Continual learning via probabilistic exchangeable sequence modelling
Authors: Hanwen Xing
Christopher Yau
Venue: Accepted by TMLR ()

Abstract: Continual learning (CL) refers to the ability to continuously learn and accumulate new knowledge while retaining useful information from past experiences. Although numerous CL methods have been proposed in recent years, it is not straightforward to deploy them directly to real-world decision-making problems due to their computational cost and lack of uncertainty quantification. To address these issues, we propose CL-BRUNO, a probabilistic, Neural Process-based CL model that performs scalable and tractable Bayesian update and prediction via probabilistic exchangeable sequence modelling. Our proposed approach uses deep-generative models to create a unified Bayesian probabilistic framework capable of handling different types of CL problems such as task- and class-incremental learning by modelling data from different tasks as sequences of exchangeable random variables, allowing users to integrate information across different CL scenarios efficiently using a single model, and give easy-to-interpret probabilistic predictions without the need of training or maintaining separate classifiers. Our approach is able to prevent catastrophic forgetting through distributional and functional regularisation without the need of retaining any previously seen samples, making it appealing to applications where data privacy or storage capacity is of concern. Experiments show that CL-BRUNO outperforms existing methods on both natural image and biomedical data sets, confirming its effectiveness in real-world applications.

Published in Transactions on Machine Learning Research (10/2025)
Continual learning via probabilistic exchangeable sequence modelling
Hanwen Xing
Jaruen.zingg@urh.oo..cm
Nuffield Department of Women's and Reproductive Health University of Orford
Christopher Yau
christopher.gaate www.h.rrrrroocc.....
Nuffield Deparbment Women's and Reproductive Health University of Oxford & Health Data Research UK
Reviewed on OpenReview: //tps:// openrevie.. net/ forum? id= fDnAsRUkOF
Abstract
Continual learning (CL) refers to the ability to contimuously learn and accumulate new knowledge while retaining useful information from past experiences. Although numerous CL methods have been proposed in recent years, it is not straightforward to deploy them directly to real-world decision-making problems due their computational cost and lack of uncertainty quantification. To address these issues, we propose CL-BRUNO, a probabilistic, Neural Process-basee CL model that performs scalable and tractable Bayesian update and prediction via probabilistic exchangeable sequence modelling. Our proposed approach models to create a unified Bayesian probabilistic framework capable uses different types of CL problems such as task- and class-incremental learning of handling by modelling data from different tasks as sequences of exchangeable random variables, allowing users to integrale information across different CL scenarios efficiently using a single model, and give easy-to-interpret probabilistic predictions without the need of training or maintaining separate classifiers. Our approach is able to prevent catastrophic forgetting through distributional and functional regularisation without the need of retaining any previously seen samples, making it appealing to applications where data privacy or storage capacity is of concern. Experiments show that CL-BRUNO outperforms existing methods on both natural image and biomedical data sets, confirming its effectiveness in real-world applications.
1 Introduction
Continual learning (CI.) enables an intelligent system to develop and refine itself adaptively in accordance with real-world dynamics by incrementally accumulatiig and exploiting knowledge gained from previous experience without the need to train any new model from scratch (Hassabis et al. 2017). The main challenge CL. has to tackle is known as catastrophic foryesting, which refers to previously learned knowledge being drastically interfered by new information (McCleland et al., 1995; McCloskey and Cohen 1989). In order to deliver accurate and trustworthy predictions, a CL model in practice should, on one hand, be able to integrate knowledge efficiently based the stream of new inputs from dynamic data distributions (learning plasticity) and, on the other hand, maximally retain relevant information from the past and prevent catastrophic forgetting (memory stability). The competition between these two conflicting objectives is known as stabilily-plasticii dilemmaa, which has been widely studied from both biological and computational perspectives DDizzler et al. 2015 Parisi et al. 2019).
Numerous methods and strategics have been developed address the CL problem under different scenarios Wang et al. b024 Regularisation-bass methods (Kirkpatrick et al.] 2017 Schwarz et al. 2018 Wang et al.

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aim to retain knowledge from history by introducing regularisation terms to balance the old and new tasks. Such regularisation can either be at a parameter level, e.g. minimising changes to key model parameters (under some data-driven parameter-wise importance measure) as new tasks are being learnt (Aljundi et al.)
2021
2018
Zenke et al. 2017). or at a functional level using c.g. knowledge distillation to prevent the model's s
performance on previous lasks from drastic deterioration (Michel et al. 2024 Rudner et al. 2022 Titsias
ct al.
2019). Architecturo-bassee CL approaches (Thaaa and Li| 2024 Gurbuz and Dovrolis, 2022 Mallya
jet al.
2018 Dhar et a 2019) seek to mitigate catastrophie forgetting and inter-task interference by allocating
specific sets of parameters to different tasks. Wortsman et al. (2020); Xue et al. (2022) Kang et al. (002
use binary masks to select and isolate the subset of dedicated parameters for different tasks in a fixed-size
model. Hung et al. (2019); Draelos et al. (2017) accommodate additional tasks by dynamically expanding the
model archilecture, providing additional model capacity before the model "saturates" as more incremental tasks are introduced. Another popular approach is rehearsal-basee methods (Robins) 1995) where historical information is retained by approximating and recovering historical data distributions. [Wen et al. (2024); [Shim et al. p0211; Aljundi al. (2019); Rebulli et al. (2017) retain distributional information by selecting and storing representative samples from the old data. Despite its conceptual simplicity, such approaches known experience replay can be infeasible due to storage or data privacy constraints. Generative replay methods (Petit et al. 2023 Chen et al. 2022 Egorov et al.
2021 Shin et al., 2017) address this issue by summarising old data distributions as generative models, and replay generated data instead of the actual samples.
In practice, experience-replay methods such as Jha et al. (2024) and Wen et al. (2024) are computationally intensive and require storing historical data as part of their memory states, which could be infeasible in
many applications due to privacy or storage concerns. Generative (Petit et al.,
2023
Gopalakrishnan et al.,
2022. Wu ct al., 2018) and regularisation-baseed CL methods (Dohare ct al.
2024 He and Zhu 2022 Li
and Hoiem, 2017) ) avoid the need of storing historical data, but are also computational costly and lack statistically principled updating or uncertainty quantification schemes. These limitations make it difficult to deploy them directly to real-world problems. To address these limitations, we propose Continual Learning Bayesian RecUrrent Neural mOdel (CI-BRUNO), a probabilistic, Neural Process- based CL model that performs scalable and tractable Bayesian update and prediction. CL-BRUNO utilises deep generative models, and extends the exchangeable sequence modelling framework given by Korshunova et al. (2020) (Conditional-BRUNN) to provide versatile probabilistic framework capable of performing probabilistic label and Lask-identily estimation, and handling different CL scenarios such as task- and class-incrementaa learning using a common, likelihood-baat problems using a single CL-BRUNO model in a statistically principled fashion, allowing knowledge to be accumulated more efficiently. Our proposed method uses generative replay (Shin et al. 2017 Wu et al. 2018 as regularisation to prevent copast forgetting without the need of retaining previously seen samples, making it more appealing in real-world applications where data privacy or storage capacity is of concern. Numerical experiments show that CL-BRUNO outperforms existing methods on both natural image and biomedical datasets, confirming its effectiveness. This paper is structured as follows: We first give technical background in See 2 then describe the proposed CL-BRUNO model in See B We highlight its connection with existing works in See and report numerical experiments in Sec We conclude the paper with a brief
updating scheme. This means that users can handle different types of CL
discussion.
2 Background
In this section, we give the technical background relevant to our proposed method.
2.1 Normalising flow
A discrete Normalising flow (NF) (Rezende and Mohamed 2015; Dinh et al. 2016: Papamakarios et al.)
2017) models a continuous probability distribution by transforming simple-structured base distribution (e.g. isotropic multivariate Normal) to the more complex target using a bijective transformation T parameterised as composition of series of smooth and invertible mappings fI, JK with easy-lo-compute Jacobians. This T is applied to the "base" random variable 20 Po, where 20 E R and is the known base density.
Code reproducing the reported results can be found in http:://ehhhbb.amm//wwwnggg///// bruno
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Let 2k = o... fi for k k= I,.,.., K. By applying change of variable repeatedly, the final output where Jr is the Jacobian of the mapping fs- The 2K has density (=() - (o( I |det (x(x=1)) final density pk can be used to approximate target distributions with complex structure, and one can sample from PK easily by applying T = fK fK-1 o .... fi to 20 Po- In order to evaluate pk efficiently, we are restricted to transformations fk whose det Jx(z) is easy to compute. For example, Real-NVP (Dinh et al.) 2016) uses the following family of transformations: For m E N such that 1 < m < d, let 21:m be the first m entries of 2 E R.,, let x be element-wiat multiplication and let Pa. Ox : R + RD- be two neural nets. The smooth and invertible transformation y = fx(z) for each step & in a Real-NVP is defined as
V1am = 21am+ Um++ = (4x(21mm) + oi (21mm) x 1md
(1)
The Jacobian Js. of fk is lower triangular, hence det Jx(=)= = D-m of on (ztm). Continuous normalising flows (Chen et al. 2018 Onken et al. 2021 Lipman et al.) 2023) further
1=1 ask (21m)) where du.(21mm) ) is the ith entry
extend model ficxibility by replacing the scries of transformations by a vector field continuously indexed by pseudo-time.
