We present Gram2Vec, a grammatical style embedding algorithm that embeds documents into a higher dimensional space by extracting the normalized relative frequencies of grammatical features present in the text. Compared to neural approaches, Gram2Vec offers inherent interpretability based on how the feature vectors are generated. In our demo, we present a way to visualize a mapping of authors to documents based on their Gram2Vec vectors and highlight the ability to drop or add features to view which authors make certain linguistic choices. Next, we use authorship attribution as an application to show how Gram2Vec can explain why a document is attributed to a certain author, using cosine similarities between the Gram2Vec feature vectors to calculate the distances between candidate documents and a query document.

Automatic Speech Assessment (ASA) has seen notable advancements with the utilization of self-supervised features (SSL) in recent research. However, a key challenge in ASA lies in the imbalanced distribution of data, particularly evident in English test datasets. To address this challenge, we approach ASA as an ordinal classification task, introducing Weighted Vectors Ranking Similarity (W-RankSim) as a novel regularization technique. W-RankSim encourages closer proximity of weighted vectors in the output layer for similar classes, implying that feature vectors with similar labels would be gradually nudged closer to each other as they converge towards corresponding weighted vectors. Extensive experimental evaluations confirm the effectiveness of our approach in improving ordinal classification performance for ASA. Furthermore, we propose a hybrid model that combines SSL and handcrafted features, showcasing how the inclusion of handcrafted features enhances performance in an ASA system.

Leveraging the infinite dimensional neural network architecture we proposed in arXiv:2109.13512v4 and which can process inputs from Fr\'echet spaces, and using the universal approximation property shown therein, we now largely extend the scope of this architecture by proving several universal approximation theorems for a vast class of input and output spaces. More precisely, the input space $\mathfrak X$ is allowed to be a general topological space satisfying only a mild condition ("quasi-Polish"), and the output space can be either another quasi-Polish space $\mathfrak Y$ or a topological vector space $E$. Similarly to arXiv:2109.13512v4, we show furthermore that our neural network architectures can be projected down to "finite dimensional" subspaces with any desirable accuracy, thus obtaining approximating networks that are easy to implement and allow for fast computation and fitting. The resulting neural network architecture is therefore applicable for prediction tasks based on functional data. To the best of our knowledge, this is the first result which deals with such a wide class of input/output spaces and simultaneously guarantees the numerical feasibility of the ensuing architectures. Finally, we prove an obstruction result which indicates that the category of quasi-Polish spaces is in a certain sense the correct category to work with if one aims at constructing approximating architectures on infinite-dimensional spaces $\mathfrak X$ which, at the same time, have sufficient expressive power to approximate continuous functions on $\mathfrak X$, are specified by a finite number of parameters only and are "stable" with respect to these parameters.

Graph Neural Networks (GNNs) have excelled in predicting graph properties in various applications ranging from identifying trends in social networks to drug discovery and malware detection. With the abundance of new architectures and increased complexity, GNNs are becoming highly specialized when tested on a few well-known datasets. However, how the performance of GNNs depends on the topological and features properties of graphs is still an open question. In this work, we introduce a comprehensive benchmarking framework for graph machine learning, focusing on the performance of GNNs across varied network structures. Utilizing the geometric soft configuration model in hyperbolic space, we generate synthetic networks with realistic topological properties and node feature vectors. This approach enables us to assess the impact of network properties, such as topology-feature correlation, degree distributions, local density of triangles (or clustering), and homophily, on the effectiveness of different GNN architectures. Our results highlight the dependency of model performance on the interplay between network structure and node features, providing insights for model selection in various scenarios. This study contributes to the field by offering a versatile tool for evaluating GNNs, thereby assisting in developing and selecting suitable models based on specific data characteristics.

Natural language processing (NLP) is utilized in a wide range of fields, where words in text are typically transformed into feature vectors called embeddings. BioConceptVec is a specific example of embeddings tailored for biology, trained on approximately 30 million PubMed abstracts using models such as skip-gram. Generally, word embeddings are known to solve analogy tasks through simple vector arithmetic. For instance, $\mathrm{\textit{king}} - \mathrm{\textit{man}} + \mathrm{\textit{woman}}$ predicts $\mathrm{\textit{queen}}$. In this study, we demonstrate that BioConceptVec embeddings, along with our own embeddings trained on PubMed abstracts, contain information about drug-gene relations and can predict target genes from a given drug through analogy computations. We also show that categorizing drugs and genes using biological pathways improves performance. Furthermore, we illustrate that vectors derived from known relations in the past can predict unknown future relations in datasets divided by year.

