Recent work \cite{arifgroup} introduced Federated Proximal Gradient \textbf{(\texttt{FedProxGrad})} for solving non-convex composite optimization problems in group fair federated learning. However, the original analysis established convergence only to a \textit{noise-dominated neighborhood of stationarity}, with explicit dependence on a variance-induced noise floor. In this work, we provide an improved asymptotic convergence analysis for a generalized \texttt{FedProxGrad}-type analytical framework with inexact local proximal solutions and explicit fairness regularization. We call this extended analytical framework \textbf{DS \texttt{FedProxGrad}} (Decay Step Size \texttt{FedProxGrad}). Under a Robbins-Monro step-size schedule \cite{robbins1951stochastic} and a mild decay condition on local inexactness, we prove that $\liminf_{r\to\infty} \mathbb{E}[\|\nabla F(\mathbf{x}^r)\|^2] = 0$, i.e., the algorithm is asymptotically stationary and the convergence rate does not depend on a variance-induced noise floor.

Recent experiments reveal that task-relevant variables are often encoded in approximately orthogonal subspaces of the neural activity space. These disentangled low-dimensional representations are observed in multiple brain areas and across different species, and are typically the result of a process of abstraction that supports simple forms of out-of-distribution generalization. The mechanisms by which such geometries emerge remain poorly understood, and the mechanisms that have been investigated are typically unsupervised (e.g., based on variational auto-encoders). Here, we show mathematically that abstract representations of latent variables are guaranteed to appear in the last hidden layer of feedforward nonlinear networks when they are trained on tasks that depend directly on these latent variables. These abstract representations reflect the structure of the desired outputs or the semantics of the input stimuli. To investigate the neural representations that emerge in these networks, we develop an analytical framework that maps the optimization over the network weights into a mean-field problem over the distribution of neural preactivations. Applying this framework to a finite-width ReLU network, we find that its hidden layer exhibits an abstract representation at all global minima of the task objective. We further extend these analyses to two broad families of activation functions and deep feedforward architectures, demonstrating that abstract representations naturally arise in all these scenarios. Together, these results provide an explanation for the widely observed abstract representations in both the brain and artificial neural networks, as well as a mathematically tractable toolkit for understanding the emergence of different kinds of representations in task-optimized, feature-learning network models.

We thank the reviewer s for the careful feedback and appreciate the time spent reading our paper. Detailed responses are as below: Literature on online L P (OLP) and the contribution of our work: (i) From the algorithmic perspective, our algorithm has a strongly polynomial O(nnz(A)) flop complexity (linear in the number of non - zero entries in A), while the previous OLP algorithms all require solving O(log n) or O(n) of LP s ( increasing to the full size over time) . For example, Agrawal e t al. (2014) solved O(log n) LPs and Kesselheim et a l . As far as we know, the algorithm is the first of its kind and the most efficient OLP algorithm so far. As mentioned by the reviewer, our algorithms share similarity with the network control algorithm in Neely, M.J. (2010), but our analysis extends their analysis (in i.i.

We present a novel approach for recommending actionable strategies by integrating strategic frameworks with decision heuristics through semantic analysis. While strategy frameworks provide systematic models for assessment and planning, and decision heuristics encode experiential knowledge,these traditions have historically remained separate. Our methodology bridges this gap using advanced natural language processing (NLP), demonstrated through integrating frameworks like the 6C model with the Thirty-Six Stratagems. The approach employs vector space representations and semantic similarity calculations to map framework parameters to heuristic patterns, supported by a computational architecture that combines deep semantic processing with constrained use of Large Language Models. By processing both primary content and secondary elements (diagrams, matrices) as complementary linguistic representations, we demonstrate effectiveness through corporate strategy case studies. The methodology generalizes to various analytical frameworks and heuristic sets, culminating in a plug-and-play architecture for generating recommender systems that enable cohesive integration of strategic frameworks and decision heuristics into actionable guidance.

