Semantic XPath: Structured Agentic Memory Access for Conversational AI

Conversational AI (ConvAI) agents increasingly maintain structured memory to support long-term, task-oriented interactions. In-context memory approaches append the growing history to the model input, which scales poorly under context-window limits. RAG-based methods retrieve request-relevant information, but most assume flat memory collections and ignore structure. We propose Semantic XPath, a tree-structured memory module to access and update structured conversational memory. Semantic XPath improves performance over flat-RAG baselines by 176.7% while using only 9.1% of the tokens required by in-context memory. We also introduce SemanticXPath Chat, an end-to-end ConvAI demo system that visualizes the structured memory and query execution details. Overall, this paper demonstrates a candidate for the next generation of long-term, task-oriented ConvAI systems built on structured memory.

Near-optimal Linear Predictive Clustering in Non-separable Spaces via Mixed Integer Programming and Quadratic Pseudo-Boolean Reductions

Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly used for LPC, alternate between clustering and linear regression but lack global optimality. While effective for separable clusters, they struggle in non-separable settings where clusters overlap in feature space. In an alternative constrained optimization paradigm, Bertsimas and Shioda (2007) formulated LPC as a Mixed-Integer Program (MIP), ensuring global optimality regardless of separability but suffering from poor scalability. This work builds on the constrained optimization paradigm to introduce two novel approaches that improve the efficiency of global optimization for LPC. By leveraging key theoretical properties of separability, we derive near-optimal approximations with provable error bounds, significantly reducing the MIP formulation's complexity and improving scalability. Additionally, we can further approximate LPC as a Quadratic Pseudo-Boolean Optimization (QPBO) problem, achieving substantial computational improvements in some settings. Comparative analyses on synthetic and real-world datasets demonstrate that our methods consistently achieve near-optimal solutions with substantially lower regression errors than greedy optimization while exhibiting superior scalability over existing MIP formulations.