Colored stochastic vertex models with U-turn boundary

In this paper, we introduce a class of colored stochastic vertex models with U-turn right boundary. The vertex weights in the models satisfy the Yang-Baxter equations and the reflection equation. Based on these equations, we derive recursive relations for partition functions of the models.Comment: 15 page

Generative Modeling for Tabular Data via Penalized Optimal Transport Network

The task of precisely learning the probability distribution of rows within tabular data and producing authentic synthetic samples is both crucial and non-trivial. Wasserstein generative adversarial network (WGAN) marks a notable improvement in generative modeling, addressing the challenges faced by its predecessor, generative adversarial network. However, due to the mixed data types and multimodalities prevalent in tabular data, the delicate equilibrium between the generator and discriminator, as well as the inherent instability of Wasserstein distance in high dimensions, WGAN often fails to produce high-fidelity samples. To this end, we propose POTNet (Penalized Optimal Transport Network), a generative deep neural network based on a novel, robust, and interpretable marginally-penalized Wasserstein (MPW) loss. POTNet can effectively model tabular data containing both categorical and continuous features. Moreover, it offers the flexibility to condition on a subset of features. We provide theoretical justifications for the motivation behind the MPW loss. We also empirically demonstrate the effectiveness of our proposed method on four different benchmarks across a variety of real-world and simulated datasets. Our proposed model achieves orders of magnitude speedup during the sampling stage compared to state-of-the-art generative models for tabular data, thereby enabling efficient large-scale synthetic data generation.Comment: 37 pages, 23 figure

Short-Term Photovoltaic Power Generation Forecasting Based on Multivariable Grey Theory Model with Parameter Optimization

Owing to the environment, temperature, and so forth, photovoltaic power generation volume is always fluctuating and subsequently impacts power grid planning and operation seriously. Therefore, it is of great importance to make accurate prediction of the power generation of photovoltaic (PV) system in advance. In order to improve the prediction accuracy, in this paper, a novel particle swarm optimization algorithm based multivariable grey theory model is proposed for short-term photovoltaic power generation volume forecasting. It is highlighted that, by integrating particle swarm optimization algorithm, the prediction accuracy of grey theory model is expected to be highly improved. In addition, large amounts of real data from two separate power stations in China are being employed for model verification. The experimental results indicate that, compared with the conventional grey model, the mean relative error in the proposed model has been reduced from 7.14% to 3.53%. The real practice demonstrates that the proposed optimization model outperforms the conventional grey model from both theoretical and practical perspectives

A Comprehensive Evaluation of GPT-4V on Knowledge-Intensive Visual Question Answering

The emergence of multimodal large models (MLMs) has significantly advanced the field of visual understanding, offering remarkable capabilities in the realm of visual question answering (VQA). Yet, the true challenge lies in the domain of knowledge-intensive VQA tasks, which necessitate not just recognition of visual elements, but also a deep comprehension of the visual information in conjunction with a vast repository of learned knowledge. To uncover such capabilities of MLMs, particularly the newly introduced GPT-4V, we provide an in-depth evaluation from three perspectives: 1) Commonsense Knowledge, which assesses how well models can understand visual cues and connect to general knowledge; 2) Fine-grained World Knowledge, which tests the model's skill in reasoning out specific knowledge from images, showcasing their proficiency across various specialized fields; 3) Comprehensive Knowledge with Decision-making Rationales, which examines model's capability to provide logical explanations for its inference, facilitating a deeper analysis from the interpretability perspective. Extensive experiments indicate that GPT-4V achieves SOTA performance on above three tasks. Interestingly, we find that: a) GPT-4V demonstrates enhanced reasoning and explanation when using composite images as few-shot; b) GPT-4V produces severe hallucinations when dealing with world knowledge, highlighting the future need for advancements in this research direction.Comment: 18 pages, 13pages; working in progres

Stochastic symplectic ice

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term "stochastic symplectic ice". The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models offers novel interacting particle systems where particles alternately jump to the right and then to the left. Two colored versions of the model and related stochastic dynamics are also introduced. Using the Yang-Baxter equations, we establish functional equations and recursive relations for the partition functions of these models. In particular, the recursive relations satisfied by the partition function of one of the colored models are closely related to Demazure-Lusztig operators of type C.Comment: 35 page