# Local Back-Propagation for Forward-Forward Networks: Independent Unsupervised Layer-Wise Training
## 4 Experiments
### Application in Federated Learning  
We conducted federated learning experiments to validate the practicality of our proposed method. Using the MNIST, CIFAR10, and CIFAR100 datasets, we compared the performance of MLP and CNN models with AE-LBP and CAE-LBP, which performed favorably among the proposed models. In total, we created 100 client models and ran 100 training rounds, randomly selecting 10 clients each round. At the end of each round, we updated the global model's weights using Federated Averaging [34], which averages the weights of the selected 10 clients. The updated global model's weights were then shared with all clients. In these experiments, the LBP cell was structured as an encoder-decoder, but to reduce communication costs and avoid reconstructing the input data, only the encoder weights were transmitted.  
In federated learning with 10 clients, the AE-LBP model (7,889,572 parameters) required 1228 MB of GPU memory, and the CAE-LBP model (12,232,103 parameters) required 1872 MB. In comparison, the MLP model (8,497,252 parameters) required 1304 MB, while the CNN model (6,373,092 parameters) required 3630 MB. These results demonstrate that the proposed LBP-based models operate with lower memory overhead than conventional architectures. In addition, since LBP models allow each layer to be trained independently, memory is only needed for a single layer at a time. On the other hand, models trained with back-propagation must load and update all layers simultaneously, resulting in much higher memory usage. Therefore, the reported memory usage for LBP models represents a conservative upper bound. In practice, when layers are processed sequentially or in a pipelined manner, the actual memory consumption can be significantly lower. This advantage becomes more significant as model size increases, making the proposed approach well suited for edge computing and federated learning environments with limited computational resources.  
Figure 8 shows the accuracy of the global model after 100 rounds. While MLP outperformed AE-LBP and CAE-LBP on MNIST, as the data became more complex, AE-LBP and CAE-LBP showed better results. Furthermore, the performance of CNN models in Figure 8 indicates that simply increasing the size of the model does not guarantee improved results. These findings confirm the practicality of our approach and suggest potential for further improvements.  
Figure 9 shows the results of federated learning experiments conducted with independent and identically distributed (IID) data, while Figures 10 and 11 show results under non-IID data conditions. The datasets were structured so that at most 20% of the total labels could be selected at any given time, and all other experimental settings remained the same.  
Figure 8: Federated learning performance for AE-LBP, CAE-LB, MLP, and CNN under independent and identically distributed (IID) settings.  
Due to the randomness in data distribution, some learning scenarios were more challenging. However, overall, LBP models generally performed better than the MLP model.  
Figure 10: Federated learning performance on CIFAR-10 under non-IID settings.  
Figure 9: Federated learning performance on CIFAR-10 under IID settings.