legal analytics teams

Abstract: Probabilities of causation (PoCs) have developed steadily, from the binary measures first introduced by Pearl to the non-binary setting recently studied by Shu et al. As the theory has matured, PoCs have found applications in a growing range of areas, including personalized medicine, marketing and legal attribution. Shu et al. proposed closed-form bounds for multi-valued treatments and outcomes and proved them valid, but left their sharpness in high dimensions open. We close this gap with a mathematical proof. We further show that $\PNS$, $\PSub$, $\PRep$ and $\PN$ are all special cases of a single, more general formula. Combined with their equivalence classes, this settles the question of sharp bounds for discrete PoCs from experimental and observational data: in every dimension, they are given in closed form by a single theorem.

Abstract: Lexical semantic change is usually summarized by a scalar distance between independently sampled period distributions. This measures how much a word changed, but does not reveal when it changed, which mechanisms and component movements carried the change, or which usages support the attribution. We introduce Coupled Usage--Sense Processes (CUSP), which derives these answers from a single marginal preserving temporal process. A hierarchical coupling relates contextual distributions through latent usage components, while Markov composition makes adjacent and longer span correspondences compatible. Displacement operators quantify change magnitude and timing, split variation exactly between movement of component centers and reorganization within components, and attribute it to transported component pairs. Word-local modes resolve distinct directions of change and their activity over time, while representative passages from attributed components ground the analysis in text. Under a Gaussian mixture specialization, we prove parametric recovery of the operators and squared distances. Synthetic experiments support the predicted rate. CUSP remains competitive on English and German DWUG and recovers controlled Janus profiles while maintaining compositionally coherent transport. A large corpus of US court opinions demonstrates transition, mode, and passage attribution in unlabeled natural text. CUSP thus makes magnitude, timing, mechanism, movement, modes, and textual evidence compatible views of one lexical history.

Abstract: Large language models (LLMs) have achieved strong performance on a wide range of natural language tasks, and recent benchmarks suggest that they are increasingly adept at multi-hop reasoning. However, these benchmarks are typically short-horizon, requiring only a small number of retrieval or inference steps, and provide limited evidence of reliability on real-world tasks that involve following manuals spanning hundreds of pages with complex, interdependent guidelines. In this paper, we introduce Tasks over Application Manuals (TAM), a benchmark for evaluating long-horizon procedural reasoning. We construct TAM by curating real-world tasks from two domains: ICD-10-CM clinical coding (mapping medical conditions to diagnostic codes) and U.S. federal sentencing (computing crime sentencing guideline outcomes, specifically offense levels), with human-validated labels. Each task requires following an authoritative manual with tens of thousands of rules and executing a sequence of interdependent steps across different sections to produce an exact answer. We evaluate general-purpose prompting approaches, including retrieval-augmented generation, ReAct-style prompting, and an agent-harness baseline on GPT-5, and find that the best exact-match performance remains extremely low: 1% on ICD-10-CM coding and 15.5% on sentencing tasks. These results show that current benchmarks may overestimate LLM reasoning ability and miss a key challenge: reliably following long, rule-based procedures. The complete TAM data and code are publicly available.