January 2026

How managing the information environment — not perfecting queries — determines whether your AI system ships or fails 1. The Fundamental Misconception Killing Production AI The AI industry has spent two years obsessed with the wrong problem. We’ve treated prompt engineering as the solution to every production challenge, iterating endlessly on phrasing, temperature parameters, and system instructions. Meanwhile, the actual bottleneck has been hiding in plain sight: information architecture. The core insight driving the shift to context engineering is brutally simple: no amount […]

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arXiv:2601.03919v2 Announce Type: replace-cross Abstract: We study when geometric simplicity of decision boundaries, used here as a notion of interpretability, can conflict with accurate approximation of axis-aligned decision trees by shallow neural networks. Decision trees induce rule-based, axis-aligned decision regions (finite unions of boxes), whereas shallow ReLU networks are typically trained as score models whose predictions are obtained by thresholding. We analyze the infinite-width, bounded-norm, single-hidden-layer ReLU class through the Radon total variation ($mathrm{R}mathrm{TV}$) seminorm, which controls the […]

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arXiv:2509.12889v3 Announce Type: replace-cross Abstract: This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework that promotes sparsity in the space of measures, to simultaneously estimate the number of components and their parameters. Our main contribution extends the BLASSO methodology to multivariate GMMs with component-specific unknown diagonal covariance matrices. This setting is significantly more flexible than previous approaches, […]

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arXiv:2506.22543v2 Announce Type: replace-cross Abstract: The Laser Interferometer Space Antenna (LISA) is expected to detect thousands of individually resolved gravitational wave sources, overlapping in time and frequency, on top of unresolved astrophysical and/or primordial backgrounds. Disentangling resolved sources from backgrounds and extracting their parameters in a computationally intensive “global fit” is normally regarded as a necessary step toward reconstructing the properties of the underlying astrophysical populations. Here, we show that it is in principle feasible to infer the […]

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arXiv:2506.01722v3 Announce Type: replace-cross Abstract: We consider the problem setting of prediction with expert advice with possibly heavy-tailed losses, i.e. the only assumption on the losses is an upper bound on their second moments, denoted by $theta$. We develop adaptive algorithms that do not require any prior knowledge about the range or the second moment of the losses. Existing adaptive algorithms have what is typically considered a lower-order term in their regret guarantees. We show that this lower-order […]

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arXiv:2506.00416v2 Announce Type: replace-cross Abstract: Federated learning (FL) is increasingly recognised for addressing security and privacy concerns in traditional cloud-centric machine learning (ML), particularly within personalised health monitoring such as wearable devices. By enabling global model training through localised policies, FL allows resource-constrained wearables to operate independently. However, conventional first-order FL approaches face several challenges in personalised model training due to the heterogeneous non-independent and identically distributed (non-iid) data by each individual’s unique physiology and usage patterns. Recently, […]

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arXiv:2505.21400v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models allow for parallel sampling, offering a promising path to accelerate generation and eliminate the left-to-right generation constraints. Despite their empirical success, theoretical understandings of diffusion language models remain underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an […]

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arXiv:2505.12225v3 Announce Type: replace-cross Abstract: Best-of-N sampling is a powerful method for improving Large Language Model (LLM) performance, but it is often limited by its dependence on massive, text-based reward models. These models are not only computationally expensive but also data-hungry, requiring extensive labeled datasets for training. This creates a significant data challenge, as they overlook a rich, readily available data source: the LLM’s own internal hidden states. To address this data and efficiency gap, we introduce SWIFT […]

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