Leo Huang

Xinran Zhu, Leo Huang, Cameron Ibrahim et al.

The Bayesian transformed Gaussian process (BTG) model, proposed by Kedem and Oliviera, is a fully Bayesian counterpart to the warped Gaussian process (WGP) and marginalizes out a joint prior over input warping and kernel hyperparameters. This fully Bayesian treatment of hyperparameters often provides more accurate regression estimates and superior uncertainty propagation, but is prohibitively expensive. The BTG posterior predictive distribution, itself estimated through high-dimensional integration, must be inverted in order to perform model prediction. To make the Bayesian approach practical and comparable in speed to maximum-likelihood estimation (MLE), we propose principled and fast techniques for computing with BTG. Our framework uses doubly sparse quadrature rules, tight quantile bounds, and rank-one matrix algebra to enable both fast model prediction and model selection. These scalable methods allow us to regress over higher-dimensional datasets and apply BTG with layered transformations that greatly improve its expressibility. We demonstrate that BTG achieves superior empirical performance over MLE-based models.

Xuanbo Su, Yingfang Zhang, Hao Luo et al.

With the growing adoption of Large Language Model (LLM) agents in persistent, real-world roles, they naturally encounter continuous streams of tasks and inevitable failures. A key limitation, however, is their inability to systematically learn from these mistakes, forcing them to repeat identical errors in similar contexts. Unlike prior training-free methods that primarily store raw instance-level experience or focus on retrieving successful trajectories, we propose Mistake Notebook Learning (MNL), a novel memory framework that enables agents to self-curate generalizable guidance from batch-clustered failures. This mechanism allows agents to distill shared error patterns into structured "mistake notes," updating an external memory only when batch performance improves to ensure stability. To further amplify adaptability, we integrate MNL with test-time scaling, leveraging aggregated failure patterns to actively steer the search process away from known pitfalls. Experiments on mathematical reasoning, Text-to-SQL, and interactive agent benchmarks show that MNL achieves competitive performance compared to existing memory mechanisms and in-context methods in both effectiveness and efficiency. These findings position structured mistake abstraction as a critical lever for robust agent evolution, enabling continuous improvement without the cost of parameter updates. The code is available at https://github.com/Bairong-Xdynamics/MistakeNotebookLearning/tree/main.

Xuanbo Su, Wenhao Hu, Le Zhan et al.

Sales dialogues require multi-turn, goal-directed persuasion under asymmetric incentives, which makes them a challenging setting for large language models (LLMs). Yet existing dialogue benchmarks rarely measure deal progression and outcomes. We introduce SalesLLM, a bilingual (ZH/EN) benchmark derived from realistic applications covering Financial Services and Consumer Goods, built from 30,074 scripted configurations and 1,805 curated multi-turn scenarios with controllable difficulty and personas. We propose a fully automatic evaluation pipeline that combines (i) an LLM-based rater for sales-process progress, and (ii) fine-tuned BERT classifiers for end-of-dialogue buying intent. To improve simulation fidelity, we train a user model, CustomerLM, with SFT and DPO on 8,000 crowdworker-involved sales conversations, reducing role inversion from 17.44% (GPT-4o) to 8.8%. SalesLLM scores correlate strongly with expert human ratings (Pearson r=0.98). Experiments across 15 mainstream LLMs reveal substantial variability: top-performance LLMs are competitive with human-level performance while the less capable ones are worse than human. SalesLLM serves as a scalable benchmark for developing and evaluating outcome-oriented sales agents.

Misha Padidar, Xinran Zhu, Leo Huang et al.

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative observations, however, comes with a dominating $O(N^3D^3)$ computational cost when training on $N$ points in $D$ input dimensions. This is intractable for even moderately sized problems. While recent work has addressed this intractability in the low-$D$ setting, the high-$N$, high-$D$ setting is still unexplored and of great value, particularly as machine learning problems increasingly become high dimensional. In this paper, we introduce methods to achieve fully scalable Gaussian process regression with derivatives using variational inference. Analogous to the use of inducing values to sparsify the labels of a training set, we introduce the concept of inducing directional derivatives to sparsify the partial derivative information of a training set. This enables us to construct a variational posterior that incorporates derivative information but whose size depends neither on the full dataset size $N$ nor the full dimensionality $D$. We demonstrate the full scalability of our approach on a variety of tasks, ranging from a high dimensional stellarator fusion regression task to training graph convolutional neural networks on Pubmed using Bayesian optimization. Surprisingly, we find that our approach can improve regression performance even in settings where only label data is available.

Leo Huang, Andrew Graven, David Bindel

A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those based on random walks and return probabilities have proven to be effective in wide-ranging applications, from bioinformatics to social networks to computer vision. However, random walk kernels generally suffer from slowness and tottering, an effect which causes walks to overemphasize local graph topology, undercutting the importance of global structure. To correct for these issues, we recast return probability graph kernels under the more general framework of density of states -- a framework which uses the lens of spectral analysis to uncover graph motifs and properties hidden within the interior of the spectrum -- and use our interpretation to construct scalable, composite density of states based graph kernels which balance local and global information, leading to higher classification accuracies on a host of benchmark datasets.

Aaron Lou, Derek Lim, Isay Katsman et al.

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for specific cases; however, these advancements hand craft layers on a manifold-by-manifold basis, restricting generality and inducing cumbersome design constraints. We overcome these issues by introducing Neural Manifold Ordinary Differential Equations, a manifold generalization of Neural ODEs, which enables the construction of Manifold Continuous Normalizing Flows (MCNFs). MCNFs require only local geometry (therefore generalizing to arbitrary manifolds) and compute probabilities with continuous change of variables (allowing for a simple and expressive flow construction). We find that leveraging continuous manifold dynamics produces a marked improvement for both density estimation and downstream tasks.