We utilize FKEA's approximated eigenspectrum of the kernel matrix to efficiently

Things to Do in L.A. Tap to enable a layout that focuses on the article. California has a strict vaccine mandate. Will it survive the Trump administration? Dr. Neville Anderson, right, tries to distract Perry Roj, 4, while nurse Breanna Kirby gives her a DTaP polio vaccination. Her mom, Devin Homsey, holds her tight at Larchmont Pediatrics.

Large-scale reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in harnessing the potential of large language models (LLMs) for single-turn reasoning tasks. In realistic reasoning scenarios, LLMs can often utilize external tools to assist in task-solving processes. However, current RL algorithms inadequately balance the models' intrinsic long-horizon reasoning capabilities and their proficiency in multi-turn tool interactions. To bridge this gap, we propose Agentic Reinforced Policy Optimization (ARPO), a novel agentic RL algorithm tailored for training multi-turn LLM-based agents. Through preliminary experiments, we observe that LLMs tend to exhibit highly uncertain behavior, characterized by an increase in the entropy distribution of generated tokens, immediately following interactions with external tools. Motivated by this observation, ARPO incorporates an entropy-based adaptive rollout mechanism, dynamically balancing global trajectory sampling and step-level sampling, thereby promoting exploration at steps with high uncertainty after tool usage. By integrating an advantage attribution estimation, ARPO enables LLMs to internalize advantage differences in stepwise tool-use interactions. Our experiments across 13 challenging benchmarks in computational reasoning, knowledge reasoning, and deep search domains demonstrate ARPO's superiority over trajectory-level RL algorithms. Remarkably, ARPO achieves improved performance using only half of the tool-use budget required by existing methods, offering a scalable solution for aligning LLM-based agents with real-time dynamic environments. Our code and datasets are released at https://github.com/dongguanting/ARPO

While standard evaluation scores for generative models are mostly reference-based, a reference-dependent assessment of generative models could be generally difficult due to the unavailability of applicable reference datasets. Recently, the reference-free entropy scores, VENDI and RKE, have been proposed to evaluate the diversity of generated data. However, estimating these scores from data leads to significant computational costs for large-scale generative models. In this work, we leverage the random Fourier features framework to reduce the computational price and propose the Fourier-based Kernel Entropy Approximation (FKEA) method. We utilize FKEA's approximated eigenspectrum of the kernel matrix to efficiently estimate the mentioned entropy scores. Furthermore, we show the application of FKEA's proxy eigenvectors to reveal the method's identified modes in evaluating the diversity of produced samples. We provide a stochastic implementation of the FKEA assessment algorithm with a complexity $O(n)$ linearly growing with sample size $n$. We extensively evaluate FKEA's numerical performance in application to standard image, text, and video datasets. Our empirical results indicate the method's scalability and interpretability applied to large-scale generative models. The codebase is available at https://github.com/aziksh-ospanov/FKEA.

Dr. Zoe Danielle Birnbaum and James Matthew Frankel are to be married Feb. 9 by Rabbi Jeffrey Sirkman at Tappan Hill Mansion in Tarrytown, N.Y. The bride and groom graduated from Colgate. Dr. Birnbaum, 30, is a third-year resident in the field of psychiatry at NYU Langone Medical Center, and received a medical degree from N.Y.U. She is a daughter of Dr. Lisa Turtz and Jesse Birnbaum of Larchmont, N.Y. The bride's father is a member of the quality assurance team at the Mahwah, N.J., manufacturing facility of Nobel Biocare, the Swiss-based maker of dental implants and individualized prosthetics.