arXiv:2603.24641v1 Announce Type: new Abstract: Mesh-free numerical methods provide flexible discretisations for complex geometries; however, classical meshless discrete differential operators typically trade low computational cost for limited accuracy or high accuracy for substantial per-stencil computation. We introduce a parametrised framework for learning mesh-free discrete differential operators using a graph neural network trained via polynomial moment constraints derived from truncated Taylor expansions. The model maps local stencils relative positions directly to discrete operator weights. The current work demonstrates that […]

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Continual learning (CL) is concerned with learning multiple tasks sequentially without forgetting previously learned tasks. Despite substantial empirical advances over recent years, the theoretical development of CL remains in its infancy. At the heart of developing CL theory lies the challenge that the data distribution varies across tasks, and we argue that properly addressing this challenge requires understanding this variation–dependency among tasks. To explicitly model task dependency, we consider nonlinear regression tasks and propose the assumption that these […]

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arXiv:2603.10056v1 Announce Type: new Abstract: Most OAuth service providers, such as Google and Microsoft, offer only a limited range of coarse-grained data access. As a result, third-party OAuth applications often end up accessing more user data than necessary, even if their developers want to minimize data access. We present OAuthHub, a development framework that leverages users’ personal devices as the intermediary controller for OAuth-based data sharing between cloud services. The key innovations of OAuthHub are: (1) the insight […]

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Python’s openai library provides the tools you need to integrate the ChatGPT API into your Python applications. With it, you can send text prompts to the API and receive AI-generated responses. You can also guide the AI’s behavior with developer role messages and handle both simple text generation and more complex code creation tasks. After watching this video course, you’ll understand how examples like this work under the hood. You’ll learn the fundamentals of using the ChatGPT API […]

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This work addresses the fundamental problem of unbounded metric movement costs in bandit online convex optimization, by considering high-dimensional dynamic quadratic hitting costs and $ell_2$-norm switching costs in a noisy bandit feedback model. For a general class of stochastic environments, we provide the first algorithm SCaLE that provably achieves a distribution-agnostic sub-linear dynamic regret, without the knowledge of hitting cost structure. En-route, we present a novel spectral regret analysis that separately quantifies eigenvalue-error driven regret and eigenbasis-perturbation driven […]

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If you’re running LLMs in production, prompt injection is the attack you can’t fully patch. Someone wraps “ignore your instructions” inside a polite customer support query, or buries a hijack command in a document your RAG pipeline retrieves, and your model follows it. The standard defenses (regex filters, classifier ensembles, guardrail APIs) catch the attacks they’ve been trained on. The ones they haven’t seen walk right through. We hit this wall ourselves. Together with George Politis, we’ve been running LLMTrace, […]

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arXiv:2511.16377v2 Announce Type: replace-cross Abstract: We investigate how to optimally design local differential privacy (LDP) mechanisms that reduce data unfairness and thereby improve fairness in downstream classification. We first derive a closed-form optimal mechanism for binary sensitive attributes and then develop a tractable optimization framework that yields the corresponding optimal mechanism for multi-valued attributes. As a theoretical contribution, we establish that for discrimination-accuracy optimal classifiers, reducing data unfairness necessarily leads to lower classification unfairness, thus providing a direct […]

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Language models trained on natural text learn to represent numbers using periodic features with dominant periods at $T=2, 5, 10$. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs, and classical word embeddings trained in different ways all learn features that have period-$T$ spikes in the Fourier domain, only some learn geometrically separable features that can be used to linearly classify a number mod-$T$. To explain this incongruity, we prove that […]

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