Randomized Neural Network with Adaptive Forward Regularization for Online Task-free Class Incremental Learning

TL;DR

The paper tackles online task-free class incremental learning (OTCIL) by introducing a Randomized NN framework with forward regularization (-F) and its generalization -$k$F, culminating in the edRVFL-$k$F and edRVFL-$k$F-Bayes algorithms. These methods deliver one-pass, closed-form incremental updates without replay, leveraging forward unsupervised knowledge and Bayesian self-adaptation to combat catastrophic forgetting in non-i.i.d. task streams. Empirical results on FashionMNIST, CIFAR-100, and large ViT backbones show that edRVFL-$k$F-Bayes consistently achieves superior accuracy and stability, closely approaching offline experts while maintaining low memory and compute. The work advances practical OTCIL by enabling rapid decision-making, reduced regret, and compatibility with pretrained transformers, albeit with considerations for potential misuse in privacy-sensitive or surveillance contexts.

Abstract

Class incremental learning (CIL) requires an agent to learn distinct tasks consecutively with knowledge retention against forgetting. Problems impeding the practical applications of CIL methods are twofold: (1) non-i.i.d batch streams and no boundary prompts to update, known as the harsher online task-free CIL (OTCIL) scenario; (2) CIL methods suffer from memory loss in learning long task streams, as shown in Fig. 1 (a). To achieve efficient decision-making and decrease cumulative regrets during the OTCIL process, a randomized neural network (Randomized NN) with forward regularization (-F) is proposed to resist forgetting and enhance learning performance. This general framework integrates unsupervised knowledge into recursive convex optimization, has no learning dissipation, and can outperform the canonical ridge style (-R) in OTCIL. Based on this framework, we derive the algorithm of the ensemble deep random vector functional link network (edRVFL) with adjustable forward regularization (-kF), where k mediates the intensity of the intervention. edRVFL-kF generates one-pass closed-form incremental updates and variable learning rates, effectively avoiding past replay and catastrophic forgetting while achieving superior performance. Moreover, to curb unstable penalties caused by non-i.i.d and mitigate intractable tuning of -kF in OTCIL, we improve it to the plug-and-play edRVFL-kF-Bayes, enabling all hard ks in multiple sub-learners to be self-adaptively determined based on Bayesian learning. Experiments were conducted on 2 image datasets including 6 metrics, dynamic performance, ablation tests, and compatibility, which distinctly validates the efficacy of our OTCIL frameworks with -kF-Bayes and -kF styles.

Figures (20)

• Figure 1: (a) The task accuracy of CIL methods on UCI dataset plant margin-100/100. Each task contained one class and replay was forbidden. EWC 6 and CRNet 29 learned in CIL while our edRVFL-$k$F and edRVFL-$k$F-Bayes learned in harsher OTCIL without task i.i.d and boundary. Classic methods show serious knowledge forgetting and intractable adjustments in long task streams, while ours achieve immediate response, high efficacy, and less loss. (b) The diagram of CIL and OTCIL. Dashed line denotes task boundary.
• Figure 2: The description to one sub-learner using -R and -$k$F styles in OTCIL process. The concentric circles denote varied Bregman divergence penalties, and the curves denote losses on data. At time $t$, the learner using -R (blue solid circle) tries to match ${\cal L}_{l,1..t}$ (crimson solid curve) and evolve into $\theta_{l,t+1}^{-R}$ and predict. The learner using optimized -$k$F (yellow solid circle) tries to meet ${{\cal L}_{l,1..t}} + k \cdot {\hat{\cal L}_{l,t + 1}}$ (pink solid curve). The -$\upsilon$F ($\upsilon \ne k$) is an instance of non-optimized -$k$F in $k$ feasible zone (gray area), shown in green dashed style. Then at time $t+1$, the same logic follows for $\theta_{l,t+2}^{-R}$. We recommend -$k$F as it reduces decision regret on new data compared to -R. $k$ should be carefully picked in the current feasible zone for better performance. -$k$F is with hard threshold $k$ and we introduce -$k$F-Bayes with soft adaptive ones later.
• Figure 3: OTCIL processes of edRVFL-$k$F and edRVFL-$k$F-Bayes. Task stream over time is shown in a varied rufous arrow. Representations inside edRVFL multiple sub-learners are painted respectively in varied brightness yellow and purple to distinguish two algorithmic styles. Clustered sub-learners are progressively updated and uncertainty is gradually removed (shown by increasing sharpness) to present improving performance as batches come.$\ \oplus$ denotes unsupervised forward knowledge participates in the current decision, where the $k_l$ is an adjustable constant in -$k$F and adaptive variable in -$k$F-Bayes.
• Figure 4: ACC curves of partial methods of Table \ref{['tab5']} on FashionMNIST-10/5. Methods learned 2 classes in each task. The edRVFL-R, edRVFL-$k$F, and edRVFL-$k$F-Bayes learned under OTCIL scenario without task boundary.
• Figure 5: $k_{l,t+1}$ and $k_{l,t}$ variation curves of -$k$F-Bayes learning 5 tasks in OTCIL. The results of the first 6 experiments are shown here, marked by superscripts. It shows the dynamic adjustments and a phase shift between the two variables. Trends illustrate the effect of maintaining the balance of penalties in changing optimization targets.

Theorems & Definitions (10)

• Lemma 1
• Lemma 2
• Theorem 1
• Theorem 2
• Remark 1
• Theorem 3
• Corollary 1
• Remark 2
• Theorem 4
• Lemma 3