Swap regret, a generic performance measure of online decision-making algorithms, plays an important role in the theory of repeated games, along with a closeconnection tocorrelated equilibria instrategicgames.

Dimension reduction methods are a fundamental class of techniques in data analysis, which aim to find a lower-dimensional representation of higher-dimensional data while preserving as much of the original information as possible. These methods are extensively used in practice, including in exploratory data analyses to visualize data--arguably, one of the first and most vital steps in any data analysis (Ray et al., 2021). Notably, in genomics, dimension reduction methods are ubiquitously applied to visualize high-dimensional single-cell RNA sequencing data in two dimensions (Becht et al., 2019). Beyond visualization, dimension reduction methods are also frequently employed to mitigate the curse of dimensionality (Bellman, 1957), engineer new features to improve downstream tasks like prediction (e.g., Massy, 1965), and enable scientific discovery in unsupervised learning settings (Chang et al., 2025). For example, many researchers have used dimension reduction in conjunction with clustering to discover new cell types and cell states (Wu et al., 2021), new cancer subtypes (Northcott et al., 2017), and other substantively-meaningful structure in a variety of domains (Bergen et al., 2019; Traven et al., 2017). Given the widespread use and need for dimension reduction methods, numerous dimension reduction techniques have been developed. Popular techniques include but are not limited to principal component analysis (PCA) (Pearson, 1901; Hotelling, 1933), multidimensional scaling (MDS) (Torgerson, 1952; Kruskal, 1964a), Isomap (Tenenbaum et al., 2000), locally linear embedding (LLE) (Roweis and Saul, 2000), t-distributed stochastic neighbor embedding (t-SNE) (van der 1

We compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the employed quantum circuits compatible with near-term quantum devices and use two distinct methodologies: applying randomized NNs on dimensionality-reduced data and applying CNNs to full image data. We evaluate these approaches on three fully-classical data sets of increasing complexity: an artificial hypercube data set, MNIST handwritten digits and industrial images. Our central goal is to shed more light on how quantum and classical models perform for various binary classification tasks and on what defines a good quantum model. Our study involves a correlation analysis between classification accuracy and quantum model hyperparameters, and an analysis on the role of entanglement in quantum models, as well as on the impact of initial training parameters. We find classical and quantum-classical hybrid models achieve statistically-equivalent classification accuracies across most data sets with no approach consistently outperforming the other. Interestingly, we observe that quantum NNs show lower variance with respect to initial training parameters and that the role of entanglement is nuanced. While incorporating entangling gates seems advantageous, we also observe the (optimizable) entangling power not to be correlated with model performance. We also observe an inverse proportionality between the number of entangling gates and the average gate entangling power. Our study provides an industry perspective on quantum machine learning for binary image classification tasks, highlighting both limitations and potential avenues for further research in quantum circuit design, entanglement utilization, and model transferability across varied applications.

Our lower bound is tight up to a constant, and resolves an open problem mentioned, e.g., in the book by Nisan

Abstract--Data dimensionality reduction techniques are often utilized in the implementation of Quantum Machine Learning models to address two significant issues: the constraints of NISQ quantum devices, which are characterized by noise and a limited number of qubits, and the challenge of simulating a large number of qubits on classical devices. It also raises concerns over the scalability of these approaches, as dimensionality reduction methods are slow to adapt to large datasets. In this article, we analyze how data reduction methods affect different QML models. We conduct this experiment over several generated datasets, quantum machine algorithms, quantum data encoding methods, and data reduction methods. All these models were evaluated on the performance metrics like accuracy, precision, recall, and F1 score. Our findings have led us to conclude that the usage of data dimensionality reduction methods results in skewed performance metric values, which results in wrongly estimating the actual performance of quantum machine learning models. There are several factors, along with data dimensionality reduction methods, that worsen this problem, such as characteristics of the datasets, classical to quantum information embedding methods, percentage of feature reduction, classical components associated with quantum models, and structure of quantum machine learning models. We consistently observed the difference in the accuracy range of 14% to 48% amongst these models, using data reduction and not using it. Apart from this, our observations have shown that some data reduction methods tend to perform better for some specific data embedding methodologies and ansatz constructions. In recent decades, there has been a significant push towards research and development of Quantum Machine Learning algorithms and models. Quantum Machine Learning has also been heralded as one of the prominent use cases for Quantum Computing devices. Several studies have shown the ability of QML models to solve difficult machine-learning problems and sometimes outperform the classical approach. Mostly, these proofs are either theoretical or simulated on classical devices. This is because the current quantum computational devices lack the required number of qubits, have questionable error correction ability, and tend to have noisy qubits.

Work in psychology has highlighted that the geometric model of similarity standard in deep learning is not psychologically plausible because its metric properties such as symmetry do not align with human perception of similarity. In contrast, Tversky (1977) proposed an axiomatic theory of similarity with psychological plausibility based on a representation of objects as sets of features, and their similarity as a function of their common and distinctive features. This model of similarity has not been used in deep learning before, in part because of the challenge of incorporating discrete set operations. In this paper, we develop a differentiable parameterization of Tversky's similarity that is learnable through gradient descent, and derive basic neural network building blocks such as the Tversky projection layer, which unlike the linear projection layer can model non-linear functions such as XOR. Through experiments with image recognition and language modeling neural networks, we show that the Tversky projection layer is a beneficial replacement for the linear projection layer. For instance, on the NABirds image classification task, a frozen ResNet-50 adapted with a Tversky projection layer achieves a 24.7% relative accuracy improvement over the linear layer adapter baseline. With Tversky projection layers, GPT-2's perplexity on PTB decreases by 7.8%, and its parameter count by 34.8%. Finally, we propose a unified interpretation of both types of projection layers as computing similarities of input stimuli to learned prototypes for which we also propose a novel visualization technique highlighting the interpretability of Tversky projection layers. Our work offers a new paradigm for thinking about the similarity model implicit in modern deep learning, and designing neural networks that are interpretable under an established theory of psychological similarity.

Our lower bound is tight up to a constant, and resolves an open problem mentioned, e.g., in the book by Nisan

Video large language models (LLMs) achieve strong video understanding by leveraging a large number of spatio-temporal tokens, but suffer from quadratic computational scaling with token count. To address this, we propose a training-free spatio-temporal token merging method, named STTM. Our key insight is to exploit local spatial and temporal redundancy in video data which has been overlooked in prior work. STTM first transforms each frame into multi-granular spatial tokens using a coarse-to-fine search over a quadtree structure, then performs directed pairwise merging across the temporal dimension. This decomposed merging approach outperforms existing token reduction methods across six video QA benchmarks. Notably, STTM achieves a 2$\times$ speed-up with only a 0.5% accuracy drop under a 50% token budget, and a 3$\times$ speed-up with just a 2% drop under a 30% budget. Moreover, STTM is query-agnostic, allowing KV cache reuse across different questions for the same video. The project page is available at https://www.jshyun.me/projects/sttm.

In this study, we focused on proposing an optimal clustering mechanism for the occupations defined in the well-known US-based occupational database, O*NET. Even though all occupations are defined according to well-conducted surveys in the US, their definitions can vary for different firms and countries. Hence, if one wants to expand the data that is already collected in O*NET for the occupations defined with different tasks, a map between the definitions will be a vital requirement. We proposed a pipeline using several BERT-based techniques with various clustering approaches to obtain such a map. We also examined the effect of dimensionality reduction approaches on several metrics used in measuring performance of clustering algorithms. Finally, we improved our results by using a specialized silhouette approach. This new clustering-based mapping approach with dimensionality reduction may help distinguish the occupations automatically, creating new paths for people wanting to change their careers.