Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we study a minimal continual learning agent designed to isolate representational dynamics from architectural complexity and optimization objectives. The agent maintains a persistent state vector across executions and incrementally updates it as new textual data is introduced. We quantify representational change using cosine similarity between successive […]

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Local class imbalance and data heterogeneity across clients often trap prototype-based federated contrastive learning in a prototype bias loop: biased local prototypes induced by imbalanced data are aggregated into biased global prototypes, which are repeatedly reused as contrastive anchors, accumulating errors across communication rounds. To break this loop, we propose Confidence-Aware Federated Contrastive Learning (CAFedCL), a novel framework that improves the prototype aggregation mechanism and strengthens the contrastive alignment guided by prototypes. CAFedCL employs a confidence-aware aggregation mechanism […]

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arXiv:2509.20993v2 Announce Type: replace-cross Abstract: We consider the problem of estimating inverse temperature parameter $beta$ of an $n$-dimensional truncated Ising model using a single sample. Given a graph $G = (V,E)$ with $n$ vertices, a truncated Ising model is a probability distribution over the $n$-dimensional hypercube ${-1,1}^n$ where each configuration $mathbf{sigma}$ is constrained to lie in a truncation set $S subseteq {-1,1}^n$ and has probability $Pr(mathbf{sigma}) propto exp(betamathbf{sigma}^top Amathbf{sigma})$ with $A$ being the adjacency matrix of $G$. We […]

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Multiple operator learning concerns learning operator families ${G[α]:Uto V}_{αin W}$ indexed by an operator descriptor $α$. Training data are collected hierarchically by sampling operator instances $α$, then input functions $u$ per instance, and finally evaluation points $x$ per input, yielding noisy observations of $G[α][u](x)$. While recent work has developed expressive multi-task and multiple operator learning architectures and approximation-theoretic scaling laws, quantitative statistical generalization guarantees remain limited. We provide a covering-number-based generalization analysis for separable models, focusing on the […]

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We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in […]

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Victoria, Seychelles, January 23, 2026 – MEXC, the world’s fastest-growing digital asset exchange and a pioneer of true zero-fee trading, successfully concluded its “Zero-Fee Gala,” attracting over 120,000 participants and generating more than $8 billion in futures trading volume. The enthusiastic participation demonstrates strong user interest in the event and deepening trust in MEXC’s commitment to creating meaningful value for its global trading community. The promotion ran from December 22, 2025, to January 21, 2026 (UTC), combining multiple […]

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How are you, hacker? 🪐Want to know what’s trending right now?: The Techbeat by HackerNoon has got you covered with fresh content from our trending stories of the day! Set email preference here. ## Should We Be Worried About Losing Jobs? Or Just Adapt Our Civilization to New Reality? By @chris127 [ 10 Min read ] The question isn’t whether jobs will disappear—it’s whether our traditional work model is still valid. Read More. **[ISO 27001 Compliance Tools in […]

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