arXiv subjects

Frank Wang

Publications and source records attributed to Frank Wang.

13 recordsLinked to original sources

arXiv2026

A formula for the $q$-character of functions on the nilpotent cone of some Lie algebra representations

Let $\mathfrak{g}$ be a reductive Lie algebra and $V$ a finite-dimensional $\mathfrak{g}$-representation. When $V$ is the representation of a cyclic quiver with equal dimensions, the representation of a cyclic quiver with two vertices, or a representation of a product of copies of $\mathfrak{sl}_2$ we call an acyclic extended quiver representation of trivial type, we prove a $q$-character formula for the nilpotent cone of $V$ analogous to Hesselink's $q$-character formula of the usual nilpotent cone of $\mathfrak{g}$. We also define a new class of representations we call Hesselink-type representations, for which we make a conjecture in relation to our formula and describe a geometric interpretation.

math.RT↗

arXiv2026

Cura 1T: Specialized Model for Agentic Healthcare

Healthcare AI agents handle patient consultation, clinical reasoning over text and images, interactive diagnosis, and electronic health record (EHR) tool use, yet specialized agentic models that cover these use cases together remain limited. These capabilities fail in different ways, and a narrow update for one task can degrade another. We present Cura 1T, a healthcare-specialized LLM built on the open-weight Kimi-K2.6 and trained through a human-gated recursive self-improvement (RSI) loop. Specifically, in each round, the RSI harness plans a target capability, trains the model, evaluates benchmark trajectories, and refines the data mixture from observed failures with targeted synthetic and curated examples rather than a single generic medical-data update. Across the healthcare evaluation suite, Cura 1T ranks at or near the top among frontier baselines while remaining competitive on out-of-domain reasoning and agentic benchmarks.

cs.AI↗

arXiv2026

CHI-Bench: Can AI Agents Automate End-to-End, Long-Horizon, Policy-Rich Healthcare Workflows?

End-to-end automation of realistic healthcare operations stresses three capabilities underrepresented in current benchmarks: policy density, decisions must be grounded in a large library of medical, insurance, and operational rules; Multi-role composition: a single task requires the agent to play multiple roles with handoffs; and multilateral interaction: intermediate workflow steps are multi-turn dialogs, such as peer-to-peer review and patient outreach. We introduce $\chi$-Bench, a benchmark of long-horizon healthcare workflows across three domains: provider prior authorization, payer utilization management, and care management. Each task hands the agent a clinical case in a high-fidelity simulator of 20 healthcare apps exposed via 87 MCP tools, which it must drive to a terminal status through tool calls and writing the role's artifacts, guided by a 1,290+ document managed-care operations handbook skill. Across 30 agent harness/models configurations, the best agent resolves only 28.0% of tasks, no agent clears 20% on strict pass^3, and executing all tasks in a single session slumps the performance to 3.8%. These results raise the hypothesis that similar gaps are likely to surface in other policy-dense, role-composed, irreversible enterprise domains.

cs.CL↗

arXiv2026

Comment on "Specific heat of an ideal Bose gas above the Bose condensation temperature," [Am. J. Phys. 72(9), 1193--1194 (2004)]

We examine the English translation of Albert Einstein's groundbreaking 1925 paper on Bose-Einstein condensation. We guide readers to execute the calculations Einstein outlined for the specific heat above the condensation temperature, correct some numerical errors, and compare his formula with a different one published in the American Journal of Physics in 2004. The history of the acceptance of Einstein's theory will be summarized.

physics.hist-ph↗

arXiv2025

Quantile Rendering: Efficiently Embedding High-dimensional Feature on 3D Gaussian Splatting

Recent advancements in computer vision have successfully extended Open-vocabulary segmentation (OVS) to the 3D domain by leveraging 3D Gaussian Splatting (3D-GS). Despite this progress, efficiently rendering the high-dimensional features required for open-vocabulary queries poses a significant challenge. Existing methods employ codebooks or feature compression, causing information loss, thereby degrading segmentation quality. To address this limitation, we introduce Quantile Rendering (Q-Render), a novel rendering strategy for 3D Gaussians that efficiently handles high-dimensional features while maintaining high fidelity. Unlike conventional volume rendering, which densely samples all 3D Gaussians intersecting each ray, Q-Render sparsely samples only those with dominant influence along the ray. By integrating Q-Render into a generalizable 3D neural network, we also propose Gaussian Splatting Network (GS-Net), which predicts Gaussian features in a generalizable manner. Extensive experiments on ScanNet and LeRF demonstrate that our framework outperforms state-of-the-art methods, while enabling real-time rendering with an approximate ~43.7x speedup on 512-D feature maps. Code will be made publicly available.

cs.CV↗

arXiv2025

Enterprise Deep Research: Steerable Multi-Agent Deep Research for Enterprise Analytics

