Chaotic dynamics are ubiquitous in many real-world systems, ranging from biological and industrial processes to climate dynamics and the spread of viruses. These systems are characterized by high sensitivity to initial conditions, making it challenging to predict their future behavior confidently. In this study, we propose a novel deep-learning framework that addresses this challenge by directly exploiting the long-term compounding of local prediction errors during model training, aiming to extend the time horizon for reliable predictions of chaotic systems. Our approach observes the future trajectories of initial errors at a time horizon, modeling the evolution of the loss to that point through the use of two major components: (1) a recurrent architecture (Error Trajectory Tracing) designed to trace the trajectories of predictive errors through phase space, and (2) a training regime, Horizon Forcing, that pushes the model’s focus out to a predetermined time horizon. We validate our method on three classic chaotic systems and six real-world time series prediction tasks with chaotic characteristics. The results show that our approach outperforms the state-of-the-art methods.

Diabetic Retinopathy (DR) is a leading cause of vision impairment globally, making accurate and efficient detection of DR stages from ophthalmological images critical for early diagnosis and treatment. In this study, we develop and evaluate the efficacy of four state-of-the-art deep learning models for classifying DR stages: a custom Convolutional Neural Network (CNN), VGG19, ResNet50, and Vision Transformer (ViT). These models are systematically applied to the Brazilian Multi-label Ophthalmological Dataset (BRSET), which consists of 16,266 retinal fundus images categorized into different DR severity levels. Each model’s performance is assessed based on metrics such as accuracy, F1-score, and AUC-ROC. Our results provide a comprehensive comparison of these architectures, highlighting their strengths and limitations in DR stage estimation, and offer insights into the suitability of these models for large-scale DR screening.

Effective early warning systems for extreme flood events in large river basins necessitate reliable long-lead streamflow forecasts. However, the inherent uncertainty within each phase of the weather system-rainfall prediction, runoff generation, and streamflow prediction-amplifies with each stage, rendering accurate long-lead streamflow estimations challenging. In response to this, our study introduces a novel deep-learning-based model, the Cascaded Spatio-Temporal Learning Deep Network (CASTLE). CASTLE synergistically integrates observed upstream precipitation, recent streamflow data, and short-term precipitation forecasts derived from a selection of quantitative climate models to produce an accurate streamflow estimate. Specifically, we employ deep residual architectures on both observed and forecasted precipitation data to model the cascading spatio-temporal processes, which begin with upstream rainfall, move to rainfall-runoff, and finally conclude with downstream discharge. Our aim is to identify hidden space-time patterns that can be used to forecast future downstream flow over extended periods. We assess CASTLE’s efficacy by forecasting the downstream discharge of the Ganges River over a long lead time. Results show that our approach outperforms the current state-of-the-art streamflow forecasting models.

The understanding of chaotic systems is challenging not only for theoretical research but also for many important applications. Chaotic behavior is found in many nonlinear dynamical systems, such as those found in climate dynamics, weather, the stock market, and the space-time dynamics of virus spread. A reliable solution for these systems must handle their complex space-time dynamics and sensitive dependence on initial conditions. We develop a deep learning framework to push the time horizon at which reliable predictions can be made further into the future by better evaluating the consequences of local errors when modeling nonlinear systems. Our approach observes the future trajectories of initial errors at a time horizon to model the evolution of the loss to that point with two major components: 1) a recurrent architecture, Error Trajectory Tracing, that is designed to trace the trajectories of predictive errors through phase space, and 2) a training regime, Horizon Forcing, that pushes the model’s focus out to a predetermined time horizon. We validate our method on classic chaotic systems and real-world time series prediction tasks with chaotic characteristics, and show that our approach outperforms the current state-of-the-art methods.

The study of model bias and variance with respect to decision boundaries is critically important in supervised learning and artificial intelligence. There is generally a tradeoff between the two, as fine-tuning of the decision boundary of a classification model to accommodate more boundary training samples (i.e., higher model complexity) may improve training accuracy (i.e., lower bias) but hurt generalization against unseen data (i.e., higher variance). By focusing on just classification boundary fine-tuning and model complexity, it is difficult to reduce both bias and variance. To overcome this dilemma, we take a different perspective and investigate a new approach to handle inaccuracy and uncertainty in the training data labels, which are inevitable in many applications where labels are conceptual entities and labeling is performed by human annotators. The process of classification can be undermined by uncertainty in the labels of the training data; extending a boundary to accommodate an inaccurately labeled point will increase both bias and variance. Our novel method can reduce both bias and variance by estimating the pointwise label uncertainty of the training set and accordingly adjusting the training sample weights such that those samples with high uncertainty are weighted down and those with low uncertainty are weighted up. In this way, uncertain samples have a smaller contribution to the objective function of the model’s learning algorithm and exert less pull on the decision boundary. In a real-world physical activity recognition case study, the data present many labeling challenges, and we show that this new approach improves model performance and reduces model variance.

It is well known that a direct parallelization of sequential optimization methods (e.g., coordinate descent and stochastic gradient methods) is often not effective. The reason is that at each iteration, the number of operations may be too small. We point out that this common understanding may not be true if the algorithm sequentially accesses the data in a feature-wise manner. For almost all real-world sparse sets we have examined, some features are much denser than others. Thus a direct parallelization of loops in a sequential method may result in excellent speedup. This approach possesses an advantage of retaining all convergence results because the algorithm is not changed at all. We apply this idea on coordinate descent (CD) methods, which are effective single-thread technique for L1-regularized classification. Further, an investigation on the shrinking technique commonly used to remove some features in the training process shows that this technique helps the parallelization of CD methods. Experiments indicate that a naive parallelization achieves better speedup than existing methods that laboriously modify the algorithm to achieve parallelism. Though a bit ironic, we conclude that the naive parallelization of the CD method is a highly competitive and robust multi-core implementation for L1-regularized classification.

Click-through rate (CTR) prediction plays an important role in computational advertising. Models based on degree-2 polynomial mappings and factorization machines (FMs) are widely used for this task. Recently, a variant of FMs, field-aware factorization machines (FFMs), outperforms existing models in some world-wide CTR-prediction competitions. Based on our experiences in winning two of them, in this paper we establish FFMs as an effective method for classifying large sparse data including those from CTR prediction. First, we propose efficient implementations for training FFMs. Then we comprehensively analyze FFMs and compare this approach with competing models. Experiments show that FFMs are very useful for certain classification problems. Finally, we have released a package of FFMs for public use.

Matrix factorization is known to be an effective method for recommender systems that are given only the ratings from users to items. Currently, stochastic gradient (SG) method is one of the most popular algorithms for matrix factorization. However, as a sequential approach, SG is difficult to be parallelized for handling web-scale problems. In this article, we develop a fast parallel SG method, FPSG, for shared memory systems. By dramatically reducing the cache-miss rate and carefully addressing the load balance of threads, FPSG is more efficient than state-of-the-art parallel algorithms for matrix factorization.

Matrix factorization is known to be an effective method for recommender systems that are given only the ratings from users to items. Currently, stochastic gradient descent (SGD) is one of the most popular algorithms for matrix factorization. However, as a sequential approach, SGD is difficult to be parallelized for handling web-scale problems. In this paper, we develop a fast parallel SGD method, FPSGD, for shared memory systems. By dramatically reducing the cache-miss rate and carefully addressing the load balance of threads, FPSGD is more efficient than state-of-the-art parallel algorithms for matrix factorization.