2.2 Conditional-BRUNe
2020: proposed Conditional Bayesian Recurrent Neural model (C-BRUNO), a Neural Korshunova et al.
Process (Garnelo et al. 2018 Kim et al. 2019 Xu et al. 2024) which models exchangeable sequences of high- dimensional observations conditionally on a set of labels. Given a set of feature-label pairs {X,, ) where X, RRD is a feature vector and y its corresponding label, C-BRUNO assumes that the joint distribution p(X1, ..... Xxlyi,..., uN) = p(Xx(1): Xa(N) -,()))))))))))) for any permutation æ. In other words, this permutation invariance implies that the model is agnostic to the ordering of the pairs {Xi, Therefore, the sequence is exchangeable as any reordering of the sequence does not change the joint distribution Xwly,... UN). C-BRUNO models
.N) by first transforming each feature vector X, into a latent variable 2; = fo(X;;y), where fo(X: RD + R is a bijoctive conditional Real- NVP depending on label y- Denote 2/ as the dth entry of 2, It then models each dimension d of the exchangeable latent sequence { as an independent 1-D Gaussian process with Var(=(")) = u(4) and ((d))= - p(()) for all i, = I,,,,,,, N, where 0 < p(a)) < p(d) are trainable covariance parameters (Note that we need 0 < p(dd) < p(d) to ensure positive definiteness of the covariance matrix). In other words, C- BRUNO assumes that p(z ZN) = I pa(1z="))N )س=1)) where pa((2("),' = (V(t
(d)
Cor(z! (d) .zj
(d) Jm=1; ON, Ea), ON is zero vector of length N, and Eg is a N N covariance matrix with diagonal clement yld) and off-diagonal element (!4), Suppose the bijective transformation So and the covariance parameters (pid), (p()),,())) _(()) )d=1 have been chosen. C-BRUNO generates a new sample from the predictive distribution "(X"lv", ..NN,, B1:N) conditioned on new label y" and previously seen feature-label pairs by first sampling z" ~ p(z" [Z1.v) and then computing x' fo (z" vz":"") The predictive likelihood p(XN+1 IN X1:N+y1:N) of a now pair (XN+1. WN+1) can be evaluated a similar fashion. Thanks to the specific covariance function used in C-BRUNO, sampling from and evaluating p(z"|z, (z using the recursive formula given in Korshunova et al. (2020) has a time complexity O(N) instcad of the general case O(N3). This greatly improves the scalability of C-BRUNO as it scales linearly with both sample size N and data dimension D.
Our proposed CL-BRUNO is built on the C-BRUNO framework: The exchangeability assumption in C- BRUNO imposes a permutaaion-invaaiann architecture to the model. It includes the conditionally identically and independently distributed (conditionally i.i.d.) assumption as a special case, therefore provides a more flexible modelling framework to reason about future samples basod on the observed ones with minimal additional computational cost, and has been proven useful in e.g. few-shot learning and anomaly detection Korshunova et al.) 2020). This feature is appealing in many CL scenarios where new datasets arrive incrementally in batches: In comparison with generative-replay methods based on i.i.d. assumption, e.g. Scardapane et al. (2020), modelling samples in each datasct as an exchangeable sequence using C-BRUNO allows users to better capture and aggregate distributional information such as sample sizes and inter-sample correlations. To see that, note C-BRUNO's Gaussian process predictive base distribution p(z") (zi.) is updated as the sample size N increascs, while models basod on the i.i.d. assumption, c.g. [Scardapane et al. (2020), ignore this dependency between z" and Zı,N, and set p(z" (ZI,N) = p(z") to be some user-specified distribution such as an isotropic Gaussian. This aggregation feature is useful for probabilistic prediction and
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inference in natural and statistically principled fashion. Furthermore, our proposed CL-BRUNO leverages the efficient and exact density evaluation feature of C-BRUNO to directly estimate probability distributions of both class and task identity of any test data (Sec 3.2). This means that compared with existing methods such as Petit et al. (2023) and Wu et al. (2018), our proposed method does not require training or maintaining separate neural network based classifiers, making computationally more efficient. Additionally, the output of CL-BRUNO can be interpreted as approximate Bayesian classifiers, which is more interpretable than the logit scores given by neural network based classifier. We give details of the proposed CL-BRUNO in the following section.
3
Method
In this section, we give technical details of our proposed method. We start by specifying the notation. Suppose there is a sequence of tasks labelled by t -= 1, ..,,...,TI Assuming all tasks are classification problems with potentially different or disjoint label spaces (extensions to regression problems are straightforward). We suppose each task & ..,, T is associated with dataset DD = (A where X; ) is the feature set, X₁, E Fd is the feature vector of the i-th sample in the t-th task, Vi (Y is the label set, Y [I.... G.} is the i-th sample's corresponding label, and Nr, C. are the sample size of Dr and the number of distinct labels in the t-th task respectively. Similar to Korshunova et al. (2020), for each dataset.
D. = J',, we assume that (a) the corresponding density function (x,, P1) factorises as
Pe(Ke. -(X.) p(XI, Xt..lt, YI.. YN..) II IPY,,)t).
(2)
i.e. Yt are generated i.i.d. from some task-specific label prior p(-1() independent to the generative process of Ne and (b) X2 is an exchangeable sequence of feature vectors conditioned on both task identity and label set De, i.c.
p(X1, ... ilt, Yi,,,.., YN..) p(Xa(1)) wn (at Ya()), Y=(N),))
(3)
for any permutation π of size N..
We propose Continual Learning BRUNO (CL-BRUNO) under the distributional assumptions given above. The key motivation of CL-BRUNO is to formulate continual learning problems as modelling streams of data (one for each task), which may come in batches, as collection of exchangeable sequences. From this perspective, once N samples from a stream of data (i.e. continual learning task) have been observed, users can then extract. distributional information from historical observations by modelling the joint distribution P(XI,N,, YiN..)) and predict a new sample and/or the associated label by inferring the one-step-ahead con- ditional distribution p(XN+1.. YN=L.l/N:: YI.N.)) or ([VN+II/XI.N4L. e). Specifically, CL-BRUNO consists of two modules: a C-BRUNO model that models feature vectors X4 from different task / as exchange- able sequences, and an approximate Bayesian inference pipeline for label and task identity estimation. Let (t, be a C-BRUNO model that approximates p(X,),,)):) the true conditional distribution of feature vectors X given (t.).). CL-BRUNO aims to train a collection of C-BRUNO models {p(X)tt. [t. )= incrementally over an expanding range of (t) by continually learning generative models p(XY [1',' )er)) from new datasets Dy, while preventing those it has learnt from previous tasks from being interfered or disrupted: If the incrementally trained C-BRUNO models could give p(X,,t, J1. that well approximates p(X, it. v.) for all previously seen tasks t throughout the continual learning process, then users could handle queries such as estimating the task identity associated with a new feature vector X*, or computing M t, Dz), the approximate posterior distribution label Y* associated with a new X* from the t-th task based on historical data any stage of the continual learning process in a statistically principled fashion.
3.1 Incremental learning scheme
In this section, we discuss the parametrisation and incremental training procedure of CL-BRUNO. Thanks to the i.i.d. assumption on labels (3r)T in 2 the task-specific label priors p( can be estimated directly using their population proportions. For the remainder of the section, we focus on learning the conditional distribution of Xr Specifically, the C-BRUNO model used in our proposed method consists of a Conditional
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+R² parameterised by 0 as bijective transformation that depends both task identity I and label Yg- We parameterise each task identity 1 and each of the unique labels {1..... Ct} in the t-th task as trainable embeddings Tr, 8 E E respectively for j = I,...,C Ct and t = 1,2..... For the rest of the paper, the embeddings (ri, {85a) C 1= ) are viewed as parts of the Conditional Real-NVP parameter 0. For t= 1.2...., let 2,, = (X,,, t, Yi,)) for all == 1...., No, 2 = {z,, 1 and px, be the task-spocific (d) latent distribution parametrised by A {vt") Pr } as described in See 2.2 Denote À A= {Ae)t=,,,.... the set of latent distribution parameters. With a slight abuse of notation, we see X1:0,1 Y1:0,0 and 21:0,1 as empty sets for the rest of the paper.
Real-NVF fo(:t,Y)) R
N.
Learning from scratch
If there is no historical information or previously seen data, then we can extract and retain information in these datasets by training a series of C-BRUNO models that approximate p(2; (1))) for all t = I,...,? T by minimising the negative log likelihood
task-wise log likelihood
Σ
(X
(4)
T N
log po.,, (X,, 114- V13-1,t)
T.N,
log Ps. (Z.:/1111)))1. det ifo(X,,it,Ye.) Vis) ))
Σ 1,=1
0Xic
as suggested by Korshunova et al. (0020) where pe, (Xelt, denotes the C-BRUNO approximation to p( Now, suppose (6, arg ming. L(,, A; (Di -T and 2 = fa( t, Yu,) for all i -....., Nr and & = 1, I....,T. T. Then for any task = 1,..., T, p(X* t, D.), the predictive distribution of new observation X given label Y and historical data D., can be summarised by a generative C-BRUNO model with bijective mapping fo and multivariate Gaussian predictive distribution Ps, (+121.N..). See also Fig (a) for schematic illustration.
