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Uniform Herding: Exemplar Replay with Representation Refresh
Krishna Subedi
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
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Summary
The paper introduces Uniform Herding, a class-incremental learning method that allocates a bounded active exemplar budget uniformly across observed classes and refreshes these exemplars using greedy herding in the current feature representation after each task. Evaluated on CIFAR-100 with a ResNet-18 backbone, Uniform Herding achieves 44.00% final average accuracy and 17.22% forgetting, outperforming iCaRL (42.33% accuracy, 24.87% forgetting) and a static bank baseline. Ablation studies highlight the importance of Nearest-Mean-of-Exemplars (NME) prediction, herding selection, and knowledge distillation for maintaining performance and reducing forgetting.
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Relation Signals (9)
Uniform Herding → evaluatedon → CIFAR-100
confidence 99% · On CIFAR-100 with ten class-incremental tasks...
Uniform Herding → outperforms → iCaRL
confidence 95% · Uniform Herding obtains 44.00±0.51% final average accuracy... compared with 42.33±1.20%... for iCaRL.
Uniform Herding → outperforms → Static Bank
confidence 95% · Uniform Herding obtains 44.00±0.51% final average accuracy... The static bank achieves 28.60±1.35%...
Uniform Herding → usesbackbone → ResNet-18
confidence 95% · a ResNet-18 backbone...
Uniform Herding → uses → Nearest-Mean-of-Exemplars
confidence 90% · At evaluation, Uniform Herding uses nearest-mean exemplar prediction.
Uniform Herding → uses → Greedy Herding
confidence 90% · rebuilds each class’s exemplar set using greedy herding 12 in the current feature space.
NME → improves → Average Accuracy
confidence 85% · NME prediction... outperform their tested alternatives on mean accuracy
Knowledge Distillation → reduces → Forgetting
confidence 85% · forgetting increased when distillation was removed.
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Abstract
Abstract:As the feature representation changes, replay must preserve the earlier classes. However, only a bounded active exemplar set can be replayed. We propose Uniform Herding, which allocates the current active set across observed classes and uses a bounded candidate pool to refresh their chosen exemplars in the current representation. On CIFAR-100 with ten class-incremental tasks, a ResNet-18 backbone, active budget $M=2{,}000$, retrieval budget $b=64$, and three seeds, Uniform Herding obtains $44.00\pm0.51\%$ final average accuracy and $17.22\pm0.43\%$ forgetting, compared with $42.33\pm1.20\%$ and $24.87\pm1.11\%$ for iCaRL. Within the Uniform Herding protocol, final accuracy decreased when NME or herding was replaced with the tested alternatives, while forgetting increased when distillation was removed. Changing the retrieval budget has a smaller effect across the tested range than changing the active budget. The comparison with iCaRL is end-to-end. It does not isolate the effect of refresh from the other protocol differences. These results are limited to the tested protocol.
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- Source: https://arxiv.org/abs/2608.13061v1
- Canonical: https://arxiv.org/abs/2608.13061v1
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Uniform Herding: Exemplar Replay with Representation Refresh Krishna Subedi Email: krishna.subedi@neryva.com Abstract As the feature representation changes, replay must preserve the earlier classes. However, only a bounded active exemplar set can be replayed. We propose Uniform Herding, which allocates the current active set across observed classes and uses a bounded candidate pool to refresh their chosen exemplars in the current representation. On CIFAR-100 with ten class-incremental tasks, a ResNet-18 backbone, active budget M=2,000M=2,000, retrieval budget b=64b=64, and three seeds, Uniform Herding obtains 44.00±0.51%44.00± 0.51\% final average accuracy and 17.22±0.43%17.22± 0.43\% forgetting, compared with 42.33±1.20%42.33± 1.20\% and 24.87±1.11%24.87± 1.11\% for iCaRL. Within the Uniform Herding protocol, final accuracy decreased when NME or herding was replaced with the tested alternatives, while forgetting increased when distillation was removed. Changing the retrieval budget has a smaller effect across the tested range than changing the active budget. The comparison with iCaRL is end-to-end. It does not isolate the effect of refresh from the other protocol differences. These results are limited to the tested protocol. 