One main challenge in time series anomaly detection for industrial IoT lies in the complex spatio-temporal couplings within multivariate data. However, traditional anomaly detection methods focus on modeling spatial or temporal dependencies independently, resulting in suboptimal representation learning and limited sensitivity to anomalous dispersion in high-dimensional spaces. In this work, we conduct an empirical analysis showing that both normal and anomalous samples tend to scatter in high-dimensional space, especially anomalous samples are markedly more dispersed. We formalize this dispersion phenomenon as scattering, quantified by the mean pairwise distance among sample representations, and leverage it as an inductive signal to enhance spatio-temporal anomaly detection. Technically, we propose ScatterAD to model representation scattering across temporal and topological dimensions. ScatterAD incorporates a topological encoder for capturing graph-structured scattering and a temporal encoder for constraining overscattering through mean squared error minimization between neighboring time steps. We introduce a contrastive fusion mechanism to ensure the complementarity of the learned temporal and topological representations. Additionally, we theoretically show that maximizing the conditional mutual information between temporal and topological views improves cross-view consistency and enhances more discriminative representations. Extensive experiments on multiple public benchmarks show that ScatterAD achieves state-of-the-art performance on multivariate time series anomaly detection.

Optical flow estimation has achieved promising results in conventional scenes but faces challenges in high-speed and low-light scenes, which suffer from motion blur and insufficient illumination. These conditions lead to weakened texture and amplified noise and deteriorate the appearance saturation and boundary completeness of frame cameras, which are necessary for motion feature matching. In degraded scenes, the frame camera provides dense appearance saturation but sparse boundary completeness due to its long imaging time and low dynamic range. In contrast, the event camera offers sparse appearance saturation, while its short imaging time and high dynamic range gives rise to dense boundary completeness. Traditionally, existing methods utilize feature fusion or domain adaptation to introduce event to improve boundary completeness.

Multi-table data integrate various entities and attributes, with potential interconnections between them. However, existing tabular learning methods often struggle to describe and leverage the underlying complementarity across distinct tables. To address this limitation, we propose the first unified paradigm for multi-table learning that systematically quantifies and integrates complementary information across tables. Specifically, we introduce a metric called complementarity strength (CS), which captures inter-table complementarity by incorporating relevance, similarity, and informativeness. For the first time, we systematically formulate the paradigm towards multi-table learning by establishing formal definitions of tasks and loss functions. Correspondingly, we present a network for multi-table learning that combines Adaptive Table encoder and Cross table Attention mechanism (ATCANet), achieving the simultaneous integration of complementary information from distinct tables. Experiments show that ATCA-Net effectively leverages complementary information and that the CS metric accurately quantifies the richness of complementarity across multiple tables. To the best of our knowledge, this is the first work to establish theoretical and practical foundations for multi-table learning.

Multi-table data integrate various entities and attributes, with potential interconnections between them. However, existing tabular learning methods often struggle to describe and leverage the underlying complementarity across distinct tables. To address this limitation, we propose the first unified paradigm for multi-table learning that systematically quantifies and integrates complementary information across tables. Specifically, we introduce a metric called complementarity strength (CS), which captures inter-table complementarity by incorporating relevance, similarity, and informativeness. For the first time, we systematically formulate the paradigm towards multi-table learning by establishing formal definitions of tasks and loss functions. Correspondingly, we present a network for multi-table learning that combines Adaptive Table encoder and Cross table Attention mechanism (ATCA-Net), achieving the simultaneous integration of complementary information from distinct tables. Extensive experiments show that ATCA-Net effectively leverages complementary information and that the CS metric accurately quantifies the richness of complementarity across multiple tables. To the best of our knowledge, this is the first work to establish theoretical and practical foundations for multi-table learning.

Protein-protein interactions (PPIs) govern nearly all cellular processes, yet computational methods for identifying binding partners typically produce ranked predictions without mechanistic justification. This creates a fundamental barrier to adoption because biologists cannot assess whether predictions reflect genuine biochemical insight or spurious correlations. We present \textbf{Protein Thoughts}, a framework that reformulates PPI discovery as an interpretable search problem with explicit reasoning. The system decomposes binding evidence into four biologically meaningful signals: sequence similarity reflecting evolutionary relationships, structural complementarity capturing geometric fit, interface balance, and chemical compatibility encoding residue-level interactions. Rather than collapsing these signals into an opaque score, we preserve their individual contributions through a transparent value function that enables both ranking and auditing. To navigate large candidate spaces efficiently, we introduce hypothesis-guided entropy-regularized Tree-of-Thoughts search. A fine-tuned language model generates search directives from embedding-derived features, classifying candidates as high-priority, exploratory, or skippable. These directives condition a Boltzmann policy that balances exploitation with entropy-driven exploration, while hypothesis-aware pruning prevents premature abandonment of promising candidates. For candidates exhibiting score disagreement, hypothesis-conditioned embedding-space flow matching transports protein embeddings toward the binder manifold. On the SHS148k benchmark, Protein Thoughts achieves mean best-binder rank of 11.2 versus 47.7 for an entropic tree search baseline, a 76% improvement, and for binding prediction the trained value function achieves $91.08 \pm 0.19$ Micro-F1, outperforming existing PPI methods on the same dataset.

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.