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Pan-sharpening algorithm utilizes panchromatic image and multispectral image to obtain a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We adopt the simple matrix equation to describe the Pan-sharpening problem. The solution existence condition and the acquirement of spectral and spatial resolution are discussed. A down-sampling enhancement method was introduced for better acquiring the spatial and spectral down-sample matrices. By the generalized inverse theory, we derived two forms of general inverse matrix formulations that can correspond to the two prominent classes of Pan-sharpening methods, that is, component substitution and multi-resolution analysis methods. Specifically, the Gram Schmidt Adaptive(GSA) was proved to follow the general inverse matrix formulation of component substitution. A model prior to the general inverse matrix of the spectral function was rendered. The theoretical errors are analyzed. Synthetic experiments and real data experiments are implemented. The proposed methods are better and sharper than other methods qualitatively in both synthetic and real experiments. The down-sample enhancement effect is shown of better results both quantitatively and qualitatively in real experiments. The generalized inverse matrix theory help us better understand the Pan-sharpening.

Many pre-trained large-scale models provided online have become highly effective in transferring to downstream tasks. At the same time, various task-specific models fine-tuned on these pre-trained models are available online for public use. In practice, as collecting task-specific data is labor-intensive and fine-tuning the large pre-trained models is computationally expensive, one can reuse task-specific finetuned models to deal with downstream tasks. However, using a model per task causes a heavy burden on storage and serving. Recently, many training-free and parameter-efficient methods have been proposed for reusing multiple fine-tuned task-specific models into a single multi-task model. However, these methods exhibit a large accuracy gap compared with using a fine-tuned model per task. In this paper, we propose Parameter-Efficient methods for ReUsing (PERU) fine-tuned models. For reusing Fully Fine-Tuned (FFT) models, we propose PERU-FFT by injecting a sparse task vector into a merged model by magnitude pruning. For reusing LoRA fine-tuned models, we propose PERU-LoRA use a lower-rank matrix to approximate the LoRA matrix by singular value decomposition. Both PERUFFT and PERU-LoRA are training-free. Extensive experiments conducted on computer vision and natural language process tasks demonstrate the effectiveness and parameter-efficiency of the proposed methods. The proposed PERU-FFT and PERU-LoRA outperform existing reusing model methods by a large margin and achieve comparable performance to using a fine-tuned model per task.

Large language models (LLMs) have shown great potential in automating significant aspects of coding by producing natural code from informal natural language (NL) intent. However, when interacting with LLMs, users have no guarantees that the code suggestions produced correctly satisfy the intent they provided. In fact, it is hard to define a notion of correctness since natural language can be ambiguous and lacks a formal semantics. In this paper, we propose the workflow of {\it interactive test-driven code generation}, which leverages lightweight user feedback to (a) formalize the user intent using generated tests that can be useful for debugging, and (b) produce an improved set of code suggestions by pruning and ranking candidate code suggestions. We describe a language-agnostic abstract algorithm and a concrete implementation TiCoder. We perform an automated evaluation of TiCoder on the \emph{MBPP} and \emph{HumanEval} code generation benchmarks. Our results are promising with using the OpenAI Codex LLM: our best algorithm improves the \passk{1} code generation accuracy (in absolute percentages) between $22.49\%$ to $37.71\%$ for MBPP and between $24.79\%$ to $53.98\%$ for HumanEval using between 1 to 5 simulated user queries.

This paper presents a comprehensive survey on deep learning-based image watermarking, a technique that entails the invisible embedding and extraction of watermarks within a cover image, aiming to offer a seamless blend of robustness and adaptability. We navigate the complex landscape of this interdisciplinary domain, linking historical foundations, current innovations, and prospective developments. Unlike existing literature, our study concentrates exclusively on image watermarking with deep learning, delivering an in-depth, yet brief analysis enriched by three fundamental contributions. First, we introduce a refined categorization, segmenting the field into Embedder-Extractor, Deep Networks as a Feature Transformation, and Hybrid Methods. This taxonomy, inspired by the varied roles of deep learning across studies, is designed to infuse clarity, offering readers technical insights and directional guidance. Second, our exploration dives into representative methodologies, encapsulating the diverse research directions and inherent challenges within each category to provide a consolidated perspective. Lastly, we venture beyond established boundaries to outline emerging frontiers, offering a detailed insight into prospective research avenues.