1 Introduction In replay-based class-incremental learning, a small exemplar set represents the training history. The backbone changes with each new task, so exemplars selected with an earlier representation may no longer approximate the class distributions well in the current representation. Existing methods combine selection, refresh timing, training objective, and readout into complete protocols; consequently, a performance gap between methods cannot isolate the refresh rule from the other design choices. We propose Uniform Herding. After each task is completed, it divides the active budget equally among all observed classes and rebuilds each class’s exemplar set using greedy herding 12 in the current feature space. Reconstruction candidates come from a bounded candidate pool, while the selected exemplars form the active replay memory. We then compare Uniform Herding with a faithful implementation of iCaRL 10 and a static replay bank on the CIFAR-100 dataset split into ten tasks. Upon arrival, iCaRL herds each new class once and preserves the resulting priority order, retaining the prefix required by the later per-class quota. The comparisons with Uniform Herding are end-to-end: the protocols also differ in training objective, readout, and storage, not only in refresh timing. We also compare Uniform Herding ablations on prediction rule, selection rule, distillation, and classifier head, in addition to active-budget and retrieval sweeps. At the default budgets (M=2,000M=2,000 active exemplars, b=64b=64 retrieval), Uniform Herding obtains higher mean final accuracy and lower mean forgetting than both baselines. Nearest-mean-of-exemplars (NME) prediction and herding selection each outperform their tested alternatives on mean accuracy; distillation primarily affects forgetting. The active-budget sweep changes the metrics more than the retrieval sweep. Contributions. • We define Uniform Herding, which divides the active budget uniformly across classes and refreshes the exemplar set from a bounded candidate pool in the current representation after each task. • We compare it against iCaRL and a static bank at matched active and retrieval budgets, with all protocol differences stated. • We ablate prediction rule, selection rule, distillation, and head geometry, and vary active-budget and retrieval sensitivity within the proposed protocol. 2 Related Work 2.1 Class-Incremental Learning Methods for class-incremental learning commonly use parameter regularization, constrained updates, distillation, or replay. EWC and Synaptic Intelligence penalize changes to parameters deemed important for earlier tasks 7; 14; GEM and A-GEM constrain gradient updates with episodic memory 9; 3. Without stored data, Learning without Forgetting distills old-task logits from the previous model 8. Uniform Herding belongs to the replay family and studies how exemplar refresh interacts with the active budget constraint. 2.2 Replay and Exemplar Selection Experience replay stores a bounded subset of earlier data and mixes it into each new task’s training 11; 4. iCaRL combines greedy herding with exemplar replay and nearest-mean-of-exemplars (NME) prediction 10; the herding step greedily builds a set of exemplars whose sample mean tracks the class mean 12. GSS and MIR select exemplars by gradient diversity and expected interference, respectively 2; 1. Uniform Herding follows the same total active budget and greedy herding as iCaRL but changes the refresh schedule. It utilizes a bounded candidate pool to re-herd every observed class in the current feature space following each task. iCaRL herds a class only once on its arrival, and thereafter truncates the ranked list as the per-class quota shrinks. Thus, the comparison is between two complete protocols, and it does not isolate refresh from the other differences. 