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Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the recently introduced empirical wavelets. We show that the adaptability of the empirical wavelet permits to reach better results than classic wavelets. In order to focus only on the textural information, we also propose to perform a cartoon + texture decomposition step before applying the segmentation algorithm. The proposed method is tested on six classic benchmarks, based on several popular texture images.

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion Models (DDMs) have been successfully adapted to solve such transport problems, resulting in CycleGAN and Bridge Matching respectively. However, these methods do not approximate Optimal Transport (OT) maps, which are known to have desirable properties. Existing techniques approximating OT maps for high-dimensional data-rich problems, such as DDM-based Rectified Flow and Schr\"odinger Bridge procedures, require fully training a DDM-type model at each iteration, or use mini-batch techniques which can introduce significant errors. We propose a novel algorithm to compute the Schr\"odinger Bridge, a dynamic entropy-regularised version of OT, that eliminates the need to train multiple DDM-like models. This algorithm corresponds to a discretisation of a flow of path measures, which we call the Schr\"odinger Bridge Flow, whose only stationary point is the Schr\"odinger Bridge. We demonstrate the performance of our algorithm on a variety of unpaired data translation tasks.

We present FLAMO, a Frequency-sampling Library for Audio-Module Optimization designed to implement and optimize differentiable linear time-invariant audio systems. The library is open-source and built on the frequency-sampling filter design method, allowing for the creation of differentiable modules that can be used stand-alone or within the computation graph of neural networks, simplifying the development of differentiable audio systems. It includes predefined filtering modules and auxiliary classes for constructing, training, and logging the optimized systems, all accessible through an intuitive interface. Practical application of these modules is demonstrated through two case studies: the optimization of an artificial reverberator and an active acoustics system for improved response smoothness.

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

Concrete domains have been introduced in the context of Description Logics to allow references to qualitative and quantitative values. In particular, the class of $\omega$-admissible concrete domains, which includes Allen's interval algebra, the region connection calculus (RCC8), and the rational numbers with ordering and equality, has been shown to yield extensions of $\mathcal{ALC}$ for which concept satisfiability w.r.t. a general TBox is decidable. In this paper, we present an algorithm based on type elimination and use it to show that deciding the consistency of an $\mathcal{ALC}(\mathfrak{D})$ ontology is ExpTime-complete if the concrete domain $\mathfrak{D}$ is $\omega$-admissible and its constraint satisfaction problem is decidable in exponential time. While this allows us to reason with concept and role assertions, we also investigate feature assertions $f(a,c)$ that can specify a constant $c$ as the value of a feature $f$ for an individual $a$. We show that, under conditions satisfied by all known $\omega$-admissible domains, we can add feature assertions without affecting the complexity., Comment: This is the extended version of a paper presented at DL 2024: 37th International Workshop on Description Logics

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

This article investigates applying advanced machine learning models, specifically LSTM and BERT, for text classification to predict multiple categories in the retail sector. The study demonstrates how applying data augmentation techniques and the focal loss function can significantly enhance accuracy in classifying products into multiple categories using a robust Brazilian retail dataset. The LSTM model, enriched with Brazilian word embedding, and BERT, known for its effectiveness in understanding complex contexts, were adapted and optimized for this specific task. The results showed that the BERT model, with an F1 Macro Score of up to $99\%$ for segments, $96\%$ for categories and subcategories and $93\%$ for name products, outperformed LSTM in more detailed categories. However, LSTM also achieved high performance, especially after applying data augmentation and focal loss techniques. These results underscore the effectiveness of NLP techniques in retail and highlight the importance of the careful selection of modelling and preprocessing strategies. This work contributes significantly to the field of NLP in retail, providing valuable insights for future research and practical applications.

Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct dynamical regimes during the backward generative diffusion process. The generative dynamics, starting from pure noise, encounters first a 'speciation' transition where the gross structure of data is unraveled, through a mechanism similar to symmetry breaking in phase transitions. It is followed at later time by a 'collapse' transition where the trajectories of the dynamics become attracted to one of the memorized data points, through a mechanism which is similar to the condensation in a glass phase. For any dataset, the speciation time can be found from a spectral analysis of the correlation matrix, and the collapse time can be found from the estimation of an 'excess entropy' in the data. The dependence of the collapse time on the dimension and number of data provides a thorough characterization of the curse of dimensionality for diffusion models. Analytical solutions for simple models like high-dimensional Gaussian mixtures substantiate these findings and provide a theoretical framework, while extensions to more complex scenarios and numerical validations with real datasets confirm the theoretical predictions., Comment: 22 pages, 11 figures

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has focused on scenarios where feasibility constraints are not given explicitly. Overlooking these constraints can lead to spurious solutions that are unrealistic in practice. To deal with such unknown constraints, we propose to perform optimization within the data manifold using diffusion models. To constrain the optimization process to the data manifold, we reformulate the original optimization problem as a sampling problem from the product of the Boltzmann distribution defined by the objective function and the data distribution learned by the diffusion model. Depending on the differentiability of the objective function, we propose two different sampling methods. For differentiable objectives, we propose a two-stage framework that begins with a guided diffusion process for warm-up, followed by a Langevin dynamics stage for further correction. For non-differentiable objectives, we propose an iterative importance sampling strategy using the diffusion model as the proposal distribution. Comprehensive experiments on a synthetic dataset, six real-world black-box optimization datasets, and a multi-objective molecule optimization dataset show that our method achieves better or comparable performance with previous state-of-the-art baselines.

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by estimating the time-reversal of this diffusion using score matching ideas. We follow here a similar strategy to sample from unnormalized probability densities and compute their normalizing constants. However, the time-reversed diffusion is here simulated by using an original iterative particle scheme relying on a novel score matching loss. Contrary to standard denoising diffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS) provides asymptotically consistent estimates under mild assumptions. We demonstrate PDDS on multimodal and high dimensional sampling tasks., Comment: To be published in ICML 2024. 37 pages, 20 figures, 3 tables, 5 algorithms

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness. We apply it to training energy-based models and finetuning denoising diffusions., Comment: 38 pages, 16 figures. Updated with additional experiments

The structure of the Small Magellanic Cloud (SMC) outside of its main body is characterised by tidal branches resulting from its interactions mainly with the Large Magellanic Cloud (LMC). Characterising the stellar populations in these tidal components helps to understand the dynamical history of this galaxy and of the Magellanic system in general. We provide full phase-space vector information for Southern Bridge clusters. We performed a photometric and spectroscopic analysis of twelve SMC clusters, doubling the number of SMC clusters with full phase-space vector information known to date. We reclassify the sample considering 3D distances and 3D velocities. We found that some of the clusters classified as Southern Bridge objects according to the projected 2D classification actually belong to the Main Body and Counter-Bridge in the background. The comparison of the kinematics of the genuine foreground Bridge clusters with those previously analysed in the same way reveals that Southern Bridge clusters are moving towards the LMC and share the kinematics of the Northern Bridge. Adding to our sample clusters from the literature with CaT metallicity determinations we compare the age-metallicity relation of the Southern Bridge with the one of the Northern Bridge. We reinforce the idea that both regions do not seem to have experienced the same chemical enrichment history and that there is a clear absence of clusters in the Northern Bridge older than 3Gyr and more metal-poor than -1.1, which would not seem to be due to a selection effect., Comment: 18 pages, 9 figures, accepted for publication in MNRAS

Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize beyond generative modeling and can be applied to learning stochastic (and deterministic) processes of arbitrary transfer tasks between two given distributions. In this paper, we highlight that while flow and bridge matching processes preserve the information of the marginal distributions, they do \emph{not} necessarily preserve the coupling information unless additional, stronger optimality conditions are met. This can be problematic if one aims at preserving the original empirical pairing. We show that a simple modification of the matching process recovers this coupling by augmenting the velocity field (or drift) with the information of the initial sample point. Doing so, we lose the Markovian property of the process but preserve the coupling information between distributions. We illustrate the efficiency of our augmentation in learning mixture of image translation tasks.