We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a stochastic differential equation evolution. The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling. We demonstrate fast convergence on various problems and show improved dimensional dependence of mixing time bounds for the case of Gaussian distributions compared to the unadjusted Langevin algorithm (ULA) and the Metropolis-adjusted Langevin algorithm (MALA). We additionally derive closed form expressions for the distributions at each iterate for quadratic potential functions, characterizing the variance reduction. Empirical results demonstrate that the particles behave in an organized manner, lying on level set contours of the potential. Moreover, the posterior mean estimator of the proposed method is shown to be closer to the maximum a-posteriori estimator compared to ULA and MALA in the context of Bayesian logistic regression. Additional examples demonstrate competitive performance for Bayesian neural network training.

We present a data structure to randomly sample rows from the Khatri-Rao product of several matrices according to the exact distribution of its leverage scores. Our proposed sampler draws each row in time logarithmic in the height of the Khatri-Rao product and quadratic in its column count, with persistent space overhead at most the size of the input matrices. As a result, it tractably draws samples even when the matrices forming the Khatri-Rao product have tens of millions of rows each. When used to sketch the linear least squares problems arising in CANDECOMP / PARAFAC tensor decomposition, our method achieves lower asymptotic complexity per solve than recent state-of-the-art methods. Experiments on billion-scale sparse tensors validate our claims, with our algorithm achieving higher accuracy than competing methods as the decomposition rank grows.

Control of surface texture in strip steel is essential to meet customer requirements during galvanizing and temper rolling processes. Traditional methods rely on post-production stylus measurements, while on-line techniques offer non-contact and real-time measurements of the entire strip. However, ensuring accurate measurement is imperative for their effective utilization in the manufacturing pipeline. Moreover, accurate on-line measurements enable real-time adjustments of manufacturing processing parameters during production, ensuring consistent quality and the possibility of closed-loop control of the temper mill. In this study, we leverage state-of-the-art machine learning models to enhance the transformation of on-line measurements into significantly a more accurate Ra surface roughness metric. By comparing a selection of data-driven approaches, including both deep learning and non-deep learning methods, to the close-form transformation, we evaluate their potential for improving surface texture control in temper strip steel manufacturing.

Most of the existing multi-modal models, hindered by their incapacity to adeptly manage interleaved image-and-text inputs in multi-image, multi-round dialogues, face substantial constraints in resource allocation for training and data accessibility, impacting their adaptability and scalability across varied interaction realms. To address this, we present the DeepSpeed-VisualChat framework, designed to optimize Large Language Models (LLMs) by incorporating multi-modal capabilities, with a focus on enhancing the proficiency of Large Vision and Language Models in handling interleaved inputs. Our framework is notable for (1) its open-source support for multi-round and multi-image dialogues, (2) introducing an innovative multi-modal causal attention mechanism, and (3) utilizing data blending techniques on existing datasets to assure seamless interactions in multi-round, multi-image conversations. Compared to existing frameworks, DeepSpeed-VisualChat shows superior scalability up to 70B parameter language model size, representing a significant advancement in multi-modal language models and setting a solid foundation for future explorations.

This paper presents a nonlinear control design for highly underactuated balance robots, which possess more numbers of unactuated degree-of-freedom (DOF) than actuated ones. To address the challenge of simultaneously trajectory tracking of actuated coordinates and balancing of unactuated coordinates, the proposed control converts a robot dynamics into a series of cascaded subsystems and each of them is considered virtually actuated. To achieve the control goal, we sequentially design and update the virtual and actual control inputs to incorporate the balance task such that the unactuated coordinates are balanced to their instantaneous equilibrium. The closed-loop dynamics are shown to be stable and the tracking errors exponentially converge towards a neighborhood near the origin. The simulation results demonstrate the effectiveness of the proposed control design by using a triple-inverted pendulum cart system.

Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the model scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, \ie node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can improve GNN for few-shot learning with theoretical analysis and illustrations. Extensive experiments show that the proposed Attentive GNN outperforms the state-of-the-art GNN-based methods for few-shot learning over the mini-ImageNet and Tiered-ImageNet datasets, with both inductive and transductive settings.