Exploring the Manifold of Neural Networks Using Diffusion Geometry

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.

On Evaluating the Integration of Reasoning and Action in LLM Agents with Database Question Answering

This study introduces a new long-form database question answering dataset designed to evaluate how Large Language Models (LLMs) interact with a SQL interpreter. The task necessitates LLMs to strategically generate multiple SQL queries to retrieve sufficient data from a database, to reason with the acquired context, and to synthesize them into a comprehensive analytical narrative. Our findings highlight that this task poses great challenges even for the state-of-the-art GPT-4 model. We propose and evaluate two interaction strategies, and provide a fine-grained analysis of the individual stages within the interaction. A key discovery is the identification of two primary bottlenecks hindering effective interaction: the capacity for planning and the ability to generate multiple SQL queries. To address the challenge of accurately assessing answer quality, we introduce a multi-agent evaluation framework that simulates the academic peer-review process, enhancing the precision and reliability of our evaluations. This framework allows for a more nuanced understanding of the strengths and limitations of current LLMs in complex retrieval and reasoning tasks.

Enhancing Few-shot Text-to-SQL Capabilities of Large Language Models: A Study on Prompt Design Strategies

In-context learning (ICL) has emerged as a new approach to various natural language processing tasks, utilizing large language models (LLMs) to make predictions based on context that has been supplemented with a few examples or task-specific instructions. In this paper, we aim to extend this method to question answering tasks that utilize structured knowledge sources, and improve Text-to-SQL systems by exploring various prompt design strategies for employing LLMs. We conduct a systematic investigation into different demonstration selection methods and optimal instruction formats for prompting LLMs in the Text-to-SQL task. Our approach involves leveraging the syntactic structure of an example's SQL query to retrieve demonstrations, and we demonstrate that pursuing both diversity and similarity in demonstration selection leads to enhanced performance. Furthermore, we show that LLMs benefit from database-related knowledge augmentations. Our most effective strategy outperforms the state-of-the-art system by 2.5 points (Execution Accuracy) and the best fine-tuned system by 5.1 points on the Spider dataset. These results highlight the effectiveness of our approach in adapting LLMs to the Text-to-SQL task, and we present an analysis of the factors contributing to the success of our strategy.