Optimization problems involve the identification of the best possible solution among several possibilities. These problems can be encountered in real-world settings, as well as in most scientific research fields. In recent years, computer scientists have developed increasingly advanced computational methods for solving optimization problems. Some of the most promising techniques developed so far are based on artificial neural networks (ANNs). Researchers at the Vector Institute, University of Waterloo and Perimeter Institute for Theoretical Physics in Canada have recently developed variational neural annealing, a new optimization method that merges recurrent neural networks (RNNs) with the principle of annealing.

Various performance measures based on the ground truth and without ground truth exist to evaluate the quality of a developed tracking algorithm. The existing popular measures - average center location error (ACLE) and average tracking accuracy (ATA) based on ground truth, may sometimes create confusion to quantify the quality of a developed algorithm for tracking an object under some complex environments (e.g., scaled or oriented or both scaled and oriented object). In this article, we propose three new auxiliary performance measures based on ground truth information to evaluate the quality of a developed tracking algorithm under such complex environments. Moreover, one performance measure is developed by combining both two existing measures ACLE and ATA and three new proposed measures for better quantifying the developed tracking algorithm under such complex conditions. Some examples and experimental results conclude that the proposed measure is better than existing measures to quantify one developed algorithm for tracking objects under such complex environments.

The idea of using quantum computers for machine learning has recently received attention both in academia and industry [1-13]. While proof of principle study have shown that some problems of mathematical interest quantum computers are useful [13], quantum advantage in machine learning algorithms for practical applications is still unclear [14]. On classical architectures, a first-principle theory of machine learning, especially the so-called deep learning that uses a large number of layers, is still in development. Early developments of the statistical learning theory provide rigorous guarantees on the learning capability in generic learning algorithms, but theoretical bounds obtained from information theory are sometimes weak in practical settings. The theory of neural tangent kernel (NTK) has been deemed an important tool to understand deep neural networks [15-21]. In the large-width limit, a generic neural network becomes nearly Gaussian when averaging over the initial weights and biases, and the learning capabilities become predictable. The NTK theory allows to derive analytical understanding of the neural networks dynamics, improving on statistical learning theory and shedding light on the underlying principle of deep learning [22-26]. In the quantum machine learning community, a similar first principle theory would help in understanding the training dynamics and selecting appropri-junyuliu@uchicago.edu

Learning how to effectively control unknown dynamical systems is crucial for intelligent autonomous systems. This task becomes a significant challenge when the underlying dynamics are changing with time. Motivated by this challenge, this paper considers the problem of controlling an unknown Markov jump linear system (MJS) to optimize a quadratic objective. By taking a model-based perspective, we consider identification-based adaptive control for MJSs. We first provide a system identification algorithm for MJS to learn the dynamics in each mode as well as the Markov transition matrix, underlying the evolution of the mode switches, from a single trajectory of the system states, inputs, and modes. Through mixing-time arguments, sample complexity of this algorithm is shown to be $\mathcal{O}(1/\sqrt{T})$. We then propose an adaptive control scheme that performs system identification together with certainty equivalent control to adapt the controllers in an episodic fashion. Combining our sample complexity results with recent perturbation results for certainty equivalent control, we prove that when the episode lengths are appropriately chosen, the proposed adaptive control scheme achieves $\mathcal{O}(\sqrt{T})$ regret, which can be improved to $\mathcal{O}(polylog(T))$ with partial knowledge of the system. Our proof strategy introduces innovations to handle Markovian jumps and a weaker notion of stability common in MJSs. Our analysis provides insights into system theoretic quantities that affect learning accuracy and control performance. Numerical simulations are presented to further reinforce these insights.

Almost all statements in knowledge bases have a temporal scope during which they are valid. Hence, knowledge base completion (KBC) on temporal knowledge bases (TKB), where each statement \textit{may} be associated with a temporal scope, has attracted growing attention. Prior works assume that each statement in a TKB \textit{must} be associated with a temporal scope. This ignores the fact that the scoping information is commonly missing in a KB. Thus prior work is typically incapable of handling generic use cases where a TKB is composed of temporal statements with/without a known temporal scope. In order to address this issue, we establish a new knowledge base embedding framework, called TIME2BOX, that can deal with atemporal and temporal statements of different types simultaneously. Our main insight is that answers to a temporal query always belong to a subset of answers to a time-agnostic counterpart. Put differently, time is a filter that helps pick out answers to be correct during certain periods. We introduce boxes to represent a set of answer entities to a time-agnostic query. The filtering functionality of time is modeled by intersections over these boxes. In addition, we generalize current evaluation protocols on time interval prediction. We describe experiments on two datasets and show that the proposed method outperforms state-of-the-art (SOTA) methods on both link prediction and time prediction.

