Wefurthermore derive, with mathematical proof and extensive numerical evidence, the scalinglawexponents inallofthese phases, inparticular computing theoptimal modelparameter-count as a function of floating point operation budget.

In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory (LSTM) network estimates the key parameters $μ>0$ and $β\in(0,1)$ from sequences of inter-arrival times, effectively modeling their temporal dependencies. Our experiments on synthetic data show that the proposed approach reduces the mean squared error (MSE) by about 55.3\% compared to the traditional method of moments (MOM) and performs reliably across different training conditions. We tested the method on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. The results show that the LSTM can effectively track daily patterns and parameter changes, indicating its effectiveness on real-world data with complex time dependencies.

Index tracking is a popular passive investment strategy aimed at optimizing portfolios, but fully replicating an index can lead to high transaction costs. To address this, partial replication have been proposed. However, the cardinality constraint renders the problem non-convex, non-differentiable, and often NP-hard, leading to the use of heuristic or neural network-based methods, which can be non-interpretable or have NP-hard complexity. To overcome these limitations, we propose a Differentiable Cardinality Constraint ($\textbf{DCC}$) for index tracking and introduce a floating-point precision-aware method ($\textbf{DCC}_{fpp}$) to address implementation issues. We theoretically prove our methods calculate cardinality accurately and enforce actual cardinality with polynomial time complexity. We propose the range of the hyperparameter $a$ ensures that $\textbf{DCC}_{fpp}$ has no error in real implementations, based on theoretical proof and experiment. Our method applied to mathematical method outperforms baseline methods across various datasets, demonstrating the effectiveness of the identified hyperparameter $a$.

Ultra-Wideband (UWB) systems are becoming increasingly popular for indoor localization, where range measurements are obtained by measuring the time-of-flight of radio signals. However, the range measurements typically suffer from a systematic error or bias that must be corrected for high-accuracy localization. In this paper, a ranging protocol is proposed alongside a robust and scalable antenna-delay calibration procedure to accurately and efficiently calibrate antenna delays for many UWB tags. Additionally, the bias and uncertainty of the measurements are modelled as a function of the received-signal power. The full calibration procedure is presented using experimental training data of 3 aerial robots fitted with 2 UWB tags each, and then evaluated on 2 test experiments. A localization problem is then formulated on the experimental test data, and the calibrated measurements and their modelled uncertainty are fed into an extended Kalman filter (EKF). The proposed calibration is shown to yield an average of 46% improvement in localization accuracy. Lastly, the paper is accompanied by an open-source UWB-calibration Python library, which can be found at https://github.com/decargroup/uwb_calibration.

Hate speech detection is a common downstream application of natural language processing (NLP) in the real world. In spite of the increasing accuracy, current data-driven approaches could easily learn biases from the imbalanced data distributions originating from humans. The deployment of biased models could further enhance the existing social biases. But unlike handling tabular data, defining and mitigating biases in text classifiers, which deal with unstructured data, are more challenging. A popular solution for improving machine learning fairness in NLP is to conduct the debiasing process with a list of potentially discriminated words given by human annotators. In addition to suffering from the risks of overlooking the biased terms, exhaustively identifying bias with human annotators are unsustainable since discrimination is variable among different datasets and may evolve over time. To this end, we propose an automatic misuse detector (MiD) relying on an explanation method for detecting potential bias. And built upon that, an end-to-end debiasing framework with the proposed staged correction is designed for text classifiers without any external resources required.

We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global and/or local geometric structure of a dataset. However, in practice one is often more interested in determining how one or multiple user-selected response function(s) can be explained by the data. To intuitively connect the responses to the data, FPP constructs 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns of the response functions. More specifically, FPP is designed to (i) produce human-interpretable embeddings; (ii) capture non-linear relationships; (iii) allow the simultaneous use of multiple response functions; and (iv) scale to millions of samples. Using FPP on real-world datasets, one can obtain fundamentally new insights about high-dimensional relationships in large-scale data that could not be achieved using existing dimension reduction methods.