This paper investigates how representation learning can enable optimal control in unknown and complex dynamics, such as chaotic and non-linear systems, without relying on prior domain knowledge of the dynamics. The core idea is to establish an equivariant geometry that is diffeomorphic to the manifold defined by a dynamical system and to perform optimal control within this corresponding geometry, which is a non-trivial task. To address this challenge, Koopman Embed to Equivariant Control (KEEC) is proposed for model learning and control. Inspired by Lie theory, KEEC begins by learning a non-linear dynamical system defined on a manifold and embedding trajectories into a Lie group. Subsequently, KEEC formulates an equivariant value function equation in reinforcement learning on the equivariant geometry, ensuring an invariant effect as the value function on the original manifold. By deriving analytical-form optimal actions on the equivariant value function, KEEC theoretically achieves quadratic convergence for the optimal equivariant value function by leveraging the differential information on the equivariant geometry. The effectiveness of KEEC is demonstrated in challenging dynamical systems, including chaotic ones like Lorenz-63. Notably, our results show that isometric functions, which maintain the compactness and completeness of geometry while preserving metric and differential information, consistently outperform loss functions lacking these characteristics.

Emotion recognition in conversations (ERC) is a rapidly evolving task within the natural language processing community, which aims to detect the emotions expressed by speakers during a conversation. Recently, a growing number of ERC methods have focused on leveraging supervised contrastive learning (SCL) to enhance the robustness and generalizability of learned features. However, current SCL-based approaches in ERC are impeded by the constraint of large batch sizes and the lack of compatibility with most existing ERC models. To address these challenges, we propose an efficient and model-agnostic SCL framework named Supervised Sample-Label Contrastive Learning with Soft-HGR Maximal Correlation (SSLCL), which eliminates the need for a large batch size and can be seamlessly integrated with existing ERC models without introducing any model-specific assumptions. Specifically, we introduce a novel perspective on utilizing label representations by projecting discrete labels into dense embeddings through a shallow multilayer perceptron, and formulate the training objective to maximize the similarity between sample features and their corresponding ground-truth label embeddings, while minimizing the similarity between sample features and label embeddings of disparate classes. Moreover, we innovatively adopt the Soft-HGR maximal correlation as a measure of similarity between sample features and label embeddings, leading to significant performance improvements over conventional similarity measures. Additionally, multimodal cues of utterances are effectively leveraged by SSLCL as data augmentations to boost model performances. Extensive experiments on two ERC benchmark datasets, IEMOCAP and MELD, demonstrate the compatibility and superiority of our proposed SSLCL framework compared to existing state-of-the-art SCL methods. Our code is available at \url{https://github.com/TaoShi1998/SSLCL}.

Automated classifiers (ACs), often built via supervised machine learning (SML), can categorize large, statistically powerful samples of data ranging from text to images and video, and have become widely popular measurement devices in communication science and related fields. Despite this popularity, even highly accurate classifiers make errors that cause misclassification bias and misleading results in downstream analyses-unless such analyses account for these errors. As we show in a systematic literature review of SML applications, communication scholars largely ignore misclassification bias. In principle, existing statistical methods can use "gold standard" validation data, such as that created by human annotators, to correct misclassification bias and produce consistent estimates. We introduce and test such methods, including a new method we design and implement in the R package misclassificationmodels, via Monte Carlo simulations designed to reveal each method's limitations, which we also release. Based on our results, we recommend our new error correction method as it is versatile and efficient. In sum, automated classifiers, even those below common accuracy standards or making systematic misclassifications, can be useful for measurement with careful study design and appropriate error correction methods.

In this work we make progress in understanding the relationship between learning models with access to entangled, separable and statistical measurements in the quantum statistical query (QSQ) model. To this end, we show the following results. $\textbf{Entangled versus separable measurements.}$ The goal here is to learn an unknown $f$ from the concept class $C\subseteq \{f:\{0,1\}^n\rightarrow [k]\}$ given copies of $\frac{1}{\sqrt{2^n}}\sum_x \vert x,f(x)\rangle$. We show that, if $T$ copies suffice to learn $f$ using entangled measurements, then $O(nT^2)$ copies suffice to learn $f$ using just separable measurements. $\textbf{Entangled versus statistical measurements}$ The goal here is to learn a function $f \in C$ given access to separable measurements and statistical measurements. We exhibit a class $C$ that gives an exponential separation between QSQ learning and quantum learning with entangled measurements (even in the presence of noise). This proves the "quantum analogue" of the seminal result of Blum et al. [BKW'03]. that separates classical SQ and PAC learning with classification noise. $\textbf{QSQ lower bounds for learning states.}$ We introduce a quantum statistical query dimension (QSD), which we use to give lower bounds on the QSQ learning. With this we prove superpolynomial QSQ lower bounds for testing purity, shadow tomography, Abelian hidden subgroup problem, degree-$2$ functions, planted bi-clique states and output states of Clifford circuits of depth $\textsf{polylog}(n)$. $\textbf{Further applications.}$ We give and $\textit{unconditional}$ separation between weak and strong error mitigation and prove lower bounds for learning distributions in the QSQ model. Prior works by Quek et al. [QFK+'22], Hinsche et al. [HIN+'22], and Nietner et al. [NIS+'23] proved the analogous results $\textit{assuming}$ diagonal measurements and our work removes this assumption.

