We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the $\phi^4$ theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Furthermore, we demonstrate that our model can learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalizations further accentuate the advantages of machine learning methods.

Robust travel time predictions are of prime importance in managing any transportation infrastructure, and particularly in rail networks where they have major impacts both on traffic regulation and passenger satisfaction. We aim at predicting the travel time of trains on rail sections at the scale of an entire rail network in real-time, by estimating trains' delays relative to a theoretical circulation plan. Predicting the evolution of a given train's delay is a uniquely hard problem, distinct from mainstream road traffic forecasting problems, since it involves several hard-to-model phenomena: train spacing, station congestion and heterogeneous rolling stock among others. We first offer empirical evidence of the previously unexplored phenomenon of delay propagation at the scale of a railway network, leading to delays being amplified by interactions between trains and the network's physical limitations. We then contribute a novel technique using the transformer architecture and pre-trained embeddings to make real-time massively parallel predictions for train delays at the scale of the whole rail network (over 3000 trains at peak hours, making predictions at an average horizon of 70 minutes). Our approach yields very positive results on real-world data when compared to currently-used and experimental prediction techniques.

We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state forward in time, and we investigate how estimators of these operators perform on long-term forecasting. Motivated by the observation that standard estimators may fail at this task, we introduce a learning paradigm that neatly combines classical techniques of eigenvalue deflation from operator theory and feature centering from statistics. This paradigm applies to any operator estimator based on empirical risk minimization, making them satisfy learning bounds which hold uniformly on the entire trajectory of future distributions, and abide to the conservation of mass for each of the forecasted distributions. Numerical experiments illustrates the advantages of our approach in practice.

Development of comprehensive prediction models are often of great interest in many disciplines of science, but datasets with information on all desired features typically have small sample sizes. In this article, we describe a transfer learning approach for building high-dimensional generalized linear models using data from a main study that has detailed information on all predictors, and from one or more external studies that have ascertained a more limited set of predictors. We propose using the external dataset(s) to build reduced model(s) and then transfer the information on underlying parameters for the analysis of the main study through a set of calibration equations, while accounting for the study-specific effects of certain design variables. We then use a generalized method of moment (GMM) with penalization for parameter estimation and develop highly scalable algorithms for fitting models taking advantage of the popular glmnet package. We further show that the use of adaptive-Lasso penalty leads to the oracle property of underlying parameter estimates and thus leads to convenient post-selection inference procedures. We conduct extensive simulation studies to investigate both predictive performance and post-selection inference properties of the proposed method. Finally, we illustrate a timely application of the proposed method for the development of risk prediction models for five common diseases using the UK Biobank study, combining baseline information from all study participants (500K) and recently released high-throughout proteomic data (# protein = 1500) on a subset (50K) of the participants.

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit intrinsic correlations over time. Capitalizing on this, we introduce Correlation Mode Decomposition (CMD). This algorithm clusters the parameter space into groups, termed modes, that display synchronized behavior across epochs. This enables CMD to efficiently represent the training dynamics of complex networks, like ResNets and Transformers, using only a few modes. Moreover, test set generalization is enhanced. We introduce an efficient CMD variant, designed to run concurrently with training. Our experiments indicate that CMD surpasses the state-of-the-art method for compactly modeled dynamics on image classification. Our modeling can improve training efficiency and lower communication overhead, as shown by our preliminary experiments in the context of federated learning.

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and editable 3D radiance field.

In many practical computer vision scenarios unlabeled data is plentiful, but labels are scarce and difficult to obtain. As a result, semi-supervised learning which leverages unlabeled data to boost the performance of supervised classifiers have received significant attention in recent literature. One major class of semi-supervised algorithms is co-training. In co-training two different models leverage different independent and sufficient "views" of the data to jointly make better predictions. During co-training each model creates pseudo labels on unlabeled points which are used to improve the other model. We show that in the common case when independent views are not available we can construct such views inexpensively using pre-trained models. Co-training on the constructed views yields a performance improvement over any of the individual views we construct and performance comparable with recent approaches in semi-supervised learning, but has some undesirable properties. To alleviate the issues present with co-training we present Meta Co-Training which is an extension of the successful Meta Pseudo Labels approach to two views. Our method achieves new state-of-the-art performance on ImageNet-10% with very few training resources, as well as outperforming prior semi-supervised work on several other fine-grained image classification datasets.

We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on algebraic properties, our algorithm exploits the regularity of the target function intrinsic in the decay of its Fourier spectrum. By defining a tractable family of models, we allow at the same time to obtain precise certificates and to leverage the advanced and powerful computational techniques developed to optimize neural networks. In this way the scalability of our approach is naturally enhanced by parallel computing with GPUs. Our approach, when applied to the case of polynomials of moderate dimensions but with thousands of coefficients, outperforms the state-of-the-art optimization methods with certificates, as the ones based on Lasserre's hierarchy, addressing problems intractable for the competitors.

Through this paper, we introduce a novel driver cognitive load assessment dataset, CL-Drive, which contains Electroencephalogram (EEG) signals along with other physiological signals such as Electrocardiography (ECG) and Electrodermal Activity (EDA) as well as eye tracking data. The data was collected from 21 subjects while driving in an immersive vehicle simulator, in various driving conditions, to induce different levels of cognitive load in the subjects. The tasks consisted of 9 complexity levels for 3 minutes each. Each driver reported their subjective cognitive load every 10 seconds throughout the experiment. The dataset contains the subjective cognitive load recorded as ground truth. In this paper, we also provide benchmark classification results for different machine learning and deep learning models for both binary and ternary label distributions. We followed 2 evaluation criteria namely 10-fold and leave-one-subject-out (LOSO). We have trained our models on both hand-crafted features as well as on raw data.

Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened our capabilities in terms of revealing common random factors from multiview datasets. In this work, we first revisit the most recent deterministic extensions of deep CCA and highlight the strengths and limitations of these state-of-the-art methods. Some methods allow trivial solutions, while others can miss weak common factors. Others overload the problem by also seeking to reveal what is not common among the views -- i.e., the private components that are needed to fully reconstruct each view. The latter tends to overload the problem and its computational and sample complexities. Aiming to improve upon these limitations, we design a novel and efficient formulation that alleviates some of the current restrictions. The main idea is to model the private components as conditionally independent given the common ones, which enables the proposed compact formulation. In addition, we also provide a sufficient condition for identifying the common random factors. Judicious experiments with synthetic and real datasets showcase the validity of our claims and the effectiveness of the proposed approach.