Deep clustering uncovers hidden patterns and groups in complex time series data, yet its opaque decision-making limits use in safety-critical settings. This survey offers a structured overview of explainable deep clustering for time series, collecting current methods and their real-world applications. We thoroughly discuss and compare peer-reviewed and preprint papers through application domains across healthcare, finance, IoT, and climate science. Our analysis reveals that most work relies on autoencoder and attention architectures, with limited support for streaming, irregularly sampled, or privacy-preserved series, and interpretability is still primarily treated as an add-on. To push the field forward, we outline six research opportunities: (1) combining complex networks with built-in interpretability; (2) setting up clear, faithfulness-focused evaluation metrics for unsupervised explanations; (3) building explainers that adapt to live data streams; (4) crafting explanations tailored to specific domains; (5) adding human-in-the-loop methods that refine clusters and explanations together; and (6) improving our understanding of how time series clustering models work internally. By making interpretability a primary design goal rather than an afterthought, we propose the groundwork for the next generation of trustworthy deep clustering time series analytics.

Accurate modeling of physical systems governed by partial differential equations is a central challenge in scientific computing. In oceanography, high-resolution current data are critical for coastal management, environmental monitoring, and maritime safety. However, available satellite products, such as Copernicus data for sea water velocity at ~0.08 degrees spatial resolution and global ocean models, often lack the spatial granularity required for detailed local analyses. In this work, we (a) introduce a supervised deep learning framework based on neural operators for solving PDEs and providing arbitrary resolution solutions, and (b) propose downscaling models with an application to Copernicus ocean current data. Additionally, our method can model surrogate PDEs and predict solutions at arbitrary resolution, regardless of the input resolution. We evaluated our model on real-world Copernicus ocean current data and synthetic Navier-Stokes simulation datasets.

Abstract--Distributed optimization is pivotal for large-scale signal processing and machine learning, yet communication overhead remains a major bottleneck. Low-rank gradient compression, in which the transmitted gradients are approximated by low-rank matrices to reduce communication, offers a promising remedy. Existing methods typically adopt either randomized or greedy compression strategies: randomized approaches project gradients onto randomly chosen subspaces, introducing high variance and degrading empirical performance; greedy methods select the most informative subspaces, achieving strong empirical results but lacking convergence guarantees. T o address this gap, we propose GreedyLore--the first Greedy L ow-R ank gradie nt compression algorithm for distributed learning with rigorous convergence guarantees. GreedyLore incorporates error feedback to correct the bias introduced by greedy compression and introduces a semi-lazy subspace update that ensures the compression operator remains contractive throughout all iterations. With these techniques, we prove that GreedyLore achieves a convergence rate of O(σ/ NT+1/T) under standard optimizers such as MSGD and Adam--marking the first linear speedup convergence rate for low-rank gradient compression. Extensive experiments are conducted to validate our theoretical findings. Index T erms--Distributed Learning, Low-Rank Compression, Communication-Efficient Optimization, Error Feedback. ISTRIBUTED optimization is a promising paradigm for addressing large-scale problems in signal processing and machine learning. In distributed algorithms, each computing node processes its local data while collaborating with others to minimize a global loss function. This approach mitigates the computational burden on individual nodes, reduces memory requirements, and enables efficient parallel computation.

Quantum federated learning (QFL) has been recently introduced to enable a distributed privacy-preserving quantum machine learning (QML) model training across quantum processors (clients). Despite recent research efforts, existing QFL frameworks predominantly focus on unimodal systems, limiting their applicability to real-world tasks that often naturally involve multiple modalities. T o fill this significant gap, we present for the first time a novel multi-modal approach specifically tailored for the QFL setting with the intermediate fusion using quantum entanglement. Furthermore, to address a major bottleneck in multimodal QFL, where the absence of certain modalities during training can degrade model performance, we introduce a Missing Modality Agnostic (MMA) mechanism that isolates untrained quantum circuits, ensuring stable training without corrupted states. Simulation results demonstrate that the proposed multimodal QFL method with MMA yields an improvement in accuracy of 6.84% in independent and identically distributed (IID) and 7.25% in non-IID data distributions compared to the state-of-the-art methods.

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments on Qwen3-14B models using math-only data but different tuning methods. We find that reinforcement learning (RL)-tuned models generalize well across domains, while supervised fine-tuning (SFT)-tuned models often forget general capabilities. Latent-space representation and token-space distribution shift analyses reveal that SFT induces substantial representation and output drift, while RL preserves general-domain structure. Our results suggest a need to rethink standard post-training recipes, particularly the reliance on SFT-distilled data for advancing reasoning models.

