The learnware paradigm aims to help users solve new tasks by reusing existing models rather than starting from scratch. A learnware consists of a model and the specification describing its capabilities. Numerous learnwares are accommodated by the learnware dock system. When users solve tasks with the system, learnwares that fully match the user task are often scarce or unavailable. This paper focuses on tabular classification tasks and explores reusing learnwares for new user tasks with significantly different feature and label spaces, leveraging the potential of numerous existing specialized tabular models developed for various tasks. Under the learnware paradigm, we find that tabular learnwares that seem semantically irrelevant can sometimes be beneficial for new user tasks. The proposed method relies solely on model-predicted probabilities and does not require gradient information, making it applicable to a wide range of tabular models. Experiments suggest that tabular learnwares can be reused beyond their original purpose across heterogeneous tasks.

The learnware paradigm focuses on leveraging numerous established high-performing models to solve machine learning tasks instead of starting from scratch. As the key concept of this paradigm, a learnware consists of a well-trained model of any structure and a specification that characterizes the model's capabilities, allowing it to be identified and reused for future tasks. Given the existence of numerous real-world models trained on diverse label spaces, effectively identifying and combining these models to address tasks involving previously unseen label spaces represents a critical challenge in this paradigm. In this paper, we make the first attempt to identify and reuse effective learnware combinations for tackling learning tasks across different label spaces, extending their applicability beyond the original purposes of individual learnwares. To this end, we introduce a statistical class-wise specification for establishing similarity relations between various label spaces. Leveraging these relations, we model the utility of a learnware combination as a minimum-cost maximum-flow problem, and further develop fine-grained learnware identification and assembly methods. Extensive experiments with thousands of heterogeneous models validate our approach, demonstrating that reusing identified learnware combinations can outperform both training from scratch and fine-tuning a generic pre-trained model.

The learnware paradigm proposed by Zhou [34] aims to solve machine learning tasks by leveraging numerous existing high-performing models instead of training from scratch. These models are accommodated in a learnware dock system, where each learnware consists of a model and a specification that characterizes the model's utility, enabling it to be identified for future tasks. A critical challenge in this paradigm remains unresolved: determining what models can be or should be admitted to the system. Without well-established admission criteria, the uncontrolled growth of uploaded models could lead to significant redundancy and inefficiency, resulting in higher storage overhead, increased computational costs, and even potential system failure. To address this gap, this paper presents the first attempt to establish learnware admission criteria and dynamically filter redundant learnwares based on model capability coverage. Specifically, we organize task information from all learnwares into a tree-based structure to assess model capabilities across a continuously expanding task set. Using this structure and model capability representation, we develop an efficient and scalable method for detecting redundant learnwares dynamically without traversing the entire system. Theoretical analysis and extensive experiments involving over ten thousand simulated learnwares validate the efficacy and efficiency of our approach.

The learnware paradigm aims to establish a market of numerous well-performed machine learning models, enabling users to leverage existing helpful models for their tasks instead of starting from scratch. Each learnware in the market is a model submitted by its developer, associated with a specification generated with the help of learnware market, representing the model's specialty and utility and enabling it to be identified for new user tasks. As the market continuously scales up, accommodating an ever-increasing number of learnwares, the critical challenge of the learnware paradigm is to effectively and efficiently identify the most helpful learnware(s) for a new user task without accessing the user's raw data. In this paper, to achieve increasingly accurate learnware characterization and identification along with a growing number of learnwares in the market, we propose an approach called Evolvable Learnware Specification with Index (ELSI). Specifically, based on the key idea of leveraging the task information within learnware specifications, we tackle the challenge of ascertaining the capabilities of models beyond their original training tasks, thereby enabling learnware specifications and the entire market to evolve continuously. Furthermore, through organizing learnwares and constructing specification indexes, we design a practical procedure to accurately and efficiently identify helpful learnwares without examining the entire market. Theoretical analysis and extensive experiments on a learnware market prototype encompassing thousands of models and covering six real-world scenarios validate the effectiveness and efficiency of our approach.

The learnware paradigm proposed by Zhou [40] aims to enable users to leverage numerous existing high-performing models instead of building machine learning models from scratch.This paradigm envisions that: Any developer worldwide can submit their well-trained models spontaneously into a learnware dock system (formerly known as learnware market).The system uniformly generates a specification for each model to form a learnware and accommodates it.As the key component, a specification should represent the capabilities of the model while preserving developer's original data.Based on the specifications, the learnware dock system can identify and assemble existing learnwares for users to solve new machine learning tasks.Recently, based on reduced kernel mean embedding (RKME) specification, a series of studies have shown the effectiveness of the learnware paradigm theoretically and empirically.However, the realization of a learnware dock system is still missing and remains a big challenge.This paper proposes Beimingwu, the first open-source learnware dock system, providing foundational support for future research.The system provides implementations and extensibility for the entire process of learnware paradigm, including the submitting, usability testing, organization, identification, deployment, and reuse of learnwares.Utilizing Beimingwu, the model development for new user tasks can be significantly streamlined, thanks to integrated architecture and engine design, specifying unified learnware structure and scalable APIs, and the integration of various algorithms for learnware identification and reuse.Notably, this is possible even for users with limited data and minimal expertise in machine learning, without compromising the raw data's security.The system facilitates the future research implementations in learnware-related algorithms and systems, and lays the ground for hosting a vast array of learnwares and establishing a learnware ecosystem.The system is fully open-source and we expect the research community

