# Local Back-Propagation for Forward-Forward Networks: Independent Unsupervised Layer-Wise Training
## 5 Discussion  
This study demonstrates that the proposed LBP method offers a viable alternative to BP by enabling deep learning without the need for backward passes. By extending the FF framework with layer-wise unsupervised learning, LBP eliminates the need for specialized inputs and non-standard loss functions, thereby addressing a key limitation of the original FF algorithm. Our results show that LBP achieves greater training stability than FF and enables practical application using standard data formats and objectives. In terms of performance, the proposed LBP models consistently outperform SLPs, and in some configurations such as CAE-LBP and AE-LBP, they also surpass MLPs trained with BP, particularly in federated learning settings. These results suggest that local unsupervised training can still facilitate meaningful information propagation between layers, even in the absence of global gradients. However, LBP generally shows lower performance than CNNs trained with BP, especially on complex datasets like CIFAR-100. We acknowledge this limitation. We believe that the relatively low performance stems from the local nature of training in LBP. Because each layer is trained independently, the model may struggle to capture sufficient semantic depth and inter-layer coherence. While BP enables multi-layer optimization through chained gradients, which can be seen as multiplicative in nature, LBP accumulates representational knowledge in an additive manner. This difference may lead to suboptimal parameter usage and reduced model expressiveness across layers. An important finding from our federated learning experiments is the notable difference in performance scaling between CAE-LBP and AE-LBP as model depth increases. Specifically, while AE-LBP exhibited diminishing returns with the addition of more layers, CAE-LBP consistently demonstrated improved accuracy with deeper architectures. We hypothesize that this trend arises from the inherent advantages of convolutional operations in capturing hierarchical spatial features. Each CAE-LBP cell serves as an effective local feature extractor, progressively constructing more abstract and informative representations from the outputs of preceding layers. The local reconstruction objective further encourages each cell to retain and refine essential spatial information before forwarding it to the next stage. In contrast, AE-LBP relies on fully connected layers that require flattening the input, which can lead to a loss of spatial structure and thus limit the benefits of increased depth. Additionally, some LBP variants, such as DAE-LBP and GAN-LBP, displayed unstable training behavior, likely due to their sensitivity to injected noise or adversarial objectives. This highlights the importance of model selection and configuration when applying LBP to different tasks. These observations suggest that the proposed LBP framework is particularly well suited for convolutional architectures, and highlight its potential for scalable and efficient training of deep vision models in distributed learning environments. From a practical standpoint, among the LBP variants, CAE-FF shows a balance between speed and performance, but other methods introduce a moderate increase in training time per epoch due to local reconstruction at each layer. However, this overhead is offset by significantly improved memory efficiency. Since each layer is trained independently and sequentially, the model can be trained with only one layer loaded into GPU memory at a time. This enables training of deep models in memory-constrained environments, such as edge devices or federated systems. Nonetheless, communication and coordination in federated settings remain open challenges. In summary, LBP bridges a gap between biologically motivated algorithms and practical deep learning. While it cannot fully replicate the performance of BP, it offers a scalable and resource-efficient alternative suitable for certain deployment scenarios.