We propose a hybrid quantum-classical reinforcement learning framework for sector rotation in the Taiwan stock market. Our system employs Proximal Policy Optimization (PPO) as the backbone algorithm and integrates both classical architectures (LSTM, Transformer) and quantum-enhanced models (QNN, QRWKV, QASA) as policy and value networks. An automated feature engineering pipeline extracts financial indicators from capital share data to ensure consistent model input across all configurations. Empirical backtesting reveals a key finding: although quantum-enhanced models consistently achieve higher training rewards, they underperform classical models in real-world investment metrics such as cumulative return and Sharpe ratio. This discrepancy highlights a core challenge in applying reinforcement learning to financial domains -- namely, the mismatch between proxy reward signals and true investment objectives. Our analysis suggests that current reward designs may incentivize overfitting to short-term volatility rather than optimizing risk-adjusted returns. This issue is compounded by the inherent expressiveness and optimization instability of quantum circuits under Noisy Intermediate-Scale Quantum (NISQ) constraints. We discuss the implications of this reward-performance gap and propose directions for future improvement, including reward shaping, model regularization, and validation-based early stopping. Our work offers a reproducible benchmark and critical insights into the practical challenges of deploying quantum reinforcement learning in real-world finance.

The growing adoption of Artificial Intelligence (AI) in Internet of Things (IoT) ecosystems has intensified the need for personalized learning methods that can operate efficiently and privately across heterogeneous, resource-constrained devices. However, enabling effective personalized learning in decentralized settings introduces several challenges, including efficient knowledge transfer between clients, protection of data privacy, and resilience against poisoning attacks. In this paper, we address these challenges by developing P4 (Personalized, Private, Peer-to-Peer) -- a method designed to deliver personalized models for resource-constrained IoT devices while ensuring differential privacy and robustness against poisoning attacks. Our solution employs a lightweight, fully decentralized algorithm to privately detect client similarity and form collaborative groups. Within each group, clients leverage differentially private knowledge distillation to co-train their models, maintaining high accuracy while ensuring robustness to the presence of malicious clients. We evaluate P4 on popular benchmark datasets using both linear and CNN-based architectures across various heterogeneity settings and attack scenarios. Experimental results show that P4 achieves 5% to 30% higher accuracy than leading differentially private peer-to-peer approaches and maintains robustness with up to 30% malicious clients. Additionally, we demonstrate its practicality by deploying it on resource-constrained devices, where collaborative training between two clients adds only ~7 seconds of overhead.

Test-Time Scaling (TTS) improves the performance of Large Language Models (LLMs) by using additional inference-time computation to explore multiple reasoning paths through search. Yet how to allocate a fixed rollout budget most effectively during search remains underexplored, often resulting in inefficient use of compute at test time. To bridge this gap, we formulate test-time search as a resource allocation problem and derive the optimal allocation strategy that maximizes the probability of obtaining a correct solution under a fixed rollout budget. Within this formulation, we reveal a core limitation of existing search methods: solution-level allocation tends to favor reasoning directions with more candidates, leading to theoretically suboptimal and inefficient use of compute. To address this, we propose Direction-Oriented Resource Allocation (DORA), a provably optimal method that mitigates this bias by decoupling direction quality from candidate count and allocating resources at the direction level. To demonstrate DORA's effectiveness, we conduct extensive experiments on challenging mathematical reasoning benchmarks including MATH500, AIME2024, and AIME2025. The empirical results show that DORA consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art accuracy. We hope our findings contribute to a broader understanding of optimal TTS for LLMs.

Physiological signals are often corrupted by motion artifacts, baseline drift, and other low-SNR disturbances, which pose significant challenges for analysis. Additionally, these signals exhibit strong non-stationarity, with sharp peaks and abrupt changes that evolve continuously, making them difficult to represent using traditional time-domain or filtering methods. To address these issues, a novel wavelet-based approach for physiological signal analysis is presented, aiming to capture multi-scale time-frequency features in various physiological signals. Leveraging this technique, two large-scale pretrained models specific to EMG and ECG are introduced for the first time, achieving superior performance and setting new baselines in downstream tasks. Additionally, a unified multi-modal framework is constructed by integrating pretrained EEG model, where each modality is guided through its dedicated branch and fused via learnable weighted fusion. This design effectively addresses challenges such as low signal-to-noise ratio, high inter-subject variability, and device mismatch, outperforming existing methods on multi-modal tasks. The proposed wavelet-based architecture lays a solid foundation for analysis of diverse physiological signals, while the multi-modal design points to next-generation physiological signal processing with potential impact on wearable health monitoring, clinical diagnostics, and broader biomedical applications. Code and data are available at: github.com/ForeverBlue816/PhysioWave

As robotic systems become increasingly integrated into real-world environments -- ranging from autonomous vehicles to household assistants -- they inevitably encounter diverse and unstructured scenarios that lead to failures. While such failures pose safety and reliability challenges, they also provide rich perceptual data for improving future performance. However, manually analyzing large-scale failure datasets is impractical. In this work, we present a method for automatically organizing large-scale robotic failure data into semantically meaningful failure clusters, enabling scalable learning from failure without human supervision. Our approach leverages the reasoning capabilities of Multimodal Large Language Models (MLLMs), trained on internet-scale data, to infer high-level failure causes from raw perceptual trajectories and discover interpretable structure within uncurated failure logs. These semantic clusters reveal patterns and hypothesized causes of failure, enabling scalable learning from experience. We demonstrate that the discovered failure modes can guide targeted data collection for policy refinement, accelerating iterative improvement in agent policies and overall safety. Additionally, we show that these semantic clusters can benefit online failure monitoring systems, offering a lightweight yet powerful safeguard for real-time operation. We demonstrate that this framework enhances robot learning and robustness by transforming real-world failures into actionable and interpretable signals for adaptation.