2.3 Distillation, Classifiers, and Readouts iCaRL distills with sigmoid binary cross-entropy on old-class targets 10; Uniform Herding pairs cross-entropy on all classes with a temperature-scaled softmax KL term constrained to old classes. Classifier choice determines the bias between old and new classes. LUCIR replaces the linear head with a normalized cosine classifier and a margin loss 6; to reduce the new-class bias, BiC and Weight Aligning post-correct the classifier outputs 13; 15. The learned head is bypassed for prediction by prototype classifiers: iCaRL makes predictions based on exemplar means, and FeCAM expands this using class-covariance weighting 10; 5. Our ablations test NME vs. head-logit prediction, distillation, and head geometry within a single training protocol. The evaluation metrics—average accuracy, backward transfer 9, and average forgetting 4—are defined in Section 3.5. 3 Uniform Herding and Experimental Setup We evaluated class-incremental learning on the CIFAR-100 dataset with a bounded active exemplar budget. Training runs through tasks t=0,…,T−1t=0,…,T-1. Each task brings a disjoint set of CnewC_new classes, and evaluation after task t covers all classes seen so far, without task identity. In the main experiments, T=10T=10 and Cnew=10C_new=10. We permute the CIFAR-100 classes using split seed 13 and remap them to contiguous internal labels. From each training class, we keep 30 images for probing and 20 for validation. None enter replay storage. Task t dataReplay from active setBackbone fθf_θHeadLossTeacher logits b samples per minibatch cosine-margin / linear CE + KD / CE only Candidate pools cQ_cHerding / randomActive set ℰENME prototypes current stream + persistent candidates rebuild in current fθf_θ active budget M; replay source selected-exemplar means Query xxBackbone fθf_θReadouty y NME / head-logit Training (t≥1t≥ 1)Memory refresh (after each task)Evaluation Figure 1: Overview of Uniform Herding. At each task boundary, class-specific candidate pools are refreshed in the current representation and herding selects the active replay set with budget M. Replay draws only from this active set, while candidate storage is bounded by ρMρ M at completed boundaries; the retrieval count is b per minibatch. Orange boxes indicate choices examined in the within-method comparisons. Dashed arrows show the replay and prototype feedback paths. Figure 1 summarizes the training, memory-refresh, and evaluation flow. 3.1 Model and Training The learner is a ResNet-18 feature extractor fθ:→ℝ512f_θ:X ^512 with base width 64 and no dropout. The default classifier is a cosine-margin classifier. For feature vector fθ(x)f_θ(x), classifier weight wjw_j, scale s, margin m, and target y, its logits are zj(x,y)=s⟨f¯θ(x),w¯j⟩−sm,j=y,s⟨f¯θ(x),w¯j⟩,j≠y,z_j(x;y)= casess f_θ(x), w_j -sm,&j=y,\\ s f_θ(x), w_j ,&j≠ y, cases where u¯=u/‖u‖2 u=u/\|u\|_2. We set s=30s=30 and m=0.35m=0.35. Each new task increases the classifier head by 10 rows. Prior to optimization, we imprint the new rows from normalized class-mean features starting with task 1. We train with SGD at learning rate 0.1, momentum 0.9, weight decay 5×10−45× 10^-4, batch size 128, gradient clipping at 1.0, mixed precision, and 70 epochs per task. Training augmentation is random crop (padding 4) and horizontal flip; evaluation applies normalization only. Our runs use seeds 1993, 2023, and 42. 3.2 Active Allocation and Candidate Refresh Uniform Herding separates the active replay set from the candidate pool used to refresh it. Let tC_t be the classes observed after task t and let Ct=|t|C_t=|C_t|. Given active budget M, the quota for the i-th class identifier is qci(t)=⌊MCt⌋+i<MmodCt,i=0,…,Ct−1.q_c_i^(t)= MC_t +1\i<M C_t\, i=0,…,C_t-1. In our experiments, every class has enough candidates, so the selected sets sum to M at each completed task boundary. When a candidate pool falls short of its quota, we select at most qc(t)q_c^(t) items. At the start of task t, let ℬc(t−1)B_c^(t-1) denote the persistent candidate pool for an old class and let c,cur(t)P_c,cur^(t) denote the raw current-task stream for a newly observed class. At the task boundary, the candidate set for class c is c(t)=ℬc(t−1)∪c,cur(t),μc(t)=1|c(t)|∑x∈c(t)fθ(x).Q_c^(t)=B_c^(t-1) _c,cur^(t), _c^(t)= 1|Q_c^(t)| _x _c^(t)f_θ(x). For each new class, the persistent pool is empty before its first rebuild. We retain the current-task