Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of transition paths using a random walk in trajectory space. This, however, comes with the drawback of strong correlations between subsequently sampled paths and with an intrinsic difficulty in parallelizing the sampling process. We propose a transition path sampling scheme based on neural-network generated configurations. These are obtained employing normalizing flows, a neural network class able to generate statistically independent samples from a given distribution. With this approach, not only are correlations between visited paths removed, but the sampling process becomes easily parallelizable. Moreover, by conditioning the normalizing flow, the sampling of configurations can be steered towards regions of interest. We show that this approach enables the resolution of both the thermodynamics and kinetics of the transition region.
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Objective: Finding events of interest is a common task in biomedical signal processing. The detection of epileptic seizures and signal artefacts are two key examples. Epoch-based classification is the typical machine learning framework to detect such signal events because of the straightforward application of classical machine learning techniques. Usually, post-processing is required to achieve good performance and enforce temporal dependencies. Designing the right post-processing scheme to convert these classification outputs into events is a tedious, and labor-intensive element of this framework. Methods: We propose an event-based modeling framework that directly works with events as learning targets, stepping away from ad-hoc post-processing schemes to turn model outputs into events. We illustrate the practical power of this framework on simulated data and real-world data, comparing it to epoch-based modeling approaches. Results: We show that event-based modeling (without post-processing) performs on par with or better than epoch-based modeling with extensive post-processing. Conclusion: These results show the power of treating events as direct learning targets, instead of using ad-hoc post-processing to obtain them, severely reducing design effort. Significance: The event-based modeling framework can easily be applied to other event detection problems in signal processing, removing the need for intensive task-specific post-processing.
In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution regression are probability measures. Then we often need to perform a second-stage sampling process to approximate the actual information of the distribution. On the other hand, the classical neural network structure requires the input variable to be a vector. When the input samples are probability distributions, the traditional deep neural network method cannot be directly used and the difficulty arises for distribution regression. A well-defined neural network structure for distribution inputs is intensively desirable. There is no mathematical model and theoretical analysis on neural network realization of distribution regression. To overcome technical difficulties and address this issue, we establish a novel fully connected neural network framework to realize an approximation theory of functionals defined on the space of Borel probability measures. Furthermore, based on the established functional approximation results, in the hypothesis space induced by the novel FNN structure with distribution inputs, almost optimal learning rates for the proposed distribution regression model up to logarithmic terms are derived via a novel two-stage error decomposition technique.
In this work we introduce $\nu^2$-Flows, an extension of the $\nu$-Flows method to final states containing multiple neutrinos. The architecture can natively scale for all combinations of object types and multiplicities in the final state for any desired neutrino multiplicities. In $t\bar{t}$ dilepton events, the momenta of both neutrinos and correlations between them are reconstructed more accurately than when using the most popular standard analytical techniques, and solutions are found for all events. Inference time is significantly faster than competing methods, and can be reduced further by evaluating in parallel on graphics processing units. We apply $\nu^2$-Flows to $t\bar{t}$ dilepton events and show that the per-bin uncertainties in unfolded distributions is much closer to the limit of performance set by perfect neutrino reconstruction than standard techniques. For the chosen double differential observables $\nu^2$-Flows results in improved statistical precision for each bin by a factor of 1.5 to 2 in comparison to the Neutrino Weighting method and up to a factor of four in comparison to the Ellipse approach.
Recently, the performance of neural image compression (NIC) has steadily improved thanks to the last line of study, reaching or outperforming state-of-the-art conventional codecs. Despite significant progress, current NIC methods still rely on ConvNet-based entropy coding, limited in modeling long-range dependencies due to their local connectivity and the increasing number of architectural biases and priors, resulting in complex underperforming models with high decoding latency. Motivated by the efficiency investigation of the Tranformer-based transform coding framework, namely SwinT-ChARM, we propose to enhance the latter, as first, with a more straightforward yet effective Tranformer-based channel-wise auto-regressive prior model, resulting in an absolute image compression transformer (ICT). Through the proposed ICT, we can capture both global and local contexts from the latent representations and better parameterize the distribution of the quantized latents. Further, we leverage a learnable scaling module with a sandwich ConvNeXt-based pre-/post-processor to accurately extract more compact latent codes while reconstructing higher-quality images. Extensive experimental results on benchmark datasets showed that the proposed framework significantly improves the trade-off between coding efficiency and decoder complexity over the versatile video coding (VVC) reference encoder (VTM-18.0) and the neural codec SwinT-ChARM. Moreover, we provide model scaling studies to verify the computational efficiency of our approach and conduct several objective and subjective analyses to bring to the fore the performance gap between the adaptive image compression transformer (AICT) and the neural codec SwinT-ChARM.
Data reduction is a fundamental challenge of modern technology, where classical statistical methods are not applicable because of computational limitations. We consider linear regression for an extraordinarily large number of observations, but only a few covariates. Subsampling aims at the selection of a given percentage of the existing original data. Under distributional assumptions on the covariates, we derive D-optimal subsampling designs and study their theoretical properties. We make use of fundamental concepts of optimal design theory and an equivalence theorem from constrained convex optimization. The thus obtained subsampling designs provide simple rules for whether to accept or reject a data point, allowing for an easy algorithmic implementation. In addition, we propose a simplified subsampling method that differs from the D-optimal design but requires lower computing time. We present a simulation study, comparing both subsampling schemes with the IBOSS method.