Two-sample testing decides whether two datasets are generated from the same distribution. This paper studies variable selection for two-sample testing, the task being to identify the variables (or dimensions) responsible for the discrepancies between the two distributions. This task is relevant to many problems of pattern analysis and machine learning, such as dataset shift adaptation, causal inference and model validation. Our approach is based on a two-sample test based on the Maximum Mean Discrepancy (MMD). We optimise the Automatic Relevance Detection (ARD) weights defined for individual variables to maximise the power of the MMD-based test. For this optimisation, we introduce sparse regularisation and propose two methods for dealing with the issue of selecting an appropriate regularisation parameter. One method determines the regularisation parameter in a data-driven way, and the other aggregates the results of different regularisation parameters. We confirm the validity of the proposed methods by systematic comparisons with baseline methods, and demonstrate their usefulness in exploratory analysis of high-dimensional traffic simulation data. Preliminary theoretical analyses are also provided, including a rigorous definition of variable selection for two-sample testing.

In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost that is orthogonal to sampling time. We tackle the question of how to improve diversity and sample efficiency by moving beyond the common assumption of independent samples. We propose particle guidance, an extension of diffusion-based generative sampling where a joint-particle time-evolving potential enforces diversity. We analyze theoretically the joint distribution that particle guidance generates, how to learn a potential that achieves optimal diversity, and the connections with methods in other disciplines. Empirically, we test the framework both in the setting of conditional image generation, where we are able to increase diversity without affecting quality, and molecular conformer generation, where we reduce the state-of-the-art median error by 13% on average.

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more generally, any target distribution whose density is known up to a normalizing constant. The key idea is to consider a forward ``noising'' diffusion initialized at the target distribution which ``transports'' this latter to a normal distribution for long diffusion times. The time-reversal of this process, the ``denoising'' diffusion, thus ``transports'' the normal distribution to the target distribution and can be approximated so as to sample from the target. To accelerate simulation, we show how one can introduce and approximate a Schr\"{o}dinger bridge between these two distributions, i.e. a diffusion which transports the normal to the target in finite time., Comment: 10 pages

Denoising diffusions are a powerful method to generate approximate samples from high-dimensional data distributions. Recent results provide polynomial bounds on their convergence rate, assuming $L^2$-accurate scores. Until now, the tightest bounds were either superlinear in the data dimension or required strong smoothness assumptions. We provide the first convergence bounds which are linear in the data dimension (up to logarithmic factors) assuming only finite second moments of the data distribution. We show that diffusion models require at most $\tilde O(\frac{d \log^2(1/\delta)}{\varepsilon^2})$ steps to approximate an arbitrary distribution on $\mathbb{R}^d$ corrupted with Gaussian noise of variance $\delta$ to within $\varepsilon^2$ in KL divergence. Our proof extends the Girsanov-based methods of previous works. We introduce a refined treatment of the error from discretizing the reverse SDE inspired by stochastic localization.

Temporal planning is an extension of classical planning involving concurrent execution of actions and alignment with temporal constraints. Durative actions along with invariants allow for modeling domains in which multiple agents operate in parallel on shared resources. Hence, it is often important to avoid resource conflicts, where temporal constraints establish the consistency of concurrent actions and events. Unfortunately, the performance of temporal planning engines tends to sharply deteriorate when the number of agents and objects in a domain gets large. A possible remedy is to use macro-actions that are well-studied in the context of classical planning. In temporal planning settings, however, introducing macro-actions is significantly more challenging when the concurrent execution of actions and shared use of resources, provided the compliance to temporal constraints, should not be suppressed entirely. Our work contributes a general concept of sequential temporal macro-actions that guarantees the applicability of obtained plans, i.e., the sequence of original actions encapsulated by a macro-action is always executable. We apply our approach to several temporal planners and domains, stemming from the International Planning Competition and RoboCup Logistics League. Our experiments yield improvements in terms of obtained satisficing plans as well as plan quality for the majority of tested planners and domains.