We stress that even though Px(T) (-121:,.a) is a multivariate Gaussian distribution whose mean and covariance depend on 2I.N... evaluating sampling from it does not require access to 21:N, see also Eqn (7) in Korshunova et al. (2020). As result, once the generative model has been trained, users can use it as proxy of (Dr)/=1, and handle queries without the need of revisiting any historical data. This learning strategy allows users to retain knowlodge and information from different tasks without storing any sample from any dataset. However, under a CL setup, such a learning scheme via joint likelihood maximisation is not feasible as datasets D,s are observed in a sequential fashion, and we do not necessarily have access any previously seen datascts. On the other hand, sequentially maximising L(0, X; D,), 1,2,... naively whenever new dalaset D, arrives will drastically disrupt what it has learni from historical data due to calastrophic soryelling [McCloskey and Cohen 1989), rendering it unusable for any prediction task except for the most recent one. To address this issue, our proposed CL-BRUNO uses generative replay to prevent catastrophic forgetting through both distributional and functional regularisation. We demonstrate our incremental learning strategy under two common CL. scenarios known as Task- and Plass-Incremental learning. Other scenarios such as Domain- or Instance- Incremental learning (Wang al. 2024) can be handled in a similar fashion.
Task-incremeet learning
Suppose our CL model has been trained on T' tasks. Let facry, (pxm (+2.,,,)) be the trained normalising flow and predictive latent distributions respectively. Suppose now a new task T + 1 and the associated dataset Dr+1 arrive. Our goal is to update the generative model so that it adapts to Dr+1 while retaining
It straightforward replace it with more sophisticated alternatives CCen al. 2018
Lipman al. 2023 Shi al.
2024 We do not consider them here for sake conceptual simplicity.
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(a)
Training/ Knowledge aggregation
Updating
Approximating
Inference/ Generation
p(X,,rl4, V1c)
p(X2a & Vins, X1c)
p(XMar VEN,, X1N
p( Y", VEN,, (18R))
Feature vector
1
11
2
N
X
Label- dependent mapping
f(-lt, x2.)
s(-1s, NN,))
Latent variable
11,t
22,4
N
0b1 pi(#1,) det 2x.1
082z pil#aal dett 2x5s
palaNallii 12) det
Ba 200
p(a (&n,,))
Du" . det 8x*
(b)
Task-incremental Learning
pl- (2I.N.a)
zi:00'1
D'
p( (112))))))
f old
frew
p(-121:N,.7)
D/r
p(-121,N7:7))
Generating pseudo datasets from old model
Dr+1
p(11 iT++1)
Inherited from old model
Generated from old model
Leamt phase
Figure 1: (a) Schematic illustration of how C-BRUNO learns the sequence distribution p(A())) II. (X.,)) 1.i-111 YIa,)). For each feature vector Xi,t in the sequence, C-BRUNO first transform to the Yr,), corresponding latent variable using the label-dependent mapping 21,0 Yr.)) then approximates the one-step-ahead conditional p( Y1...) by po(21_c(210-11) det ax,,
Exchangeability is guaranteed by the specific covariance function in the latent distribution p(2I.N.) In the inttoratioonnffeeenn phase, given a label Y", a new latent variable z" is first generated from p(-121.N.), multivariate Gaussian whose mcan and covariance depend on the observed sequence, and then transformed to the generated feature vector X f-= Y*) under label Y*. (b) Schematic illustration of TIL in CL-BRUNO. Pseudo datasets are generated from the previous latent predictive distributions p(-121.N,.)) and the bijective mapping fold- Note that in the TIL phase, the new bijectíve mapping fnew learns to 1) map the new dataset DT+1 to a series of latent variables and compute the corresponding latent predictive p(- (2..N+..,44) (i.e. learning from new data) and 2) map the pseudo-datasets D. back to latent variables that resemble samples drawn from the previous latent predictive distributions p(-121.N..)) (i.e. retaining learnt knowledge).
0#..1
the historical knowledge the old generative model has learnt regarding the previous T tasks. This scenario is known as
learning (TIL) (Van de Ven and Tolias 2019).
To achieve this goal, update the old CL-BRUNO by estimating 1) new bijective transformation fo parametrised by 0, and 2) Ar+1 for the latent distribution of the T'+ 1-th task. The rest of the old CL-BRUNO model (i.c. latent distributions associated with previous tasks) are kept unchanged. Specifically, we first ,
generale pseudo datasets D'- = {X,,, Y "'' for each previously seen task = 1, 2..,..77 T from the old CL-BRUNO model as follows. Denote N' the size of pseudo datasets, for each D/ and j = 1,"..,,', the pscudo label Yi, associated with the t-th task is sampled according to the population label proportion of D,, then the pscudo feature vector X/,, is generated by first drawing latent variable z Ps. (-22...,.))) then set X/,6- fgcry (2), Y/,)) Once the T pseudo datasets based the old CL-BRUNO has been generated, one

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then update the CL-BRUNO by updating parameters {0, Ar+1) using the joint likelihood optimisation approach in Eg based on the augmented dataset. To further prevent the historical knowledge in facry from being disrupted by the new dataset Dr+1. 1. we adopt the functional regularisation technique in Wu et al. (2018) that penalises the L2 distance between outputs of the old and new models generated from the same set of imput noises. Specifically, for new bijective Se parametrised by 8, the regularisation takes the form
UD++1 See Fig (b) for schematic illustration.
T.N' R(0; (C)) (DD)) = Σ (4,,t -x,,1 t,=1
where ( Yi,) and X1, are the outputs of the new and old normalising flows based on the common noise z Combining the augmented datasets and the functional regularisation, the new generative model fo and the base distribution parameter λT+1 of the new task T ++1 1 under the TIL scenario is chosen by solving Aing (O,,(0, AT+1) where (on,(0, Ar41) is the regularised joint negative log likelihood
neg log likelihood of new task
Ltn. (0, AT+1) = L(0, 11 Dr+i) + on (1 (T. (PUTL)) +a2R(0;00) (PD)L
(6)
distributional regulariser
functional regulariser
where
T.N' L'(0, L'00 1T: =- Σ log Px(r) (fo Yj,) Ne)
T.N' Σ b==1
Ofe(X) ( ox,
log
det
(7)
is the negative log likelihood associated with the T pseudo datasets and 0r 02 > 0 controls the strength of regularisation. Note that in comparison with Eqn 4 the latent distributions in T are informed by historical samples (2I.N,.) we expect fa to be able map X',, back to latent variables that resemble samples drawn from p(-121:N.1). See also Fig 1 (b).
class-nncrmental learning
So far focused task-incremental learning where all samples associated with task are presented to the model as single dataset Dr+1. It is not always the case in practice samples associated with the same task may also come in batches. In particular, each batch may contain labels not seen in any previous batches. This scenario is known as CL-BRUNO handles CIL under the sccnario where labels different data batches are disjoint (the extension to the non-disjoint case is straightforward).
learning (CIL) (Zhou et al. 2024). We here demonstrate how
Our goal now is to learn from a new batch of data D( (x M MO)
3 3, associated with previously seen and known task & E {1, such that Y, * YG for all y in D.") and YG,x in Da (i.e. disjoint labels). Such problem can be addressed by updating the normalising flow fo using the same regularisation approach as in Sec 3.1 Similar to LTn. in Equ 6 CL-BRUNO under the CIL scenario is updated by finding a So that minimizes a regularised augmented negative log likelihood
neg log lkd of new batch given old
(e) log Po.
Po,x (or (z. (() D2) L', (2 + (DD))_)).
(8)
where
1 2..)..) x det asx(X x,(
Yixk
log Po Po,ser
(2 1k. (0) Dx)) Σ
log
PRTTi (2 11)
(9)
oxp1)
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is the conditional likelihood of the new feature set x = (x J given the corresponding label set (1)
D = (x No and previous data batch D& associated with the same task, and 2 fo Y( is the transformed latent variable generated by the normalising flow fo. Note that given the prodictive (1) (1)
latent distribution Pxcr (-121:N,.k) from the old CI-BRUNO, Pxcro (2,,k Pi 1,k7 21)Ne.))) in 9 can be evaluated
efficiently using the recursive formula in Korshunova al. (2020) for all i= I,..,, N without access to Kk In comparison with 6. the parameter of latent distribution X( associated with task k in Len is taken from the old CL-BRUNO and not updated alongside with 0. We choose to do so as it simplifies the computation and ensures the tractability Px(r) (-121:N,.k). This choice can also viewed as an additional regularisation that aims to mitigate the impact of catastrophic forgetting. See Supplementary material A.1 for additional discussion Len.
