Forecast-Then-Optimize Deep Learning Methods

Time series forecasting underpins vital decision-making across various sectors, yet raw predictions from sophisticated models often harbor systematic errors and biases. We examine the Forecast-Then-Optimize (FTO) framework, pioneering its systematic synopsis. Unlike conventional Predict-Then-Optimize (PTO) methods, FTO explicitly refines forecasts through optimization techniques such as ensemble methods, meta-learners, and uncertainty adjustments. Furthermore, deep learning and large language models have established superiority over traditional parametric forecasting models for most enterprise applications. This paper surveys significant advancements from 2016 to 2025, analyzing mainstream deep learning FTO architectures. Focusing on real-world applications in operations management, we demonstrate FTO's crucial role in enhancing predictive accuracy, robustness, and decision efficacy. Our study establishes foundational guidelines for future forecasting methodologies, bridging theory and operational practicality.

Parallel Algorithms for Exact Enumeration of Deep Neural Network Activation Regions

A feedforward neural network using rectified linear units constructs a mapping from inputs to outputs by partitioning its input space into a set of convex regions where points within a region share a single affine transformation. In order to understand how neural networks work, when and why they fail, and how they compare to biological intelligence, we need to understand the organization and formation of these regions. Step one is to design and implement algorithms for exact region enumeration in networks beyond toy examples. In this work, we present parallel algorithms for exact enumeration in deep (and shallow) neural networks. Our work has three main contributions: (1) we present a novel algorithm framework and parallel algorithms for region enumeration; (2) we implement one of our algorithms on a variety of network architectures and experimentally show how the number of regions dictates runtime; and (3) we show, using our algorithm's output, how the dimension of a region's affine transformation impacts further partitioning of the region by deeper layers. To our knowledge, we run our implemented algorithm on networks larger than all of the networks used in the existing region enumeration literature. Further, we experimentally demonstrate the importance of parallelism for region enumeration of any reasonably sized network.