reviews: 
Comments: This paper considers the problem of clustered federated learning. Inspired by a Bayesian modeling of clustered FL, the provides three clustering heuristics. The paper evaluates the proposed heuristics and shows that in practice they outperform  WeCFL, which is the state-of-the-art FL clustering method.
Strengths: - The proposed clustering heuristics exhibit superior performance compared to the current state-of-the-art WeCFL in federated learning.
- The experimental results section is well-crafted, providing a thorough evaluation of the proposed methods.
- BCFL distinguishes itself from other clustering federated learning methods by dynamically adjusting clusters, offering a unique approach that departs from hierarchical clustering strategies.
Weaknesses: - The paper's overall clarity is compromised due to unnecessarily complex and at times undefined notation, making it challenging to follow.
- The update mechanism for the parameters of the Bayesian model lacks explicit explanation, leaving a crucial aspect of the methodology unclear.
- The comparison and discussion of related work are superficial, lacking a fundamental exploration of how the proposed method differs from other clustering approaches. 
- The claim that the paper provides a "unified framework with a rigorous formulation" and offers "new theoretical insights and algorithms" is disputed, as the paper fails to present any novel theoretical contributions.
- Section 3 contains derivations that are deemed obvious, contributing minimally to the understanding of the proposed approach.
- The content in Sections 3 and 4.1 communicates a message that, in my interpretation, appears rather straightforward. The outlined two-step iteration involves computing the "optimal" association $\theta^{*}_{t}$ given cluster weights $\Omega$ and updating cluster weights based on the current association rule. Furthermore, the solution presented in equation (16) suggests associating a client $j$ with a cluster $i$ that maximizes $\log(D^j|w^i)$. While these concepts are essential, the simplicity of the presented message does not seem commensurate with the extensive coverage given to these sections (four pages). The detailed explanation does not justify the space allocated, and as such, Sections 3 and 4.1 may be perceived as overextended for the relatively straightforward content they provide. 
- In light of the preceding remark, it might be beneficial for the paper to discuss soft clustering approaches based on the EM algorithm.
- The proposed methods lack theoretical guarantees, relying solely on heuristics without a solid theoretical foundation.
- The success of the proposed method heavily depends on the higher computational cost of BCFL-MH, raising concerns about the practicality and efficiency of the cheaper variants (BCFL-G and BCFL-C). In fact,  BCFL-G and BCFL-C do not show a significant improvement over FedAvg and WeCFL; the improvement never exceeds $1$ p.p., and is often lower then $0.1$ p.p.   
- Several minor issues, including inconsistent citation style, grammatical errors, and unclear notation choices, need attention for a more polished presentation: 
     - The paper seems to use the wrong citation style. It refers to the authors when it should refer to the paper. For example, the sentence "FL allows collaborative model training without data sharing across clients, thus preserving their privacy McMahan et al. (2017)" should be "FL allows collaborative model training without data sharing across clients, thus preserving their privacy (McMahan et al., 2017). "
    - In Section 1, "the is a lack" -> "there is a lack". 
    - What is the reason behind using $\mathbb{P}$ instead of $P$ in page 3?
    -In Page 4, "to denote the a particular" -> "to denote a particular".
     - In Page 7, "both feature- and label- skew" -> "both feature---and label---skew"
Recommendation: 5: marginally below the acceptance threshold
Reviewer confidence: 2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 2 fair
Clarity: 1 poor