3.2 Label and task identity prediction
In the previous section, we discussed a unified incremental learning strategy for both task- and class- incremental learning. In particular, we focused on incrementally modelling the feature vectors p(Xelt, for tasks I....,T. T. In this section, we discuss the probabilistic inference pipeline for label and task identity prediction. Let Jacr: (Px (-Br...) over 7" tasks. Let X be generic test point and Y* be the unknown label of interest. We start from the case where the task identity t known. Under the assumption given in we approximate the posterior label distribution p( X*, (D) by
be the normalising flow and predietive latent distributions trained
pty"lt, (D)))) x P (X" D.)p(Y 8) x Px, (zy.,,, det afger, (X*;t, ax*
p(Y*)t), (10)
for all Y (l, C,), where 2y.,- = Sscry (X*; YY) is the transformed latent variable associated with X* conditioned on label Y", and (t) is the prior distribution over the C2 classes associated with the t-th task.
However, the lask identity associated with X in practice ice is not always available, and task identity estimation is itself a challenging problem in CL (Lee et al.) 2020). Here we give an mosy-to-interpret probabilistic estimate of task identity of test point X under the assumption that X* is indoed sample from the underlying generative process of one of the T previously seen datasets {Dr)T= (See Supplementary material A.2 for discussion on other possibilities). Denote p(t) user specified prior the T tasks, and C, {1...., Ct) the label set associated with the t-th task. We approximate the task identity distribution p(X* from task {((D))=)) for = -,....,T by
P(X* from task {((D))=>) x p(t)
Σ Parcy & (X* Y YCE
Y,",, (D))))(("())
(11)
which can be interpreted as the predictive likelihood of observing X the next new sample given previous ones D, averaged over all possible labels Y*. We summarise the training and inference procedures of CL- BRUNO for TIL in Alg T CL-BRUNO for CTL and their combination work similarly. In addition, if all tasks share the same label space, we can then further marginalise out the uncertainty of task identity label prediction by
T p(Y*X' (DIT - p( D.) x p(X* from task t({D.)?
(12)
This is particularly useful in biomedical settings where a single CL model incrementally learns distinguish healthy vs unhealthy from a sequence of datasets collected from patients from different hospitals or regions (i.e. different tasks).
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Algorithm 1: CI-BRUNO for TIL.
Data: Dataset (Dr)i= of the initial T' tasks; Regularisation parameters 02 2 0; Pseudo data size N' E N+ Datascts (Dr+e I of the subsequent (T + 1)th to (T + T' tasks.
Result: Predicted label and task identity a generic input X
Train the initial model from scratch by finding (6(T), Å} minimising L(O, X: (Di)=1) in Eq using stochastic gradient descent.
for f- 1 to T do
/* Here we assume that the model incorporates one new task DT+ at a time. Incorporating multiple tasks the same time works similarly.
Update the imitial model by finding (Ô(T+e') Ar+e) minimising LTIL Ar+e) given by Eq 6 which depends on the regularisation hyperparameters 01, 02, N', using stochastic gradient descent.
end
return The predicted lask identity distribution p(X* from task ((DD)) in Eq 11 and label distributions p(Y X", Dz) in Eq 10 for all .,, (I' + T) of some generic data X".
4
Related works
4.1 Bayesian continual learning
Various Bayesian continual learning methods have been developed for different tasks (Adel 2025 :: Bonnet
ct al.] (2025) and Yan et al. (2022) use sequential Bayesian inference to update paramcters of Bayesian neural networks while retaining the knowledge learnt from historical data. Raichur et al. (2025 combines Bayesian lcarning-driven dynamic weighting mechanism (Kendall et al. 2018) and contrastive learning to continually update both the parameters and the architectures of a neural network model in a CIL setting. [ha al. (2244) propose Neural Process Continual Learning (NPCL), which combines attentive Neural Processes (Kim) et al. 2019) and experience replay (Chaudhry et al. 2019), under Bayesian updating framework. Both CL-BRUNO and NPCL use Neural processes to capture uncertainty in prediction. However, we would like to highlight that NPCL uses Neural Processes to model the posterior distributions of labels p( , -prew) as a random function of task identity t, test point X* and historical data D Ppree- In contrast, our approach uses Neural Processes to model the distribution of fcature vectors p(X; ft, V+) associated with different tasks and labels. Unlike NPCL, our method leverages generative replay to retain learned knowledge without the need for storing any previous samples, making it more appealing to applications where data privacy or storage is of concern. In addition, thanks to the specific covariance function used in C-BRUNO, our proposed method scales linearly with both the sample size and the dimension of feature vector. In contrast, NPCL exhibits quadratic complexity relative to the training sample size due to the attention architecture.
4.2 Conditional generative continual learning
The generative replay strategy used in our proposed method is closely related to Continual Learning for Conditional Generation (CICCG (Wang et al. 2024), which also aims to mitigate catastrophic forgetting by recovering previously-learned data distributions. Recent CLCG methods such as MeRGANs Wu al.
(2018). BAE (Egorov et al.) 2021 Hyper-LifelongGAN (Zhai et al. 2021 and FILIT (Chen et al. 2022
use GAN [Goodfellow et al. 2020 VAE (Kingma and Welling 2013 as their underlying conditional generative models and require soparate discriminative models for label prediction. Scardapanc et al. (020) uses normalizing flows lo retain distributional information at the feature embedding level, but still requires separate encoders and discriminators. In comparison, CL- BL-BUNNO utilises a tractable deep generative model that supports both conditional gencration and density estimation on feature vectors. This enables tractable, efficient, and statistically principled label prediction and task identity estimation without the need for separate discriminators or any other modules, improving both interpretability and computational efficiency.
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5
Experiments
In this section, we first empirically evaluate our algorithm on four image benchmarking datasets. We then demonst.aae the efficacy and versatility of CL-BRUNO using two real-world biomedical datasets.
5.1 Benchmarking on image classification tasks
We evaluate the proposed method on both class and task incremental learning (IL) settings. For class- (CIT.), we use three public datasets: incremental CIFAR1O (iCTFAR-10) (Lopez-Paz and Ranzato 2017 incremental CLFARIO0(CCIAAR-
(Zenke al. 2017), and sequential Tiny ImageNet (5-TinyImage.V [Chaudhry et al. 2019 For task-IL(TIL),, we use the MNIST dataset (LeCun 1998). iCIFAR- 10, iCIFAR100, and S-Tiny ImageNee Net contain 3-channel images of size 32 x 32, 32 x 32 and 64 x 64 from 10, 100 and 200 classes, and each class includes 5000, 500, 500 training images and 500, 50, 50 test images. The MNIST dataset consists of single-channel 28 x 28 images of handwritten digits from 0 to 9, and each digit includes ~ 6000 training images and ~ 1000 test images. Under the CIL setting, the mumbers of sequential batches for iCIFAR-10, iCIFAR-100 and S-Tiny-ImageNet are (2 classes per batch), 10 (10 classes per batch) and 10 (20 classes per batch) respectively. Under the TIL setting, we follow the experiment setup in Egorov et al. (202)), and split the MNIST dataset into 5 batches, where each batch consists of images of two digits. We view each batch a binary classification task (0 vs 1, 2 3, ..... 8 9).
We compare CL-BRUNO with both experience replay-based methods including ER (Riemer et al. 2018
DER Buzzega et al. 2020), NPCL (Jha et al. 2024) and CSReL-LODE (Tong et. al. 2025 and exemplar-fie arrfeere OEWC-MACL (Wang and Huang 2024). LwF (Li and Hoiem| 2017), SSRE (Zhu et al. 2022). DS-AL (Zhuang et al. 2024). McRGAN (Wu et al. 2018). FeTRIL
methods including EWC (Kirkpatrick et al.
2017),
Petit et al. ) NICE (Gurbuz al. 2024 PRER (Scardapane et al. 2020 ReReLRR (Bogacka el. al.,
2025) and Boo-VAE (Egorov et al.) 2021 The default or recommended settings are used for all the above
methods. For all experience replay- based methods, fix the buffer size MM 500.
