This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition where the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor is constrained to a preset value $Q$ much smaller than the size of the core. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. AL$\ell_0$CORE -- i.e., $allo$cated $\ell_0$-$co$nstrained $core$-- thus enjoys both the computational tractability of CP decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that AL$\ell_0$CORE typically requires only tiny fractions (e.g.,~1%) of the full core to achieve the same results as full Tucker decomposition at only a correspondingly tiny fraction of the cost.

Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As such, they encompass a broad class of statistical inference tasks, and provide a rich template to study statistical and computational trade-offs in the high-dimensional regime. While the information-theoretic sample complexity to recover the hidden direction is linear in the dimension $d$, we show that computationally efficient algorithms, both within the Statistical Query (SQ) and the Low-Degree Polynomial (LDP) framework, necessarily require $\Omega(d^{k^\star/2})$ samples, where $k^\star$ is a "generative" exponent associated with the model that we explicitly characterize. Moreover, we show that this sample complexity is also sufficient, by establishing matching upper bounds using a partial-trace algorithm. Therefore, our results provide evidence of a sharp computational-to-statistical gap (under both the SQ and LDP class) whenever $k^\star>2$. To complete the study, we provide examples of smooth and Lipschitz deterministic target functions with arbitrarily large generative exponents $k^\star$.

The Yemen-based branch of Al Qaeda said on Sunday that its leader, Khaled Batarfi, had died. Al Qaeda in the Arabian Peninsula, known as A.Q.A.P., released a video announcing Mr. Batarfi's death, showing images of him wrapped in a white funeral shroud overlaid with a black Al Qaeda flag. It did not explain how he had died. The United States government once considered Al Qaeda in the Arabian Peninsula to be one of the world's most dangerous terrorist organizations. The group tried and failed at least three times to blow up American airliners, and has been targeted by American drone strikes for two decades.

This wasn't the first year that the Academy Awards fell on the second Sunday in March, forcing the good citizens of Hollywood to manage their hair appointments and limousine pickups around the annual scourge that is daylight-saving time. Even so, the ninety-sixth annual Oscars ceremony wrought more than its expected share of havoc on schedules. The Academy of Motion Picture Arts and Sciences, hoping to broaden its reach among those with strict curfews and short attention spans, opted to kick off the show at the previously unheard-of time of 4 P.M. Or, as this year's host, Jimmy Kimmel, quipped in his opening monologue, "The show, as you know, is starting an hour early this year, but don't worry. It will still end very, very late." Such temporal dislocation was surely a good omen, not that any were needed, for Christopher Nolan and "Oppenheimer."

In this study, we investigate stochastic optimization on Riemannian manifolds, focusing on the crucial variance reduction mechanism used in both Euclidean and Riemannian settings. Riemannian variance-reduced methods usually involve a double-loop structure, computing a full gradient at the start of each loop. Determining the optimal inner loop length is challenging in practice, as it depends on strong convexity or smoothness constants, which are often unknown or hard to estimate. Motivated by Euclidean methods, we introduce the Riemannian Loopless SVRG (R-LSVRG) and PAGE (R-PAGE) methods. These methods replace the outer loop with probabilistic gradient computation triggered by a coin flip in each iteration, ensuring simpler proofs, efficient hyperparameter selection, and sharp convergence guarantees. Using R-PAGE as a framework for non-convex Riemannian optimization, we demonstrate its applicability to various important settings. For example, we derive Riemannian MARINA (R-MARINA) for distributed settings with communication compression, providing the best theoretical communication complexity guarantees for non-convex distributed optimization over Riemannian manifolds. Experimental results support our theoretical findings.

