Ethan Hsu

Ethan Hsu, Hong Meng Yam, Ivan Ge

Partial differential equation (PDE) solvers underpin scientific computing, but real-world deployment is bounded by compute. Classical Monte Carlo solvers such as Walk-on-Spheres (WoS) are unbiased and geometry-agnostic but are slow. Learned solvers are fast but biased and brittle under distribution shift. We present \textbf{MC$^2$}, a hybrid WoS-Neural Network (WoS-NN) PDE solver that treats a low-budget Monte Carlo solution as a structured estimator of the true field and learns a single-pass neural correction to recover a high-fidelity solution. MC$^2$ matches the accuracy of solutions using over $1000\times$ more Monte Carlo compute, outperforming all evaluated classical, denoising, and neural-operator baselines. To enable reproducible study of finite-compute PDE solving, we additionally release \textbf{PDEZoo}, the largest standardized elliptic PDE benchmark to date: 2M PDEs spanning five elliptic families and unlimited geometric compositions, with analytic ground truth and multi-budget Monte Carlo trajectories. Together \textbf{MC$^2$} and \textbf{PDEZoo} (1) empirically establish that finite-sample Monte Carlo error is structured, learnable, and correctable in a single forward pass, (2) show that we can solve PDEs $\sim$\textbf{1000x} faster than with just WoS, and (3) provide the evaluation infrastructure the field has so far lacked.

Ethan Hsu, Hong Meng Yam, Ines Bouissou et al.

A large portion of real-world data science tasks are complex and require multi-hop web-based interactions: finding appropriate data available on the internet, synthesizing real-time data of various modalities from different locations, and producing summarized analyses. Existing web benchmarks often focus on simplistic interactions, such as form submissions or e-commerce transactions, and often do not require diverse tool-using capabilities required for web based data science. Conversely, traditional data science benchmarks typically concentrate on static, often textually bound datasets and do not assess end-to-end workflows that encompass data acquisition, cleaning, analysis, and insight generation. In response, we introduce WebDS, the first end-to-end web-based data science benchmark. It comprises 870 web-based data science tasks across 29 diverse websites from structured government data portals to unstructured news media, challenging agents to perform complex, multi-step operations requiring the use of tools and heterogeneous data formats that better reflect the realities of modern data analytics. Evaluations of current SOTA LLM agents indicate significant performance gaps in accomplishing these tasks. For instance, Browser Use, which accomplishes 80% of tasks on Web Voyager, successfully completes only 15% of tasks in WebDS, which our analysis suggests is due to new failure modes like poor information grounding, repetitive behavior and shortcut-taking that agents performing WebDS' tasks display. By providing a more robust and realistic testing ground, WebDS sets the stage for significant advances in the development of practically useful LLM-based data science.

Ethan Hsu, Harry Chen, Chudi Zhong et al.

Real-world machine learning (ML) pipelines rarely produce a single model; instead, they produce a Rashomon set of many near-optimal ones. We show that this multiplicity reshapes key aspects of trustworthiness. At the individual-model level, sparse interpretable models tend to preserve privacy but are fragile to adversarial attacks. In contrast, the diversity within a large Rashomon set enables reactive robustness: even when an attack breaks one model, others often remain accurate. Rashomon sets are also stable under small distribution shifts. However, this same diversity increases information leakage, as disclosing more near-optimal models provides an attacker with progressively richer views of the training data. Through theoretical analysis and empirical studies of sparse decision trees and linear models, we characterize this robustness-privacy trade-off and highlight the dual role of Rashomon sets as both a resource and a risk for trustworthy ML.

Shihan Feng, Cheng Zhang, Michael Xi et al.

Modern neural networks rarely have a single way to be right. For many tasks, multiple models can achieve identical performance while relying on different features or reasoning patterns, a property known as the Rashomon Effect. However, uncovering this diversity in deep architectures is challenging as their continuous parameter spaces contain countless near-optimal solutions that are numerically distinct but often behaviorally similar. We introduce Rashomon Concept Bottleneck Models, a framework that learns multiple neural networks which are all accurate yet reason through distinct human-understandable concepts. By combining lightweight adapter modules with a diversity-regularized training objective, our method constructs a diverse set of deep concept-based models efficiently without retraining from scratch. The resulting networks provide fundamentally different reasoning processes for the same predictions, revealing how concept reliance and decision making vary across equally performing solutions. Our framework enables systematic exploration of data-driven reasoning diversity in deep models, offering a new mechanism for auditing, comparison, and alignment across equally accurate solutions.