The world has recently witnessed an unprecedented acceleration in demands for Machine Learning and Artificial Intelligence applications. This spike in demand has imposed tremendous strain on the underlying technology stack in supply chain, GPU-accelerated hardware, software, datacenter power density, and energy consumption. If left on the current technological trajectory, future demands show insurmountable spending trends, further limiting market players, stifling innovation, and widening the technology gap. To address these challenges, we propose a fundamental change in the AI training infrastructure throughout the technology ecosystem. The changes require advancements in supercomputing and novel AI training approaches, from high-end software to low-level hardware, microprocessor, and chip design, while advancing the energy efficiency required by a sustainable infrastructure. This paper presents the analytical framework that quantitatively highlights the challenges and points to the opportunities to reduce the barriers to entry for training large language models.

Analysis of longitudinal changes in imaging studies often involves both segmentation of structures of interest and registration of multiple timeframes. The accuracy of such analysis could benefit from a tailored framework that jointly optimizes both tasks to fully exploit the information available in the longitudinal data. Most learning-based registration algorithms, including joint optimization approaches, currently suffer from bias due to selection of a fixed reference frame and only support pairwise transformations. We here propose an analytical framework based on an unbiased learning strategy for group-wise registration that simultaneously registers images to the mean space of a group to obtain consistent segmentations. We evaluate the proposed method on longitudinal analysis of a white matter tract in a brain MRI dataset with 2-3 time-points for 3249 individuals, i.e., 8045 images in total. The reproducibility of the method is evaluated on test-retest data from 97 individuals. The results confirm that the implicit reference image is an average of the input image. In addition, the proposed framework leads to consistent segmentations and significantly lower processing bias than that of a pair-wise fixed-reference approach. This processing bias is even smaller than those obtained when translating segmentations by only one voxel, which can be attributed to subtle numerical instabilities and interpolation. Therefore, we postulate that the proposed mean-space learning strategy could be widely applied to learning-based registration tasks. In addition, this group-wise framework introduces a novel way for learning-based longitudinal studies by direct construction of an unbiased within-subject template and allowing reliable and efficient analysis of spatio-temporal imaging biomarkers.

The artificial intelligence community (AI) has recently engaged in activism in relation to their employers, other members of the community, and their governments in order to shape the societal and ethical implications of AI. It has achieved some notable successes, but prospects for further political organising and activism are uncertain. We survey activism by the AI community over the last six years; apply two analytical frameworks drawing upon the literature on epistemic communities, and worker organising and bargaining; and explore what they imply for the future prospects of the AI community. Success thus far has hinged on a coherent shared culture, and high bargaining power due to the high demand for a limited supply of AI talent. Both are crucial to the future of AI activism and worthy of sustained attention.

We present a preference learning framework for multiple criteria sorting. We consider sorting procedures applying an additive value model with diverse types of marginal value functions (including linear, piecewise-linear, splined, and general monotone ones) under a unified analytical framework. Differently from the existing sorting methods that infer a preference model from crisp decision examples, where each reference alternative is assigned to a unique class, our framework allows to consider valued assignment examples in which a reference alternative can be classified into multiple classes with respective credibility degrees. We propose an optimization model for constructing a preference model from such valued examples by maximizing the credible consistency among reference alternatives. To improve the predictive ability of the constructed model on new instances, we employ the regularization techniques. Moreover, to enhance the capability of addressing large-scale datasets, we introduce a state-of-the-art algorithm that is widely used in the machine learning community to solve the proposed optimization model in a computationally efficient way. Using the constructed additive value model, we determine both crisp and valued assignments for non-reference alternatives. Moreover, we allow the Decision Maker to prioritize importance of classes and give the method a flexibility to adjust classification performance across classes according to the specified priorities. The practical usefulness of the analytical framework is demonstrated on a real-world dataset by comparing it to several existing sorting methods.

The use of Big Data has continued to grow and mature, with some organizations reaping considerable rewards. The processing of Big Data has recently advanced to a new level of evolution, in the form of AI (Artificial Intelligence) platforms. AI platforms promise significant impact (and disruptions) over the next decade. The use of AI to process massive datasets will bring previously unknown improvements to Business Intelligence and Analytics among innumerable other technologies. According to Anil Kaul, CEO and co-founder of Absolutdata, In mid-2000s, the concept of using Big Data to "train" Artificial Intelligence was developed, and advanced with several successes.