stream until the boundary. Once a class has a known quota, we maintain its persistent candidate pool with class-local bounded reservoir insertion. Herding selects the active exemplars from c(t)Q_c^(t). With S0=0S_0=0, the k-th exemplar is xk∈argminx∈c(t)∖x1,…,xk−1‖fθ(x)−(kμc(t)−Sk−1)‖22,Sk=Sk−1+fθ(xk).x_k∈ *argmin_x _c^(t) \x_1,…,x_k-1\ \|f_θ(x)- (k _c^(t)-S_k-1 ) \|_2^2, S_k=S_k-1+f_θ(x_k). The selected set is ℰc(t)=x1,…,xqc(t)E_c^(t)=\x_1,…,x_q_c^(t)\, and the NME prototype is μ^c(t)=1|ℰc(t)|∑x∈ℰc(t)fθ(x). μ_c^(t)= 1|E_c^(t)| _x _c^(t)f_θ(x). This rebuild runs for every observed class after every task. After selection, the candidate pool keeps the selected items plus a bounded set of leftover candidates. At the default ρ=pool_multiplier=3ρ= pool\_multiplier=3, each task boundary stores at most ρqc(t)ρ q_c^(t) candidates per class and at most ρMρ M in total in the reported runs. This bound excludes the transient full stream of a class before its first rebuild. M is therefore the active replay budget and ρMρ M is the boundary storage candidate bound. The method does not have a total storage budget of M. The candidate pool is a bounded buffer, not a claim of uniform sampling over the entire historical stream. Replay draws only from the selected sets. We use the default ρ=3ρ=3 and did not sweep it. 3.3 Replay, Distillation, and Prediction At t=0t=0, training uses only the current-task minibatches. For t≥1t≥ 1, each minibatch is augmented with b exemplars drawn with replacement from earlier classes. Sampling is uniform over stored items, not over classes. Retrieved raw images are re-augmented before concatenation. We set M=2,000M=2,000 and b=64b=64. The loss combines cross-entropy over the expanded label space with a distillation on old classes. We copy a snapshot of the teacher just before expanding the head. For t≥1t≥ 1, ℒt _t =ℒCE(z(x,y),y)+λTKD2KL(pteach(x)∥p(x)), =L_CE(z(x;y),y)+λ T_KD^2KL\! (p^teach(x)\, \|\,p(x) ), pteach(x) p^teach(x) =softmax(zteach0:Ct−1−1(x)/TKD), =softmax\! (z^teach_0:C_t-1-1(x)/T_KD ), p(x) p(x) =softmax(z~0:Ct−1−1(x;y)/TKD), =softmax\! ( z_0:C_t-1-1(x;y)/T_KD ), where z~ z is the student’s logit vector after undoing the target-dependent cosine margin for the KD comparison. We set λ=1λ=1 and TKD=2T_KD=2; at t=0t=0 there is no distillation term. At evaluation, Uniform Herding uses nearest-mean exemplar prediction. Given the final representation, the prediction is y^(x)=argminc∈T−1‖f¯θ(x)−μ^¯c(T−1)‖2. y(x)= *argmin_c _T-1 \| f_θ(x)- μ_c^(T-1) \|_2. The head-logit rule is used in the corresponding ablation and in the static-bank baseline’s own protocol. The no-replay baseline has no exemplar readout. 3.4 Baselines and Supporting Analyses The iCaRL baseline herds each new class once from its full current-task pool, stores the prioritized order, and later keeps the prefix required by the new quota. It does not re-herd old classes. It recomputes NME means in the current feature space over the retained exemplars and discards the transient current task pool at the task boundary. Training uses iCaRL-style sigmoid binary cross-entropy targets for old classes. The static-bank baseline uses random replacement within class pools, the same nominal active budget and retrieval count, and cross-entropy training with head-logit prediction. At task boundaries, it reduces its active store to the nominal budget, unlike Uniform Herding’s additional candidate pool. Every Uniform Herding ablation changes one choice at a time. We remove KD, swap NME for head-logit prediction, swap the cosine-margin head for a linear head, or swap herding for random selection. Resource sweeps vary M∈500,2000,4000M∈\500,2000,4000\ and b∈32,64,128b∈\32,64,128\ around the default. T1 compares full protocols. Among the replay rows, nominal active and retrieval budgets match, but total retained storage, training objective, and readout differ. The no-replay baseline has neither replay storage nor retrieval. 