With the long term accumulation of high quality educational data, artificial intelligence has shown excellent performance in knowledge tracing. However, due to the lack of interpretability and transparency of some algorithms, this approach will result in reduced stakeholder trust and a decreased acceptance of intelligent decisions. Therefore, algorithms need to achieve high accuracy, and users need to understand the internal operating mechanism and provide reliable explanations for decisions. This paper thoroughly analyzes the interpretability of KT algorithms. First, the concepts and common methods of explainable artificial intelligence and knowledge tracing are introduced. Next, explainable knowledge tracing models are classified into two categories: transparent models and black box models. Then, the interpretable methods used are reviewed from three stages: ante hoc interpretable methods, post hoc interpretable methods, and other dimensions. It is worth noting that current evaluation methods for explainable knowledge tracing are lacking. Hence, contrast and deletion experiments are conducted to explain the prediction results of the deep knowledge tracing model on the ASSISTment2009 by using three XAI methods. Moreover, this paper offers some insights into evaluation methods from the perspective of educational stakeholders. This paper provides a detailed and comprehensive review of the research on explainable knowledge tracing, aiming to offer some basis and inspiration for researchers interested in the interpretability of knowledge tracing.

A critical component when developing question-answering AIs is an adversarial dataset that challenges models to adapt to the complex syntax and reasoning underlying our natural language. Present techniques for procedurally generating adversarial texts are not robust enough for training on complex tasks such as answering multi-sentence trivia questions. We instead turn to human-generated data by introducing an interface for collecting adversarial human-written trivia questions. Our interface is aimed towards question writers and players of Quiz Bowl, a buzzer-based trivia competition where paragraph-long questions consist of a sequence of clues of decreasing difficulty. To incentivize usage, a suite of machine learning-based tools in our interface assist humans in writing questions that are more challenging to answer for Quiz Bowl players and computers alike. Not only does our interface gather training data for the groundbreaking Quiz Bowl AI project QANTA, but it is also a proof-of-concept of future adversarial data collection for question-answering systems. The results of performance-testing our interface with ten originally-composed questions indicate that, despite some flaws, our interface's novel question-writing features as well as its real-time exposure of useful responses from our machine models could facilitate and enhance the collection of adversarial questions. The code for our interface is available at: https://github.com/Zefan-Cai/QAML

Direct image-to-graph transformation is a challenging task that solves object detection and relationship prediction in a single model. Due to the complexity of this task, large training datasets are rare in many domains, which makes the training of large networks challenging. This data sparsity necessitates the establishment of pre-training strategies akin to the state-of-the-art in computer vision. In this work, we introduce a set of methods enabling cross-domain and cross-dimension transfer learning for image-to-graph transformers. We propose (1) a regularized edge sampling loss for sampling the optimal number of object relationships (edges) across domains, (2) a domain adaptation framework for image-to-graph transformers that aligns features from different domains, and (3) a simple projection function that allows us to pretrain 3D transformers on 2D input data. We demonstrate our method's utility in cross-domain and cross-dimension experiments, where we pretrain our models on 2D satellite images before applying them to vastly different target domains in 2D and 3D. Our method consistently outperforms a series of baselines on challenging benchmarks, such as retinal or whole-brain vessel graph extraction.

Data generated by edge devices has the potential to train intelligent autonomous systems across various domains. Despite the emergence of diverse machine learning approaches addressing privacy concerns and utilizing distributed data, security issues persist due to the sensitive storage of data shards in disparate locations. This paper introduces a potentially groundbreaking paradigm for machine learning model training, specifically designed for scenarios with only a single magnetic image and its corresponding label image available. We harness the capabilities of Deep Learning to generate concise yet informative samples, aiming to overcome data scarcity. Through the utilization of deep learning's internal representations, our objective is to efficiently address data scarcity issues and produce meaningful results. This methodology presents a promising avenue for training machine learning models with minimal data.

Existing communication methods for multi-agent reinforcement learning (MARL) in cooperative multi-robot problems are almost exclusively task-specific, training new communication strategies for each unique task. We address this inefficiency by introducing a communication strategy applicable to any task within a given environment. We pre-train the communication strategy without task-specific reward guidance in a self-supervised manner using a set autoencoder. Our objective is to learn a fixed-size latent Markov state from a variable number of agent observations. Under mild assumptions, we prove that policies using our latent representations are guaranteed to converge, and upper bound the value error introduced by our Markov state approximation. Our method enables seamless adaptation to novel tasks without fine-tuning the communication strategy, gracefully supports scaling to more agents than present during training, and detects out-of-distribution events in an environment.