DebateQA: Evaluating Question Answering on Debatable Knowledge

The rise of large language models (LLMs) has enabled us to seek answers to inherently debatable questions on LLM chatbots, necessitating a reliable way to evaluate their ability. However, traditional QA benchmarks assume fixed answers are inadequate for this purpose. To address this, we introduce DebateQA, a dataset of 2,941 debatable questions, each accompanied by multiple human-annotated partial answers that capture a variety of perspectives. We develop two metrics: Perspective Diversity, which evaluates the comprehensiveness of perspectives, and Dispute Awareness, which assesses if the LLM acknowledges the question's debatable nature. Experiments demonstrate that both metrics align with human preferences and are stable across different underlying models. Using DebateQA with two metrics, we assess 12 popular LLMs and retrieval-augmented generation methods. Our findings reveal that while LLMs generally excel at recognizing debatable issues, their ability to provide comprehensive answers encompassing diverse perspectives varies considerably.

Truthful Dataset Valuation by Pointwise Mutual Information

A common way to evaluate a dataset in ML involves training a model on this dataset and assessing the model's performance on a test set. However, this approach has two issues: (1) it may incentivize undesirable data manipulation in data marketplaces, as the self-interested data providers seek to modify the dataset to maximize their evaluation scores; (2) it may select datasets that overfit to potentially small test sets. We propose a new data valuation method that provably guarantees the following: data providers always maximize their expected score by truthfully reporting their observed data. Any manipulation of the data, including but not limited to data duplication, adding random data, data removal, or re-weighting data from different groups, cannot increase their expected score. Our method, following the paradigm of proper scoring rules, measures the pointwise mutual information (PMI) of the test dataset and the evaluated dataset. However, computing the PMI of two datasets is challenging. We introduce a novel PMI measuring method that greatly improves tractability within Bayesian machine learning contexts. This is accomplished through a new characterization of PMI that relies solely on the posterior probabilities of the model parameter at an arbitrarily selected value. Finally, we support our theoretical results with simulations and further test the effectiveness of our data valuation method in identifying the top datasets among multiple data providers. Interestingly, our method outperforms the standard approach of selecting datasets based on the trained model's test performance, suggesting that our truthful valuation score can also be more robust to overfitting.

The Evolution of the Interplay Between Input Distributions and Linear Regions in Networks

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of deep neural networks remains uncertain. For ReLU (Rectified Linear Unit) networks with piecewise linear activations, the number of linear convex regions serves as a natural metric to gauge the network's expressivity. In this paper, we count the number of linear convex regions in deep neural networks based on ReLU. In particular, we prove that for any one-dimensional input, there exists a minimum threshold for the number of neurons required to express it. We also empirically observe that for the same network, intricate inputs hinder its capacity to express linear regions. Furthermore, we unveil the iterative refinement process of decision boundaries in ReLU networks during training. We aspire for our research to serve as an inspiration for network optimization endeavors and aids in the exploration and analysis of the behaviors exhibited by deep networks.