Relationships among teachers are known to influence their teaching-related perceptions. We study whether and how teachers' advising relationships (networks) are related to their perceptions of satisfaction, students, and influence over educational policies, recorded as their responses to a questionnaire (item responses). We propose a novel joint model of network and item responses (JNIRM) with correlated latent variables to understand these co-varying ties. This methodology allows the analyst to test and interpret the dependence between a network and item responses. Using JNIRM, we discover that teachers' advising relationships contribute to their perceptions of satisfaction and students more often than their perceptions of influence over educational policies. In addition, we observe that the complementarity principle applies in certain schools, where teachers tend to seek advice from those who are different from them. JNIRM shows superior parameter estimation and model fit over separately modeling the network and item responses with latent variable models.

As model sizes in machine learning continue to scale, distributed training is necessary to accommodate model weights within each device and to reduce training time. However, this comes with the expense of increased communication overhead due to the exchange of gradients and activations, which become the critical bottleneck of the end-to-end training process. In this work, we motivate the design of multi-dimensional networks within machine learning systems as a cost-efficient mechanism to enhance overall network bandwidth. We also identify that optimal bandwidth allocation is pivotal for multi-dimensional networks to ensure efficient resource utilization. We introduce LIBRA, a framework specifically focused on optimizing multi-dimensional fabric architectures. Through case studies, we demonstrate the value of LIBRA, both in architecting optimized fabrics under diverse constraints and in enabling co-optimization opportunities.