In deep learning, classification models don’t just need to make predictions—they need to express confidence. That’s where the Softmax activation function comes in. Softmax takes the raw, unbounded scores produced by a neural network and transforms them into a well-defined probability distribution, making it possible to interpret each output as the likelihood of a specific class.  This property makes Softmax a cornerstone of multi-class classification tasks, from image recognition to language modeling. In this article, we’ll build an […]

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Many real world applications employ multi-variate performance measures and each example can belong to multiple classes. The currently most popular approaches train an SVM for each class, followed by ad hoc thresholding. Probabilistic models using Bayesian decision theory are also commonly adopted. In this paper, we propose a Bayesian online multi-label classification framework (BOMC) which learns a probabilistic linear classifier. The likelihood is modeled by a graphical model similar to TrueSkill$^text{TM}$, and inference is based on Gaussian density […]

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arXiv:2512.22473v2 Announce Type: replace Abstract: Transformers empirically perform precise probabilistic reasoning in carefully constructed “Bayesian wind tunnels” and in large-scale language models, yet the mechanisms by which gradient-based learning creates the required internal geometry remain opaque. We provide a complete first-order analysis of how cross-entropy training reshapes attention scores and value vectors in a transformer attention head. Our core result is an emph{advantage-based routing law} for attention scores, [ frac{partial L}{partial s_{ij}} = alpha_{ij}bigl(b_{ij}-mathbb{E}_{alpha_i}[b]bigr), qquad b_{ij} := u_i^top […]

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arXiv:2601.05404v1 Announce Type: new Abstract: Optimal damping aims at determining a vector of damping coefficients $nu$ that maximizes the decay rate of a mechanical system’s response. This problem can be formulated as the minimization of the trace of the solution of a Lyapunov equation whose coefficient matrix depends on $nu$. For physical relevance, the damping coefficients must be nonnegative and the resulting system must be asymptotically stable. We identify conditions under which the system is never stable or […]

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Placental abruption is detachment of the placenta before delivery from the implantation site that may have a potential to develop life-threating emergency clinic syptoms. The multifactorial nature of this disorder and no lab testing or procedures that can diagnose placental abruption. makes it difficult to predict. Artificial intelligence (AI) and machine learning (ML) have the potential to enhance clinical decision-making and enable precise assessments. This study purposed on predictive 15 ML models for placental abruption high-lighting input characteristics, […]

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The integration of game theory and AI-driven reinforcement learning into blockchain-enabled sustainable renewable energy power systems represents a transformative approach to decentralized energy management, addressing the intermittency of sources like solar and wind while ensuring equitable resource allocation. Game theory models prosumers simultaneous producers and consumers as rational agents in competitive markets, employing Nash equilibria for non-cooperative bidding in double auctions and cooperative mechanisms like Shapley values for fair profit sharing in peer-to-peer networks.Reinforcement learning enhances this framework […]

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arXiv:2601.15347v1 Announce Type: new Abstract: The rash development of knowledge graph research has brought big driving force to its application in many areas, including the medicine and healthcare domain. However, we have found that the application of some major information processing techniques on knowledge graph still lags behind. This defect includes the failure to make sufficient use of advanced logic reasoning, advanced artificial intelligence techniques, special-purpose programming languages, modern probabilistic and statistic theories et al. on knowledge graphs […]

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arXiv:2601.02412v1 Announce Type: new Abstract: Recommender systems shape online interactions by matching users with creators content to maximize engagement. Creators, in turn, adapt their content to align with users preferences and enhance their popularity. At the same time, users preferences evolve under the influence of both suggested content from the recommender system and content shared within their social circles. This feedback loop generates a complex interplay between users, creators, and recommender algorithms, which is the key cause of […]

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Multi-task learning (MTL) is critical in real-world applications such as autonomous driving and robotics, enabling simultaneous handling of diverse tasks. However, obtaining fully annotated data for all tasks is impractical due to labeling costs. Existing methods for partially labeled MTL typically rely on predictions from unlabeled tasks, making it difficult to establish reliable task associations and potentially leading to negative transfer and suboptimal performance. To address these issues, we propose a prototype-based knowledge retrieval framework that achieves robust […]

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