Extreme central values of quadratic Dirichlet LL-functions with prime conductors

In this paper we prove a lower bound result for extremely large values of $L(\frac{1}{2},\chi_p)$ with prime numbers $p\equiv 1\pmod 8$.Comment: 21 pages. Comments welcome

Convergence of Two-Layer Regression with Nonlinear Units

Large language models (LLMs), such as ChatGPT and GPT4, have shown outstanding performance in many human life task. Attention computation plays an important role in training LLMs. Softmax unit and ReLU unit are the key structure in attention computation. Inspired by them, we put forward a softmax ReLU regression problem. Generally speaking, our goal is to find an optimal solution to the regression problem involving the ReLU unit. In this work, we calculate a close form representation for the Hessian of the loss function. Under certain assumptions, we prove the Lipschitz continuous and the PSDness of the Hessian. Then, we introduce an greedy algorithm based on approximate Newton method, which converges in the sense of the distance to optimal solution. Last, We relax the Lipschitz condition and prove the convergence in the sense of loss value

Unmasking Transformers: A Theoretical Approach to Data Recovery via Attention Weights

In the realm of deep learning, transformers have emerged as a dominant architecture, particularly in natural language processing tasks. However, with their widespread adoption, concerns regarding the security and privacy of the data processed by these models have arisen. In this paper, we address a pivotal question: Can the data fed into transformers be recovered using their attention weights and outputs? We introduce a theoretical framework to tackle this problem. Specifically, we present an algorithm that aims to recover the input data $X \in \mathbb{R}^{d \times n}$ from given attention weights $W = QK^\top \in \mathbb{R}^{d \times d}$ and output $B \in \mathbb{R}^{n \times n}$ by minimizing the loss function $L(X)$. This loss function captures the discrepancy between the expected output and the actual output of the transformer. Our findings have significant implications for the Localized Layer-wise Mechanism (LLM), suggesting potential vulnerabilities in the model's design from a security and privacy perspective. This work underscores the importance of understanding and safeguarding the internal workings of transformers to ensure the confidentiality of processed data

ASAG: Building Strong One-Decoder-Layer Sparse Detectors via Adaptive Sparse Anchor Generation

Recent sparse detectors with multiple, e.g. six, decoder layers achieve promising performance but much inference time due to complex heads. Previous works have explored using dense priors as initialization and built one-decoder-layer detectors. Although they gain remarkable acceleration, their performance still lags behind their six-decoder-layer counterparts by a large margin. In this work, we aim to bridge this performance gap while retaining fast speed. We find that the architecture discrepancy between dense and sparse detectors leads to feature conflict, hampering the performance of one-decoder-layer detectors. Thus we propose Adaptive Sparse Anchor Generator (ASAG) which predicts dynamic anchors on patches rather than grids in a sparse way so that it alleviates the feature conflict problem. For each image, ASAG dynamically selects which feature maps and which locations to predict, forming a fully adaptive way to generate image-specific anchors. Further, a simple and effective Query Weighting method eases the training instability from adaptiveness. Extensive experiments show that our method outperforms dense-initialized ones and achieves a better speed-accuracy trade-off. The code is available at \url{https://github.com/iSEE-Laboratory/ASAG}.Comment: Accepted to ICCV 202

MoWE: Mixture of Weather Experts for Multiple Adverse Weather Removal

Currently, most adverse weather removal tasks are handled independently, such as deraining, desnowing, and dehazing. However, in autonomous driving scenarios, the type, intensity, and mixing degree of the weather are unknown, so the separated task setting cannot deal with these complex conditions well. Besides, the vision applications in autonomous driving often aim at high-level tasks, but existing weather removal methods neglect the connection between performance on perceptual tasks and signal fidelity. To this end, in upstream task, we propose a novel \textbf{Mixture of Weather Experts(MoWE)} Transformer framework to handle complex weather removal in a perception-aware fashion. We design a \textbf{Weather-aware Router} to make the experts targeted more relevant to weather types while without the need for weather type labels during inference. To handle diverse weather conditions, we propose \textbf{Multi-scale Experts} to fuse information among neighbor tokens. In downstream task, we propose a \textbf{Label-free Perception-aware Metric} to measure whether the outputs of image processing models are suitable for high level perception tasks without the demand for semantic labels. We collect a syntactic dataset \textbf{MAW-Sim} towards autonomous driving scenarios to benchmark the multiple weather removal performance of existing methods. Our MoWE achieves SOTA performance in upstream task on the proposed dataset and two public datasets, i.e. All-Weather and Rain/Fog-Cityscapes, and also have better perceptual results in downstream segmentation task compared to other methods. Our codes and datasets will be released after acceptance

