## 4 Types of FL
### Vertical FL (VFL)  
Vertical federated learning (VFL) is a specialized variant of federated learning designed for scenarios where local parties have diverse attributes within the same user cohort, unlike general FL systems that deal with numerous records sharing the same feature space. In VFL, there are two main types of participants: the active party, which initiates the training task and holds the primary label for data samples, and the passive participants, which contribute additional features for the same set. For instance, a bank with limited transactional features can use VFL with another entity possessing complementary data to predict default risks and credit scores [34; 57]. VFL differs from horizontal FL (HFL) by focusing on scenarios where entities possess complementary datasets (data from B parts), while HFL deals with entities having similar types of data but from different users (data from A parts). In VFL, parties target the same user set but with significantly different features, such as one entity having demographic data and another focusing on online behavior. A common identifier, like user IDs, allows collaboration without compromising data privacy. Throughout this process, the feature values remain undisclosed, ensuring data confidentiality. A key feature of VFL is its emphasis on combining different features of the same user set, in contrast to HFL's approach, where data are distributed across numerous users. This cooperative approach in VFL aids in assembling AI models that use each participant's contribution, streamlining the model training process in settings where traditional averaging methods might fall short [58]. An illustrative real-world application of VFL would be the following. Consider a scenario whereby a financial institution, with abundant transactional data, partners with an e-commerce platform, which tracks users' browsing and purchasing behaviors. Historically, insights from either of these entities would remain in isolated repositories. However, VFL introduces the potential for a transformative, symbiotic relationship. Using common user identifiers, these entities can collaboratively design predictive models, giving rise to insights such as predictions of purchasing likelihoods based on a mixture of financial history and online behavior [57]. To further illustrate this concept, consider a multi-party, multi-class VFL (MMVFL) system. This framework takes into account the distribution of labels across VFL participants while ensuring data privacy. It empowers multiple entities to collaborate and share labels, thereby enhancing the overall learning experience. A more simplified approach reduces the complexity of the VFL system architecture and coordination requirements by eliminating the need for a central coordinator. Such advancements elevate the efficiency and adaptability of VFL frameworks. Nonetheless, VFL, despite being innovative, has its own complexities. Challenges in federated learning (FL) include aligning data across different parties, upholding privacy standards, and integrating models trained on varied datasets. [PERSON] et al. [59] stress that the goal is not merely combining data but creating actionable insights. To handle issues such as diverse and unreliable network connections, asynchronous VFL architectures are being used. These allow model updates without synchronizing data sharing. Modern VFL approaches balance protection, competition, and efficiency [60], shifting away from solely cryptographic methods. Traditional VFL uses a central coordinator to securely aggregate the results, preventing data breaches. However, new methods propose removing this coordinator to improve the efficiency, with direct communication between the participants. While this could enhance the efficiency, it requires careful attention to security to prevent breaches and resist attacks. In VFL, entities (such as businesses or institutions) exchange diverse aspects of the same data topic, such as demographic data from a bank paired with purchasing activity data from an e-commerce platform.