Generative models can be categorized into two types: explicit generative models that define explicit density forms and allow exact likelihood inference, such as score-based diffusion models (SDMs) and normalizing flows; implicit generative models that directly learn a transformation from the prior to the data distribution, such as generative adversarial nets (GANs). While these two types of models have shown great success, they suffer from respective limitations that hinder them from achieving fast sampling and high sample quality simultaneously. In this paper, we propose a unified theoretic framework for SDMs and GANs. We shown that: i) the learning dynamics of both SDMs and GANs can be described as a novel SDE named Discriminator Denoising Diffusion Flow (DiffFlow) where the drift can be determined by some weighted combinations of scores of the real data and the generated data; ii) By adjusting the relative weights between different score terms, we can obtain a smooth transition between SDMs and GANs while the marginal distribution of the SDE remains invariant to the change of the weights; iii) we prove the asymptotic optimality and maximal likelihood training scheme of the DiffFlow dynamics; iv) under our unified theoretic framework, we introduce several instantiations of the DiffFLow that provide new algorithms beyond GANs and SDMs with exact likelihood inference and have potential to achieve flexible trade-off between high sample quality and fast sampling speed.
The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional Boussinesq-Abbott system. The problem can be reduced to a transmission problem for this Boussinesq system, in which the transmission conditions between the components of the domain at the left and at the right of the object are determined through the resolution of coupled forced ODEs in time satisfied by the vertical displacement of the object and the average discharge in the portion of the fluid located under the object. We propose a new extended formulation in which these ODEs are complemented by two other forced ODEs satisfied by the trace of the surface elevation at the contact points. The interest of this new extended formulation is that the forcing terms are easy to compute numerically and that the surface elevation at the contact points is furnished for free. Based on this formulation, we propose a second order scheme that involves a generalization of the MacCormack scheme with nonlocal flux and a source term, which is coupled to a second order Heun scheme for the ODEs. In order to validate this scheme, several explicit solutions for this wave-structure interaction problem are derived and can serve as benchmark for future codes. As a byproduct, our method provides a second order scheme for the generation of waves at the entrance of the numerical domain for the Boussinesq-Abbott system.
Transshipment, also known under the names of earth mover's distance, uncapacitated min-cost flow, or Wasserstein's metric, is an important and well-studied problem that asks to find a flow of minimum cost that routes a general demand vector. Adding to its importance, recent advancements in our understanding of algorithms for transshipment have led to breakthroughs for the fundamental problem of computing shortest paths. Specifically, the recent near-optimal $(1+\varepsilon)$-approximate single-source shortest path algorithms in the parallel and distributed settings crucially solve transshipment as a central step of their approach. The key property that differentiates transshipment from other similar problems like shortest path is the so-called \emph{boosting}: one can boost a (bad) approximate solution to a near-optimal $(1 + \varepsilon)$-approximate solution. This conceptually reduces the problem to finding an approximate solution. However, not all approximations can be boosted -- there have been several proposed approaches that were shown to be susceptible to boosting, and a few others where boosting was left as an open question. The main takeaway of our paper is that any black-box $\alpha$-approximate transshipment solver that computes a \emph{dual} solution can be boosted to an $(1 + \varepsilon)$-approximate solver. Moreover, we significantly simplify and decouple previous approaches to transshipment (in sequential, parallel, and distributed settings) by showing all of them (implicitly) obtain approximate dual solutions. Our analysis is very simple and relies only on the well-known multiplicative weights framework. Furthermore, to keep the paper completely self-contained, we provide a new (and arguably much simpler) analysis of multiplicative weights that leverages well-known optimization tools to bypass the ad-hoc calculations used in the standard analyses.
Machine Learning (ML) models in Robotic Assembly Sequence Planning (RASP) need to be introspective on the predicted solutions, i.e. whether they are feasible or not, to circumvent potential efficiency degradation. Previous works need both feasible and infeasible examples during training. However, the infeasible ones are hard to collect sufficiently when re-training is required for swift adaptation to new product variants. In this work, we propose a density-based feasibility learning method that requires only feasible examples. Concretely, we formulate the feasibility learning problem as Out-of-Distribution (OOD) detection with Normalizing Flows (NF), which are powerful generative models for estimating complex probability distributions. Empirically, the proposed method is demonstrated on robotic assembly use cases and outperforms other single-class baselines in detecting infeasible assemblies. We further investigate the internal working mechanism of our method and show that a large memory saving can be obtained based on an advanced variant of NF.
Deep generative modelling is a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which making trade-offs including run-time, diversity, and architectural restrictions. In particular, this compendium covers energy-based models, variational autoencoders, generative adversarial networks, autoregressive models, normalizing flows, in addition to numerous hybrid approaches. These techniques are drawn under a single cohesive framework, comparing and contrasting to explain the premises behind each, while reviewing current state-of-the-art advances and implementations.
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