3.5 Evaluation Metrics After each task i, we evaluate separately on every task j≤ij≤ i, producing an accuracy matrix R. Final average accuracy is ACC=1T∑j=0T−1RT−1,j.ACC= 1T _j=0^T-1R_T-1,j. Forgetting is the mean drop from each old task’s best observed accuracy to its final accuracy: F=1T−1∑j=0T−2(maxi∈j,…,T−1Ri,j−RT−1,j).F= 1T-1 _j=0^T-2 ( _i∈\j,…,T-1\R_i,j-R_T-1,j ). Backward transfer is BWT=1T−1∑j=0T−2(RT−1,j−Rj,j).BWT= 1T-1 _j=0^T-2 (R_T-1,j-R_j,j ). We report all scalar metrics as the mean and population standard deviation over the three seeds. For ablation and sensitivity rows, we compute deltas per seed against the matched Uniform Herding run before averaging. 4 Results All results follow the protocol in Section 3 and are reported as mean ± population standard deviation over three seeds. The main comparison in Table 1 uses active budget M=2,000M=2,000 and retrieval budget b=64b=64. 4.1 Main Method Comparison At the common nominal active budget, Uniform Herding obtains 44.00±0.51%44.00± 0.51\% final average accuracy and 17.22±0.43%17.22± 0.43\% forgetting. iCaRL reaches 42.33±1.20%42.33± 1.20\% accuracy and 24.87±1.11%24.87± 1.11\% forgetting. The static bank achieves 28.60±1.35%28.60± 1.35\% and 55.86±1.42%55.86± 1.42\%. The comparison is end-to-end. The baselines differ in candidate retention and training objective, and the static bank also uses a different readout. The appendix details these protocol differences. Figure 2 shows final per-task accuracies. Table 1: Main comparison on CIFAR-100. All methods use a nominal active exemplar budget of 2,000 and retrieval budget of 64. Uniform Herding also retains candidate storage for refresh. Method Average accuracy (%) Forgetting (%) BWT (%) iCaRL 42.33±1.2042.33± 1.20 24.87±1.1124.87± 1.11 −24.87±1.11-24.87± 1.11 Static bank 28.60±1.3528.60± 1.35 55.86±1.4255.86± 1.42 −55.86±1.42-55.86± 1.42 Uniform Herding 44.00±0.5144.00± 0.51 17.22±0.4317.22± 0.43 −16.91±0.41-16.91± 0.41 Figure 2: Final per-task accuracies. Panel (a) compares the baselines with Uniform Herding. Panel (b) shows the within-method variants. 4.2 Supporting Analyses of Uniform Herding Table 2 reports matched within-method ablations of the prediction rule, selection rule, distillation, and classifier head. Replacing NME with head-logit evaluation drops accuracy by 10.4610.46 p and raises forgetting by 30.3630.36 p. Replacing herding with random selection costs 2.392.39 p in accuracy and 1.161.16 p in forgetting. Removing KD decreases accuracy by 1.481.48 p but increases forgetting by 11.6611.66 p. Replacing the cosine-margin head with a linear head decreases accuracy by 0.790.79 p and increases forgetting by 0.120.12 p. These comparisons describe the current configuration; they do not establish effects beyond it. Appendix Figure 9 shows the per-seed deltas. Figure 3 plots forgetting by task. From tasks 0–8, forgetting is 5151–5959 p for the static bank and 2727–5555 p for head-logit evaluation, compared to 8.18.1–30.130.1 p for Uniform Herding. The pattern is consistent with recency bias: both unfavorable settings maintain good accuracy on the most recent task despite their aggregate forgetting. Task 9 has zero forgetting by definition since no subsequent training degrades it. Figure 3: Forgetting by task index for Uniform Herding and two adverse configurations. The final task has zero forgetting by definition because no subsequent task is learned. Table 2: Matched within-method comparisons for Uniform Herding. Deltas are paired by seed against the main configuration. Variant Average accuracy (%) Forgetting (%) Δ accuracy (p) Δ forgetting (p) Without KD 42.52±0.6142.52± 0.61 28.88±0.1928.88± 0.19 −1.48-1.48 +11.66+11.66 Head-logit evaluation 33.54±0.3933.54± 0.39 47.58±0.8447.58± 0.84 −10.46-10.46 +30.36+30.36 Linear head 43.22±0.3643.22± 0.36 17.34±0.6817.34± 0.68 −0.79-0.79 +0.12+0.12 Random selection 41.61±0.5341.61± 0.53 18.38±0.4718.38± 0.47 −2.39-2.39 +1.16+1.16 4.3 Active-Budget and Retrieval Sensitivity Because Uniform Herding uses ρ=3ρ=3, changing the active budget changes the candidate-pool capacity as well. Reducing M from 2,000 to 500 lowers accuracy by 10.0510.05 p and raises forgetting by 13.2613.26 p. Increasing M to 4,000 raises accuracy by 3.323.32 p and lowers forgetting by 3.913.91 p. Three tested points do not establish a scaling law. With M=2,000M=2,000 fixed, reducing retrieval from 64 to 32 decreases accuracy by 1.531.53 p and decreases forgetting by 0.010.01 p. Increasing retrieval to 128 increases accuracy by 0.160.16 p and increases forgetting by 0.590.59 p. The retrieval sweep produces a smaller