However, they cause another problem: space waste for personal tasks.

We study a systematic approach to a popular Statistical Arbitrage technique: Pairs Trading. Instead of relying on two highly correlated assets, we replace the second asset with a replication of the first using risk factor representations. These factors are obtained through Principal Components Analysis (PCA), exchange traded funds (ETFs), and, as our main contribution, Long Short Term Memory networks (LSTMs). Residuals between the main asset and its replication are examined for mean reversion properties, and trading signals are generated for sufficiently fast mean reverting portfolios. Beyond introducing a deep learning based replication method, we adapt the framework of Avellaneda and Lee (2008) to the Polish market. Accordingly, components of WIG20, mWIG40, and selected sector indices replace the original S&P500 universe, and market parameters such as the risk free rate and transaction costs are updated to reflect local conditions. We outline the full strategy pipeline: risk factor construction, residual modeling via the Ornstein Uhlenbeck process, and signal generation. Each replication technique is described together with its practical implementation. Strategy performance is evaluated over two periods: 2017-2019 and the recessive year 2020. All methods yield profits in 2017-2019, with PCA achieving roughly 20 percent cumulative return and an annualized Sharpe ratio of up to 2.63. Despite multiple adaptations, our conclusions remain consistent with those of the original paper. During the COVID-19 recession, only the ETF based approach remains profitable (about 5 percent annual return), while PCA and LSTM methods underperform. LSTM results, although negative, are promising and indicate potential for future optimization.

Model merging has emerged as a practical paradigm for integrating multiple independently trained models into a single model without joint retraining. Previous studies have demonstrated the effectiveness of combining parameters through strategies such as parameter decomposition, coefficient optimization, and subspace learning, significantly reducing the need for expensive joint training and achieving strong empirical performance across diverse tasks. However, these approaches predominantly treat merging as a problem of parameter space decomposition or fusion coefficient optimization, while overlooking the critical role of directional information in both parameter and feature spaces. In practice, naïve merging introduces inconsistencies in dominant parameter directions and disrupts structural coherence across models, which can degrade performance. Moreover, coefficient-based optimization methods implicitly assume compatible feature-space directions across models. However, Neural Collapse indicates that class features follow structured directional patterns, which may differ across independently trained models, making coefficient optimization alone insufficient. In this work, we emphasize the importance of \emph{directional alignment} and introduce a unified geometric framework, \emph{Merging with Directional Alignment} (\method{}), which aligns directional structures consistently in both the parameter and feature spaces. Our analysis shows that directional alignment improves structural coherence, and extensive experiments across benchmarks, model scales, and task configurations further validate the effectiveness of our approach.

Built upon Eq. 7, we have The architecture of surrogate models is modified to avoid overfitting. To make the conclusion clearer, we also report the performance of a general surrogate model, which is trained on the training set of target models. Specifically, the common sense in black-box attacks is that mounting attacks requires a surrogate model, which generalizes well on the test set. Similarly, "First" means only applying ETF to the first layer. We conduct experiments using GEFORCE RTX 2080 Ti, CPU AMD Ryzen 7 3700X @3.6 GHz.

Then the same solution in the Lemma 1 is obtained. We will prove that if Assumptions 1 and 2 hold, the stochastic gradients cannot be uniformly bounded. However, FedGELA might reach better local optimal by adapting the feature structure. Here we complete the proof. "existing angle" as the angle of classifier vectors belonging to classes that exist in a local client In Fed-ISIC2019, there exists a true PCDD situation that needs to be solved.

Accurately measuring portfolio similarity is critical for a wide range of financial applications, including Exchange-traded Fund (ETF) recommendation, portfolio trading, and risk alignment. Existing similarity measures often rely on exact asset overlap or static distance metrics, which fail to capture similarities among the constituents (e.g., securities within the portfolio) as well as nuanced relationships between partially overlapping portfolios with heterogeneous weights. We introduce STRAPSim (Semantic, Two-level, Residual-Aware Portfolio Similarity), a novel method that computes portfolio similarity by matching constituents based on semantic similarity, weighting them according to their portfolio share, and aggregating results via residual-aware greedy alignment. We benchmark our approach against Jaccard, weighted Jaccard, as well as BERTScore-inspired variants across public classification, regression, and recommendation tasks, as well as on corporate bond ETF datasets. Empirical results show that our method consistently outperforms baselines in predictive accuracy and ranking alignment, achieving the highest Spearman correlation with return-based similarity. By leveraging constituent-aware matching and dynamic reweighting, portfolio similarity offers a scalable, interpretable framework for comparing structured asset baskets, demonstrating its utility in ETF benchmarking, portfolio construction, and systematic execution.

Continual learning (CL) involves acquiring and accumulating knowledge from evolving tasks while alleviating catastrophic forgetting. Recently, leveraging contrastive loss to construct more transferable and less forgetful representations has been a promising direction in CL. Despite advancements, their performance is still limited due to confusion arising from both inter-task and intra-task features. To address the problem, we propose a simple yet effective contrastive strategy named \textbf{G}lobal \textbf{P}re-fixing, \textbf{L}ocal \textbf{A}djusting for \textbf{S}upervised \textbf{C}ontrastive learning (GPLASC). Specifically, to avoid task-level confusion, we divide the entire unit hypersphere of representations into non-overlapping regions, with the centers of the regions forming an inter-task pre-fixed \textbf{E}quiangular \textbf{T}ight \textbf{F}rame (ETF). Meanwhile, for individual tasks, our method helps regulate the feature structure and form intra-task adjustable ETFs within their respective allocated regions. As a result, our method \textit{simultaneously} ensures discriminative feature structures both between tasks and within tasks and can be seamlessly integrated into any existing contrastive continual learning framework. Extensive experiments validate its effectiveness.