Tabular data is hard to acquire and is subject to missing values. This paper introduces a novel approach for generating and imputing mixed-type (continuous and categorical) tabular data utilizing score-based diffusion and conditional flow matching. In contrast to prior methods that rely on neural networks to learn the score function or the vector field, we adopt XGBoost, a widely used Gradient-Boosted Tree (GBT) technique. To test our method, we build one of the most extensive benchmarks for tabular data generation and imputation, containing 27 diverse datasets and 9 metrics. Through empirical evaluation across the benchmark, we demonstrate that our approach outperforms deep-learning generation methods in data generation tasks and remains competitive in data imputation. Notably, it can be trained in parallel using CPUs without requiring a GPU. Our Python and R code is available at \url{https://github.com/SamsungSAILMontreal/ForestDiffusion}.

The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce \foldflow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions---i.e. the group $\mathrm{SE(3)}$---enabling accurate modeling of protein backbones. We first introduce $\text{FoldFlow-Base}$, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\mathrm{SE(3)}$. We next accelerate training by incorporating Riemannian optimal transport to create $\text{FoldFlow-OT}$, leading to the construction of both more simple and stable flows. Finally, we design \foldflowsfm, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\mathrm{SE(3)}$. Our family of $\text{FoldFlow}$, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\mathrm{SE(3)}$. Empirically, we validate $\text{FoldFlow}$, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples.

Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural networks. This efficiency, however, contrasts with the non-convex and seemingly complex structure of neural loss landscapes. In this study, we delve into the fundamental geometric properties of sampled gradients along optimization paths. We focus on two key quantities, the restricted secant inequality and error bound, as well as their ratio γ, which hold high significance for first-order optimization. Our analysis reveals that these quantities exhibit predictable, consistent behavior throughout training, despite the stochasticity induced by sampling minibatches. Our findings suggest that not only do optimization trajectories never encounter significant obstacles, but they also maintain stable dynamics during the majority of training. These observed properties are sufficiently expressive to theoretically guarantee linear convergence and prescribe learning rate schedules mirroring empirical practices. We conduct our experiments on image classification, semantic segmentation and language modeling across different batch sizes, network architectures, datasets, optimizers, and initialization seeds. We discuss the impact of each factor. Our work provides novel insights into the properties of neural network loss functions, and opens the door to theoretical frameworks more relevant to prevalent practice.

Proteins are essential for almost all biological processes and derive their diverse functions from complex $3 \rm D$ structures, which are in turn determined by their amino acid sequences. In this paper, we exploit the rich biological inductive bias of amino acid sequences and introduce FoldFlow++, a novel sequence-conditioned $\text{SE}(3)$-equivariant flow matching model for protein structure generation. FoldFlow++ presents substantial new architectural features over the previous FoldFlow family of models including a protein large language model to encode sequence, a new multi-modal fusion trunk that combines structure and sequence representations, and a geometric transformer based decoder. To increase diversity and novelty of generated samples -- crucial for de-novo drug design -- we train FoldFlow++ at scale on a new dataset that is an order of magnitude larger than PDB datasets of prior works, containing both known proteins in PDB and high-quality synthetic structures achieved through filtering. We further demonstrate the ability to align FoldFlow++ to arbitrary rewards, e.g. increasing secondary structures diversity, by introducing a Reinforced Finetuning (ReFT) objective. We empirically observe that FoldFlow++ outperforms previous state-of-the-art protein structure-based generative models, improving over RFDiffusion in terms of unconditional generation across all metrics including designability, diversity, and novelty across all protein lengths, as well as exhibiting generalization on the task of equilibrium conformation sampling. Finally, we demonstrate that a fine-tuned FoldFlow++ makes progress on challenging conditional design tasks such as designing scaffolds for the VHH nanobody.

Noisy labels often occur in vision datasets, especially when they are obtained from crowdsourcing or Web scraping. We propose a new regularization method, which enables learning robust classifiers in presence of noisy data. To achieve this goal, we propose a new adversarial regularization scheme based on the Wasserstein distance. Using this distance allows taking into account specific relations between classes by leveraging the geometric properties of the labels space. Our Wasserstein Adversarial Regularization (WAR) encodes a selective regularization, which promotes smoothness of the classifier between some classes, while preserving sufficient complexity of the decision boundary between others. We first discuss how and why adversarial regularization can be used in the context of noise and then show the effectiveness of our method on five datasets corrupted with noisy labels: in both benchmarks and real datasets, WAR outperforms the state-of-the-art competitors.

Over the last years, remote sensing image (RSI) analysis has started resorting to using deep neural networks to solve most of the commonly faced problems, such as detection, land cover classification, or segmentation. As far as critical decision-making can be based upon the results of RSI analysis, it is important to clearly identify and understand potential security threats occurring in those machine learning algorithms. Notably, it has recently been found that neural networks are particularly sensitive to carefully designed attacks, generally crafted given the full knowledge of the considered deep network. In this article, we consider the more realistic but challenging case where one wants to generate such attacks in the case of a black-box neural network. In this case, only the prediction score of the network is accessible, on a specific dataset. Examples that lure away the network’s prediction, while being perceptually similar to real images, are called natural or unrestricted adversarial examples. We present an original method to generate such examples based on a variant of the Wasserstein generative adversarial network. We demonstrate its effectiveness on natural adversarial hyperspectral image generation and image modification for fooling a state-of-the-art detector. Among others, we also conduct a perceptual evaluation with human annotators to better assess the effectiveness of the proposed method. Our code is available for the community:https://github.com/PythonOT/ARWGAN.

Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, i.e. minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behaviors. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.

Optimal transport has recently been reintroduced to the machine learning community thanks in part to novel efficient optimization procedures allowing for medium to large scale applications. We propose a Python toolbox that implements several key optimal transport ideas for the machine learning community. The toolbox contains implementations of a number of founding works of OT for machine learning such as Sinkhorn algorithm and Wasserstein barycenters, but also provides generic solvers that can be used for conducting novel fundamental research. This toolbox, named POT for Python Optimal Transport, is open source with an MIT license.

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this challenge, practitioners compute these distances on minibatches i.e., they average the outcome of several smaller optimal transport problems. We propose in this paper an analysis of this practice, which effects are not well understood so far. We notably argue that it is equivalent to an implicit regularization of the original problem, with appealing properties such as unbiased estimators, gradients and a concentration bound around the expectation, but also with defects such as loss of distance property. Along with this theoretical analysis, we also conduct empirical experiments on gradient flows, GANs or color transfer that highlight the practical interest of this strategy.

Despite the raise to fame of stochastic variance reduced methods like SAGA and ProxSVRG, their use in non-smooth optimization is still limited to a few simple cases. Existing methods require to compute the proximal operator of the non-smooth term at each iteration, which, for complex penalties like the total variation, overlapping group lasso or trend filtering, is an iterative process that becomes unfeasible for moderately large problems. In this work we propose and analyze VRTOS, a variance-reduced method to solve problems with an arbitrary number of non-smooth terms. Like other variance reduced methods, it only requires to evaluate one gradient per iteration and converges with a constant step size, and so is ideally suited for large scale applications. Unlike existing variance reduced methods, it admits multiple non-smooth terms whose proximal operator only needs to be evaluated once per iteration. We provide a convergence rate analysis for the proposed methods that achieves the same asymptotic rate as their full gradient variants and illustrate its computational advantage on 4 different large scale datasets.