Do Not Imitate, Reinforce: Iterative Classification via Belief Refinement

Class-incremental learning requires a model to learn new classes while preserving decision regions for old ones. This is difficult when raw old samples are no longer available. We propose Prototype Latent World Model Replay, a memory-free framework that stores old classes as distributions over stable hidden states rather than as images. A frozen ImageNet-pretrained encoder maps each image into a latent state space. In this space, each class is summarized by several prototype-centered distributions with class-specific variances. When new classes arrive, the model samples old latent states from this prototype world model. It then trains a lightweight adapter and classifier using both sampled old states and real new-class features. We also add a supervised contrastive term in the adapter space to promote intra-class compactness and old-new class separation. On Split CIFAR-100, our method improves over fine-tuning under Inc5, Inc10, and Inc20 without storing raw exemplars. The full Ours-LWM+Con model raises LastAcc from 4.55% to 31.64%, from 9.06% to 37.06%, and from 16.96% to 43.10% in Inc5, Inc10, and Inc20, respectively. It also achieves AvgAcc of 45.86%, 52.19%, and 56.18%. Ablation and retention analyses show that stable latent-state replay is the main source of the gain. Contrastive separation further refines the old-new geometry. These results suggest that prototype latent memory preserves reusable class-state distributions, rather than only fitting the current classifier.

A prediction that is both confident and wrong is a critical reliability failure because it can bypass abstention and human review precisely when the model is mistaken. Empirical risk minimization (ERM) controls average loss but not this failure directly, while calibration, uncertainty estimation, conformal risk control, and selective prediction methods target related reliability properties rather than bounding the joint failure event during training. We propose ReliableNet, which constrains the Joint Confident-Wrong (JCW) probability, the probability that a prediction is simultaneously confident and incorrect, below a user-specified risk budget $α\in(0,1)$. We formulate this as a chance-constrained ERM problem, use a conservative smooth inner approximation whose population feasibility implies the original JCW constraint. Across four tabular and two image datasets, ReliableNet is the only method certified within the JCW budget for every dataset and seed in distribution, when compared against baselines spanning ERM, post-hoc calibration, conformal risk control, and selective prediction. Under demographic, ambiguity, spurious-correlation, novel-class, and covariate shifts, it achieves the lowest empirical JCW among the compared methods while remaining very competitive in accuracy, coverage, calibration, and selective prediction. Risk-coverage results further indicate that ReliableNet achieves better selective ranking than the benchmark methods on most datasets. Overall, ReliableNet provides a principled approach to trustworthy classification.

This paper proposes a novel loss concept for supervised classification tasks. Rather than enforcing a direct mapping from each input sample to a single assigned label, we define an optimization objective over all classifier outputs as a bimodal Gaussian distribution. This softer target formulation implicitly captures class ambiguity, mitigates overfitting, and encourages the learning of more robust decision boundaries, all without requiring additional label information. Experimental results demonstrate consistent improvements in robustness, with particularly pronounced gains in low-data regimes, while requiring only minimal modifications to standard training pipelines.