Many real-world vehicle routing problems involve rich sets of constraints with respect to the capacities of the vehicles, time windows for customers etc. While in recent years first machine learning models have been developed to solve basic vehicle routing problems faster than optimization heuristics, complex constraints rarely are taken into consideration. Due to their general procedure to construct solutions sequentially route by route, these methods generalize unfavorably to such problems. In this paper, we develop a policy model that is able to start and extend multiple routes concurrently by using attention on the joint action space of several tours. In that way the model is able to select routes and customers and thus learns to make difficult trade-offs between routes. In comprehensive experiments on three variants of the vehicle routing problem with time windows we show that our model called JAMPR works well for different problem sizes and outperforms the existing state-of-the-art constructive model. For two of the three variants it also creates significantly better solutions than a comparable meta-heuristic solver.

Model noise is known to have detrimental effects on neural networks, such as training instability and predictive distributions with non-calibrated uncertainty properties. These factors set bottlenecks on the expressive potential of Neural Stochastic Differential Equations (NSDEs), a model family that employs neural nets on both drift and diffusion functions. We introduce a novel algorithm that solves a generic NSDE using only deterministic approximation methods. Given a discretization, we estimate the marginal distribution of the It\^{o} process implied by the NSDE using a recursive scheme to propagate deterministic approximations of the statistical moments across time steps. The proposed algorithm comes with theoretical guarantees on numerical stability and convergence to the true solution, enabling its computational use for robust, accurate, and efficient prediction of long sequences. We observe our novel algorithm to behave interpretably on synthetic setups and to improve the state of the art on two challenging real-world tasks.

We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs must instead be learned from observations of optimal decisions. Learning from optimal decisions is a particularly challenging bi-level problem, and much of the related inverse optimization literature is dedicated to special cases. We tackle the general problem, learning all parameters jointly while allowing flexible parametrizations of costs, constraints, and loss functions. We also address challenges specific to learning linear programs, such as empty feasible regions and non-unique optimal decisions. Experiments show that our method successfully learns synthetic linear programs and minimum-cost multi-commodity flow instances for which previous methods are not directly applicable. We also provide a fast batch-mode PyTorch implementation of the homogeneous interior point algorithm, which supports gradients by implicit differentiation or backpropagation.

To increase the trustworthiness of deep neural network (DNN) classifiers, an accurate prediction confidence that represents the true likelihood of correctness is crucial. Towards this end, many post-hoc calibration methods have been proposed to leverage a lightweight model to map the target DNN's output layer into a calibrated confidence. Nonetheless, on an out-of-distribution (OOD) dataset in practice, the target DNN can often mis-classify samples with a high confidence, creating significant challenges for the existing calibration methods to produce an accurate confidence. In this paper, we propose a new post-hoc confidence calibration method, called CCAC (Confidence Calibration with an Auxiliary Class), for DNN classifiers on OOD datasets. The key novelty of CCAC is an auxiliary class in the calibration model which separates mis-classified samples from correctly classified ones, thus effectively mitigating the target DNN's being confidently wrong. We also propose a simplified version of CCAC to reduce free parameters and facilitate transfer to a new unseen dataset. Our experiments on different DNN models, datasets and applications show that CCAC can consistently outperform the prior post-hoc calibration methods.

Neural networks have historically been built layerwise from the set of functions in ${f: \mathbb{R}^n \to \mathbb{R}^m }$, i.e. with activations and weights/parameters represented by real numbers, $\mathbb{R}$. Our work considers a richer set of objects for activations and weights, and undertakes a comprehensive study of alternative algebras as number representations by studying their performance on two challenging problems: large-scale image classification using the ImageNet dataset and language modeling using the enwiki8 and WikiText-103 datasets. We denote this broader class of models as AlgebraNets. Our findings indicate that the conclusions of prior work, which explored neural networks constructed from $\mathbb{C}$ (complex numbers) and $\mathbb{H}$ (quaternions) on smaller datasets, do not always transfer to these challenging settings. However, our results demonstrate that there are alternative algebras which deliver better parameter and computational efficiency compared with $\mathbb{R}$. We consider $\mathbb{C}$, $\mathbb{H}$, $M_{2}(\mathbb{R})$ (the set of $2\times2$ real-valued matrices), $M_{2}(\mathbb{C})$, $M_{3}(\mathbb{R})$ and $M_{4}(\mathbb{R})$. Additionally, we note that multiplication in these algebras has higher compute density than real multiplication, a useful property in situations with inherently limited parameter reuse such as auto-regressive inference and sparse neural networks. We therefore investigate how to induce sparsity within AlgebraNets. We hope that our strong results on large-scale, practical benchmarks will spur further exploration of these unconventional architectures which challenge the default choice of using real numbers for neural network weights and activations.

In this paper, we develop an efficient sketchy empirical natural gradient method for large-scale finite-sum optimization problems from deep learning. The empirical Fisher information matrix is usually low-rank since the sampling is only practical on a small amount of data at each iteration. Although the corresponding natural gradient direction lies in a small subspace, both the computational cost and memory requirement are still not tractable due to the curse of dimensionality. We design randomized techniques for different neural network structures to resolve these challenges. For layers with a reasonable dimension, a sketching can be performed on a regularized least squares subproblem. Otherwise, since the gradient is a vectorization of the product between two matrices, we apply sketching on low-rank approximation of these matrices to compute the most expensive parts. Global convergence to stationary point is established under some mild assumptions. Numerical results on deep convolution networks illustrate that our method is quite competitive to the state-of-the-art methods such as SGD and KFAC.

Neural architecture search (NAS) is a widely popular area of machine learning, with the goal of automating the development of the best neural network for a given dataset. Hundreds of NAS algorithms have been proposed [10, 40], and with the release of two NAS benchmark datasets [8, 39], the extreme computational cost for NAS is no longer a barrier, and it is easier to fairly compare different NAS algorithms. Most of the recently proposed state-of-the-art algorithms are becoming increasingly more complex, many of which use neural networks as subroutines [35, 36]. This trend is problematic because as the complexity of NAS algorithms increases, the amount of necessary "hyper-hyperparameter tuning", or tuning the NAS algorithm itself, increases. Not only is this a vicious cycle (will we start using AutoML algorithms to tune AutoML algorithms?), but the runtime for any hyper-hyperparameter tuning on a new dataset must be added to the total runtime of the NAS algorithm [19, 38]. Since this information is not always recorded, some NAS algorithms may have under-reported runtimes, making it harder to compare different algorithms.

Abstract: We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals, giving rise to a powerful new approach for answering causal questions in imaging applications and beyond. The code for all our experiments is available at this https URL.

The original AI Dungeon was made just over a year ago, the result of a curious gamer, a hackathon, and the GPT-2 text transformer. Fast forward to the present day, and AI Dungeon has expanded into a unique example of creative AI technology. The game now boasts 1.5 million players, multiple genres for stories, and even multiplayer adventures. AI Dungeon is an AI-generated text adventure game in which players progress through the game by typing whatever they want. The game responds to player input thanks to a novel adaptation of GPT-2, an AI text transformer.

Running short on images to train your model? Here's how to increase your dataset size multi-fold with synthetic images using Image… It is quite a known fact that the quality and quantity of dataset used to train your model will have a direct effect on the model's performance. Availability of an extensive, versatile dataset could seal the deal, and you could jump to the next step of your Machine Learning / Deep Learning pipeline. But often you might end up in a situation where the dataset you need is just not readily available. Or the data you have is not enough to train a heavy duty model.