Training large neural networks and merging task-specific models both exploit low-rank structure and require parameter importance estimation, yet these challenges have been pursued in isolation. Current workflows compute curvature information during training, discard it, then recompute similar information for merging—wasting computation and discarding valuable trajectory data. We introduce a unified framework that maintains factorized momentum and curvature statistics during training, then reuses this information for geometry-aware model composition. The proposed method incurs modest memory overhead (approximately 30% over AdamW) to accumulate task saliency scores that enable curvature-aware merging. These scores, computed as a byproduct of optimization, provide importance estimates comparable to post-hoc Fisher computation while producing merge-ready models directly from training. We establish convergence guarantees for non-convex objectives with approximation error bounded by gradient singular value decay. On natural language understanding benchmarks, curvature-aware parameter selection outperforms magnitude-only baselines across all sparsity levels, with multi-task merging improving 1.6% over strong baselines. The proposed framework exhibits rank-invariant convergence and superior hyperparameter robustness compared to existing low-rank optimizers. By treating the optimization trajectory as a reusable asset rather than discarding it, our approach demonstrates that training-time curvature information suffices for effective model composition, enabling a unified training-merging pipeline.

Time series forecasting has become indispensable for multiple applications and industrial processes. Currently, a large number of algorithms have been developed to forecast time series, all of which are suitable depending on the characteristics and patterns to be inferred in each case. In this work, a new algorithm is proposed to predict both univariate and multivariate time series based on a combination of clustering, classification and forecasting techniques. The main goal of the proposed algorithm is first to group windows of time series values with similar patterns by applying a clustering process. Then, a specific forecasting model for each pattern is built and training is only conducted with the time windows corresponding to that pattern. The new algorithm has been designed using a flexible framework that allows the model to be generated using any combination of approaches within multiple machine learning techniques. To evaluate the model, several experiments are carried out using different configurations of the clustering, classification and forecasting methods that the model consists of. The results are analyzed and compared to classical prediction models, such as autoregressive, integrated, moving average and Holt-Winters models, to very recent forecasting methods, including deep, long short-term memory neural networks, and to well-known methods in the literature, such as k nearest neighbors, classification and regression trees, as well as random forest.

This paper presents a new approach to forecast the behavior of time series based on similarity of pattern sequences. First, clustering techniques are used with the aim of grouping and labeling the samples from a data set. Thus, the prediction of a data point is provided as follows: first, the pattern sequence prior to the day to be predicted is extracted. Then, this sequence is searched in the historical data and the prediction is calculated by averaging all the samples immediately after the matched sequence. The main novelty is that only the labels associated with each pattern are considered to forecast the future behavior of the time series, avoiding the use of real values of the time series until the last step of the prediction process. Results from several energy time series are reported and the performance of the proposed method is compared to that of recently published techniques showing a remarkable improvement in the prediction.

A new approach is presented in this work with the aim of predicting time series behaviors. A previous labeling of the samples is obtained utilizing clustering techniques and the forecasting is applied using the information provided by the clustering. Thus, the whole data set is discretized with the labels assigned to each data point and the main novelty is that only these labels are used to predict the future behavior of the time series, avoiding using the real values of the time series until the process ends. The results returned by the algorithm, however, are not labels but the nominal value of the point that is required to be predicted. The algorithm based on labeled (LBF) has been tested in several energy-related time series and a notable improvement in the prediction has been achieved.