We generalize the framework of Fredholm Neural Networks, to learn non-expansive integral operators arising in Fredholm Integral Equations (FIEs) of the second kind in arbitrary dimensions. We first present the proposed Fredholm Integral Neural Operators (FREDINOs), for FIEs and prove that they are universal approximators of linear and non-linear integral operators and corresponding solution operators. We furthermore prove that the learned operators are guaranteed to be contractive, thereby strictly satisfying the mathematical property required for the convergence of […]

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Two years ago, I posted a list of Hello World examples for machine learning and AI on social. Here, the Hello World means beginner-friendly examples to showcase a method. I set a biennial calendar alert to revisit and append to it. I was thinking pretty hard about what a 2025 example could look like. So, here is a short post with the updated list and some explanations for more context.

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arXiv:2601.19756v1 Announce Type: cross Abstract: The empirical success of deep learning is often attributed to deep networks’ ability to exploit hierarchical structure in data, constructing increasingly complex features across layers. Yet despite substantial progress in deep learning theory, most optimization results sill focus on networks with only two or three layers, leaving the theoretical understanding of hierarchical learning in genuinely deep models limited. This leads to a natural question: can we prove that deep networks, trained by gradient-based […]

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The decentralized finance sector keeps expanding as tech giants including Google, OpenAI, Amazon, Meta, xAI, and Oracle signed a White House Ratepayer Protection Pledge to cover their AI data center energy costs. Tracking bitcoin hyper news is routine for Layer 2 watchers, but better opportunities exist during consolidation, and Pepeto with $7.5M raised and advancing exchange infrastructure offers returns that bitcoin hyper news cannot deliver. Tech Giants Sign White House Pledge to Cover AI Data Center Energy Costs […]

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Large Reasoning Models (LRMs) achieve impressive performance on complex reasoning tasks via Chain-of-Thought (CoT) reasoning, which enables them to generate intermediate thinking tokens before arriving at the final answer. However, LRMs often suffer from significant overthinking, spending excessive compute time even after the answer is generated early on. Prior work has identified the existence of an optimal reasoning length such that truncating reasoning at this point significantly shortens CoT outputs with virtually no change in performance. However, determining […]

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arXiv:2601.19964v1 Announce Type: new Abstract: We discuss Google’s journey in developing and refining two internal AI-based IDE features: code completion and natural-language-driven code transformation (Transform Code). We address challenges in latency, user experience and suggestion quality, all backed by rigorous experimentation. The article serves as an example of how to refine AI developer tools across the user interface, backend, and model layers, to deliver tangible productivity improvements in an enterprise setting.

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The systematic construction of expansive fictional universes, known as worldbuilding, faces significant challenges in maintaining long-range structural consistency, particularly within generative AI architectures prone to “ontological drift”. This paper introduces WorldPT, a novel framework and dataset that formalizes worldbuilding through Directed Multilayer Attributed Graphs. By implementing a Grounding Directionality Axiom and a hexapartite layering system (Structural, Causal, Temporal, Social, Ontological, and Symbolic), we transition from unstructured text-centric models to machine-verifiable narrative structures. The dataset is uniquely curated in […]

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