This paper explores the application of non-standard geometry to computational geometry, focusing on the development of a novel method for defining and computing geometric properties for complex systems, particularly fluid dynamics and protein folding. Traditional geometric computation often struggles with the inherent complexity and self-organization of these systems, necessitating the creation of intricate geometric constructs. We propose a 'geometric language' – a system of rules and symbolic representations – that enables efficient manipulation and analysis of these complex shapes. The core mechanism involves establishing a hierarchical structure within this language, allowing for the generation of novel geometric configurations through a combination of geometric transformations and parametric modeling. This approach aims to overcome limitations in current computational geometry by offering a framework for tackling problems that are currently computationally intractable. The paper will detail the conceptualization of this language, its implementation through a set of rules and algorithms, and initial explorations into its potential for solving specific problems within fluid dynamics and protein folding. Finally, we present preliminary results demonstrating the feasibility of this approach, highlighting its potential for advancing the field of computational geometry.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Predicting the folding pathway of a protein – the process by which a linear chain of amino acids adopts its functional three-dimensional structure – is a central challenge in computational biology. Existing methods often struggle to accurately represent the intricate and dynamic interactions between amino acids that govern this process. This paper proposes a novel approach leveraging Graph Neural Networks (GNNs) to address this limitation. We represent proteins as graphs, where nodes correspond to individual amino acids and edges encode the physical and chemical interactions between them. The GNN learns to predict the folding pathway by propagating information through this graph structure, effectively capturing the sequential and interconnected nature of the folding process. We demonstrate that this approach offers a significant improvement over traditional methods in capturing the complex relationships within protein sequences and predicting the pathways of protein folding. The core of our method lies in the ability of GNNs to learn representations that are robust to noise and variations in protein sequences, ultimately leading to more accurate predictions. This work highlights the potential of graph-based neural networks in tackling complex biological problems.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Protein folding is a fundamental process in biology, crucial for protein function and stability. Traditional methods often rely on rigid, predefined folding rules, limiting flexibility and efficiency. This paper introduces a novel computational approach – a dynamic modeling algorithm – that adapts protein structure during folding, significantly enhancing stability. We propose a model leveraging self-adaptive mechanisms to dynamically adjust the protein's conformation, achieving a more robust and versatile folding process. This research addresses the limitations of existing methods by offering a flexible framework for predicting and controlling protein folding.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper presents a novel approach to protein structure prediction leveraging the principles of quantum entanglement. Traditional protein structure prediction methods are often limited by the computational complexity of simulating large biomolecular systems. We propose a framework that utilizes quantum entanglement to model the complex correlations inherent in protein folding, potentially overcoming these limitations. The core idea involves translating the amino acid sequence of a protein into a quantum state and employing quantum computation, specifically entanglement-based algorithms, to predict the protein's three-dimensional structure. The theoretical framework outlines the transformation process, the quantum algorithm design, and the methods for interpreting the results. We explore the potential advantages of this approach, focusing on its ability to capture long-range interactions and conformational flexibility that are difficult to model accurately with classical methods. The ultimate goal is to establish a new paradigm for protein structure prediction, offering improved accuracy and efficiency.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Resonance-Based Probability Distribution Modeling presents a novel probabilistic modeling framework predicated on the principles of resonant frequencies and vibrational modes within complex systems. This approach aims to enhance predictive accuracy across diverse domains, including protein folding, fluid dynamics, and other systems exhibiting dynamic behavior. The core mechanism involves constructing a complex, multi-dimensional resonance function to represent system stability and predict outcomes, offering a departure from conventional statistical approaches. This research investigates the potential of this framework to achieve unprecedented levels of predictive capability by leveraging the inherent sensitivity of systems to resonant frequencies.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Reinforcement learning (RL) has achieved remarkable success in various domains, but its "black box" nature poses a significant challenge for real-world deployment. Understanding the rationale behind an RL agent's decisions is crucial for trust, debugging, and improving performance. This paper proposes a novel approach to explainable AI (XAI) within reinforcement learning by leveraging causal reasoning. We model the environment and the agent's policy using a causal Bayesian network. By performing inference through this network, we trace the causal chain of events leading to a specific action, providing a transparent explanation. This method moves beyond simply observing the agent's behavior to understanding the underlying reasons for its choices. The core of our approach lies in identifying and representing the causal relationships within the RL system, enabling us to dissect the decision-making process and ultimately build more robust and reliable RL agents. The proposed framework offers a significant step toward interpretable RL and addresses a critical limitation of current techniques. ---