We study non-episodic Reinforcement Learning for Lipschitz MDPs in which state-action space is a metric space, and the transition kernel and rewards are Lipschitz functions. We develop computationally efficient UCB-based algorithm, $\textit{ZoRL-}\epsilon$ that adaptively discretizes the state-action space and show that their regret as compared with $\epsilon$-optimal policy is bounded as $\mathcal{O}(\epsilon^{-(2 d_\mathcal{S} + d^\epsilon_z + 1)}\log{(T)})$, where $d^\epsilon_z$ is the $\epsilon$-zooming dimension. In contrast, if one uses the vanilla $\textit{UCRL-}2$ on a fixed discretization of the MDP, the regret w.r.t. a $\epsilon$-optimal policy scales as $\mathcal{O}(\epsilon^{-(2 d_\mathcal{S} + d + 1)}\log{(T)})$ so that the adaptivity gains are huge when $d^\epsilon_z \ll d$. Note that the absolute regret of any 'uniformly good' algorithm for a large family of continuous MDPs asymptotically scales as at least $\Omega(\log{(T)})$. Though adaptive discretization has been shown to yield $\mathcal{\tilde{O}}(H^{2.5}K^\frac{d_z + 1}{d_z + 2})$ regret in episodic RL, an attempt to extend this to the non-episodic case by employing constant duration episodes whose duration increases with $T$, is futile since $d_z \to d$ as $T \to \infty$. The current work shows how to obtain adaptivity gains for non-episodic RL. The theoretical results are supported by simulations on two systems where the performance of $\textit{ZoRL-}\epsilon$ is compared with that of '$\textit{UCRL-C}$,' the fixed discretization-based extension of $\textit{UCRL-}2$ for systems with continuous state-action spaces.

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited node-level expressivity. To address these limitations we propose Bundle Neural Networks (BuNN), a new type of GNN that operates via message diffusion over flat vector bundles - structures analogous to connections on Riemannian manifolds that augment the graph by assigning to each node a vector space and an orthogonal map. A BuNN layer evolves the features according to a diffusion-type partial differential equation. When discretized, BuNNs are a special case of Sheaf Neural Networks (SNNs), a recently proposed MPNN capable of mitigating over-smoothing. The continuous nature of message diffusion enables BuNNs to operate on larger scales of the graph and, therefore, to mitigate over-squashing. Finally, we prove that BuNN can approximate any feature transformation over nodes on any (potentially infinite) family of graphs given injective positional encodings, resulting in universal node-level expressivity. We support our theory via synthetic experiments and showcase the strong empirical performance of BuNNs over a range of real-world tasks, achieving state-of-the-art results on several standard benchmarks in transductive and inductive settings.

In this paper, we address the classification of instances each characterized not by a singular point, but by a distribution on a vector space. We employ the Wasserstein metric to measure distances between distributions, which are then used by distance-based classification algorithms such as k-nearest neighbors, k-means, and pseudo-mixture modeling. Central to our investigation is dimension reduction within the Wasserstein metric space to enhance classification accuracy. We introduce a novel approach grounded in the principle of maximizing Fisher's ratio, defined as the quotient of between-class variation to within-class variation. The directions in which this ratio is maximized are termed discriminant coordinates or canonical variates axes. In practice, we define both between-class and within-class variations as the average squared distances between pairs of instances, with the pairs either belonging to the same class or to different classes. This ratio optimization is achieved through an iterative algorithm, which alternates between optimal transport and maximization steps within the vector space. We conduct empirical studies to assess the algorithm's convergence and, through experimental validation, demonstrate that our dimension reduction technique substantially enhances classification performance. Moreover, our method outperforms well-established algorithms that operate on vector representations derived from distributional data. It also exhibits robustness against variations in the distributional representations of data clouds.

This paper studies batched bandit learning problems for nondegenerate functions. We introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally. More specifically, we introduce an algorithm, called Geometric Narrowing (GN), whose regret bound is of order $\widetilde{{\mathcal{O}}} ( A_{+}^d \sqrt{T} )$. In addition, GN only needs $\mathcal{O} (\log \log T)$ batches to achieve this regret. We also provide lower bound analysis for this problem. More specifically, we prove that over some (compact) doubling metric space of doubling dimension $d$: 1. For any policy $\pi$, there exists a problem instance on which $\pi$ admits a regret of order ${\Omega} ( A_-^d \sqrt{T})$; 2. No policy can achieve a regret of order $ A_-^d \sqrt{T} $ over all problem instances, using less than $ \Omega ( \log \log T ) $ rounds of communications. Our lower bound analysis shows that the GN algorithm achieves near optimal regret with minimal number of batches.

When comparing speech sounds across languages, scholars often make use of feature representations of individual sounds in order to determine fine-grained sound similarities. Although binary feature systems for large numbers of speech sounds have been proposed, large-scale computational applications often face the challenges that the proposed feature systems -- even if they list features for several thousand sounds -- only cover a smaller part of the numerous speech sounds reflected in actual cross-linguistic data. In order to address the problem of missing data for attested speech sounds, we propose a new approach that can create binary feature vectors dynamically for all sounds that can be represented in the the standardized version of the International Phonetic Alphabet proposed by the Cross-Linguistic Transcription Systems (CLTS) reference catalog. Since CLTS is actively used in large data collections, covering more than 2,000 distinct language varieties, our procedure for the generation of binary feature vectors provides immediate access to a very large collection of multilingual wordlists. Testing our feature system in different ways on different datasets proves that the system is not only useful to provide a straightforward means to compare the similarity of speech sounds, but also illustrates its potential to be used in future cross-linguistic machine learning applications.