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Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers. The proper choice of the integrator of the Hamiltonian dynamics is key to the efficiency of HMC. It is becoming increasingly clear that multi-stage splitting integrators are a good alternative to the Verlet method, traditionally used in HMC. Here we propose a principled way of finding optimal, problem-specific integration schemes (in terms of the best conservation of energy for harmonic forces/Gaussian targets) within the families of 2- and 3-stage splitting integrators. The method, which we call Adaptive Integration Approach for statistics, or s-AIA, uses a multivariate Gaussian model and simulation data obtained at the HMC burn-in stage to identify a system-specific dimensional stability interval and assigns the most appropriate 2-/3-stage integrator for any user-chosen simulation step size within that interval. s-AIA has been implemented in the in-house software package HaiCS without introducing computational overheads in the simulations. The efficiency of the s-AIA integrators and their impact on the HMC accuracy, sampling performance and convergence are discussed in comparison with known fixed-parameter multi-stage splitting integrators (including Verlet). Numerical experiments on well-known statistical models show that the adaptive schemes reach the best possible performance within the family of 2-, 3-stage splitting schemes.

Diffusion models have recently emerged as a promising framework for Image Restoration (IR), owing to their ability to produce high-quality reconstructions and their compatibility with established methods. Existing methods for solving noisy inverse problems in IR, considers the pixel-wise data-fidelity. In this paper, we propose SaFaRI, a spatial-and-frequency-aware diffusion model for IR with Gaussian noise. Our model encourages images to preserve data-fidelity in both the spatial and frequency domains, resulting in enhanced reconstruction quality. We comprehensively evaluate the performance of our model on a variety of noisy inverse problems, including inpainting, denoising, and super-resolution. Our thorough evaluation demonstrates that SaFaRI achieves state-of-the-art performance on both the ImageNet datasets and FFHQ datasets, outperforming existing zero-shot IR methods in terms of LPIPS and FID metrics.

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics. Wasserstein estimators are defined as solutions of variational problems whose objective function involves the use of an optimal transport cost between probability measures. Such estimators can be regularized by replacing the optimal transport cost by its regularized version using an entropy penalty on the transport plan. The use of such a regularization has a potentially significant smoothing effect on the resulting estimators. In this work, we investigate its potential benefits on the approximation and estimation properties of regularized Wasserstein estimators. Our main contribution is to discuss how entropic regularization may reach, at a lower computational cost, statistical performances that are comparable to those of un-regularized Wasserstein estimators in statistical learning problems involving distributional data analysis. To this end, we present new theoretical results on the convergence of regularized Wasserstein estimators. We also study their numerical performances using simulated and real data in the supervised learning problem of proportions estimation in mixture models using optimal transport.

Wasserstein distortion is a one-parameter family of distortion measures that was recently proposed to unify fidelity and realism constraints. After establishing continuity results for Wasserstein in the extreme cases of pure fidelity and pure realism, we prove the first coding theorems for compression under Wasserstein distortion focusing on the regime in which both the rate and the distortion are small.

While generative AI is now widespread and useful in society, there are potential risks of misuse, e.g., unconsciously influencing cognitive processes or decision-making. Although this causes a security problem in the cognitive domain, there has been no research about neural and computational mechanisms counteracting the impact of malicious generative AI in humans. We propose DecNefGAN, a novel framework that combines a generative adversarial system and a neural reinforcement model. More specifically, DecNefGAN bridges human and generative AI in a closed-loop system, with the AI creating stimuli that induce specific mental states, thus exerting external control over neural activity. The objective of the human is the opposite, to compete and reach an orthogonal mental state. This framework can contribute to elucidating how the human brain responds to and counteracts the potential influence of generative AI.

Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict trust assumption. In the context of computation and storage, it is required that honest nodes outnumber adversarial ones by a certain margin. However, in several emerging real-world cases, particularly, in decentralized blockchain-oriented applications, such assumptions are often unrealistic. Consequently, despite the important role of coding in addressing significant challenges within decentralized systems, its applications become constrained. Still, in decentralized platforms, a distinctive characteristic emerges, offering new avenues for secure coding beyond the constraints of conventional methods. In these scenarios, the adversary benefits when the legitimate decoder recovers the data, and preferably with a high estimation error. This incentive motivates them to act rationally, trying to maximize their gains. In this paper, we propose a game theoretic formulation, called game of coding, that captures this unique dynamic where each of the adversary and the data collector (decoder) have a utility function to optimize. The utility functions reflect the fact that both the data collector and the adversary are interested to increase the chance of data being recoverable at the data collector. Moreover, the utility functions express the interest of the data collector to estimate the input with lower estimation error, but the opposite interest of the adversary. As a first, still highly non-trivial step, we characterize the equilibrium of the game for the repetition code with repetition factor of 2, for a wide class of utility functions with minimal assumptions.

Faithfully summarizing the knowledge encoded by a deep neural network (DNN) into a few symbolic primitive patterns without losing much information represents a core challenge in explainable AI. To this end, Ren et al. (2023c) have derived a series of theorems to prove that the inference score of a DNN can be explained as a small set of interactions between input variables. However, the lack of generalization power makes it still hard to consider such interactions as faithful primitive patterns encoded by the DNN. Therefore, given different DNNs trained for the same task, we develop a new method to extract interactions that are shared by these DNNs. Experiments show that the extracted interactions can better reflect common knowledge shared by different DNNs.

By formulating the floorplanning of VLSI as a mixed-variable optimization problem, this paper proposes to solve it by memetic algorithms, where the discrete orientation variables are addressed by the distribution evolutionary algorithm based on a population of probability model (DEA-PPM), and the continuous coordination variables are optimized by the conjugate sub-gradient algorithm (CSA). Accordingly, the fixed-outline floorplanning algorithm based on CSA and DEA-PPM (FFA-CD) and the floorplanning algorithm with golden section strategy (FA-GSS) are proposed for the floorplanning problems with and without fixed-outline constraint. %FF-CD is committed to optimizing wirelength targets within a fixed profile. FA-GSS uses the Golden Section strategy to optimize both wirelength and area targets. The CSA is used to solve the proposed non-smooth optimization model, and the DEA-PPM is used to explore the module rotation scheme to enhance the flexibility of the algorithm. Numerical experiments on GSRC test circuits show that the proposed algorithms are superior to some celebrated B*-tree based floorplanning algorithms, and are expected to be applied to large-scale floorplanning problems due to their low time complexity.

The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman's asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research.

In this work, a Generalized Finite Difference (GFD) scheme is presented for effectively computing the numerical solution of a parabolic-elliptic system modelling a bacterial strain with density-suppressed motility. The GFD method is a meshless method known for its simplicity for solving non-linear boundary value problems over irregular geometries. The paper first introduces the basic elements of the GFD method, and then an explicit-implicit scheme is derived. The convergence of the method is proven under a bound for the time step, and an algorithm is provided for its computational implementation. Finally, some examples are considered comparing the results obtained with a regular mesh and an irregular cloud of points.