We analyze task orderings in continual learning for linear regression, assuming joint realizability of training data. We focus on orderings that greedily maximize dissimilarity between consecutive tasks, a concept briefly explored in prior work but still surrounded by open questions. Using tools from the Kaczmarz method literature, we formalize such orderings and develop geometric and algebraic intuitions around them. Empirically, we demonstrate that greedy orderings converge faster than random ones in terms of the average loss across tasks, both for linear regression with random data and for linear probing on CIFAR-100classification tasks. Analytically, in a high-rank regression setting, we prove a loss bound for greedy orderings analogous to that of random ones. However, under general rank, we establish a repetition-dependent separation. Specifically, while prior work showed that for random orderings, with or without replacement, the average loss after k iterations is bounded by O(1/ k)--we prove that single-pass greedy orderings may fail catastrophically, whereas those allowing repetition converge at rate O(1/ 3 k). Overall, we reveal nuances within and between greedy and random orderings.

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In this work, we introduce TreeGen, a novel generative framework modeling distributions over hierarchies. We extend Bayesian Flow Networks (BFNs) to enable transitions between probabilistic and discrete hierarchies parametrized via categorical distributions. Our proposed scheduler provides smooth and consistent entropy decay across varying numbers of categories. We empirically evaluate TreeGen on the jet-clustering task in high-energy physics, demonstrating that it consistently generates valid trees that adhere to physical constraints and closely align with ground-truth log-likelihoods. Finally, by comparing TreeGen's samples to the exact posterior distribution and performing likelihood maximization via rejection sampling, we demonstrate that TreeGen outperforms various baselines.

Watermarking the outputs of generative models has emerged as a promising approach for tracking their provenance. Despite significant interest in autoregressive image generation models and their potential for misuse, no prior work has attempted the first such to watermark approach their by adapting outputs language at the tok model en level.

Mobile agents rely on Large Language Models (LLMs) to plan and execute tasks on smartphone user interfaces (UIs). While cloud-based LLMs achieve high task accuracy, they require uploading the full UI state at every step, exposing unnecessary and often irrelevant information. In contrast, local LLMs avoid UI uploads but suffer from limited capacity, resulting in lower task success rates. We propose CORE, a COllaborative framework that combines the strengths of cloud and local LLMs to Reduce UIExposure, while maintaining task accuracy for mobile agents. CORE comprises three key components: (1) Layout-aware block partitioning, which groups semantically related UI elements based on the XML screen hierarchy; (2) Co-planning, where local and cloud LLMs collaboratively identify the current sub-task; and (3) Co-decision-making, where the local LLM ranks relevant UI blocks, and the cloud LLM selects specific UI elements within the top-ranked block. CORE further introduces a multi-round accumulation mechanism to mitigate local misjudgment or limited context. Experiments across diverse mobile apps and tasks show that CORE reduces UI exposure by up to 55.6% while maintaining task success rates slightly below cloud-only agents, effectively mitigating unnecessary privacy exposure to the cloud.2

Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available information is irrelevant, and effective deductive inference requires identifying and ignoring such distractions. We propose a framework for assessing LM reasoning efficiency through the lens of logic programming, introducing a simple method to align proofs written in natural language--as generated by an LM--with shortest proofs found by executing the logic program. Efficiency is quantified by measuring how well a model avoids unnecessary inference. Empirically, we construct a dataset of math word problems injected with various number of irrelevant axioms that vary in semantic overlap with the goal theorem. We find that current LMs show marked accuracy declines under such conditions--even with minimal, domainconsistent distractions--and the proofs they generate frequently exhibit detours through irrelevant inferences.2

Anthropic's design assistant now works better with its coding agent Anthropic's design assistant now works better with its coding agent Exactly two months after releasing a preview of Claude Design to subscribers, Anthropic has begun rolling out a major update for its design assistant that brings better integration with its other apps. To start, Claude Design can now begin working from a local codebase, meaning any assets it generates will contain elements that already exist in your front-facing products. From there, the app can hand off a design to Claude Code, allowing the coding agent to program an interface without the need to start from scratch. You also don't need to provide it with screenshots to give it an idea of your intent. And if you want to skip Claude Design, you can do that too, with Anthropic adding the option to create and edit designs directly from Claude Code. Outside of more robust integration with Anthropic's other apps, today's update brings with it quality of life improvements, starting with a more flexible import tool that can build entire design systems from GitHub and raw files.

The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational efficiency. To overcome these issues, we first introduce a new duality between the spectral density and the kernel function. By modeling the spectral density with a bivariate Gaussian mixture, we then derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. To address the inherent computational inefficiency of the NG-SM kernel, we design a new form of random Fourier feature approximation. Combined with a tailored reparameterization trick, this approximation enables scalable variational inference for both the model and the unified latent representations. Numerical evaluations across a diverse range of multi-view datasets demonstrate that our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this challenge by dynamically relocating mesh nodes to rapidly-varying regions, enhancing both simulation accuracy and computational efficiency. However, traditional approaches suffer from high computational complexity and geometric inflexibility, limiting their applicability, and existing supervised learning-based approaches face challenges in zero-shot generalization across diverse PDEs and mesh topologies. In this paper, we present an Unsupervised and Generalizable Mesh Movement Network (UGM2N). We first introduce unsupervised mesh adaptation through localized geometric feature learning, eliminating the dependency on pre-adapted meshes. We then develop a physics-constrained loss function, M-Uniform loss, that enforces mesh equidistribution at the nodal level. Experimental results demonstrate that the proposed network exhibits equation-agnostic generalization and geometric independence in efficient mesh adaptation. It demonstrates consistent superiority over existing methods, including robust performance across diverse PDEs and mesh geometries, scalability to multi-scale resolutions and guaranteed error reduction without mesh tangling.

There has been a surge of interest in assistive wearable agents: agents embodied in wearable form factors (e.g., smart glasses) who take assistive actions toward a user's goal/query (e.g. "Where did I leave my keys?"). In this work, we consider the important complementary problem of inferring that goal from multi-modal contextual observations. Solving this "goal inference" problem holds the promise of eliminating the effort needed to interact with such an agent. This work focuses on creating WAGIBench, a strong benchmark to measure progress in solving this problem using vision-language models (VLMs). Given the limited prior work in this area, we collected a novel dataset comprising 29 hours of multimodal data from 348 participants across 3,477 recordings, featuring ground-truth goals alongside accompanying visual, audio, digital, and longitudinal contextual observations. We validate that human performance exceeds model performance, achieving 93% multiple-choice accuracy compared with 84% for the best-performing VLM. Generative benchmark results that evaluate several families of modern vision-language models show that larger models perform significantly better on the task, yet remain far from practical usefulness, as they produce relevant goals only 55% of the time. Through a modality ablation, we show that models benefit from extra information in relevant modalities with minimal performance degradation from irrelevant modalities.