The application of large language models (LLMs) in domain-specific contexts, including finance, has expanded rapidly. Domain-specific LLMs are typically evaluated based on their performance in various downstream tasks relevant to the domain. In this work, we present a detailed analysis of fine-tuning LLMs for such tasks. Somewhat counterintuitively, we find that in domain-specific cases, fine-tuning exclusively on the target task is not always the most effective strategy. Instead, multi-task finetuning - where models are trained on a cocktail of related tasks - can significantly enhance performance. We demonstrate how this approach enables a small model, such as Phi-3-Mini, to achieve state-of-the-art results, even surpassing the much larger GPT-4-o model on financial benchmarks. Our study involves a large-scale experiment, conducting over 200 training experiments using several widely adopted LLMs as baselines, and empirically confirms the benefits of multi-task fine-tuning. Additionally, we explore the use of general instruction data as a form of regularization, suggesting that it helps minimize performance degradation. We also investigate the inclusion of mathematical data, finding improvements in numerical reasoning that transfer effectively to financial tasks. Finally, we note that while fine-tuning for downstream tasks leads to targeted improvements in task performance, it does not necessarily result in broader gains in domain knowledge or complex domain reasoning abilities.

Large language models (LLMs) encapsulate a vast amount of factual information within their pre-trained weights, as evidenced by their ability to answer diverse questions across different domains. However, this knowledge is inherently limited, relying heavily on the characteristics of the training data. Consequently, using external datasets to incorporate new information or refine the capabilities of LLMs on previously seen information poses a significant challenge. In this study, we compare two common approaches: unsupervised fine-tuning and retrieval-augmented generation (RAG). We evaluate both approaches on a variety of knowledge-intensive tasks across different topics. Our findings reveal that while unsupervised fine-tuning offers some improvement, RAG consistently outperforms it, both for existing knowledge encountered during training and entirely new knowledge. Moreover, we find that LLMs struggle to learn new factual information through unsupervised fine-tuning, and that exposing them to numerous variations of the same fact during training could alleviate this problem.

Extrapolation remains a grand challenge in deep neural networks across all application domains. We propose an operator learning method to solve time-dependent partial differential equations (PDEs) continuously and with extrapolation in time without any temporal discretization. The proposed method, named Diffusion-inspired Temporal Transformer Operator (DiTTO), is inspired by latent diffusion models and their conditioning mechanism, which we use to incorporate the temporal evolution of the PDE, in combination with elements from the transformer architecture to improve its capabilities. Upon training, DiTTO can make inferences in real-time. We demonstrate its extrapolation capability on a climate problem by estimating the temperature around the globe for several years, and also in modeling hypersonic flows around a double-cone. We propose different training strategies involving temporal-bundling and sub-sampling and demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals as well as zero-shot super-resolution in time.

This paper presents a comprehensive comparison of various machine learning models, namely U-Net [12], U-Net integrated with Vision Transformers (ViT) [11], and Fourier Neural Operator (FNO) [4], for time-dependent forward modelling in groundwater systems. Through testing on synthetic datasets, it is demonstrated that U-Net and U-Net + ViT models outperform FNO in accuracy and efficiency, especially in sparse data scenarios. These findings underscore the potential of U-Net-based models for groundwater modelling in real-world applications where data scarcity is prevalent.