Artificial Intelligence
Publications
Stochasticity Is Not the Hard Part: Reduction and Complexity in Instructional Sequencing over Prerequisite DAGs
When a student must learn concepts connected by prerequisite dependencies, when does the order of instruction matter, and what does it cost to find the best one? We study instructional sequencing as a stochastic shortest-path problem in which attempting a concept succeeds with a state-dependent probability and failure leaves the learner state unchanged. We first prove that this stochasticity can be eliminated exactly: the problem collapses to a deterministic shortest-path problem on the lattice of prerequisite order ideals, preserving optimal values and actions. The collapse removes stochastic complexity but not combinatorial complexity: optimal sequencing remains NP-hard -- via reduction from feedback arc set in tournaments -- even with no prerequisite edges, unit costs, uniform binary nonnegative transfer, and success probabilities at least $1/2$. Hardness is not uniform: when realizable transfer preferences remain jointly acyclic with the prerequisites, any topological order of the residual joint graph is optimal, and fixed prerequisite width yields polynomial-time exact dynamic programming. A computable diagnostic, $mΔ$, bounds the value of sequencing before optimization. On 70,893 interactions from an introductory CS course, the diagnostic certifies a doubly easy regime -- little value to optimize and little space to search -- while constructed transfer instances realize the challenging regime, where myopic sequencing suffers large regret yet exact A* with a consistent heuristic expands only linearly many states on that family.
Autonomous Knowledge Graph Exploration with Adaptive Breadth-Depth Retrieval
Retrieving evidence for language model queries from knowledge graphs requires balancing broad search across the graph with multi-hop traversal to follow relational links. Similarity-based retrievers provide coverage but remain shallow, whereas traversal-based methods rely on selecting seed nodes to start exploration, which can fail when queries span multiple entities and relations. We introduce ARK: Adaptive Retriever of Knowledge, an agentic KG retriever that gives a language model control over this breadth-depth tradeoff using a two-operation toolset: global lexical search over node descriptors and one-hop neighborhood exploration that composes into multi-hop traversal. ARK alternates between breadth-oriented discovery and depth-oriented expansion without depending on a fragile seed selection, a pre-set hop depth, or requiring retrieval training. ARK adapts tool use to queries, using global search for language-heavy queries and neighborhood exploration for relation-heavy queries. On STaRK, ARK reaches 59.1% average Hit@1 and 67.4 average MRR, improving average Hit@1 by up to 31.4% and average MRR by up to 28.0% over retrieval-based and agentic training-free methods. Finally, we distill ARK's tool-use trajectories from a large teacher into an 8B model via label-free imitation, improving Hit@1 by +7.0, +26.6, and +13.5 absolute points over the base 8B model on AMAZON, MAG, and PRIME datasets, respectively, while retaining up to 98.5% of the teacher's Hit@1 rate.