The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this work we provide an error analysis for the deep Kolmogorov method for heat PDEs. Specifically, we reveal convergence with convergence rates for the overall mean square distance between the exact solution of the heat PDE and the realization function of the approximating deep neural network (DNN) associated with a stochastic optimization algorithm in terms of the size of the architecture (the depth/number of hidden layers and the width of the hidden layers) of the approximating DNN, in terms of the number of random sample points used in the loss function (the number of input-output data pairs used in the loss function), and in terms of the size of the optimization error made by the employed stochastic optimization method.

Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for similarity-based search, the geometry of Euclidean embeddings often fails to capture the hierarchical structure and fine-grained affinity variations intrinsic to molecular interactions. In this work, we propose HypSeek, a hyperbolic representation learning framework that embeds ligands, protein pockets, and sequences into Lorentz-model hyperbolic space. By leveraging the exponential geometry and negative curvature of hyperbolic space, HypSeek enables expressive, affinity-sensitive embeddings that can effectively model both global activity and subtle functional differences-particularly in challenging cases such as activity cliffs, where structurally similar ligands exhibit large affinity gaps. Our mode unifies virtual screening and affinity ranking in a single framework, introducing a protein-guided three-tower architecture to enhance representational structure. HypSeek improves early enrichment in virtual screening on DUD-E from 42.63 to 51.44 (+20.7%) and affinity ranking correlation on JACS from 0.5774 to 0.7239 (+25.4%), demonstrating the benefits of hyperbolic geometry across both tasks and highlighting its potential as a powerful inductive bias for protein-ligand modeling.

We study cost-aware routing for large language models across diverse and dynamic pools of models. Existing approaches often overlook prompt-specific context, rely on expensive model profiling, assume a fixed set of experts, or use inefficient trial-and-error strategies. We introduce Cost-Spectrum Contrastive Routing (CSCR), a lightweight framework that maps both prompts and models into a shared embedding space to enable fast, cost-sensitive selection. CSCR uses compact, fast-to-compute logit footprints for open-source models and perplexity fingerprints for black-box APIs. A contrastive encoder is trained to favor the cheapest accurate expert within adaptive cost bands. At inference time, routing reduces to a single k-NN lookup via a FAISS index, requiring no retraining when the expert pool changes and enabling microsecond latency. Across multiple benchmarks, CSCR consistently outperforms baselines, improving the accuracy-cost tradeoff by up to 25%, while generalizing robustly to unseen LLMs and out-of-distribution prompts.

Fault intensity diagnosis (FID) plays a pivotal role in monitoring and maintaining mechanical devices within complex industrial systems. As current FID methods are based on chain of thought without considering dependencies among target classes. To capture and explore dependencies, we propose a hierarchical knowledge guided fault intensity diagnosis framework (HKG) inspired by the tree of thought, which is amenable to any representation learning methods. The HKG uses graph convolutional networks to map the hierarchical topological graph of class representations into a set of interdependent global hierarchical classifiers, where each node is denoted by word embeddings of a class. These global hierarchical classifiers are applied to learned deep features extracted by representation learning, allowing the entire model to be end-to-end learnable. In addition, we develop a re-weighted hierarchical knowledge correlation matrix (Re-HKCM) scheme by embedding inter-class hierarchical knowledge into a data-driven statistical correlation matrix (SCM) which effectively guides the information sharing of nodes in graphical convolutional neural networks and avoids over-smoothing issues. The Re-HKCM is derived from the SCM through a series of mathematical transformations. Extensive experiments are performed on four real-world datasets from different industrial domains (three cavitation datasets from SAMSON AG and one existing publicly) for FID, all showing superior results and outperform recent state-of-the-art FID methods.

Recommendation systems are essential tools in modern e-commerce, facilitating personalized user experiences by suggesting relevant products. Recent advancements in generative models have demonstrated potential in enhancing recommendation systems; however, these models often exhibit limitations in optimizing retrieval tasks, primarily due to their reliance on autoregressive generation mechanisms. Conventional approaches introduce sequential dependencies that impede efficient retrieval, as they are inherently unsuitable for generating multiple items without positional constraints within a single request session. To address these limitations, we propose TBGRecall, a framework integrating Next Session Prediction (NSP), designed to enhance generative retrieval models for e-commerce applications. Our framework reformulation involves partitioning input samples into multi-session sequences, where each sequence comprises a session token followed by a set of item tokens, and then further incorporate multiple optimizations tailored to the generative task in retrieval scenarios. In terms of training methodology, our pipeline integrates limited historical data pre-training with stochastic partial incremental training, significantly improving training efficiency and emphasizing the superiority of data recency over sheer data volume. Our extensive experiments, conducted on public benchmarks alongside a large-scale industrial dataset from TaoBao, show TBGRecall outperforms the state-of-the-art recommendation methods, and exhibits a clear scaling law trend. Ultimately, NSP represents a significant advancement in the effectiveness of generative recommendation systems for e-commerce applications.

Advanced reasoning in LLMs on challenging domains like mathematical reasoning can be tackled using verifiable rewards based reinforced fine-tuning (ReFT). In standard ReFT frameworks, a behavior model generates multiple completions with answers per problem, for the answer to be then scored by a reward function. While such RL post-training methods demonstrate significant performance improvements across challenging reasoning domains, the computational cost of generating completions during training with multiple inference steps makes the training cost non-trivial. To address this, we draw inspiration from off-policy RL, and speculative decoding to introduce a novel ReFT framework, dubbed Nested-ReFT, where a subset of layers of the target model acts as the behavior model to generate off-policy completions during training. The behavior model configured with dynamic layer skipping per batch during training decreases the inference cost compared to the standard ReFT frameworks. Our theoretical analysis shows that Nested-ReFT yields unbiased gradient estimates with controlled variance. Our empirical analysis demonstrates improved computational efficiency measured as tokens/sec across multiple math reasoning benchmarks and model sizes. Additionally, we explore three variants of bias mitigation to minimize the off-policyness in the gradient updates that allows for maintaining performance that matches the baseline ReFT performance.

