Backpropagation-Free Continual Learning: A Unified Energy-Based Framework, Reproducible Benchmark, and Open Challenges

Backpropagation has been the dominant credit-assignment mechanism behind the deep-learning revolution, yet it is global, memory-hungry, biologically implausible, and costly on hardware dominated by data movement. In parallel, predictive coding, equilibrium propagation, contrastive Hebbian learning and forward-only schemes have shown that useful credit assignment can also arise from local variables and the relaxation of an energy function. This manuscript is a review with a reproducible benchmark, not a proposal of a new learning rule. We organise existing backpropagation-free methods and continual-learning strategies under a common Local Equilibrium Learning (LEL) formulation, re-validate the core theoretical links numerically, and use a controlled continual-learning benchmark as an auditable case study within the review. The theoretical contribution is unification and verification, not priority over predictive coding, equilibrium propagation or replay. The empirical contribution is diagnostic rather than exhaustive: a benchmark of catastrophic forgetting with local networks that makes the review reproducible. We compare regularisation (EWC, SI), noise replay and generative “dreaming” across MNIST, Fashion-MNIST and CIFAR-10 in two independent implementations. Generative replay with local generators turns class-incremental Split-MNIST forgetting (chance level, the same as EWC and SI) into 86.8±0.2%, which is 96% of the joint-training ceiling and 97.4% in the task-incremental setting; the same mechanism reaches 82.0% on Fashion-MNIST and 37.0% on CIFAR-10. A matched control that holds the retention mechanism fixed and swaps only the learning rule shows that backpropagation with the same generative replay reaches a comparable or slightly higher accuracy than LEL (90.3% vs. 86.7% class-incremental); the benefit is attributable to generative replay as a retention mechanism, not to the local learning rule itself, which we state plainly rather than let the headline number imply otherwise. The CIFAR-10 number is intentionally reported as a limitation of a shallow raw-pixel local model, not as a claim of competitiveness with modern CNNs or transformers trained by backpropagation. We separate positive results; negative results and open limitations; and release scripts, seeds, dataset preparation and configuration files so that this paper can serve as an honest entry point for backpropagation-free continual learning.