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural sciences. While many of these problems stand to benefit from the ability to specify arbitrary, domain-informed constraints, this setting is not covered by the existing (Riemannian) diffusion model methodology. Recent work has attempted to address this issue by constructing novel noising processes based on the reflected Brownian motion and logarithmic barrier methods. However, the associated samplers are either computationally burdensome or only apply to convex subsets of Euclidean space. In this paper, we introduce an alternative, simple noising scheme based on Metropolis sampling that affords substantial gains in computational efficiency and empirical performance compared to the earlier samplers. Of independent interest, we prove that this new process corresponds to a valid discretisation of the reflected Brownian motion. We demonstrate the scalability and flexibility of our approach on a range of problem settings with convex and non-convex constraints, including applications from geospatial modelling, robotics and protein design., Comment: NeurIPS 2023

Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many problems in the natural sciences incorporate symmetries and involve data living in non-Euclidean spaces. In this work, we extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We do so by a) constructing a noising process which admits, as limiting distribution, a geometric Gaussian process that transforms under the symmetry group of interest, and b) approximating the score with a neural network that is equivariant w.r.t. this group. We show that with these conditions, the generative functional model admits the same symmetry. We demonstrate scalability and capacity of the model, using a novel Langevin-based conditional sampler, to fit complex scalar and vector fields, with Euclidean and spherical codomain, on synthetic and real-world weather data.

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.

Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time due to the emergence of new species or birth and death events. However, existing neural parameterizations of SBs such as diffusion Schr\"odinger bridges (DSBs) are restricted to settings in which the endpoints of the stochastic process are both probability measures and assume conservation of mass constraints. To address this limitation, we introduce unbalanced DSBs which model the temporal evolution of marginals with arbitrary finite mass. This is achieved by deriving the time reversal of stochastic differential equations with killing and birth terms. We present two novel algorithmic schemes that comprise a scalable objective function for training unbalanced DSBs and provide a theoretical analysis alongside challenging applications on predicting heterogeneous molecular single-cell responses to various cancer drugs and simulating the emergence and spread of new viral variants.

The formation scenario of the Magellanic Bridge during an encounter between the Large and Small Magellanic Clouds $\sim200\,$Myr ago, as proposed by $N$-body models, would be imprinted in the chemical enrichment and kinematics of its stars, and sites of ongoing star formation along its extension. We present an analysis of 33 Bridge star clusters using photometry obtained with the SOAR 4-m telescope equipped with adaptive optics for the VISCACHA survey. We performed a membership selection and derived self-consistent ages, metallicities, distances and reddening values via statistical isochrone fitting, as well as tidal radii and integrated masses from structure analysis. Two groups are clearly detected: 13 well-studied clusters older than the Bridge, with $0.5-6.8\,$Gyr and $\rm{[Fe/H]}<-0.6\,$dex; and 15 clusters with $< 200\,$Myr and $\rm{[Fe/H]}>-0.5\,$dex, probably formed in-situ. The old clusters follow the overall age and metallicity gradients of the SMC, whereas the younger ones are uniformly distributed along the Bridge. The main results are as follows: $(i)$ we derive ages and metallicities for the first time for 9 and 18 clusters, respectively; $(ii)$ we detect two metallicity dips in the age-metallicity relation of the Bridge at $\sim 200\,$Myr and $1.5\,$Gyr ago for the first time, possibly chemical signatures of the formation of the Bridge and Magellanic Stream; $(iii)$ we estimate a minimum stellar mass for the Bridge of $3-5 \times 10^5\,M_\odot$; $(iv)$ we confirm that all the young Bridge clusters at $\rm{RA} < 3^h$ are metal-rich $\rm{[Fe/H]} \sim -0.4\,$dex., Comment: 15 pages, 13 figures + appendix. Accepted for publication in MNRAS