The learnware paradigm aims to enable users to leverage numerous existing well-trained models instead of building machine learning models from scratch. In this paradigm, developers worldwide can submit their well-trained models spontaneously into a learnware dock system, and the system helps developers generate specification for each model to form a learnware. As the key component, a specification should characterize the capabilities of the model, enabling it to be adequately identified and reused, while preserving the developer's original data. Recently, the RKME (Reduced Kernel Mean Embedding) specification was proposed and most commonly utilized. This paper provides a theoretical analysis of RKME specification about its preservation ability for developer's training data. By modeling it as a geometric problem on manifolds and utilizing tools from geometric analysis, we prove that the RKME specification is able to disclose none of the developer's original data and possesses robust defense against common inference attacks, while preserving sufficient information for effective learnware identification.

The learnware paradigm aims to help users leverage numerous existing high-performing models instead of starting from scratch, where a learnware consists of a well-trained model and the specification describing its capability. Numerous learnwares are accommodated by a learnware dock system. When users solve tasks with the system, models that fully match the task feature space are often rare or even unavailable. However, models with heterogeneous feature space can still be helpful. This paper finds that label information, particularly model outputs, is helpful yet previously less exploited in the accommodation of heterogeneous learnwares. We extend the specification to better leverage model pseudo-labels and subsequently enrich the unified embedding space for better specification evolvement. With label information, the learnware identification can also be improved by additionally comparing conditional distributions. Experiments demonstrate that, even without a model explicitly tailored to user tasks, the system can effectively handle tasks by leveraging models from diverse feature spaces.

The learnware paradigm aims to construct a market of numerous well-performing machine learning models, which enables users to leverage these models to accomplish specific tasks without having to build models from scratch. Each learnware in the market is a model associated with a specification, representing the model’s utility and enabling it to be identified according to future users’ requirements. In the learnware paradigm, due to the vast and ever-increasing number of models in the market, a significant challenge is to identify helpful learnwares efficiently for a specific user task without leaking data privacy. However, existing identification methods require examining the whole market, which is computationally unaffordable in a large market. In this paper, we propose a new framework for identifying helpful learnwares without examining the whole market. Specifically, using the Reduced Kernel Mean Embedding (RKME) specification, we derive a novel learnware scoring criterion for assessing the helpfulness of a learnware, based on which we design an anchor-based framework to identify helpful learnwares by examining only a small portion of learnwares in the market. Theoretical analyses are provided for both the criterion and the anchor-based method. Empirical studies on market containing thousands of learnwares from real-world datasets confirm the effectiveness of our proposed approach.

The learnware paradigm proposed by Zhou [2016] devotes to constructing a market of numerous well-performed models, enabling users to solve problems by reusing existing efforts rather than starting from scratch. A learnware comprises a trained model and the specification which enables the model to be adequately identified according to the user's requirement. Previous studies concentrated on the homogeneous case where models share the same feature space based on Reduced Kernel Mean Embedding (RKME) specification. However, in real-world scenarios, models are typically constructed from different feature spaces. If such a scenario can be handled by the market, all models built for a particular task even with different feature spaces can be identified and reused for a new user task. Generally, this problem would be easier if there were additional auxiliary data connecting different feature spaces, however, obtaining such data in reality is challenging. In this paper, we present a general framework for accommodating heterogeneous learnwares without requiring additional auxiliary data. The key idea is to utilize the submitted RKME specifications to establish the relationship between different feature spaces. Additionally, we give a matrix factorization-based implementation and propose the overall procedure for constructing and exploiting the heterogeneous learnware market. Experiments on real-world tasks validate the efficacy of our method.

Recently complex-valued neural networks have received increasing attention due to successful applications in various tasks and the potential advantages of better theoretical properties and richer representational capacity. However, the training dynamics of complex networks compared to real networks remains an open problem. In this paper, we investigate the dynamics of deep complex networks during real-valued backpropagation in the infinite-width limit via neural tangent kernel (NTK). We first extend the Tensor Program to the complex domain, to show that the dynamics of any basic complex network architecture is governed by its NTK under real-valued backpropagation. Then we propose a way to investigate the comparison of training dynamics between complex and real networks by studying their NTKs. As a result, we surprisingly prove that for most complex activation functions, the commonly used real-valued backpropagation reduces the training dynamics of complex networks to that of ordinary real networks as the widths tend to infinity, thus eliminating the characteristics of complex-valued neural networks. Finally, the experiments validate our theoretical findings numerically.