The recent explosion of interest in multimodal applications has resulted in a wide selection of datasets and methods for representing and integrating information from different modalities. Despite these empirical advances, there remain fundamental research questions: How can we quantify the interactions that are necessary to solve a multimodal task? Subsequently, what are the most suitable multimodal models to capture these interactions? To answer these questions, we propose an information-theoretic approach to quantify the degree of redundancy, uniqueness, and synergy relating input modalities with an output task. We term these three measures as the PID statistics of a multimodal distribution (or PID for short), and introduce two new estimators for these PID statistics that scale to high-dimensional distributions. To validate PID estimation, we conduct extensive experiments on both synthetic datasets where the PID is known and on large-scale multimodal benchmarks where PID estimations are compared with human annotations. Finally, we demonstrate their usefulness in (1) quantifying interactions within multimodal datasets, (2) quantifying interactions captured by multimodal models, (3) principled approaches for model selection, and (4) three real-world case studies engaging with domain experts in pathology, mood prediction, and robotic perception where our framework helps to recommend strong multimodal models for each application.

In this paper, we consider a theoretical model for injecting data bias, namely, under-representation and label bias (Blum & Stangl, 2019). We empirically study the effect of varying data biases on the accuracy and fairness of fair classifiers. Through extensive experiments on both synthetic and real-world datasets (e.g., Adult, German Credit, Bank Marketing, COMPAS), we empirically audit pre-, in-, and post-processing fair classifiers from standard fairness toolkits for their fairness and accuracy by injecting varying amounts of under-representation and label bias in their training data (but not the test data). Our main observations are: 1. The fairness and accuracy of many standard fair classifiers degrade severely as the bias injected in their training data increases, 2. A simple logistic regression model trained on the right data can often outperform, in both accuracy and fairness, most fair classifiers trained on biased training data, and 3. A few, simple fairness techniques (e.g., reweighing, exponentiated gradients) seem to offer stable accuracy and fairness guarantees even when their training data is injected with under-representation and label bias. Our experiments also show how to integrate a measure of data bias risk in the existing fairness dashboards for real-world deployments.

Adversarial training is widely acknowledged as the most effective defense against adversarial attacks. However, it is also well established that achieving both robustness and generalization in adversarially trained models involves a trade-off. The goal of this work is to provide an in depth comparison of different approaches for adversarial training in language models. Specifically, we study the effect of pre-training data augmentation as well as training time input perturbations vs. embedding space perturbations on the robustness and generalization of transformer-based language models. Our findings suggest that better robustness can be achieved by pre-training data augmentation or by training with input space perturbation. However, training with embedding space perturbation significantly improves generalization. A linguistic correlation analysis of neurons of the learned models reveals that the improved generalization is due to 'more specialized' neurons. To the best of our knowledge, this is the first work to carry out a deep qualitative analysis of different methods of generating adversarial examples in adversarial training of language models.

We study the problem of post-processing a supervised machine-learned regressor to maximize fair binary classification at all decision thresholds. By decreasing the statistical distance between each group's score distributions, we show that we can increase fair performance across all thresholds at once, and that we can do so without a large decrease in accuracy. To this end, we introduce a formal measure of Distributional Parity, which captures the degree of similarity in the distributions of classifications for different protected groups. Our main result is to put forward a novel post-processing algorithm based on optimal transport, which provably maximizes Distributional Parity, thereby attaining common notions of group fairness like Equalized Odds or Equal Opportunity at all thresholds. We demonstrate on two fairness benchmarks that our technique works well empirically, while also outperforming and generalizing similar techniques from related work.

The use of tensors is progressively widespread in the realms of data analytics and machine learning. As an extension of vectors and matrices, a tensor is a multi-dimensional array of numbers that provides a means to represent data across multiple dimensions. As an illustration, Figure 1 shows an image stream that can be seen as a three-dimensional tensor, where the first two dimensions denote the pixels within each image, while the third dimension represents the distinct images in the sequence. One of the advantages of representing data as a tensor, as opposed to reshaping it into a vector or matrix, lies in its ability to capture intricate relationships within the data, especially when interactions occur across multiple dimensions. For instance, the image stream depicted in Figure 1 exhibits a spatiotemporal correlation structure. Specifically, pixels within each image have spatial correlation, and pixels at the same location across multiple images are temporally correlated. Transforming the image stream into a vector or matrix would disrupt the spatiotemporal correlation structure, whereas representing it as a three-dimensional tensor preserves this correlation. In addition to capturing intricate relationships, other benefits of using tensors include compatibility with multi-modal data (i.e., accommodating diverse types of data in a unified structure) and facilitating parallel processing (i.e., enabling the parallelization of operations), etc. As a result, the volume of research in tensor-based data analytics has been rapidly increasing in recent years (Shen et al., 2022; Gahrooei et al., 2021; Yan et al., 2019; Hu et al., 2023; Zhen et al., 2023; Zhang et al., 2023).

This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse optimisation problems on measures. By formulating the CPGD steps within a variational framework, we provide rigorous mathematical proofs demonstrating the following key findings: (i) The total variation norms of the solution measures along the descent trajectory remain bounded, ensuring stability and preventing undesirable divergence; (ii) We establish a global convergence guarantee with a convergence rate of $\mathcal{O}(\log(K)/\sqrt{K})$ over $K$ iterations, showcasing the efficiency and effectiveness of our algorithm; (iii) Additionally, we analyze and establish local control over the first-order condition discrepancy, contributing to a deeper understanding of the algorithm's behavior and reliability in practical applications.