Our CL-BRUNO is specified as follows: We use Resnet18 (He et al. 2016) as a feature extractor (i.e. using the output of the second-last layer of Resnet18, a 512-dimensional real vector, as the transformed feature of the corresponding input image) and apply CL-BRUNO to the 512-dimensional feature vectors. Specifically, the Resnet18 feature extractor here is only trained using the images from the first batch of data in the initial state, and is then frozen for the reminder of the class- task-incremental learning process. Similar strategies have been used in exemplar-free methods such as Petit et al. (023).. (In principle, generalive model on raw images instead of feature vectors. However, we do not consider it here as our method is motivated by tabular rather than image data.) In this example, we set the mumber of coupling layers in CL-BRUNO to be 6, the dimension of class embedding to be 128, size of pscudo data N' = 128 (i.c. N' pseudo samples are generated to compute the distributional regulariser in Eq t or S for every gradient descent step) and regularisation strength a1 = 02 = 1. We report the classification accuracy on test set for each of the methods in Table [ We see that CL-BRUNO either outperforms existing exemplar-free methods achieves competitive performance across multiple experimental settings. We further report the ranking of the performance of different. methods in Supp Fig + Note that CI-BRUNO does not perform as well on S- S-Tinylmages Imagent. This is likely due to the fact that the fixed feature extractor trained on the first batch may not be sufficient to capture the distributional difference in the fortheoming data.
could directly specify
Memory overhead
We then investigate the memory overhead of CL-BRUNO in comparison with other methods using the iCIFAR100 dataset as example. Since we follow the setup in Jha et al. (2024) and Boschini et all (2022) CL-BRUNO use Resnet18, which consists of 11.7M paramcters, as backbone model. In addition to the backbone model, CL-BRUNO also maintains a C-BRUNO model consisting of ~133MM parameters, and 100 class embeddings (12.8K parameters). As a result, CL-BRUNO in total requires storing ~1.39M extra parameters in addition to the backbone Resnet18 model. In comparison, the replay-basod method requires storing exemplar samples from historical datasets instead of extra model parameters. In our setup where the buffer size is fixed at 500, maintaining this buffer requires storing 11.4MM floating point numbers, which
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iCIFAR10
iCIFAR100
S-TinyImagenet CIL
MNIST
Турe
Method
CIL
CIL
TIL
(a)
ER
0.577
0.221
0.099
0.972
DER
0.705
0.366
0.178
0.983
NPCL
0.702
0.198
0.135
CSReL-LODE
0.398
0.420
0.228
(b)
EWC
0.182
0.092
0.056
0.441
oFWC-MACT.
0.206
0.088
0.079
LwF
0.196
0.145
0.094
0.472
SSRE
0.355
0.179
0.110
DS-AL
0.408
0.205
0.122
McRGAN
0.251
0.122
0.078
0.670
FeTriL
0.417
0.208
0.115
NICE
0.551
0.203
0.120
PRER
0.412
0.197
0.108
ReReLRP
0.399
0.058
0.033
Boo- Boo-VAF
0.892
CL-BRUNO
0.257
0.146
0.056
0.734
CL-BRUNO 0.421
0.212
0.117
0.947
Table 1: Classification accuracy of different CL methods iCIFAR10, iCIFAR100, S-Tinylmagenet and MNIST. indicates method is not applicable to the problem setting. (a) Experience replay with buffer size M 500 (b) Exemplar-free. The best and second best results in (b) are highlighted in boldface and underline respectively. CL-BRUNO refers to CL-BRUNO without functional regulariser.
is larger than the memory required by CL-BRUNO. In addition to exemplar samples, NPCL also requires maintaining an attention-based network consisting of another ~12.8 parameters. Among exemplar- free models, FWC, LwF, oFWC-MACL. and DS-AT, maintain single discriminative models based on Resnet18 or Resnet34, which consists of ~ 11.7M and 21.1M parameters respectively. MeRGAN requires ~7.15M parameters under the default setting. FeTriL has a smaller extra memory requirement (~0.3M parameters) in addition to the backbone Resnet18 or Resnet34 it encodes and stores historical data sets fixed-length vectors instcad of a full generative model. Although McRGAN and FeTriL require less memory than CL- BRUNO, we see that CL-BRUNO outperforms them in terms of classification accuracy. In addition, we would like to highlight that CL-BRUNO is more versatile than exemplar-free CTL methods as it offers additional functionalities such as task incremental learning (Sec 3.1, task identity estimation (Sec 3.2 and outlier detection (Supplementary material A.2)
Prediction calibration
To demonstrate CL-BRUNO's uncertainty quantification feature, compare the Expected Calibration Error (ECE) (Guo et al. 2017) of CL-BRUNO with both experience-replay and exemplar-free CL baselines in a similar fashion to (Jha et al. 2024). In Table 2 we see CL-BRUNO attains lower EGE than exemplar-free CL methods with similar accuracios (FeTriL and NICE), and show comparable performance to experience- replay methods on both iCIFARIO and iCIFAR100 datasets. This suggests that the probabilistic nature of CL-BRUNO benefits it in terms of prediction calibration.
Tha ct (2024) reported classification accuracy 37.4% and 15.3% the iCIFAR100 and S-TinyImagend datasct. Our independent using the publicly available implementation provided by the authors under the sctup gave classification accuracies 19.8% and 13.5% respectively. Our code reproducing the NPCL results iCTFAR100 and TinyImageeet can be found here
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Experience replay
Exemplar-free
Dataset/ /alaset/Method Method
ER
DER
NPCL
FeTriL
NICE
CL-BRUNO
iCIFARIO
0.455
0.299
0.210
0.310
0.268
0.245
iCTFAR100
0.646
0.248
0.199
0.358
0.472
0.303
Table 2: Expected Calibration Error (ECE) of different methods. Lowest ECE in Exemplar-free methods is highlighted in boldface.
Ablation study
In Sec 2 we have demonstrated how the distributional regulariser L' naturally arises from the Bayesian updating rule. However, the inclusion of the functional regulariser R is not justified. Therefore, we first investigate the role of the functional regulariser R in the training CL-BRUNO. We apply CL-BRUNO without the functional regulariser (CI-BRUNOn.=o)) to the same datasets described above, and report the classification accuracies in Table [ We see that the default CL-BRUNO outperforms CL-BRUNO by a large margin across all experimental settings. This confirms that the functional regulariser R contributes to the performance of CL-BRUNO.
We next investigate the size of pseudo data N'. We use the iCIFAR100 dataset and run CL-BRUNO under four choices of pseudo samples N = 32, N = 64, N2 = 128 and N2- = 256. The final classification accuracy of the four models is 10.9%, 17.1%, 21.2% and 22.8%, respectively, showing that increasing N' leads to a diminishing increase in classífication accuracy. We further investigate the impact of N' on the computational cost of the proposed method. The rumning times of the four models are 2569s, 2726s, 2917s, and 3562s, respectively. We see that increasing N' by factor of 8 (from 32 to 256) leads to 40% increase in the rumning time of CL-BRUNO. This also confirms that increasing N' does not drastically increase the computational cost of CL-BRUNO.
5.2 Pan-Cancer Atlas dataset
We here demonstrate CL-BRUNO under CIL scenario using the Pan-Cancer Atlas (PANCAN) dataset (Hoadley et al. 2018). The PANCAN dataset consists of pre-processed RNAscq readings of N = 10, 535 tumour samples from 33 cancer types. In our analysis, we use only the top P = 2, 000 most. variable genes as the feature vector associated with each tumour sample, and split the PANCAN dataset into groups according their cancer types: the first consists of 8 cancer types, while each of the rest consists of cancer types. Cancer types are partitioned in a way such that all 6 groups of data have similar sample sizes. Our goal is to predict cancer type from the RNAseq data of tumour under CIL scenario, where groups of data are presented to the model sequentially. In this example, CL-BRUNO to be 6, the dimension of task and label embedding to be 256, size of pseudo data N' = 128 (i.e. N' pseudo samples are generated to compute the distributional regulariser in Eq 0 or for every gradient descent step) and regularisation strength a1 = a2 = 1. Each group of data is randomly split into a training set consisting of 80% of the samples and a lest set containing the rest, and the performance measured by the misclassification rate on all test sets after the model has been incrementally trained on all training sets. We compare CL-BRUNO with three exemplar-fie CL methods: EWC (Kirkpatrick et al. 2017):
set the number of coupling layers in
LwF (Li and Hoiem
2017) and MeR-GAN (Wu et. al. 2018 under default or recommended settings. The misclassification rates on test sets are reported in Table We also demonstrate in Fig 2 aa) how CI-BRUNO
retains previously learnt knowledge by reporting the misclassification rate associated with each of the 6 test sets at each incremental learning step, and compare them with results from an oracle CL-BRUNO model that has access to all historical data (i.e. trained by directly minimising Eqn 4 at each incremental learning step. Figure 2 (a) shows how CL-BRUNO retains historical knowledge in terms of prediction accuracy compared to the oracle model.
5.3 Immune Checkpoint Inhibitors dataset
We also tested CL-BRUNO under TIL scenario using the Molecular Response to Immune Checkpoint Inhibitors (ICT) dataset (Eddy et al.) 2020). Immune Checkpoint Inhibitors designed to block (checkpoint)
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(a)
PANCAN data under CIL scenario
(b)
ICI data under TIL scenario
CIL
0.25
Oracle
Oracle
0.20
Group
Atezo
Nivo
Group
Misclassificatonn rate
Group
Misclasifiiacoon rate
0.15
Group
ti
Group
0.15
Ii+ Pembro
Group
Ii++ Nivo
0.10
0.10
0.05
0.05
0.00
0.00
Incremental step
Incremental step
(c)
(d)
1-SNE visualisation of ICI dataset Therapy
Task identity estimation
80
Alezo
Atezo
predictive a Rebasaen
Ipi Nivo
-088
30
Ipi Pembro
True task identity
Pembro
Nive
None
None
dim 2
Pembro
-0.4
Ipi Pembro
0.2
Cancer_Tyy
Bladder
Ipi+ Nivo
Atezo
Nivo
Rembro
None
Ipi
Pembro
Ipi+Nivo
Kidney
-60
Skin
Predicted identity
Stomach
dim
Figure 2: (a-b) Evolution of misclassification rate specific to each incremental PANCAN batch. Each point represents the misclassification rate specific an incremental dataset evaluated at specific training step using the incrementally trained CL-BRUNO. Each triangle represents the same quantity given by CL-BRUNO who has access to all historical datasets (oracle).