mean change than the active-budget sweep (Table 3). Figure 4 plots both sweeps. Table 3: Resource sensitivity relative to Uniform Herding at M=2,000M=2,000 and retrieval budget 64. Active-budget changes also change the candidate-pool capacity through ρ=3ρ=3; deltas are paired by seed. Axis Value Average accuracy (%) Forgetting (%) Δ accuracy (p) Δ forgetting (p) Active budget 500 33.95±1.5133.95± 1.51 30.48±0.5430.48± 0.54 −10.05-10.05 +13.26+13.26 Active budget 2,000 44.00±0.5144.00± 0.51 17.22±0.4317.22± 0.43 0.000.00 0.000.00 Active budget 4,000 47.32±0.2447.32± 0.24 13.31±0.5913.31± 0.59 +3.32+3.32 −3.91-3.91 Retrieval 32 42.47±0.6342.47± 0.63 17.22±0.4717.22± 0.47 −1.53-1.53 −0.01-0.01 Retrieval 64 44.00±0.5144.00± 0.51 17.22±0.4317.22± 0.43 0.000.00 0.000.00 Retrieval 128 44.16±0.5944.16± 0.59 17.81±0.3817.81± 0.38 +0.16+0.16 +0.59+0.59 Figure 4: Sensitivity to active exemplar budget and replay retrieval budget. Error bars denote population standard deviation over three seeds. 5 Discussion Uniform Herding achieves higher mean final accuracy and lower mean forgetting than the faithful iCaRL implementation and the static-bank baseline in the evaluated protocol. This is a complete-method result. Because the protocols differ in refresh policy, training objective, and retained candidate storage and the static bank also uses a different readout, the comparison does not estimate the effect of refresh alone. 5.1 Evidence About the Proposed Configuration Within Uniform Herding, NME evaluation is strongly favored over head-logit evaluation by 10.4610.46 p in accuracy and 30.3630.36 p in forgetting. Since both variants share the training procedure, the gap points to the value of matching the readout to the selected exemplar representation in this protocol. Herding selection yields 2.392.39 p higher accuracy and reduces mean forgetting by 1.161.16 p relative to random selection; this small difference is not estimated reliably with three seeds. Removing KD decreases accuracy by 1.481.48 p but increases forgetting by 11.6611.66 p, suggesting that distillation serves a retention role in this objective. Replacing the cosine-margin head with a linear head produces the smallest shift among these ablations (−0.79-0.79 p accuracy, +0.12+0.12 p forgetting). These comparisons describe the current configuration and they do not establish effects beyond it. 5.2 Resource and Storage Implications Reducing the active budget from 2,000 to 500 lowers accuracy by 10.0510.05 p and raises forgetting by 13.2613.26 p. Raising retrieval from 64 to 128 increases mean accuracy by 0.160.16 p but also increases mean forgetting by 0.590.59 p. Because ρ=3ρ=3, the active-budget sweep simultaneously changes candidate capacity. Uniform Herding therefore trades additional candidate storage and refresh computation for an active replay set of size M. The comparison with iCaRL or the static bank is not storage-matched. The observed pattern is conditional on the backbone, data stream, and budget range. 5.3 Limitations All experiments use the CIFAR-100 dataset, one ten-task partition (split seed 13), one ResNet-18 backbone, and three training seeds. No variation in class order, task granularity, dataset, or architecture is tested. The active-budget and retrieval sweeps cover only the reported values, and the default ρ=3ρ=3 was not swept separately. A new class retains its full transient stream before its first rebuild, so the boundary candidate storage bound does not capture all mid-task storage. The iCaRL comparison does not isolate refresh from the objective and storage differences between the two protocols. No matched experiment varies only the refresh policy while retaining the objective, head, readout, active budget, candidate multiplier, data order, and seed set fixed. Three matched seeds are used in the paired supporting comparisons, so tiny effects are not estimated reliably. The next experiment should use one common objective, head, readout, active budget, candidate multiplier, data order, and seed set, then replace arrival-time prefix truncation with refresh-all-class candidate reselection. That design would support a refresh-specific claim. 