Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of class distributions ($n=\infty$) the problem is solved optimally by the likelihood-ratio test; when $m=1$ it corresponds to binary classification; and when $m\approx n$ it is equivalent to two-sample testing. The intermediate settings occur in the field of likelihood-free inference, where labeled samples are obtained by running forward simulations and the unlabeled sample is collected experimentally. In recent work it was discovered that there is a fundamental trade-off between $m$ and $n$: increasing the data sample $m$ reduces the amount $n$ of training/simulation data needed. In this work we (a) introduce a generalization where unlabeled samples come from a mixture of the two classes -- a case often encountered in practice; (b) study the minimax sample complexity for non-parametric classes of densities under \textit{maximum mean discrepancy} (MMD) separation; and (c) investigate the empirical performance of kernels parameterized by neural networks on two tasks: detection of the Higgs boson and detection of planted DDPM generated images amidst CIFAR-10 images. For both problems we confirm the existence of the theoretically predicted asymmetric $m$ vs $n$ trade-off.

A common forecasting setting in real world applications considers a set of possibly heterogeneous time series of the same domain. Due to different properties of each time series such as length, obtaining forecasts for each individual time series in a straight-forward way is challenging. This paper proposes a general framework utilizing a similarity measure in Dynamic Time Warping to find similar time series to build neighborhoods in a k-Nearest Neighbor fashion, and improve forecasts of possibly simple models by averaging. Several ways of performing the averaging are suggested, and theoretical arguments underline the usefulness of averaging for forecasting. Additionally, diagnostics tools are proposed allowing a deep understanding of the procedure.

While the application of Artificial Intelligence in Finance has a long tradition, its potential in Entrepreneurship has been intensively explored only recently. In this context, Entrepreneurial Finance is a particularly fertile ground for future Artificial Intelligence proliferation. To support the latter, the study provides a bibliometric review of Artificial Intelligence applications in (1) entrepreneurial finance literature, and (2) corporate finance literature with implications for Entrepreneurship. Rigorous search and screening procedures of the scientific database Web of Science Core Collection resulted in the identification of 1890 relevant journal articles subjected to analysis. The bibliometric analysis gives a rich insight into the knowledge field's conceptual, intellectual, and social structure, indicating nascent and underdeveloped research directions. As far as we were able to identify, this is the first study to map and bibliometrically analyze the academic field concerning the relationship between Artificial Intelligence, Entrepreneurship, and Finance, and the first review that deals with Artificial Intelligence methods in Entrepreneurship. According to the results, Artificial Neural Network, Deep Neural Network and Support Vector Machine are highly represented in almost all identified topic niches. At the same time, applying Topic Modeling, Fuzzy Neural Network and Growing Hierarchical Self-organizing Map is quite rare. As an element of the research, and before final remarks, the article deals as well with a discussion of certain gaps in the relationship between Computer Science and Economics. These gaps do represent problems in the application of Artificial Intelligence in Economic Science. As a way to at least in part remedy this situation, the foundational paradigm and the bespoke demonstration of the Monte Carlo randomized algorithm are presented.

After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then, an overview of two modern mathematical formulations of organization -- intrinsic computation and evolution operators -- lays out a way to overcome these challenges. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function $y(x)$. We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels $y(x)$ are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

Amidst ongoing market recalibration and increasing investor optimism, the U.S. stock market is experiencing a resurgence, prompting the need for sophisticated tools to protect and grow portfolios. Addressing this, we introduce "Stockformer," a cutting-edge deep learning framework optimized for swing trading, featuring the TopKDropout method for enhanced stock selection. By integrating STL decomposition and self-attention networks, Stockformer utilizes the S&P 500's complex data to refine stock return predictions. Our methodology entailed segmenting data for training and validation (January 2021 to January 2023) and testing (February to June 2023). During testing, Stockformer's predictions outperformed ten industry models, achieving superior precision in key predictive accuracy indicators (MAE, RMSE, MAPE), with a remarkable accuracy rate of 62.39% in detecting market trends. In our backtests, Stockformer's swing trading strategy yielded a cumulative return of 13.19% and an annualized return of 30.80%, significantly surpassing current state-of-the-art models. Stockformer has emerged as a beacon of innovation in these volatile times, offering investors a potent tool for market forecasting. To advance the field and foster community collaboration, we have open-sourced Stockformer, available at https://github.com/Eric991005/Stockformer.

This study presents an unsupervised machine learning approach for optimizing Profit and Loss (PnL) in quantitative finance. Our algorithm, akin to an unsupervised variant of linear regression, maximizes the Sharpe Ratio of PnL generated from signals constructed linearly from exogenous variables. The methodology employs a linear relationship between exogenous variables and the trading signal, with the objective of maximizing the Sharpe Ratio through parameter optimization. Empirical application on an ETF representing U.S. Treasury bonds demonstrates the model's effectiveness, supported by regularization techniques to mitigate overfitting. The study concludes with potential avenues for further development, including generalized time steps and enhanced corrective terms.

Datasets, the cornerstone of modern machine learning (ML) systems, have been increasingly sold and purchased for different ML pipelines [2]. Several data marketplaces have emerged to serve different stages of building ML-enhanced data applications. For example, NASDAQ Data Link [3] offers financial datasets cleaned and structured for model training, Amazon AWS data exchange [4] focuses on generic tabular datasets, and Databricks Marketplace [5] integrates raw datasets and ML pipelines to deliver insights. The data-as-a-service market size was more than 30 billions and is expected to double in the next five years [6]. While the data marketplaces are increasingly expanding, unfortunately, data acquisition for ML remains challenging, partially due to its ad-hoc nature: Based on discussions with real-world users, data acquirers often need to negotiate varying contracts with different data providers first, then purchase multiple datasets with different formats, and finally filtering out unnecessary data from the purchased datasets.

Institutional bias can impact patient outcomes, educational attainment, and legal system navigation. Written records often reflect bias, and once bias is identified; it is possible to refer individuals for training to reduce bias. Many machine learning tools exist to explore text data and create predictive models that can search written records to identify real-time bias. However, few previous studies investigate large language model embeddings and geometric models of biased text data to understand geometry's impact on bias modeling accuracy. To overcome this issue, this study utilizes the RedditBias database to analyze textual biases. Four transformer models, including BERT and RoBERTa variants, were explored. Post-embedding, t-SNE allowed two-dimensional visualization of data. KNN classifiers differentiated bias types, with lower k-values proving more effective. Findings suggest BERT, particularly mini BERT, excels in bias classification, while multilingual models lag. The recommendation emphasizes refining monolingual models and exploring domain-specific biases.

Traditional methods of linking large language models (LLMs) to knowledge bases via the semantic similarity search often fall short of capturing complex relational dynamics. To address these limitations, we introduce AutoKG, a lightweight and efficient approach for automated knowledge graph (KG) construction. For a given knowledge base consisting of text blocks, AutoKG first extracts keywords using a LLM and then evaluates the relationship weight between each pair of keywords using graph Laplace learning. We employ a hybrid search scheme combining vector similarity and graph-based associations to enrich LLM responses. Preliminary experiments demonstrate that AutoKG offers a more comprehensive and interconnected knowledge retrieval mechanism compared to the semantic similarity search, thereby enhancing the capabilities of LLMs in generating more insightful and relevant outputs.