Predictive Business Process Monitoring (PBPM) aims to forecast future events in ongoing cases based on historical event logs. While Graph Neural Networks (GNNs) are well suited to capture structural dependencies in process data, existing GNN-based PBPM models remain underdeveloped. Most rely either on short prefix subgraphs or global architectures that overlook temporal relevance and transition semantics. We propose a unified, interpretable GNN framework that advances the state of the art along three key axes. First, we compare prefix-based Graph Convolutional Networks(GCNs) and full trace Graph Attention Networks(GATs) to quantify the performance gap between localized and global modeling. Second, we introduce a novel time decay attention mechanism that constructs dynamic, prediction-centered windows, emphasizing temporally relevant history and suppressing noise. Third, we embed transition type semantics into edge features to enable fine grained reasoning over structurally ambiguous traces. Our architecture includes multilevel interpretability modules, offering diverse visualizations of attention behavior. Evaluated on five benchmarks, the proposed models achieve competitive Top-k accuracy and DL scores without per-dataset tuning. By addressing architectural, temporal, and semantic gaps, this work presents a robust, generalizable, and explainable solution for next event prediction in PBPM.

Recent advances in vision-language models (VLMs) have significantly enhanced the visual grounding task, which involves locating objects in an image based on natural language queries. Despite these advancements, the security of VLM-based grounding systems has not been thoroughly investigated. This paper reveals a novel and realistic vulnerability: the first multi-target backdoor attack on VLM-based visual grounding. Unlike prior attacks that rely on static triggers or fixed targets, we propose IAG, a method that dynamically generates input-aware, text-guided triggers conditioned on any specified target object description to execute the attack. This is achieved through a text-conditioned UNet that embeds imperceptible target semantic cues into visual inputs while preserving normal grounding performance on benign samples. W e further develop a joint training objective that balances language capability with perceptual reconstruction to ensure imperceptibility, effectiveness, and stealth. Extensive experiments on multiple VLMs (e.g., LLaVA, InternVL, Ferret) and benchmarks (RefCOCO, RefCOCO+, RefCOCOg, Flickr30k Entities, and ShowUI) demonstrate that IAG achieves the best ASRs compared with other baselines on almost all settings without compromising clean accuracy, maintaining robustness against existing defenses, and exhibiting transferability across datasets and models. These findings underscore critical security risks in grounding-capable VLMs and highlight the need for further research on trustworthy multi-modal understanding.

Denoising Diffusion Probabilistic Models (DDPMs) show promising potential in one-step Real-World Image Super-Resolution (Real-ISR). Current one-step Real-ISR methods typically inject the low-quality (LQ) image latent representation at the start or end timestep of the DDPM scheduler. Recent studies have begun to note that the LQ image latent and the pre-trained noisy latent representations are intuitively closer at a mid-timestep. However, a quantitative analysis of these latent representations remains lacking. Considering these latent representations can be decomposed into signal and noise, we propose a method based on the Signal-to-Noise Ratio (SNR) to pre-compute an average optimal mid-timestep for injection. To better approximate the pre-trained noisy latent representation, we further introduce the Latent Representation Refinement (LRR) loss via a LoRA-enhanced VAE encoder. We also fine-tune the backbone of the DDPM-based generative model using LoRA to perform one-step denoising at the average optimal mid-timestep. Based on these components, we present OMGSR, a GAN-based Real-ISR framework that employs a DDPM-based generative model as the generator and a DINOv3-ConvNeXt model with multi-level discriminator heads as the discriminator. We also propose the DINOv3-ConvNeXt DISTS (Dv3CD) loss, which is enhanced for structural perception at varying resolutions. Within the OMGSR framework, we develop OMGSR-S based on SD2.1-base. An ablation study confirms that our pre-computation strategy and LRR loss significantly improve the baseline. Comparative studies demonstrate that OMGSR-S achieves state-of-the-art performance across multiple metrics. Code is available at \hyperlink{Github}{https://github.com/wuer5/OMGSR}.

Person re-identification (ReID) aims to retrieve images of a target person from the gallery set, with wide applications in medical rehabilitation and public security. However, traditional person ReID models are typically uni-modal, resulting in limited generalizability across heterogeneous data modalities. Recently, the emergence of multi-modal large language models (MLLMs) has shown a promising avenue for addressing this issue. Despite this potential, existing methods merely regard MLLMs as feature extractors or caption generators, leaving their capabilities in person ReID tasks largely unexplored. To bridge this gap, we introduce a novel benchmark for \underline{\textbf{V}}ersatile \underline{\textbf{P}}erson \underline{\textbf{Re}}-\underline{\textbf{ID}}entification, termed VP-ReID. The benchmark includes 257,310 multi-modal queries and gallery images, covering ten diverse person ReID tasks. In addition, we propose two task-oriented evaluation schemes for MLLM-based person ReID. Extensive experiments demonstrate the impressive versatility, effectiveness, and interpretability of MLLMs in various person ReID tasks. Nevertheless, they also have limitations in handling a few modalities, particularly thermal and infrared data. We hope that VP-ReID can facilitate the community in developing more robust and generalizable cross-modal foundation models for person ReID.