6 Conclusion We proposed Uniform Herding, a replay method that allocates a uniform active exemplar budget and refreshes every observed class in the current feature representation. Selected exemplars form the replay set, while a bounded candidate pool retains examples for future reselection. At M=2,000M=2,000 and b=64b=64, Uniform Herding reaches 44.00±0.51%44.00± 0.51\% final average accuracy and 17.22±0.43%17.22± 0.43\% forgetting, against 42.33±1.20%42.33± 1.20\% and 24.87±1.11%24.87± 1.11\% for iCaRL, and 28.60±1.35%28.60± 1.35\% and 55.86±1.42%55.86± 1.42\% for the static bank. 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Appendix A Reproducibility Details The source code to reproduce all experiments is available at https://github.com/neryva-lab/uniform-herding. All experiments used CIFAR-100 in a fixed ten-task class-incremental partition of ten classes per task. The class partition was created by split seed 13 and shared by all runs. The three reported seeds therefore vary training randomness rather than class order. Each task used a ResNet-18 with 64 base filters and no dropout, batch size 128, mixed-precision arithmetic, and SGD with learning rate 0.1, momentum 0.9, weight decay 5×10−45× 10^-4, and gradient clipping at 1.0. No learning-rate schedule or warm-up was used. The configured task length was 70 epochs. Run metadata records 71 epochs for every seed because the trainer’s epoch counter was incremented once after the final configured epoch. This recording discrepancy does not alter the configured schedule. Until a variant changes a setting, Uniform Herding uses a cosine-margin head (scale 30, margin 0.35), weight imprinting for each new task’s head rows after task 0, distillation weight 1 at temperature 2, and retrieval budget 64. The no-distillation ablation sets the distillation weight to zero. The linear-head variant replaces the cosine-margin head. The static bank and head-logit variant use head-logit prediction. All replay configurations other than these use NME prediction. The no-replay baseline has no replay readout. Uniform Herding replays only its selected exemplars. Its implementation default is ρ=pool_multiplier=3ρ= pool\_multiplier=3: the candidate pool is bounded by ρMρ M at completed task boundaries in the reported setting, while the current-task stream before a class’s first rebuild is transient and may exceed that bound. Table 4: Protocol settings shared across runs unless an ablation explicitly changes them. Setting Value Dataset and partition CIFAR-100; 10 tasks × 10 classes; split seed 13 Probe / validation split 30 / 20 Backbone ResNet-18; 64 base filters; dropout 0 Optimizer SGD; lr 0.1; momentum 0.9; weight decay 5×10−45× 10^-4 Training 70 configured epochs per task; batch size 128; gradient clip 1.0 Precision 16-mixed Random seeds 1993, 2023, 42 Active exemplar budget 2,000 for replay configurations; not used by no replay Retrieval budget 64 for replay configurations; not used by no replay Candidate multiplier (ρ) 3 for Uniform Herding; implementation default Replay source Selected active exemplars; candidate pool used only for refresh Hardware Tesla T4 Software Python 3.12.13; PyTorch 2.11.0+cu128; Lightning 2.6.5 Appendix B Task-Level Results For task i, reported forgetting is the difference between the best accuracy attained on task i during training and its accuracy after the final task. Figure 5 gives this quantity for every evaluated configuration and task. The final task has zero forgetting by construction, so the figure separates aggregate retention from its distribution over task. Figure 5: Per-task forgetting, in percentage points, for all evaluated configurations. Each entry is the drop from the task’s best observed accuracy to its final accuracy. Task T9 is zero by definition because it is introduced last. Figures 7 and 7 show the complete task-by-time accuracy matrices for Uniform Herding and iCaRL. Row i, column t is the accuracy on task i after learning through task t; cells with i>ti>t are undefined and omitted. These matrices are the underlying trajectories from which task-level forgetting is calculated. Figure 6: Task-evolution accuracy matrix for Uniform Herding with NME prediction. Figure 7: Task-evolution accuracy matrix for iCaRL. Figure 8 provides a seed-level view of the stability comparison. For each earlier task and seed, it connects accuracy at