.973   0.978   0.982   0.980   0.984   0.958   -       -       -    \n      0.987   0.976   0.976   0.979   0.979   0.983   0.955   0.988   -       -    \n      0.985   0.973   0.977   0.979   0.979   0.983   0.957   0.984   0.951   -    \n      0.986   0.973   0.977   0.978   0.981   0.983   0.955   0.984   0.947   0.979\n\n  We chose the TIL setting for this analysis because it provides clearer insight into forgetting. In CIL, accuracy will naturally drop as more tasks are learned, not necessarily due to forgetting, but because the classification problem becomes increasingly more difficult (e.g., distinguishing between 100 classes is harder than between 10).\n\n  In contrast, TIL keeps the classification difficulty fixed because the task ID is provided at inference time. For example, task 1 always involves classifying among the same 10 classes, regardless of how many tasks have been learned. If forgetting occurred, it would show as a drop in earlier task accuracy. However, as seen in the matrix, the first column (task 1 accuracy) remains nearly constant across all steps. The same applies to other columns, indicating our method retains prior knowledge effectively.\n\n\nWe appreciate your comments. If we have addressed your concerns, we would be grateful if you could consider updating your score."}]

Author rebuttal:

Meta-review: This paper proposes Analytical Contrastive Projection (ACP), a novel class-incremental continual learning method that combines analytical closed-form updates with contrastive feature adaptation. The approach leverages frozen pre-trained models, a contrastive projection layer, and pseudo-replay with shared covariance, achieving strong results across multiple benchmarks. Reviewers praised the method’s conceptual elegance, efficiency, and thorough experimental validation, with ablations confirming the contributions of key components. Main concerns included the readability of Lemma 4.1, reliance on strong PTMs, fairness of some comparisons, and clarity of presentation; however, the rebuttal provided convincing clarifications, additional experiments, and commitments to improve the exposition. Overall, the reviewers agreed that the strengths outweigh the weaknesses, and the paper makes a solid and impactful contribution to continual learning. The simplicity and elegance of the method make it stand out of the other submissions, especially given how many papers achieve performance improvements at the cost of overcomplicated setups.
Decision: Accept (spotlight)