Blockchain application in recycling: from the supply chain perspective

Recycling chains face evident challenges, including surging waste generation, insufficient recycling incentives and enforcement, fragmented traceability, and limited recycling network coordination. These challenges are particularly pronounced in the complex structures of multi-tier sustainable supply chains (MT-SSCM), where Blockchain technology (BCT) is often lauded as a potential ‘game-changer’. However, the transformative potential of BCT lacks empirical evidence, especially regarding how it can be effectively applied to recycling chains. The study commences with a comprehensive review of BCT functionalities, application drivers, technical feasibility, and potential performance. Subsequently, it employs a multiple-case study method to examine three companies that have successfully integrated BCT into their multi-tier recycling chains. Employing the Organisational Information Processing Theory (OIPT) as a framework, the study identifies three levels of information processing needs—firm, supply chain, and industry—and explores how BCT augments capabilities in transparency, immutability, integration, and trust. Additionally, the research delineates knowledge integration phases—transferring, translating, and transforming—while pinpointing visionary and structural boundary objects that facilitate this intricate process. This research stands as an early exploration into BCT application in the recycling sector, advancing the application of BCT in SSCM. It expands the body of knowledge by delineating a diverse multi-tier recycling framework. Theoretically, the study emphasises the critical role of information processing fit mechanisms, which are pivotal for enhancing performance in this domain. By employing a knowledge integration perspective, the research delineates how BCT can be effectively applied, thereby broadening the discourse on knowledge integration and the utility of boundary objects within recycling chains. The findings have been synthesised into a conceptual framework that incorporates the theoretical constructs of uncertainty in recycling chains, the capabilities enabled by BCT for information processing, and the mechanisms of knowledge integration. Practically, this study offers actionable insights for practitioners. It showcases a viable BCT-based recycling chain model that can aid practitioners in their pursuit of digital transformation towards sustainability. Additionally, it outlines further considerations for blockchain companies looking to pioneer feasible applications. For regulatory associations and other verification entities, BCT emerges as an invaluable tool to enhance supervision and trust

Dataset in support of the University of Southampton Doctoral thesis 'Blockchain application in recycling: from the supply chain perspective'

Dataset in support of the University of Southampton Doctoral thesis &#39;Blockchain application in recycling: from the supply chain perspective &#39; The dataset format is qdpx format, it includes the raw data for PhD research, such as interview transcripts for interviews, internal documents for case companies, qualitative data coding structure. It should be opened with software NVivo. This project strictly enforces the research ethical principles to ensure integrity, quality and transparency, and has been approved by the university, with the Ethics and Research Governance Online (ERGO) code of 67322. </span

Multi-tier sustainable supply chain management and blockchain technology solutions

More organizations are realizing that implementing sustainability strategies cannot rely on internal operations or first-tier suppliers alone; they also need to engage cross-tier suppliers to coordinate sustainability initiatives. However, a multi-tier sustainable supply chain (MT-SSCM) involves complex network structures, and sub-suppliers are often perceived as the ‘iceberg’, creating invisible threats to promoting sustainability practices and supplier compliance. Brands usually do not have direct leveraging power over sub-suppliers, including lack of contractual relationships and limited information, resulting in the limited rollout of sustainable initiatives. Blockchain technology (BCT) offers innovative solutions to disrupt traditional MT-SSCM. The inherent transparency, immutability, decentralized, and smart contract features of BCT are expected to tackle the bottlenecks of MT-SSCM implementation. However, research on BCT is still in its early stages, and there is even less about the BCT application in SSCM from a multi-tier perspective. Therefore, this chapter explores how BCT drives effective MT-SSCM implementations. This chapter first reviews the existing MT-SSCM research, including conceptual frameworks, empirical practices, and theoretical perspectives. This is then followed by discussions of the underlying concepts of BCT, SSCM applications, and potential MT-SSCM solutions with a case study

Blockchain‐based recycling and its impact on recycling performance: A network theory perspective

The purpose of this study is to explore the application of blockchain technology (BCT) in recycling. This research applies a multiple case study approach with six pioneer organisations, based on secondary data. We found that BCT is an effective approach to promote recycling performance: it can provide tokenisation, waste flow tracking and recycling chain integration. The benefits include ‘Eco-friendly’, ‘Stimulate participation’, ‘Social inclusion’, ‘Transparent recycling chains’ and ‘Extended producer responsibility accountability’. However, the majority of existing BCT-based initiatives are in the pilot stage and face cognitive, technology, internal and external barriers. Our research is one of the first studies on blockchain-based recycling. We applied the network theory of ‘Reachability’, ‘Richness’ and ‘Receptivity’ and ‘network formation’ barriers to propose a conceptual framework of BCT-based recycling, which serves as a practical reference for the recycling industry

Untangling the critical success factors of the latest compulsory waste sorting initiative in Shanghai: the role of accountability governance

Municipal solid waste sorting is an essential element of urban sustainability as cities transition to a circular economy. As a mega-city, Shanghai has achieved remarkable milestones in its latest compulsory waste sorting program. This success has garnered widespread attention, and most studies have primarily focused on policy interventions from either a macro perspective or micro-analysis of individual behaviours. However, these studies have often overlooked the intricacies of multi-stakeholder coordination and the division of responsibilities, which frequently contributed to the failure of waste sorting initiatives. Furthermore, existing research lacks a systematic theoretical framework to elucidate multi-stakeholder accountability mechanisms. Therefore, this research adopts a case study approach to untangle the factors that led to Shanghai's success. Through the lens of accountability theory, this study systematically elaborates stakeholder accountability mechanisms and offers a distinctive multi-stakeholder perspective to explain Shanghai's success across vertical, horizontal, and felt accountability dimensions. This informative exemplar provides crucial empirical insights for other cities, especially those grappling with challenges in promoting and managing waste sorting initiatives.</p