introduction with final accuracy. It visualizes the per-seed quantities used for the stability comparison and is not an additional statistical test. Figure 8: Seed-level task trajectories for Uniform Herding and the no-distillation ablation. Lines connect task-introduction accuracy to final accuracy for the same task and seed. Appendix C Additional Diagnostics The following figures provide supplementary views of the matched within-method comparisons (Figure 9) and the joint accuracy–forgetting distribution (Figure 10). The exact per-configuration values remain in Tables 2 and 3. Figure 9: Matched per-seed changes relative to Uniform Herding. Negative accuracy changes and positive forgetting changes are unfavorable. Figure 10: Average accuracy versus forgetting for baselines, within-method variants, and resource configurations. Higher accuracy and lower forgetting are preferred. The points do not define a causal trade-off curve. Appendix D Exemplar Quotas After task t, the active budget is divided among the 10(t+1)10(t+1) observed classes. Table 5 lists the resulting per-class quotas. When the budget is not divisible by the number of observed classes, floor rounding assigns the remainder to the first classes in identifier order. Table 5: Per-class active exemplar quota after each task. Ranges indicate the one-exemplar difference induced by floor rounding. Active budget T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 500 50 25 16–17 12–13 10 8–9 7–8 6–7 5–6 5 2,000 200 100 66–67 50 40 33–34 28–29 25 22–23 20 4,000 400 200 133–134 100 80 66–67 57–58 50 44–45 40 Appendix E Seed-Level Outcomes and Compute Table 6 reports the raw aggregate metrics for every run and seed. Values are in percentages. The table makes the reported means and standard deviations auditable without treating the three training seeds as independent task-level observations. Table 6: Per-seed final average accuracy, forgetting, and backward transfer. ID Configuration / seed Average accuracy Forgetting BWT B0 No replay / 1993 7.79 80.73 -80.73 B0 No replay / 2023 8.05 78.94 -78.94 B0 No replay / 42 7.89 80.97 -80.97 B1 iCaRL / 1993 40.88 25.83 -25.83 B1 iCaRL / 2023 43.82 25.46 -25.46 B1 iCaRL / 42 42.29 23.32 -23.32 B2 Static bank / 1993 28.15 56.34 -56.34 B2 Static bank / 2023 30.43 53.93 -53.93 B2 Static bank / 42 27.22 57.31 -57.31 B3 Uniform Herding / 1993 43.64 16.68 -16.41 B3 Uniform Herding / 2023 44.72 17.26 -16.91 B3 Uniform Herding / 42 43.65 17.73 -17.41 a1 No KD / 1993 41.72 29.10 -29.10 a1 No KD / 2023 42.66 28.90 -28.90 a1 No KD / 42 43.19 28.64 -28.64 a2 Head-logit / 1993 34.09 46.39 -46.39 a2 Head-logit / 2023 33.34 48.12 -48.12 a2 Head-logit / 42 33.20 48.22 -48.22 a3 Linear head / 1993 43.32 17.73 -17.73 a3 Linear head / 2023 43.60 17.91 -17.87 a3 Linear head / 42 42.73 16.39 -16.39 a4 Random selection / 1993 40.87 18.59 -18.59 a4 Random selection / 2023 42.03 18.82 -18.82 a4 Random selection / 42 41.94 17.73 -17.43 s1 Active budget 500 / 1993 32.08 31.18 -31.18 s1 Active budget 500 / 2023 35.79 29.86 -29.86 s1 Active budget 500 / 42 33.98 30.41 -30.41 s2 Active budget 4000 / 1993 47.03 12.52 -12.02 s2 Active budget 4000 / 2023 47.61 13.93 -13.59 s2 Active budget 4000 / 42 47.33 13.48 -12.62 s3 Retrieval 32 / 1993 41.93 16.91 -16.79 s3 Retrieval 32 / 2023 43.36 17.88 -17.41 s3 Retrieval 32 / 42 42.13 16.86 -16.40 s4 Retrieval 128 / 1993 43.41 17.48 -17.21 s4 Retrieval 128 / 2023 44.84 18.34 -18.01 s4 Retrieval 128 / 42 44.24 17.62 -17.23 Table 7 reports elapsed wall-clock time per run on a Tesla T4. These timings describe the implementation and hardware used here. They are not hardware-independent efficiency comparisons. Table 7: Wall-clock time per run in seconds (mean ± standard deviation across three seeds), measured on a Tesla T4. ID Configuration Seconds B0 No replay 2022.4±79.42022.4± 79.4 B1 iCaRL 3649.3±26.13649.3± 26.1 B2 Static bank 2756.4±109.32756.4± 109.3 B3 Uniform Herding 4635.4±47.54635.4± 47.5 a1 No KD 3446.0±43.73446.0± 43.7 a2 Head-logit 4332.4±33.34332.4± 33.3 a3 Linear head 3957.4±17.83957.4± 17.8 a4 Random selection 4336.8±18.54336.8± 18.5 s1 Active budget 500 4237.0±55.44237.0± 55.4 s2 Active budget 4000 4309.4±15.34309.4± 15.3 s3 Retrieval 32 3516.5±25.33516.5± 25.3 s4 Retrieval 128 5285.7±40.75285.7± 40.7