We give a precise trade-off between the rank of the SVDs required and the radius of the ball in which we need to initialize the method.

Second, TMA constrains the variance of the teachers to be small to avoid inconsistent labels produced during twoadjacent updates.

Time series classification faces a fundamental trade-off between accuracy and computational efficiency. While comprehensive ensembles like HIVE-COTE 2.0 achieve state-of-the-art accuracy, their 340-hour training time on the UCR benchmark renders them impractical for large-scale datasets. We investigate whether targeted combinations of two efficient algorithms from complementary paradigms can capture ensemble benefits while maintaining computational feasibility. Combining Hydra (competing convolutional kernels) and Quant (hierarchical interval quantiles) across six ensemble configurations, we evaluate performance on 10 large-scale MONSTER datasets (7,898 to 1,168,774 training instances). Our strongest configuration improves mean accuracy from 0.829 to 0.836, succeeding on 7 of 10 datasets. However, prediction-combination ensembles capture only 11% of theoretical oracle potential, revealing a substantial meta-learning optimization gap. Feature-concatenation approaches exceeded oracle bounds by learning novel decision boundaries, while prediction-level complementarity shows moderate correlation with ensemble gains. The central finding: the challenge has shifted from ensuring algorithms are different to learning how to combine them effectively. Current meta-learning strategies struggle to exploit the complementarity that oracle analysis confirms exists. Improved combination strategies could potentially double or triple ensemble gains across diverse time series classification applications.

Multi-view multi-label data offers richer perspectives for artificial intelligence, but simultaneously presents significant challenges for feature selection due to the inherent complexity of interrelations among features, views and labels. Attention mechanisms provide an effective way for analyzing these intricate relationships. They can compute importance weights for information by aggregating correlations between Query and Key matrices to focus on pertinent values. However, existing attention-based feature selection methods predominantly focus on intra-view relationships, neglecting the complementarity of inter-view features and the critical feature-label correlations. Moreover, they often fail to account for feature redundancy, potentially leading to subop-timal feature subsets. To overcome these limitations, we propose a novel method based on R edundancy-optimized Multi-head A ttention Networks for Multi-view Multi-label F eature Selection (RMAN-MMFS). Specifically, we employ each individual attention head to model intra-view feature relationships and use the cross-attention mechanisms between different heads to capture inter-view feature complementarity. Furthermore, we design static and dynamic feature redundancy terms: the static term mitigates redundancy within each view, while the dynamic term explicitly models redundancy between unselected and selected features across the entire selection process, thereby promoting feature compactness. Comprehensive evaluations on six real-world datasets, compared against six multi-view multi-label feature selection methods, demonstrate the superior performance of the proposed method.

While LLMs excel at general tasks, they struggle in specialized domains like finance, requiring diverse skills in domain knowledge, mathematical reasoning, and multilingual processing. Merging domain-specific Continual Pre-training (CPT) "experts" offers a practical alternative to costly and unstable multi-skill training. However, unlike established Supervised Fine-Tuning (SFT) model-based merging, CPT model merging remains largely unexplored. We address this gap by creating financial LLMs from experts in finance, math, and Japanese. We propose a three-stage evaluation focusing on knowledge recovery, complementarity, and emergence, and assess three merging methods (Task Arithmetic, TIES, and DARE-TIES) on a comprehensive financial benchmark curated from 18 tasks across 8 established datasets. Results show that merging an expert with its base model recovers general knowledge lost during CPT, while merging experts improves performance and can yield emergent cross-domain skills. Among the methods, Task Arithmetic performs strongly but is hyperparameter-sensitive, whereas TIES is more robust. Our findings also suggest that while model similarity correlates with merging success, emergent skills depend on more complex factors. This work presents the first foundational analysis of CPT model merging, establishing a principled framework and providing clear guidance for building multi-skill LLMs from existing assets.

Today's pursuit of a single Large Language Model (LMM) for all software engineering tasks is resource-intensive and overlooks the potential benefits of complementarity, where different models contribute unique strengths. However, the degree to which coding LLMs complement each other and the best strategy for maximizing an ensemble's potential are unclear, leaving practitioners without a clear path to move beyond single-model systems. To address this gap, we empirically compare ten individual LLMs from five families, and three ensembles of these LLMs across three software engineering benchmarks covering code generation and program repair. We assess the complementarity between models and the performance gap between the best individual model and the ensembles. Next, we evaluate various selection heuristics to identify correct solutions from an ensemble's candidate pool. We find that the theoretical upperbound for an ensemble's performance can be 83% above the best single model. Our results show that consensus-based strategies for selecting solutions fall into a "popularity trap," amplifying common but incorrect outputs. In contrast, a diversity-based strategy realizes up to 95% of this theoretical potential, and proves effective even in small two-model ensembles, enabling a cost-efficient way to enhance performance by leveraging multiple LLMs.

AI predictive systems are increasingly embedded in decision making pipelines, shaping high stakes choices once made solely by humans. Yet robust decisions under uncertainty still rely on capabilities that current AI lacks: domain knowledge not captured by data, long horizon context, and reasoning grounded in the physical world. This gap has motivated growing efforts to design collaborative frameworks that combine the complementary strengths of humans and AI. This work advances this vision by identifying the fundamental principles of Human AI collaboration within uncertainty quantification, a key component of reliable decision making. We introduce Human AI Collaborative Uncertainty Quantification, a framework that formalizes how an AI model can refine a human expert's proposed prediction set with two goals: avoiding counterfactual harm, ensuring the AI does not degrade correct human judgments, and complementarity, enabling recovery of correct outcomes the human missed. At the population level, we show that the optimal collaborative prediction set follows an intuitive two threshold structure over a single score function, extending a classical result in conformal prediction. Building on this insight, we develop practical offline and online calibration algorithms with provable distribution free finite sample guarantees. The online method adapts to distribution shifts, including human behavior evolving through interaction with AI, a phenomenon we call Human to AI Adaptation. Experiments across image classification, regression, and text based medical decision making show that collaborative prediction sets consistently outperform either agent alone, achieving higher coverage and smaller set sizes across various conditions.