(a) PANCAN dataset under CIL scenario, (b) ICT dataset under TIL scenario. Note that TCT dataset contains tasks with only one class, which leads to zero test error. (c)-(d) ICI dataset. (c): Heat map of predicted task identity. Each row corresponds to the calegorical lask identity distribution 11 averaged over lest samples from each task. (d): t-SNE (Van der Maaten and Hinton 2008) projection of the pre-processed RNAseq measurement associated with different therapy types ICI dataset.
proteins expressed by some cancers which allow it avoid detection by the immune system. Blocking the checkpoints, reactivates the immune system to target the cancer. The ICI dataset contains pre-processed RNAseq data from N 1, 142 patients' tumour samples under 7 different types of immunotherapy treatments. This included four single therapy only regimes: Atezolizumab (Atezo), Nivolumab (Nivo), Pembrolizumab (Pembro), Ipilimumab (Ipi), two combination therapies (Ipi+Pembro, Ipi+Nivo) and a non-treatment pllaceoo group (None). Each ICI designed to block a certain checkpoint protein. As a consequence, ICIs are only effective against those cancers that express the targeted chockpoint protein. Our goal is determine if CL.- BRUNO could learn the molecular signatures associated with immunthhrappy effectiveness which is by proxy cancer type prediction problem given the RNAseq data. In this example, split the dataset into 7 groups
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Mathod/Data
PANCAN
ICI 0.118 (..11)
CL-BRUNO
0.139(0.028))
EWC
(.569())0265)
0.331(0.088)
LWF
(.322(0.0217)
0.157 (0.0433)
MeR-GAN
0.518(0.0521)
Table 3: Misclassification rate of different methods on PANCAN and ICI datasets. Results are averaged over 5 repeated runs. Standard deviations of the misclassification rates are reported in brackets.- indicates method is not applicable to the problem setting. Best results are in boldface.
according the therapy the patients reccived, and treat the classification problem under each therapy as an individual lask. The 7 lasks consists of N1 524, N₂ 224, N3- = 218, N₂ = 89, Ng 42, No. = 32, N, 13 samples and C1 2 ((Bladder, Kidney)), }); C2 3 ((Brain, Skin, Kidney)), C3 3 ([Stomach, Brain, Skin)), C. = ([Kidney)), O 1 ([Skin}), C. = 1 ([Skin)), C7 = 2 ((Kidney, Skin)) unique cancer types respectively. We use the same set of hyperparameters and training strategy as in the last example to train the CI-BRUNO, and compare its performance with EWC and LwF under default or recommended settings This example is challenging due to the relatively small and imbalanced sample sizes. We report the misclassification rates given by different methods in Table g The knowledge retention curves compared to the oracle model is reported in Fig b). We report the task identity estimates given by the trained Cc) We that the task identity estimates put most of the probability mass on the correct task identities (the diagonal line), indicating good prediction accuracy.
CL-BRUNO model under uniform task prior in Fig 2
In addition to prediction accuracy, we also demonstrate that CL-BRUNO is able to give probabilistic predictions that correctly reflects the uncertainty when tasks are indeed indistinguishable: Pal et al. (2022) report that Atezo is ineffective for kidney cancers. Hence we expect patients given Atezo for kidney cancer to be indistinguishable from patients who received no ICT treatment None as both are effectively equivalent. to no treatment. To verify if CL-BRUNO captures this relationship, we first split the test set of Atezo into subgroups depending on their cancer type (Kidney Non-kidncy) and response to the therapy (Responder Non-responder), then compute the averaged predicted probabilities separately. From Fig 3(c) we see CL-BRUNO is much more likely to assign kidney cancer patients given Atezo to None in comparison with non-kidney cancer patients regardless of the response status. This agrees with previous studies, and is also confirmed by visualisation, as we see from Fig (a) that patients from None overlap with a cluster of kidney cancer samples in Atezo.
By the same rationale, since both Nivo and Ipi are given to patients with skin cancer, we expect non- responders in Nivo with skin cancer to be indistinguishable from non-responders in Ipi, which consists of solely patients with skin cancer. To verify if CL-BRUNO captures this relationship, we split the test set of Nivo and compute the averaged predicted probabilitics in similar fashion as before. From Fig 3 (d) we see non-responders in Nivo with skin cancer are much more likely to be classified as Ipi in comparison with the rest. This is supported by the visualisation in Fig 3 (b) as we can see a clear overlap between the non-responders to Nivo and Ipi with skin cancer. This unique pattern suggests that CL-BRUNO accurately captures the inter-task relationship between Nivo and Ipi, and further confirms that CL-BRUNO is capable of capturing inter-task relationships under TIL scenario.
6 Conclusion
We propose CL-BRUNO, probabilistic, exemplar-free CL model based on exchangeable sequence modelling. Compared with existing generative continual learning methods, our proposed method provides a unified probabilistic framework capable of handling different types of CL problems such as TIL and CIL, and giving easy-to-interpret probabilistic predictions without the need of training or maintaining a separate classifier. These fcatures make our approach appcaling in applications where data privacy and uncortainty quantification are of concern.
WW did not include MeR-GAN here as is designed for CIT.
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(a)
t-SNE visualisation of ICI dataset, Atezo/None
(b)
t-SNE visualisation ICI dataset, Nivo/lpi
Therapy
20
Therapy
30-
Nivo
None
Responder
Responder
di__
FALSE
FALSE
TRUE
-20
TRUE
Cancer_ Type
Cancer Type
Brain
Diadder
Kicney
Kidnay
Skin
-50
60
dim_1
dim
(c)
(d)
Avg. predicted probability, Task Atezo
Avg. predicted probability, Task Nivo
Non-responder
Non kidney,
0.8
Aaprrrcoa Sarpronn pabeeang
Non-responder
03
Kidney, Non-responder
0.4
Non-responder
0.3
Non kidney,
Non skin, Responder
Responder
Kidney, Responder
Skin, Responder
0.1
Atezo Nivo Pembro None
Ipi
loi+ Pembro Nivo
Ip+
0.0
Pembro
Pembro Nivo
Candidate tasks
Figure 3: Visualisation of subsets of ICI dataset (a): L-SNE projection of samples from Atezo and None. (b): t-SNE projection of samples from Nivo and Ipi. (c): Averaged predicted probabilities for different groups paticnts under treatment Atezo. Patients are split into four groups based on cancer type (Kidney cancer Non-kidney cancer) and responsiveness to treatment (Responder Non-responder). (d): Averaged predicted probabilities for groups of patients under treatment Nivo. Patients are split into four groups in similar fashion to (c).
Broader Impact Statement
In this work, propose CL-BRUNO, gencrative-replay approach for continual learning that avoids storing explicit exemplar samples, thereby offering potential advantage in privacy-sensitive applications. We acknowledge that generative models trained real data can encode and reproduce distributional and/or identifiable patterns of the training data. One potential solution to this issue is to incorporate pretrained feature extractors in a similar fashion to the image datasets. By doing so, the model would only remember the distributi patterns the feature vectors instead of the original data, hence preventing the model from reproducing the original training data. Although our experiments do not involve user-specific or sensitive biometric data (PANCAN and ICI datasets both non-identifiable data sets made available for research), recognise that applying such models to real-world, rrivacy-criticn domains would necessitate more rigorous safeguards. Future work should incorporate privacy-preserving techniques, e.g. differential privacy, to ensure that generated samples do not leak sensitive information.
We also recognise the potential for bias amplification continual learning settings, particularly when using biometric datascts that may exhibit class imbalance uneven demographic representation. Although our current study focuses on methodological contributions rather than fairness-specific evaluations, we believe that integrating fairness-award strategies is essential for real-world deployment. Addressing these
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ethical considerations is key direction for future research, particularly for applications involving socially demographically sensitive data.
Acknowledgements
The authors are supported by an EPSRC Turing Al Acceleration Fellowship (Grant Ref: GPPVV22333/D 1).
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A Additional discussion on CL-BRUNO
A.1 Discussion on CIL loss
In this section, we justify the choice of LEIL in Sec 3.1 LELL takes the form
neg log lkd of new batch given old
(o) - log Po,ieri (2 ( D D2) (., (0. +2 (DD)
(6)
where
det 0Se(x Fi ikik, vir
log PogPo s
Ik, (1)) (k ( Dx) = Σ log (pxe (2 212-1,1 1, &1.Ne.))
(7)
ox! f
Recall that under the TIL scenario, the trained CL-BRUNO does not depend on the ordering of samples in each dataset, as we assumed that samples within each task are exchangeable. Similarly, under the CIL scenario, we also expect the trained model to not depend on the ordering of data batches the model has been trained on (e.g. model first trained on (Kx.3%) and then (x , should be the same a model trained on the reverse order). This requirement is easily satisfied by our CL-BRUNO model under the assumption that the concatenated {Xx, 21 is jointly exchangeable given (Dk,,)))) i.e. the two data batches {& ( associated with the k-th task are "segments' of sequence generated from an underlying exchangeable generative process.