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper presents a novel approach to neuro-symbolic reasoning by integrating attentive graph neural networks (GNNs) with rule extraction techniques. The core idea is to leverage the pattern recognition capabilities of GNNs for initial data processing while simultaneously extracting symbolic rules that encapsulate domain knowledge. The attentive mechanism within the GNN allows for selective focus on relevant graph features, improving both the accuracy and interpretability of the learned representations. These representations are then used as the basis for logical reasoning and decision-making, providing a more robust and explainable AI system compared to purely neural or symbolic approaches. We demonstrate the effectiveness of this hybrid system through a detailed explanation of the architecture and its theoretical underpinnings. The key contribution lies in the synergistic combination of graph representation learning and symbolic knowledge discovery, resulting in a system capable of handling complex reasoning tasks.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper presents a novel approach to neuro-symbolic reasoning by integrating attentive graph neural networks (GNNs) with rule extraction techniques. The core idea is to leverage the pattern recognition capabilities of GNNs for initial data processing while simultaneously extracting symbolic rules that encapsulate domain knowledge. The attentive mechanism within the GNN allows for selective focus on relevant graph features, improving both the accuracy and interpretability of the learned representations. These representations are then used as the basis for logical reasoning and decision-making, providing a more robust and explainable AI system compared to purely neural or symbolic approaches. We demonstrate the effectiveness of this hybrid system through a detailed explanation of the architecture and its theoretical underpinnings. The key contribution lies in the synergistic combination of graph representation learning and symbolic knowledge discovery, resulting in a system capable of handling complex reasoning tasks.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Current Explainable AI (XAI) methods frequently deliver post-hoc explanations that lack a fundamental understanding of the causal relationships underpinning AI decision-making. This paper proposes a novel approach to XAI that integrates causal inference and counterfactual analysis, aiming to generate more insightful and actionable explanations. Our methodology leverages causal discovery techniques to identify the key causal factors driving a model's decisions, moving beyond merely highlighting correlations. Furthermore, we employ counterfactual analysis to simulate "what-if" scenarios, allowing us to assess the potential impact of altering specific input features and understand the sensitivity of the model. This approach provides a deeper understanding of the AI system's behavior, ultimately leading to more robust and trustworthy AI models. We demonstrate the potential of this integrated framework through conceptual arguments and a detailed outline of the proposed methodology.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper proposes a novel deep learning model incorporating symbolic reasoning for enhanced visual understanding. The core idea is to bridge the gap between deep learning's ability to extract intricate visual features and symbolic reasoning's capacity for logical deduction. The model consists of two key components: a deep learning module for feature extraction and a symbolic reasoning engine for logical inference. We explore the architecture and training strategies to effectively integrate these components, aiming to achieve more robust and explainable visual understanding. The model is designed to handle tasks requiring not just pattern recognition, but also the ability to interpret relationships and constraints expressed in symbolic form. This work represents a significant step towards more intelligent and reliable AI systems by combining the strengths of both paradigms.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Federated learning (FL) offers a promising approach to training machine learning models on decentralized data sources without direct data sharing, thus addressing privacy concerns. However, FL is still susceptible to privacy breaches and suffers from significant information loss during model aggregation, a phenomenon addressed by the information bottleneck (IB) principle. This paper proposes a novel framework that integrates the IB technique with differential privacy (DP) within the FL setting. We formulate the problem as a constrained optimization, minimizing information loss while simultaneously satisfying DP guarantees. Our approach utilizes a compressed representation of local data, learned through an IB objective, and introduces noise to protect individual data points, ensuring privacy. The core contribution lies in the synergistic combination of these two techniques, leading to enhanced privacy protection and improved model accuracy compared to standard FL. We demonstrate the effectiveness of our framework through a theoretical analysis and outline potential implementation strategies. The primary goal is to achieve a balance between model performance and privacy preservation, a critical aspect often overlooked in current FL methodologies. The theoretical framework provides a foundation for future research and practical deployment in privacy-sensitive applications.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Federated learning (FL) offers a promising approach to training machine learning models on decentralized data sources without directly exchanging the data itself. However, existing FL systems are susceptible to Byzantine attacks, where malicious participants can inject faulty model updates, compromising the global model's integrity. This paper proposes a novel decentralized federated learning framework incorporating Byzantine Fault Tolerant (BFT) consensus protocols. Our system utilizes cryptographic consensus mechanisms to validate and authenticate model updates from each participant before aggregation, thereby mitigating the risks posed by Byzantine nodes. The core innovation lies in the integration of FL with robust BFT consensus, ensuring secure and reliable model training even when faced with adversarial behavior. We introduce a framework utilizing verifiable computation and consensus-based proofs to achieve this. This approach allows for the detection and rejection of malicious updates, ultimately leading to a more trustworthy and resilient global model. The system is designed for scalability and adaptability, addressing key challenges in practical FL deployments. The key mathematical concepts underlying the system are represented through the following notation: (x_i, m_i), where x_i represents the data sample from participant i, and m_i represents the model update generated by participant i. The aggregation function is denoted as (Σ_{i=1}^K (α_i * m_i)), where α_i represents the learning rate for participant i, and K is the total number of participants. The BFT consensus protocol relies on a threshold number of participants (T) to reach agreement, and the proof of correctness is represented as P(m_true, m_agg), where m_true is the true global model, and m_agg is the aggregated model. Byzantine faults are represented as f_i, where f_i is the faulty model update from participant i. The probability of a successful consensus is denoted as P_success. The security level is characterized by the parameter β, representing the probability of successfully detecting a Byzantine update.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
