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Gregory Li

Publications and source records attributed to Gregory Li.

5 recordsLinked to original sources

TripScore: Benchmarking and rewarding real-world travel planning with fine-grained evaluation

Travel planning is a valuable yet complex task that poses significant challenges even for advanced large language models (LLMs). While recent benchmarks have advanced in evaluating LLMs' planning capabilities, they often fall short in evaluating feasibility, reliability, and engagement of travel plans. We introduce a comprehensive benchmark for travel planning that unifies fine-grained criteria into a single reward, enabling direct comparison of plan quality and seamless integration with reinforcement learning (RL). Our evaluator achieves moderate agreement with travel-expert annotations (60.75%) and outperforms multiple LLM-as-judge baselines. We further release a large-scale dataset of 4,870 queries including 219 real-world, free-form requests for generalization to authentic user intent. Using this benchmark, we conduct extensive experiments across diverse methods and LLMs, including test-time computation, neuro-symbolic approaches, supervised fine-tuning, and RL via GRPO. Across base models, RL generally improves itinerary feasibility over prompt-only and supervised baselines, yielding higher unified reward scores.

cs.AI

Hyperbolic Handlebody Complements in 3-Manifolds

Let $M_0$ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold $M$ contains handlebodies of arbitrary genus such that the closure of their complement is hyperbolic. We then extend the octahedral decomposition to obtain bounds on volume for some of these handlebody complements.

math.GT

Hyperbolicity and Volume of Hyperbolic Bongles

We consider a simple but infinite class of staked links known as bongles. We provide necessary and sufficient conditions for these bongles to be hyperbolic. Then, we prove that all balanced hyperbolic $n$-bongles have the same volume and the corresponding volume is an upper bound on the volume of any hyperbolic $n$-bongle for $n$ even. Moreover, all hyperbolic $n$-bongles have volume strictly less than $5n(1.01494\dots)$. We also include explicit volume calculations for all hyperbolic 3-bongles through 6-bongles.

math.GT

Intrinsically knotted graphs and connected domination

We classify all the maximal linklessly embeddable graphs of order 12 and show that their complements are all intrinsically knotted. We derive results about the connected domination numbers of a graph and its complement. We provide an answer to an open question about the minimal order of a 3-non-compliant graph. We prove that the complements of knotlessly embeddable graphs of order at least 15 are all intrinsically knotted. We provide results on general $k$-non-compliant graphs and leave a set of open questions for further exploration of the subject.

math.CO

Complete Minors in Complements of Non-Separating Planar Graphs

We prove that the complement of any non-separating planar graph of order $2n-3$ contains a $K_n$ minor, and argue that the order $2n-3$ is lowest possible with this property. To illustrate the necessity of the non-separating hypothesis, we give an example of a planar graph of order 11 whose complement does not contain a $K_7$ minor. We argue that the complements of planar graphs of order 11 are intrinsically knotted. We compute the Hadwiger numbers of complements of wheel graphs.

math.CO