Equitable Access to Justice: Logical LLMs Show Promise

The costs and complexity of the American judicial system limit access to legal solutions for many Americans. Large language models (LLMs) hold great potential to improve access to justice. However, a major challenge in applying AI and LLMs in legal contexts, where consistency and reliability are crucial, is the need for System 2 reasoning. In this paper, we explore the integration of LLMs with logic programming to enhance their ability to reason, bringing their strategic capabilities closer to that of a skilled lawyer. Our objective is to translate laws and contracts into logic programs that can be applied to specific legal cases, with a focus on insurance contracts. We demonstrate that while GPT-4o fails to encode a simple health insurance contract into logical code, the recently released OpenAI o1-preview model succeeds, exemplifying how LLMs with advanced System 2 reasoning capabilities can expand access to justice.

Identifiability of Product of Experts Models

Product of experts (PoE) are layered networks in which the value at each node is an AND (or product) of the values (possibly negated) at its inputs. These were introduced as a neural network architecture that can efficiently learn to generate high-dimensional data which satisfy many low-dimensional constraints -- thereby allowing each individual expert to perform a simple task. PoEs have found a variety of applications in learning. We study the problem of identifiability of a product of experts model having a layer of binary latent variables, and a layer of binary observables that are iid conditional on the latents. The previous best upper bound on the number of observables needed to identify the model was exponential in the number of parameters. We show: (a) When the latents are uniformly distributed, the model is identifiable with a number of observables equal to the number of parameters (and hence best possible). (b) In the more general case of arbitrarily distributed latents, the model is identifiable for a number of observables that is still linear in the number of parameters (and within a factor of two of best-possible). The proofs rely on root interlacing phenomena for some special three-term recurrences.