A Unified Framework for Interpretable Transformers Using PDEs and Information Theory

This paper presents a novel unified theoretical framework for understanding Transformer architectures by integrating Partial Differential Equations (PDEs), Neural Information Flow Theory, and Information Bottleneck Theory. We model Transformer information dynamics as a continuous PDE process, encompassing diffusion, self-attention, and nonlinear residual components. Our comprehensive experiments across image and text modalities demonstrate that the PDE model effectively captures key aspects of Transformer behavior, achieving high similarity (cosine similarity > 0.98) with Transformer attention distributions across all layers. While the model excels in replicating general information flow patterns, it shows limitations in fully capturing complex, non-linear transformations. This work provides crucial theoretical insights into Transformer mechanisms, offering a foundation for future optimizations in deep learning architectural design. We discuss the implications of our findings, potential applications in model interpretability and efficiency, and outline directions for enhancing PDE models to better mimic the intricate behaviors observed in Transformers, paving the way for more transparent and optimized AI systems.

Unraveling Text Generation in LLMs: A Stochastic Differential Equation Approach

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each step depends on previously generated content and model parameters, sampling the next word from a vocabulary distribution. We represent this generation process using SDE to capture both deterministic trends and stochastic perturbations. The drift term describes the deterministic trends in the generation process, while the diffusion term captures the stochastic variations. We fit these functions using neural networks and validate the model on real-world text corpora. Through numerical simulations and comprehensive analyses, including drift and diffusion analysis, stochastic process property evaluation, and phase space exploration, we provide deep insights into the dynamics of text generation. This approach not only enhances the understanding of the inner workings of LLMs but also offers a novel mathematical perspective on language generation, which is crucial for diagnosing, optimizing, and controlling the quality of generated text.

Unveiling LLM Mechanisms Through Neural ODEs and Control Theory

This study presents a novel approach that leverages Neural Ordinary Differential Equations (Neural ODEs) to unravel the intricate relationships between inputs and outputs in Large Language Models (LLMs), and employs robust control to fine-tune outputs to meet predefined standards. Central to our methodology is the transformation of LLM inputs and outputs into a lower-dimensional latent space, facilitating a detailed examination of the information processing pathways within LLMs. Neural ODEs play a pivotal role in this investigation by providing a dynamic model that captures the continuous evolution of data within the LLMs. Additionally, robust control mechanisms are applied to strategically adjust the model's outputs, ensuring they not only maintain high quality and reliability but also adhere to specific performance criteria. This fusion of Neural ODEs and robust control represents a significant advancement in LLM interpretability, offering a comprehensive framework that elucidates the previously opaque mechanisms of these complex models. Our empirical results validate the effectiveness of this integrated approach, making a substantial contribution to the field of explainable AI by merging advanced machine learning techniques with the critical need for transparency and control in AI outputs.

Dynamic interactive group decision making method on two-dimensional language

The language evaluation information of the interactive group decision method at present is based on the one-dimension language variable. At the same time, multi-attribute group decision making method based on two-dimension linguistic information only use single-stage and static evaluation method. In this paper, we propose a dynamic group decision making method based on two-dimension linguistic information, combining dynamic interactive group decision making methods with two-dimensional language evaluation information The method first use Two-Dimensional Uncertain Linguistic Generalized Weighted Aggregation (DULGWA) Operators to aggregate the preference information of each decision maker, then adopting dynamic information entropy method to obtain weights of attributes at each stage. Finally we propose the group consistency index to quantify the termination conditions of group interaction. One example is given to verify the developed approach and to demonstrate its effectiveness

Learning Multi-modal Information for Robust Light Field Depth Estimation

Light field data has been demonstrated to facilitate the depth estimation task. Most learning-based methods estimate the depth infor-mation from EPI or sub-aperture images, while less methods pay attention to the focal stack. Existing learning-based depth estimation methods from the focal stack lead to suboptimal performance because of the defocus blur. In this paper, we propose a multi-modal learning method for robust light field depth estimation. We first excavate the internal spatial correlation by designing a context reasoning unit which separately extracts comprehensive contextual information from the focal stack and RGB images. Then we integrate the contextual information by exploiting a attention-guide cross-modal fusion module. Extensive experiments demonstrate that our method achieves superior performance than existing representative methods on two light field datasets. Moreover, visual results on a mobile phone dataset show that our method can be widely used in daily life.

Dynamic Fusion Network For Light Field Depth Estimation

Focus based methods have shown promising results for the task of depth estimation. However, most existing focus based depth estimation approaches depend on maximal sharpness of the focal stack. Out of focus information in the focal stack poses challenges for this task. In this paper, we propose a dynamically multi modal learning strategy which incorporates RGB data and the focal stack in our framework. Our goal is to deeply excavate the spatial correlation in the focal stack by designing the spatial correlation perception module and dynamically fuse multi modal information between RGB data and the focal stack in a adaptive way by designing the multi modal dynamic fusion module. The success of our method is demonstrated by achieving the state of the art performance on two datasets. Furthermore, we test our network on a set of different focused images generated by a smart phone camera to prove that the proposed method not only broke the limitation of only using light field data, but also open a path toward practical applications of depth estimation on common consumer level cameras data.

Fairness Assessment for Artificial Intelligence in Financial Industry

Artificial Intelligence (AI) is an important driving force for the development and transformation of the financial industry. However, with the fast-evolving AI technology and application, unintentional bias, insufficient model validation, immature contingency plan and other underestimated threats may expose the company to operational and reputational risks. In this paper, we focus on fairness evaluation, one of the key components of AI Governance, through a quantitative lens. Statistical methods are reviewed for imbalanced data treatment and bias mitigation. These methods and fairness evaluation metrics are then applied to a credit card default payment example.