In particular, under the distributional assumption above, CL-BRUNO aims to learn the joint distribution p(x;") Xe .3%) of the concatenated exchangeable sequence {x A. given the label ( 343 while retaining the marginal Paer),x A (&& [t. V4) the model has lcarnt from historical datasct. In other words, terms in LOI associated with the k-th task can be interpreted learning the joint
p( Melt, Di (4) = p(( |t,
1 1/ &e. Da)
under the constraint that
p(Aalt Parri X (K)),,
Note that the first term in LCIL forces the normalising flow to learn the conditional p(*) x() under the marginal constraint, while the regularisers ICIL related to the k-th task in enforce the marginal constraint by penalising both distributional and functional deviation between the new Po (Xalt, and
[t 20 Ny 3%k
the old P&rt, (A)). The latent distribution parameter
X(77) not updated alongside with the normalising flow parameter 0. We choose to do so as it simplifies the computation and ensures the tractability of Px(r) (12)1:N,. This choice can also be viewed as an additional regularisation that aims to mitigate the impact of catastrophic forgetting.
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NICE
CL-BRUNO
DS-AL
CL-BRUNO
FeTriL
NICE
FeTril
DS-AL
CL-BRUNO
PRER
NICE
FeTriL
Rank
DS-AL
PRER
SSRE
ReReLAP
SSRE
PRER
SSRE
MeRGAN
LWF
MeRGAN
LwF
dEWC-MACL
OEWC-MACL
EWC
MeRGAN
OEWC-MACL
EWC
ReReLRP
ReReLRP
ICIFAR10
ICIFAR100
S-Tinyimage
Datasets
Figure 4: Rankings performance of exemplar-free methods based on their accuracies in Table 1 Note that our proposed CL-BRUNO show competitive performance across all experiments.
A.2 Outlier detection using CL-BRUNO
In Sec 3.1 we give task-identity estimate of generic test point X under the assumption that X is indeed drawn from the generative process of one of the previously seen D,s. This assumption no longer holds when X c.g. outlier. Thanks to the tractable generative modelling framework of CL-BRUNO, users identify outliers in straightforward fashion using e.g. level sets (Hyndman) 1996): For each task 4, we first generate a pseudo dataset Dr as in Sec 3.1 and discard the pseudo labels Y.,, then for each generated pseudo feature vector X 1,... N', we evaluate
((L.)) Pacr,, & (X (t,ttDD) D:)
(8)
=E Part ( Y'EC,
(9)
the approximate predictive density of obscrving X,, as the next sample conditioned on D3 marginalisod over all labels Y* E C. where p(-lt) is the prior that generates the pseudo labels Y,,- Note that by definition, each Xx is indeod sample drawn from Pger), (-1t, D,), the approximate marginal predictive distribution of feature vectors from the 1-th task learnt by CI-BRUNO under the chosen label prior p(-(t). Let E (0, 1) and Pa.t be the a% quantile of {p, (&,,)) By Hyndman (1996), level set S, {X' px())) > pa.1) defines a (1 - a)% approximate highest density region of Pacm, 3, (-1t, D.). As a result, one could test if X is typical feature vector associated with the t-th task in natural and interpretable fashion by comparing (X(*) with the threshold Pa.t.
B Additional experiments
We include additional synthetic and real-world examples in this section.
B.1 Synthetic data
Here we demonstrate CL-BRUNO using synthetic dataset. We set data dimension D = 1000, and consider T = 4 tasks. Fach lask = 1,..., T is associated with a classification problem with C, = L+ 1 distinct classes. Each syuthetic dataset D, consists of N, = 500 samples, where labels Y,, Unif([I, C.}), and features (d) Ya ~ N(ui, 0.5Ip) with ID being a D D identity matrix, pt, = {1 Jiz and (d)
pi (2ssn(2
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Task 1
Task 3
3
1-
Dim 2
Dim 2
-3
-3
Class
Class
Class
Task 2
Task 4
Generated
3
3-
Test set
1-
Dim 2
Dmm 2
-3
-3
Figure 5: Scatter plots of the first two dimensions of samples in the test set (cross) and samples generated from the trained CL-BRUNO (circle) for each of the tasks.
(d) vt cos(YYY... if d is even. See Fig for an illustration of the synthetic datasets. if d odd and mi, We first initialise proposed model on task 1 by training the generative D1, then incrementally present task (D2) and 3 (Dz) to the model. We then demonstrate the innemmnnremettal scenario using task 4: We split D4 into two groups, one containing data associated with the first three out of the five classes in D4, and the other containing the rest two classes. We then present the two groups of data sequentially to the model. As a result, the example consists for task-incremental learning and 2 for iaas-incremental learning). We parameterise task ID and each distinct label associated with task for cach task 1,..., T trainable emboddings of length 16. After the training phase, we test the classification accuracy on all four tasks using separate test sets drawn from the generative process. Note that samples in training data {D)T= is retained in trained model.
incremental training steps in total (1 for initialisation,
For all four tasks, the trained model attains < 1% misclassification rate on test sets of size 1000 samples. CL-BRUNO is also able lo accurately predict task identities of samples from test sets, attaining < 5% misclassification rate on all tasks. To visualise the of CL-BRUNO, we report scatter plots of the first two dimension samples from the test set and samples generated by the trained CL-BRUNO in Fig We see CL-BRUNO able accurately capture the feature distributions associated with each class within each task. This confirms the effectiveness of CL-BRUNO.
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B.2 Discussion computational cost
We inspect the computational cost of CL-BRUNO in terms of wall clock time using the same S-CIFAR-100 example. All examples are executed on our machine with an AMD Ryzen7 2700 CPU and NVIDIA RIX 2060 GPU. Under the experiment sctup described above, CL-BRUNO takes around 2.9 x 10 to complete. In comparison, the running time of non-generative. exemplar-free LwF and EWC are around 2.4 x 10's, whereas the generative, exemplar-free FeTriL takes around 3.2 10Ss. The experience replay-based NPCT. takes around 3.5 10's run. We see in this example that the computational cost of CL-BRUNO is scale comparable to the existing exemplar-free CL models.
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Reviews:
[{"review_id": "KaI2WrQV2i", "reviewer": "Reviewer_w7vW", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n* The idea seems novel, interesting and relevant for handling CL. CL is in its core a problem about learning from non-i.i.d. data as the different tasks come in sequentially. In that context, viewing CL under the lens of exchangeable sequence modelling, which relaxes the i.i.d. assumption, seems pretty novel and interesting, and can provide a new set of tools to tackle sequential learning in a CL scenario.\n* The paper is generally very nicely written, the notation is consistent, thorough and clear.\n\nWeaknesses:\n\n* A clear and strong motivation for the method in the CL context is missing. As I see, the main motivation is given at the end of 2.2 but this is very short and high level. Can you be more concrete in justifying how you are using the added flexibility of the exchangeability assumption in this CL setting, what it brings compared to other methods? In the abstract the main points for motivating the method are 1) not storing data and 2) having uncertainty quantification, but many other methods have already solved these problems. What else does this method bring? The abstract does not even mention exchangeability.\n* The chosen experiments do not seem to demonstrate the advantages of this particular method. The paper highlights scalability (but is CIFAR100 really a dataset that demonstrates scalability?), ability to quantify uncertainty (but as I can see only the ECE table uses this, and there is no other mention to uncertainty in the results?), and the chosen datasets do not constitute cases where, within a given dataset, the exchangeability assumption is important? (e.g. the provided vision experiments to not need it, can you clarify if the biomedical experiments benefit from this somehow?).\n* Certain statements are not supported by the reported results. E.g. Section 5.2. states “we see no abrupt interference or deterioration in prediction accuracy in the training steps”, this is a very vague statement and actually when looking at Fig 2(a) I would state the opposite. Same for 5.3 statement “Fig 2(b) show no drastic performance deterioration in any task”. There is clearly a drop in performance. Anyways these results are hard to interpret as there is no other baseline and no error bars. Also not sure if I understand correctly, but it seems the hyperparameters for the baselines were not tuned? If this is the case, it’s not a very fair comparison. Also, the paper mentions as motivation that TIL and CIL can be merged under a framework, but no experiments seem to demonstrate this (only potentially in appendix, but in a very ad-hoc synthetic dataset that is hard to judge, and that is never mentioned in the main).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper adapts Conditional-BRUNO method to the continual learning setting (CL-BRUNO) and aims to demonstrate that it can perform competitively in a set of computer vision and biomedical CL datasets. More specifically, the C-BRUNO core allows generating pseudo-samples of a given task conditioned on a given label (using normalising flows), and these can then be used to mitigate forgetting of previously learned tasks. To further mitigate forgetting, the stability of the conditional generation is controlled by adding an L2 loss on the generated samples, to make sure they don’t differ much from the generated samples based on the previous state of the normalising flow.  \n\nThe main contributions of the paper are:\n\n* viewing CL under the lens of exchangeable sequence modelling\n* proposing a probabilistic framework that allows unifying task-incremental learning and class-incremental learning", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* Improve the motivation of the method in the CL context both in the abstract and the introduction (see comments above)\n* Improve the positioning of CL-BRUNO relative to BRUNO/C-BRUNO. i.e. understanding that BRUNO/C-BRUNO are useful in contexts like few-shot learning can help. Also, the condition $0 < \\rho < v$ is given without context, can you add a short explanation why it’s necessary in C-BRUNO? Maybe also add some extra short sentence on what the permutation/exchangeability means so that it’s easier to parse. Also notation in this Section is not consistent with the CL-BRUNO section (i.e. $h_i$ instead of $y_i$).\n* Maybe adding a box with the algorithm would help the reader quickly know 1) how training happens, 2) how inference happens. It can also be a good place to clarify the process for getting $X_i$ samples, inferring task identity, and inferring $Y_i$.