In this tutorial, we build a RAG-Anything workflow and use it to explore how multimodal retrieval works across text, tables, equations, and images. We start by preparing the Colab environment, installing the required packages, and securely entering our OpenAI API key at runtime to keep the notebook practical and safe to run. We then create a synthetic multimodal report, generate a chart and PDF, convert the content into RAG-Anything’s direct content_list format, and insert it into the retrieval […]

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Reachability analysis has become increasingly important in robotics to distinguish safe from unsafe states. Unfortunately, existing reachability and safety analysis methods often fall short, as they typically require known system dynamics or large datasets to estimate accurate system models, are computationally expensive, and assume full state information. A recent method, called MORALS, aims to address these shortcomings by using topological tools to estimate3DR-eEgnciodnesr of Attraction (ROA) in a low-dimensional latent space. However, MORALS still relies on full state […]

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arXiv:2603.06660v1 Announce Type: new Abstract: Approximate Nearest Neighbor Search (ANNS) is fundamental to modern AI applications. Most existing solutions optimize query efficiency but fail to align with the practical requirements of modern workloads. In this paper, we outline six critical demands of modern AI applications: high query efficiency, fast indexing, low memory footprint, scalability to high dimensionality, robustness across varying retrieval sizes, and support for online insertions. To satisfy all these demands, we introduce Projection-Augmented Graph (PAG), a […]

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arXiv:2601.07535v1 Announce Type: new Abstract: Clustering with bandit feedback refers to the problem of partitioning a set of items, where the clustering algorithm can sequentially query the items to receive noisy observations. The problem is formally posed as the task of partitioning the arms of an N-armed stochastic bandit according to their underlying distributions, grouping two arms together if and only if they share the same distribution, using samples collected sequentially and adaptively. This setting has gained attention […]

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In this month’s episode of Functional Futures, our guest is David Christiansen, the Executive Director of the Haskell Foundation, a contributor to a number of dependently typed languages, and a dependent type advocate that has managed to introduce many people to the topic today through his work, talks, and texts. We cover topics such as dependent types, theorem proving, metaprogramming, and many more. We also discuss the book he co-authored with Daniel P. Friedman, The Little Typer, and […]

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arXiv:2606.05242v1 Announce Type: new Abstract: Stochastic-gradient Langevin algorithms often use tamed denominators to stabilize non-globally Lipschitz drifts. This paper shows that when the denominator depends on the same stochastic-gradient realization as the numerator, the taming step changes the stochastic oracle itself and can create a stationary bias even if the original stochastic gradient is unbiased. We propose a structure-preserving framework for designing tamed denominators. It fixes the denominator before the oracle noise is sampled and uses localized deterministic […]

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arXiv:2602.00997v1 Announce Type: new Abstract: Automatic Prompt Optimization (APO) is a powerful approach for extracting performance from large language models without modifying their weights. Many existing methods rely on trial-and-error, testing different prompts or in-context examples until a good configuration emerges, often consuming substantial compute. Recently, natural language feedback derived from execution logs has shown promise as a way to identify how prompts can be improved. However, most prior approaches operate in a bottom-up manner, iteratively adjusting the […]

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Scientific discovery increasingly requires learning on federated datasets, fed by streams from high-resolution instruments, that have extreme class imbalance. Current ML approaches either require impractical data aggregation or fail due to class imbalance. Existing coreset selection methods rely on local heuristics, making them unaware of the global data landscape and prone to sub-optimal and non-representative pruning. To overcome these challenges, we introduce SCOPE (Semantic Coreset using Orthogonal Projection Embeddings for Federated learning), a coreset framework for federated data […]

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This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and neural network approximations. Next, it illustrates fundamental performance limits in terms of sample size by adopting a minimax perspective and considering various notions of regularity beyond holomorphy. The paper ends with a discussion on the interplay between these two perspectives and related open questions.

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