However, a topology with a fast consensus rate, e.g., the exponential graph, generally has a large maximum degree, which incurs significant communication

The cubic regularization method (CR) is a popular algorithm for unconstrained non-convex optimization. At each iteration, CR solves a cubically regularized quadratic problem, called the cubic regularization subproblem (CRS). One way to solve the CRS relies on solving the secular equation, whose computational bottleneck lies in the computation of all eigenvalues of the Hessian matrix. In this paper, we propose and analyze a novel CRS solver based on an approximate secular equation, which requires only some of the Hessian eigenvalues and is therefore much more efficient. Two approximate secular equations (ASEs) are developed.

Large Language Models (LLMs) exhibit impressive capabilities, but remain susceptible to a growing spectrum of safety risks, including jailbreaks, toxic content, hallucinations, and bias. Existing defenses often address only a single threat type or resort to rigid outright rejection, sacrificing user experience and failing to generalize across diverse and novel attacks. This paper introduces Adversarial Scenario Extrapolation (ASE), a novel inference-time computation framework that leverages Chain-of-Thought (CoT) reasoning to simultaneously enhance LLM robustness and seamlessness. ASE guides the LLM through a self-generative process of contemplating potential adversarial scenarios and formulating defensive strategies before generating a response to the user query. Comprehensive evaluation on four adversarial benchmarks with four latest LLMs shows that ASE achieves near-zero jailbreak attack success rates and minimal toxicity, while slashing outright rejections to <4%. ASE outperforms six state-of-the-art defenses in robustness-seamlessness trade-offs, with 92-99% accuracy on adversarial Q&A and 4-10x lower bias scores. By transforming adversarial perception into an intrinsic cognitive process, ASE sets a new paradigm for secure and natural human-AI interaction.

However, a topology with a fast consensus rate, e.g., the exponential graph, generally has a large maximum degree, which incurs significant communication

In Figure 2, we examine the probability of acquiring a '7' as a function of the number of acquired We see that XWED initially focuses on 7s but then diversifies. The XWED behavior is preferable: we are initially unsure about the loss of these points, but once the loss is well characterized for the 7s we should explore other areas as well. B.2 Constant π Fails for Distribution Shift. Figure B.1 (a) shows that, for LURE suffered high variance in Figure 3. In Figure B.1 (b), we observe that ASE continues to Figure B.2 demonstrates that ASEs continue to outperform all other baselines for the task of This result highlights the importance of the adaptive nature of both ASE-and LUREbased active testing. Figure B.2: V ariant of the experiments of 7.3 where we estimate the accuracy of the main model. We here investigate a variation of the experiments in 7.3: reducing the size of the training set to Despite this, Figure B.3 demonstrates that ASEs continue to outperform all baselines.

This paper presents a comparison of the performance of Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) in the task of multi-classifying images containing lesions of psoriasis and diseases similar to it. Models pre-trained on ImageNet were adapted to a specific data set. Both achieved high predictive metrics, but the ViTs stood out for their superior performance with smaller models. Dual Attention Vision Transformer-Base (DaViT-B) obtained the best results, with an f1-score of 96.4%, and is recommended as the most efficient architecture for automated psoriasis detection. This article reinforces the potential of ViTs for medical image classification tasks.

As modern software systems expand in scale and complexity, the challenges associated with their modeling and formulation grow increasingly intricate. Traditional approaches often fall short in effectively addressing these complexities, particularly in tasks such as design pattern detection for maintenance and assessment, as well as code refactoring for optimization and long-term sustainability. This growing inadequacy underscores the need for a paradigm shift in how such challenges are approached and resolved. This paper presents Analytical Software Engineering (ASE), a novel design paradigm aimed at balancing abstraction, tool accessibility, compatibility, and scalability. ASE enables effective modeling and resolution of complex software engineering problems. The paradigm is evaluated through two frameworks Behavioral-Structural Sequences (BSS) and Optimized Design Refactoring (ODR), both developed in accordance with ASE principles. BSS offers a compact, language-agnostic representation of codebases to facilitate precise design pattern detection. ODR unifies artifact and solution representations to optimize code refactoring via heuristic algorithms while eliminating iterative computational overhead. By providing a structured approach to software design challenges, ASE lays the groundwork for future research in encoding and analyzing complex software metrics.