arXiv:2510.22068v2 Announce Type: replace-cross Abstract: Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate modeling. Existing approaches often struggle to capture complex nonlinear relationships and/or provide reliable uncertainty quantification when data are noisy, sparse, or irregularly sampled. To address these challenges, we propose Deep Gaussian Processes for Functional Maps (DGPFM). Our method constructs a sequence of GP-based linear and […]

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arXiv:2601.19942v1 Announce Type: new Abstract: We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where $C^{(ell)}=mathbb{E}[h^{(ell)}h^{(ell)top}]$, and track deviations from a random-matrix bulk. Across model scales (1.5B–30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, $Omega(h)=1-|h|_1/(sqrt{d}|h|_2)$, exhibits a […]

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Table Of Links Abstract 1 Introduction 2 Background 3 Privacy-Relevant Methods 4 Identifying API Privacy-relevant Methods 5 Labels for Personal Data Processing 6 Process of Identifying Personal Data 7 Data-based Ranking of Privacy-relevant Methods 8 Application to Privacy Code Review 9 Related Work Conclusion, Future Work, Acknowledgement And References Identifying API Privacy-Relevant Methods Native privacy-relevant methods form the basis for identifying what we refer to as API privacyrelevant methods. These are methods found in third-party libraries and frameworks […]

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Reinforcement Learning (RL) has become essential for eliciting complex reasoning capabilities in Large Language Models (LLMs). However, the substantial memory overhead of storing Key-Value (KV) caches during long-horizon rollouts acts as a critical bottleneck, often prohibiting efficient training on limited hardware. While existing KV compression techniques offer a remedy for inference, directly applying them to RL training induces a severe policy mismatch, leading to catastrophic performance collapse. To address this, we introduce Sparse-RL empowers stable RL training under […]

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The life of a prescription at Amazon Pharmacy From pricing estimation and regulatory compliance to inventory management and chatbot assistants, machine learning models help Amazon Pharmacy customers stay healthy and save time and money. Conversational AI Alexandre Alves Anita Vila September 30, 01:32 PM October 02, 11:42 AM Pharmacies play a vital role in ensuring patients health, but the process of dispensing medications is far more complex than it may appear. At Amazon Pharmacy, we are using artificial […]

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Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive implicit generative models such as diffusion and flow-based methods, these approaches are often data-hungry, computationally costly, and misaligned with the structured solution spaces frequently found in scientific problems. We demonstrate that Mixture Density Networks (MDNs) provide a principled yet largely overlooked alternative for multimodal uncertainty quantification in SciML. As explicit […]

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arXiv:2601.20989v1 Announce Type: new Abstract: Identifying the top-$k$ items is fundamental but often prohibitive when exact valuations are expensive. We study a two-oracle setting with a fast, noisy weak oracle and a scarce, high-fidelity strong oracle (e.g., human expert verification or expensive simulation). We first analyze a simple screen-then-certify baseline (STC) and prove it makes at most $m(4varepsilon_{max})$ strong calls given jointly valid weak confidence intervals with maximum radius $varepsilon_{max}$, where $m(cdot)$ denotes the near-tie mass around the […]

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Large Reasoning Models (LRMs) have shown exceptional reasoning capabilities, but they also suffer from the issue of overthinking, often generating excessively long and redundant answers. For problems that exceed the model’s capabilities, LRMs tend to exhibit the overconfidence phenomenon, generating overly short but incorrect answers, which may contribute to suboptimal performance. To address these issues, we propose Difficulty-Differentiated Policy Optimization (DDPO), an efficient reinforcement learning algorithm that optimizes simple and complex tasks separately based on the overconfidence phenomenon. […]

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