January 2026

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems. However, unlike classical numerical methods that offer established convergence guarantees, neural network-based approximations typically lack rigorous error bounds. Furthermore, the non-deterministic nature of their optimization makes it difficult to mathematically certify their accuracy. To address these challenges, we propose a "Learn and Verify" framework that […]

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Every entrepreneur talks about vision, resilience, and execution. But beneath all of these traits lies a quieter, less visible skill that ultimately determines success or failure: decision-making under uncertainty. Markets shift, data is incomplete, and outcomes are rarely guaranteed. The leaders who endure are not those who wait for certainty—but those who learn how to think clearly without it. According to Alessio Vinassa, serial entrepreneur and business advisor, uncertainty is not an obstacle to leadership—it is the environment […]

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The Hidden Tax of Dirty Data on AI Performance — and a Developer’s Shortcut to Fixing It You’ve trained a customer segmentation model, but it’s clustering addresses from different states together. Your recommendation engine is suggesting products to customers in countries you don’t ship to. Your fraud detection system keeps flagging legitimate international transactions. Sound familiar? Here’s the uncomfortable truth: Your model isn’t failing. Your data is. As we discussed in my previous piece on data quality’s role in […]

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Unsupervised pre-training can equip reinforcement learning agents with prior knowledge and accelerate learning in downstream tasks. A promising direction, grounded in human development, investigates agents that learn by setting and pursuing their own goals. The core challenge lies in how to effectively generate, select, and learn from such goals. Our focus is on broad distributions of downstream tasks where solving every task zero-shot is infeasible. Such settings naturally arise when the target tasks lie outside of the pre-training […]

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Hi everyone, I’m a beginner who is just starting with Python and slowly learning about Reinforcement Learning (RL). I have a basic doubt and wanted guidance from people already in the field: Is a PhD or Master’s degree mandatory to get a job in Reinforcement Learning? Are there industry roles where a Bachelor’s + strong skills/projects are enough? Which type of RL roles usually require PhD, and which don’t? I’m not aiming for research right now — more […]

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Anyone who works with PyTorch model code starts asking the same questions: Why is this taking so long? How do I make my training loop faster? Whether you’re an ML engineer, a researcher or just decided to play around with a random ML repository over the weekend, you will eventually try to understand how to speed your code up. However, before we can do that, we need to learn how to measure performance correctly. And then draw the […]

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Federated Continual Learning (FCL) leverages inter-client collaboration to balance new knowledge acquisition and prior knowledge retention in non-stationary data. However, existing batch-based FCL methods lack adaptability to streaming scenarios featuring category overlap between old and new data and absent task identifiers, leading to indistinguishability of old and new knowledge, uncertain task assignments for samples, and knowledge confusion.To address this, we propose streaming federated continual learning setting: per federated learning (FL) round, clients process streaming data with disjoint samples […]

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Continual learning is a challenge for models with static architecture, as they fail to adapt to when data distributions evolve across tasks. We introduce a mathematical framework that jointly models architecture and weights in a Sobolev space, enabling a rigorous investigation into the role of neural network architecture in continual learning and its effect on the forgetting loss. We derive necessary conditions for the continual learning solution and prove that learning only model weights is insufficient to mitigate […]

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