Parameter-level model merging is an emerging paradigm in multi-task learning with significant promise. Previous research has explored its connections with prediction-level model ensembling-commonly viewed as the upper bound for merging-to reveal the potential of achieving performance consistency between the two. However, this observation relies on certain preconditions, such as being limited to two models, using ViT-based models, and all models are fine-tuned from the same pre-trained checkpoint. To further understand the intrinsic connections between model merging and model ensembling, this paper explores an interesting possibility: If these restrictions are removed, can performance consistency still be achieved between merging and ensembling? To answer this question, we first theoretically establish a performance correlation between merging and ensembling. We find that even when previous restrictions are not met, there is still a way for model merging to attain a near-identical and superior performance similar to that of ensembling. To verify whether our findings are practical, we introduce a validation framework termed Neural Ligand (NeuLig). The learning process of NeuLig is meticulously designed with a specialized loss function supported by theoretical foundations. Experimental results demonstrate the robust resilience of NeuLig in terms of both model scale and the number of collaborating models. For instance, for the case involving 5 CLIP-ViT-B/32 models, parameter-level merging achieves the same performance as prediction-level ensembling (merging: 95.44% vs. ensembling: 95.46%).

Following the financial crisis of 2007-2008, regulators issued specific guidance to help banks reduce the risk of financial losses or other adverse consequences stemming from decisions based on incorrect or misused financial models. Since then, the guidance has become the model risk management bible for financial institutions. It is used to ensure that model validation, typically performed annually, can identify vulnerabilities in the models and manage them effectively. Recently, the rapid advance and broader adoption of machine learning (ML) models have added more complexity and time to the model validation process. Specifically, ML models have highlighted expertise gaps in in-house model validation teams trained in traditional modeling techniques.

The added risk brought on by the complexity of machine-learning models can be mitigated by making well-targeted modifications to existing validation frameworks. Machine learning and artificial intelligence are set to transform the banking industry, using vast amounts of data to build models that improve decision making, tailor services, and improve risk management. According to the McKinsey Global Institute, this could generate value of more than $250 billion in the banking industry.1 1.For the purposes of this article machine learning is broadly defined to include algorithms that learn from data without being explicitly programmed, including, for example, random forests, boosted decision trees, support-vector machines, deep learning, and reinforcement learning. The definition includes both supervised and unsupervised algorithms. For a full primer on the applications of artificial intelligence, we refer the reader to "An executive's guide to AI."

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley-Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.