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Objectives: This study aims to provide a comprehensive overview of the role of quadratic polynomials in data modeling and analysis, particularly in representing the curvature of natural phenomena. Methods: We begin with a fundamental explanation of quadratic polynomials and describe their general forms and theoretical significance. We then explored the application of these polynomials in regression analysis, detailing the process of fitting quadratic models to the data using Python libraries NumPy and Matplotlib. The methodology also included calculation of the coefficient of determination (R-squared) to evaluate the polynomial model fit. Results: Using practical examples accompanied by Python scripts, this study demonstrated the application of quadratic polynomials to analyze data patterns. These examples illustrate the utility of quadratic models in applied analytics. Conclusions: This study bridges the gap between theoretical mathematical concepts and practical data analysis, thereby enhancing the understanding and interpretation of the data patterns. Furthermore, its implementation in Python, released under MIT license, offers an accessible tool for public use.

As deep neural networks are more commonly deployed in high-stakes domains, their black-box nature makes uncertainty quantification challenging. We investigate the presentation of conformal prediction sets--a distribution-free class of methods for generating prediction sets with specified coverage--to express uncertainty in AI-advised decision-making. Through a large online experiment, we compare the utility of conformal prediction sets to displays of Top-1 and Top-k predictions for AI-advised image labeling. In a pre-registered analysis, we find that the utility of prediction sets for accuracy varies with the difficulty of the task: while they result in accuracy on par with or less than Top-1 and Top-k displays for easy images, prediction sets offer some advantage in assisting humans in labeling out-of-distribution (OOD) images in the setting that we studied, especially when the set size is small. Our results empirically pinpoint practical challenges of conformal prediction sets and provide implications on how to incorporate them for real-world decision-making.

With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.

We introduce a hybrid method that integrates deep learning with model-analog forecasting, a straightforward yet effective approach that generates forecasts from similar initial climate states in a repository of model simulations. This hybrid framework employs a convolutional neural network to estimate state-dependent weights to identify analog states. The advantage of our method lies in its physical interpretability, offering insights into initial-error-sensitive regions through estimated weights and the ability to trace the physically-based temporal evolution of the system through analog forecasting. We evaluate our approach using the Community Earth System Model Version 2 Large Ensemble to forecast the El Ni\~no-Southern Oscillation (ENSO) on a seasonal-to-annual time scale. Results show a 10% improvement in forecasting sea surface temperature anomalies over the equatorial Pacific at 9-12 months leads compared to the traditional model-analog technique. Furthermore, our hybrid model demonstrates improvements in boreal winter and spring initialization when evaluated against a reanalysis dataset. Our deep learning-based approach reveals state-dependent sensitivity linked to various seasonally varying physical processes, including the Pacific Meridional Modes, equatorial recharge oscillator, and stochastic wind forcing. Notably, disparities emerge in the sensitivity associated with El Ni\~no and La Ni\~na events. We find that sea surface temperature over the tropical Pacific plays a more crucial role in El Ni\~no forecasting, while zonal wind stress over the same region exhibits greater significance in La Ni\~na prediction. This approach has broad implications for forecasting diverse climate phenomena, including regional temperature and precipitation, which are challenging for the traditional model-analog forecasting method.

In the context of imitation learning applied to dexterous robotic hands, the high complexity of the systems makes learning complex manipulation tasks challenging. However, the numerous datasets depicting human hands in various different tasks could provide us with better knowledge regarding human hand motion. We propose a method to leverage multiple large-scale task-agnostic datasets to obtain latent representations that effectively encode motion subtrajectories that we included in a transformer-based behavior cloning method. Our results demonstrate that employing latent representations yields enhanced performance compared to conventional behavior cloning methods, particularly regarding resilience to errors and noise in perception and proprioception. Furthermore, the proposed approach solely relies on human demonstrations, eliminating the need for teleoperation and, therefore, accelerating the data acquisition process. Accurate inverse kinematics for fingertip retargeting ensures precise transfer from human hand data to the robot, facilitating effective learning and deployment of manipulation policies. Finally, the trained policies have been successfully transferred to a real-world 23Dof robotic system.

Domain generalization focuses on leveraging knowledge from multiple related domains with ample training data and labels to enhance inference on unseen in-distribution (IN) and out-of-distribution (OOD) domains. In our study, we introduce a two-phase representation learning technique using multi-task learning. This approach aims to cultivate a latent space from features spanning multiple domains, encompassing both native and cross-domains, to amplify generalization to IN and OOD territories. Additionally, we attempt to disentangle the latent space by minimizing the mutual information between the prior and latent space, effectively de-correlating spurious feature correlations. Collectively, the joint optimization will facilitate domain-invariant feature learning. We assess the model's efficacy across multiple cybersecurity datasets, using standard classification metrics on both unseen IN and OOD sets, and juxtapose the results with contemporary domain generalization methods.

The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

Influenced by the stunning success of deep learning in computer vision and language understanding, research in recommendation has shifted to inventing new recommender models based on neural networks. In recent years, we have witnessed significant progress in developing neural recommender models, which generalize and surpass traditional recommender models owing to the strong representation power of neural networks. In this survey paper, we conduct a systematic review on neural recommender models, aiming to summarize the field to facilitate future progress. Distinct from existing surveys that categorize existing methods based on the taxonomy of deep learning techniques, we instead summarize the field from the perspective of recommendation modeling, which could be more instructive to researchers and practitioners working on recommender systems. Specifically, we divide the work into three types based on the data they used for recommendation modeling: 1) collaborative filtering models, which leverage the key source of user-item interaction data; 2) content enriched models, which additionally utilize the side information associated with users and items, like user profile and item knowledge graph; and 3) context enriched models, which account for the contextual information associated with an interaction, such as time, location, and the past interactions. After reviewing representative works for each type, we finally discuss some promising directions in this field, including benchmarking recommender systems, graph reasoning based recommendation models, and explainable and fair recommendations for social good.