Even as economies struggle with the chaos of the pandemic, the AI startup space continues to grow stronger with increased investments and M&A deals. According to the latest State of AI report from CB Insights, the global funding in the segment has seen a significant surge, growing from $16.6 billion across 588 deals in Q2 2021 (figures show $20B due to the inclusion of two public subsidiary fundings) to $17.9 billion across 841 deals in the third quarter. Throughout the year (which is yet to end), AI startups around the world raised $50 billion across 2000 deals with 138 mega-rounds of 100 million. As much as $8.5 billion of the total investment went into healthcare AI, $3.1 billion went into fintech AI, while $2.6 billion went into retail AI. The findings show how AI has become a driving force across nearly every industry and is drawing significant attention from VCs, CVCs, and other investors.

The global AI in fintech market size is projected to increase to $46,881.9 million by 2030 from $7,702.7 million in 2020, at a 19.8% CAGR between 2020 and 2030. With AI, the efficiency of financial processes and the security of money-related data can be improved massively. For instance, in regard to fraud detection, AI monitors people's online transactional behavior so that any deviation and a potential fraud can be identified in real time and stopped right there. Moreover, AI helps in automating several processes in the banking, financial services, and insurance (BFSI) sector, such as online customer engagement via chatbots, claims processing, and answering frequently asked questions (FAQs). This not only allows BFSI companies to reduce their expenditure in hiring humans for these tasks but also engage these employees in more-important tasks, such as decision making and strategizing. AI solutions have been in a higher demand than managed and professional services because the former conduct question and answer (Q&A) processing, natural language processing (NLP) and generation, facial recognition, video and image analysis, and speech recognition.

NVIDIA opened the door for enterprises worldwide to develop and deploy large language models (LLM) by enabling them to build their own domain-specific chatbots, personal assistants and other AI applications that understand language with unprecedented levels of subtlety and nuance. The company unveiled the NVIDIA NeMo Megatron framework for training language models with trillions of parameters, the Megatron 530B customizable LLM that can be trained for new domains and languages, and NVIDIA Triton Inference Server with multi-GPU, multinode distributed inference functionality. Combined with NVIDIA DGX systems, these tools provide a production-ready, enterprise-grade solution to simplify the development and deployment of large language models. "Large language models have proven to be flexible and capable, able to answer deep domain questions, translate languages, comprehend and summarize documents, write stories and compute programs, all without specialized training or supervision," said Bryan Catanzaro, vice president of Applied Deep Learning Research at NVIDIA. "Building large language models for new languages and domains is likely the largest supercomputing application yet, and now these capabilities are within reach for the world's enterprises."

Retrieving a signal from the Fourier transform of its third-order statistics or bispectrum arises in a wide range of signal processing problems. Conventional methods do not provide a unique inversion of bispectrum. In this paper, we present a an approach that uniquely recovers signals with finite spectral support (band-limited signals) from at least $3B$ measurements of its bispectrum function (BF), where $B$ is the signal's bandwidth. Our approach also extends to time-limited signals. We propose a two-step trust region algorithm that minimizes a non-convex objective function. First, we approximate the signal by a spectral algorithm. Then, we refine the attained initialization based upon a sequence of gradient iterations. Numerical experiments suggest that our proposed algorithm is able to estimate band/time-limited signals from its BF for both complete and undersampled observations.

Multimodal regression is a fundamental task, which integrates the information from different sources to improve the performance of follow-up applications. However, existing methods mainly focus on improving the performance and often ignore the confidence of prediction for diverse situations. In this study, we are devoted to trustworthy multimodal regression which is critical in cost-sensitive domains. To this end, we introduce a novel Mixture of Normal-Inverse Gamma distributions (MoNIG) algorithm, which efficiently estimates uncertainty in principle for adaptive integration of different modalities and produces a trustworthy regression result. Our model can be dynamically aware of uncertainty for each modality, and also robust for corrupted modalities. Furthermore, the proposed MoNIG ensures explicitly representation of (modality-specific/global) epistemic and aleatoric uncertainties, respectively. Experimental results on both synthetic and different real-world data demonstrate the effectiveness and trustworthiness of our method on various multimodal regression tasks (e.g., temperature prediction for superconductivity, relative location prediction for CT slices, and multimodal sentiment analysis).