As information grows exponentially, enterprises face increasing pressure to transform unstructured data into coherent, actionable insights. While autonomous agents show promise, they often struggle with domain-specific nuances, intent alignment, and enterprise integration. We present Enterprise Deep Research (EDR), a multi-agent system that integrates (1) a Master Planning Agent for adaptive query decomposition, (2) four specialized search agents (General, Academic, GitHub, LinkedIn), (3) an extensible MCP-based tool ecosystem supporting NL2SQL, file analysis, and enterprise workflows, (4) a Visualization Agent for data-driven insights, and (5) a reflection mechanism that detects knowledge gaps and updates research direction with optional human-in-the-loop steering guidance. These components enable automated report generation, real-time streaming, and seamless enterprise deployment, as validated on internal datasets. On open-ended benchmarks including DeepResearch Bench and DeepConsult, EDR outperforms state-of-the-art agentic systems without any human steering. We release the EDR framework and benchmark trajectories to advance research on multi-agent reasoning applications. Code at https://github.com/SalesforceAIResearch/enterprise-deep-research and Dataset at https://huggingface.co/datasets/Salesforce/EDR-200

cs.CL↗

arXiv2025

The Amazing Journey of Lars Ahlfors' Fields Medal

This is the story of the first Fields Medal awarded to Lars Ahlfors. It was smuggled out of Finland in 1944, pawned in Sweden during World War II, and returned to Helsinki in 2004. This article is based on an interview with Ahlfors' second daughter Vanessa Gruen, and established biographical sources.

math.HO↗

arXiv2024

Hilbert Series of $S_3$-Quasi-Invariant Polynomials in Characteristics 2, 3

We compute the Hilbert series of the space of $n=3$ variable quasi-invariant polynomials in characteristic $2$ and $3$, capturing the dimension of the homogeneous components of the space, and explicitly describe the generators in the characteristic $2$ case. In doing so we extend the work of the first author in 2023 on quasi-invariant polynomials in characteristic $p>n$ and prove that a sufficient condition found by Ren-Xu in 2020 on when the Hilbert series differs between characteristic $0$ and $p$ is also necessary for $n=3$, $p=2,3$. This is the first description of quasi-invariant polynomials in the case, where the space forms a modular representation over the symmetric group, bringing us closer to describing the quasi-invariant polynomials in all characteristics and numbers of variables.

math.RT↗

arXiv2024

Transformation Between the Schwarzschild Coordinates and Local Inertial Coordinates

We present a transformation between the Schwarzschild coordinates and local inertial coordinates, and demonstrate the effect of gravitational bending of light near a massive body in a small region. When a photon is emitted from a point near the Earth's surface with an initial horizontal direction, its parabolic trajectory would have a vertical deflection that is about three times that of a non-relativistic Newtonian particle would trace.

physics.gen-ph↗

arXiv2022

Toward explicit Hilbert series of quasi-invariant polynomials in characteristic $p$ and $q$-deformed quasi-invariants

We study the spaces $Q_m$ of $m$-quasi-invariant polynomials of the symmetric group $S_n$ in characteristic $p$. Using the representation theory of the symmetric group we describe the Hilbert series of $Q_m$ for $n=3$, proving a conjecture of Ren and Xu [arXiv:1907.13417]. From this we may deduce the palindromicity and highest term of the Hilbert polynomial and the freeness of $Q_m$ as a module over the ring of symmetric polynomials, which are conjectured for general $n$. We also prove further results in the case $n=3$ that allow us to compute values of $m,p$ for which $Q_m$ has a different Hilbert series over characteristic 0 and characteristic $p$, and what the degrees of the generators of $Q_m$ are in such cases. We also extend various results to the spaces $Q_{m,q}$ of $q$-deformed $m$-quasi-invariants and prove a sufficient condition for the Hilbert series of $Q_{m,q}$ to differ from the Hilbert series of $Q_m$.

math.RT↗

arXiv2021

The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization

We introduce four new real-world distribution shift datasets consisting of changes in image style, image blurriness, geographic location, camera operation, and more. With our new datasets, we take stock of previously proposed methods for improving out-of-distribution robustness and put them to the test. We find that using larger models and artificial data augmentations can improve robustness on real-world distribution shifts, contrary to claims in prior work. We find improvements in artificial robustness benchmarks can transfer to real-world distribution shifts, contrary to claims in prior work. Motivated by our observation that data augmentations can help with real-world distribution shifts, we also introduce a new data augmentation method which advances the state-of-the-art and outperforms models pretrained with 1000 times more labeled data. Overall we find that some methods consistently help with distribution shifts in texture and local image statistics, but these methods do not help with some other distribution shifts like geographic changes. Our results show that future research must study multiple distribution shifts simultaneously, as we demonstrate that no evaluated method consistently improves robustness.

cs.CV↗

arXiv2020

The integral shuffle algebra and the $K$-theory of the Hilbert scheme of points in $\mathbb{A}^2$

We examine the shuffle algebra defined over the ring $\mathbf{R} = \mathbb{C}[q_1^{\pm 1}, q_2^{\pm 1}]$, also called the integral shuffle algebra, which was found by Schiffmann and Vasserot to act on the equivariant $K$-theory of the Hilbert scheme of points in the plane. We find that the modules of 2 and 3 variable elements of the integral shuffle algebra are finitely generated and prove a necessary condition for an element to be in the integral shuffle algebra for arbitrarily many variables.

math.RT↗

arXiv2019

A Nonlinear Model for Time Synchronization

The current algorithms are based on linear model, for example, Precision Time Protocol (PTP) which requires frequent synchronization in order to handle the effects of clock frequency drift. This paper introduces a nonlinear approach to clock time synchronize. This approach can accurately model the frequency shift. Therefore, the required time interval to synchronize clocks can be longer. Meanwhile, it also offers better performance and relaxes the synchronization process. The idea of the nonlinear algorithm and some numerical examples will be presented in this paper in detail.

cs.LG↗