Multi-objective optimization (MOO) has become an important method in machine learning, which involves solving multiple competing objective problems simultaneously. Nowadays, many MOO algorithms assume that gradient information is easily available and use this information to optimize functions. However, when encountering situations where gradients are not available, such as black-box functions or non-differentiable functions, these algorithms become ineffective. In this paper, we propose a zeroth-order MOO algorithm named SZMG (stochastic zeroth-order multi-gradient algorithm), which approximates the gradient of functions by finite difference methods. Meanwhile, to avoid conflicting gradients between functions and reduce stochastic multi-gradient direction bias caused by stochastic gradients, an SGD-type method is adopted to acquire weight parameters. Under the non-convex setting and mild assumptions, the convergence rate is established for the SZMG algorithm. Simulation results demonstrate the effectiveness of the SZMG algorithm.

In the domain of natural language processing (NLP), a primary challenge pertains to the process of Chinese tokenization, which remains challenging due to the lack of explicit word boundaries in written Chinese. The existing tokenization methods often treat each Chinese character as an indivisible unit, neglecting the finer semantic features embedded in the characters, such as radicals. To tackle this issue, we propose a novel token representation method that integrates radical-based features into the process. The proposed method extends the vocabulary to include both radicals and original character tokens, enabling a more granular understanding of Chinese text. We also conduct experiments on seven datasets covering multiple Chinese natural language processing tasks. The results show that our method significantly improves model performance on downstream tasks. Specifically, the accuracy of BERT on the BQ Croups dataset was enhanced to 86.95%, showing an improvement of 1.65% over the baseline. Additionally, the BERT-wwm performance demonstrated a 1.28% enhancement, suggesting that the incorporation of fine-grained radical features offers a more efficacious solution for Chinese tokenization and paves the way for future research in Chinese text processing.

Accurately detecting lane lines is a hot topic in computer vision. How to effectively utilize the relationship between lane features for detection is still an open question. In this paper, we propose a novel lane detection model based on convolutional neural network (CNN), namely, the BSCNNLaneNet (Bidirectional Spatial CNN Lane Detection Network). The proposed model is based on the spatial CNN method and incorporates a bidirectional recurrent neural network (BRNN) block to learn the spatial relationships between slice features. Additionally, a convolutional block attention mechanism is introduced to gain global features, which enhance the global connection between slice features in different directions. We conduct extensive experiments on the TuSimple dataset. The results demonstrate that the proposed method surpasses the original spatial CNN method, achieving an increase in accuracy from 96.53% to 96.86%.

To optimize expensive black-box functions over networks, one of the most dominant frameworks is distributed Bayesian optimization (DBO), where local information can be exchanged among agents. However, DBO suffers from low evaluation efficiency due to limited data in the initial stage and the high cost of evaluations among multiple objectives. To tackle these obstacles, we propose a prior-informed multi-task collaborative Bayesian optimization (PMCBO) algorithm over networks. Concretely, PMCBO integrates expert prior knowledge about the location of optimum into the distributed multi-task Bayesian optimization framework to reduce the cost of evaluations. Meanwhile, PMCBO combines multi-task Bayesian optimization with a collaborative mechanism to improve the evaluation efficiency. Furthermore, we rigorously prove that the cumulative regret bound of PMCBO can achieve sub-linearly with high probability, where the acquisition functions employ expected improvement (EI) and upper-confidence bound (UCB) based on a Gaussian process surrogate. Finally, we implement various experiments to evaluate the effectiveness of PMCBO. The experimental results demonstrate that PMCBO can achieve state-of-the-art performance and benefit all clients based on diverse benchmarks and prior characteristics.

Spatial transcriptomics (ST) has emerged as an essential technology for interpreting the molecular profiles underlying pathological tissue morphology. Most existing ST analyses are limited to 2D sections, which ignore the complex structural and molecular heterogeneity of biological tissues in 3D space and may cause diagnostic oversights. Since acquiring complete 3D ST volumes is resource-intensive, recent 3D imputation paradigms provide a cost-effective alternative by integrating 3D whole-slide images (WSIs) with sparse 2D ST references (e.g., a single slide). Despite this methodological advancement, effectively modeling complex cross-layer spatial dependencies remains challenging. Current mainstream solutions predominantly adopt standard Transformers for cross-scale feature aggregation, which may bring computational overhead and higher overfitting risk while having limited explicit mechanisms for hierarchical anatomical guidance. To address these limitations, we propose a Hierarchical MambaOut-based Spatial Imputation Graph Network (HM-ASIGN) for anatomy-aware 3D spatial transcriptomics imputation. Our architecture leverages MambaOut’s dynamic gated 1D convolutions as a parameter-efficient alternative to dense global self-attention. This design captures the depth-wise evolution of pathological features while reducing over-parameterization. Inspired by the macro-to-micro diagnostic reasoning of clinical pathologists, HM-ASIGN introduces a multi-scale recursive guidance mechanism. It constructs a top-down information flow by extracting global anatomical priors at macroscopic scales and injecting them as contextual anchors into regional and spot-level features in a cascaded manner. This helps ensure that fine-grained molecular predictions are properly constrained by global morphological structures. Evaluation experiments on multiple public breast cancer datasets demonstrate that HM-ASIGN achieves competitive reference-level performance against existing baselines, reaching a Pearson Correlation Coefficient (PCC) of 0.772. Specifically, when evaluated against the foundational ASIGN framework, it improves predictive accuracy while reducing the total parameter count by approximately 33.3% and improving inference throughput. Our results suggest that HM-ASIGN provides a computationally efficient approach for 3D spatial molecular mapping.