Limits for Learning with Language Models

With the advent of large language models (LLMs), the trend in NLP has been to train LLMs on vast amounts of data to solve diverse language understanding and generation tasks. The list of LLM successes is long and varied. Nevertheless, several recent papers provide empirical evidence that LLMs fail to capture important aspects of linguistic meaning. Focusing on universal quantification, we provide a theoretical foundation for these empirical findings by proving that LLMs cannot learn certain fundamental semantic properties including semantic entailment and consistency as they are defined in formal semantics. More generally, we show that LLMs are unable to learn concepts beyond the first level of the Borel Hierarchy, which imposes severe limits on the ability of LMs, both large and small, to capture many aspects of linguistic meaning. This means that LLMs will continue to operate without formal guarantees on tasks that require entailments and deep linguistic understanding.

Adequate and fair explanations

Explaining sophisticated machine-learning based systems is an important issue at the foundations of AI. Recent efforts have shown various methods for providing explanations. These approaches can be broadly divided into two schools: those that provide a local and human interpreatable approximation of a machine learning algorithm, and logical approaches that exactly characterise one aspect of the decision. In this paper we focus upon the second school of exact explanations with a rigorous logical foundation. There is an epistemological problem with these exact methods. While they can furnish complete explanations, such explanations may be too complex for humans to understand or even to write down in human readable form. Interpretability requires epistemically accessible explanations, explanations humans can grasp. Yet what is a sufficiently complete epistemically accessible explanation still needs clarification. We do this here in terms of counterfactuals, following [Wachter et al., 2017]. With counterfactual explanations, many of the assumptions needed to provide a complete explanation are left implicit. To do so, counterfactual explanations exploit the properties of a particular data point or sample, and as such are also local as well as partial explanations. We explore how to move from local partial explanations to what we call complete local explanations and then to global ones. But to preserve accessibility we argue for the need for partiality. This partiality makes it possible to hide explicit biases present in the algorithm that may be injurious or unfair.We investigate how easy it is to uncover these biases in providing complete and fair explanations by exploiting the structure of the set of counterfactuals providing a complete local explanation.

Bias in Semantic and Discourse Interpretation

In this paper, we show how game-theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias. Interpretive bias is an essential feature of learning and understanding but also something that can be used to pervert or subvert the truth. The framework we develop here provides tools for understanding and analyzing the range of interpretive biases and the factors that contribute to them.