\n* Improve quality/visibility of plots: at the moment the font size is too small. \n* Bayesian CL literature seems to be missing, and this seems relevant given that one main motivation mentioned in the paper is the probabilistic nature of the method. \n* At the moment it’s not clear to me why second paragraph in section 5.3 is interesting. These inter-task relationship results seem to come a bit out of nowhere, and take a lot of space in the main text. Can you add some explanation of why we care about these results, in the light of the specific method that you are proposing?\n* Clarification: If indeed the default parameters were taken for the baselines, at least some hyperaparameter tuning seems necessary.\n* Clarification: in 5.1 (training?) runtimes are given. In 5.2 you mention samples need to be generated for every gradient descent step. Can you explain why just in this experiment, and whether this has a significant impact on runtime?\n\nTypos:\n\n* 2.2: (as supposed to i.i.d.) → opposed\n* 3.1: CL-BRUNO loss equation has no label that one can refer to, and in the last line of page 6, I think it should refer to that one and not to Eqn 6 as currently is\n* 5.1: Ablation study: CL-RUNO_{dist}\n* Figure 2 caption. ICI dataset consists of tasks with only one class - contains? As far as I understand, only some of them. As it’s currently written it seems all of them are.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "qfU9sYttlJ", "reviewer": "Reviewer_pAhH", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\n- The paper conducts experiments in a medical application, a real-world continual learning scenario beyond synthetic benchmarks like MNIST, and demonstrates the good performance of the proposed method\n- The proposed method does not retain previously seen samples, making it suitable for sensitive applications such as biomedical data analysis.\n- The proposed method provides a unified probabilistic framework that can handle both task- and class-incremental CL problems.\n\n### Weaknesses\n- I think the paper lacks a thorough comparison with baseline methods. For example, the work by Scardapane et al. (2020) (also mentioned by the authors in the related work section), which employs normalizing flow for generative replay in continual learning, is not included in the comparisons. While the authors claim that their proposed method is more unified and scalable in the related work section, this is less convincing without concrete supporting evidence. Furthermore, the baseline results presented in Table 1 appear to be lower than those reported in the original publications. For instance, NPCL is reported at 0.198 by the authors, whereas the original paper reports a value of 0.3743. Is there a difference in the experimental setup that could account for this discrepancy?\n- The paper does not include a systematic ablation study to explain the effectiveness of the proposed components. This omission limits the insights into why the proposed method would excel in performance compared to previous methods.\n- The authors claim that uncertainty quantification is a weakness of existing methods and a strength of the proposed method. However, the experimental section does not adequately demonstrate how the proposed method improves in this area. There is no clear evidence or results related to uncertainty quantification of the proposed method, e.g., whether the method is better calibrated. \n- The equation in the Method section on page 3 requires some clarification, particularly , the RHS because the right-hand side would include the term X_{1:0,t} when i =1 which can be confusing.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose CL-BRUNO, a CL method that leverages probabilistic, Neural Process-based models to address challenges such as catastrophic forgetting and uncertainty quantification in CL applications. \n\nThe method employs deep-generative models, specifically normalizing flows, to capture the joint density function of inputs and labels across a sequence of CL tasks, supporting generative replay without the need to store previously seen training examples. During CL, the model is iteratively trained using a combined objective, including  1) maximum likelihood on the union of training examples from the current task and synthetic examples from previous tasks through conditional generation, and 2) a functional regularization term to penalize discrepancies in the predictive outputs between the old and updated models. Inference is conducted by task-id prediction followed by label prediction, using the posterior task and label distributions. \n\nThe authors demonstrate the efficacy of CL-BRUNO through experiments on both standard CL benchmarks (MNIST and Split CIFAR-100) and biomedical datasets, showing that it outperforms baseline CL methods.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please kindly refer to the weaknesses mentioned above.", "broader_impact_concerns": "n/a", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "VorjQnR51n", "reviewer": "Reviewer_SE8t", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n\n1. The framework presented in the paper is novel, which frames continual learning as inference over exchangeable sequences.\n2. The method is task-agnostic and replay-free.\n3. The paper is clearly written and provides strong theoritical analysis for the proposed approach. \n\n## Weakness\n1. The experimental evaluation is not comprehensive. Most experiments are conducted on two biometric datasets that are uncommon in the continual learning literature. Evaluation on standard CL benchmarks is limited to only MNIST and CIFAR-100, which weakens the generalizability claims. Moreover, a substantial portion of the manuscript in the experiment section is occupied by large figures and tables, some of which could be compressed or relocated to the appendix to improve clarity and space efficiency.\n2. The compared methods are quite old. On their biometric datasets, the authors only compare with 3 baselines published before 2018. This is insufficient for a 2025 submission and does not convincingly demonstrate the method’s advantage over recent state-of-the-art approaches.\n3. The empirical results are not particularly strong, and the experimental analysis is relatively shallow. More detailed discussion, interpretation, and ablation studies would strengthen the empirical contribution.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes CL-BRUNO, a continual learning method based on exchangeable sequence modeling with Neural Processes. The key idea is to treat data observed across tasks as samples from an exchangeable sequence, enabling a unified probabilistic view of continual learning without requiring explicit task identities.\n\nMain contributions include:\n* Probabilistic Formulation: The proposed method is modeled as Bayesian inference over exchangeable sequences, enabling task-agnostic continual learning.\n\n* Neural Process-based Implementation: CL-BRUNO uses Neural Processes to amortize inference, achieving scalability and flexibility across tasks.\n\n* No Replay or Task IDs: The method avoids storing past data or relying on task boundaries, relying instead on functional and distributional regularization to mitigate forgetting.\n\n* Empirical Results: Experiments on vision and biomedical datasets show that CL-BRUNO achieves good performance compared to baselines across task-incremental and class-incremental CL settings.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. I would suggest shifting the focus from your biometric datasets to widely-used benchmarks in the continual learning literature. The current datasets are quite unfamiliar to other researchers and difficult to evaluate. For example, consider adding results on datasets such as ImageNet-200, CORe50, or iCIFAR-100 to enhance the credibility and generalizability of the method.\n2. Provide more detailed analysis of the results. The current presentation of results, especially on standard CL benchmarks like Split MNIST and CIFAR-100, is limited to numerical tables without sufficient discussion. Please include in-depth analysis of the performance, comparison across methods and failure cases to help readers better understand the method’s behavior.\n3. Include more recent and stronger baselines. Most of the compared baselines are outdated.  Incorporating more recent continual learning methods would strengthen the empirical comparison and better position your contribution within the current state of the field.\n4. Some entries in Table 1 are incomplete. If certain methods could not be run for specific settings, please explicitly state the reason.\n5. An ablation study is necessary to evaluate the contribution of key components of your proposed framework. Please provide such an analysis to justify the design choices.\n6. Please enhance the clarity and readability of the figures. For example, in Figure 1(b), it is difficult to distinguish instances from different classes. There are also seemingly misplaced texts in that figure.", "broader_impact_concerns": "The submission does not include a Broader Impact Statement, and currently lacks a discussion on the potential ethical implications of deploying continual learning systems in real-world settings. While the proposed framework is primarily evaluated in academic benchmarks, continual learning methods—particularly those designed for biometric data or long-term user modeling—can raise important privacy, fairness, and misuse concerns. \n\nIn particular: \n* **Privacy risks**: Although the proposed method avoids storing explicit memory samples, it relies on generating synthetic samples for replay. It remains unclear whether these generated samples are truly anonymized and free from privacy leakage. Can such samples inadvertently preserve or reconstruct identifiable information about users? A discussion on the safety and privacy guarantees of the generative module is warranted.\n\n* **Bias amplification**: Continual learning performance is often sensitive to task ordering and task difficulty. This issue is especially pronounced in biometric datasets, which often exhibit class imbalance or uneven data distributions. The manuscript does not address how such biases may affect model behavior or what strategies (e.g., curriculum learning, re-weighting) could be employed to mitigate them. This is important for ensuring fairness across different user groups or identity classes.\n\nI recommend that the authors add a Broader Impact Statement to reflect on these issues, even if only to clarify the intended scope and limitations of their method under ethical considerations.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)