Finding low-dimensional interpretable models of complex physical fields such as turbulence remains an open question, 80 years after the pioneer work of Kolmogorov. Estimating high-dimensional probability distributions from data samples suffers from an optimization and an approximation curse of dimensionality. It may be avoided by following a hierarchic probability flow from coarse to fine scales. This inverse renormalization group is defined by conditional probabilities across scales, renormalized in a wavelet basis. For a $\varphi^4$ scalar potential, sampling these hierarchic models avoids the critical slowing down at the phase transition. An outstanding issue is to also approximate non-Gaussian fields having long-range interactions in space and across scales. We introduce low-dimensional models with robust multiscale approximations of high order polynomial energies. They are calculated with a second wavelet transform, which defines interactions over two hierarchies of scales. We estimate and sample these wavelet scattering models to generate 2D vorticity fields of turbulence, and images of dark matter densities.

Distributed approaches have many computational benefits, but they are vulnerable to attacks from a subset of devices transmitting incorrect information. This paper investigates Byzantine-resilient algorithms in a decentralized setting, where devices communicate directly with one another. We leverage the so-called dual approach to design a general robust decentralized optimization method. We provide both global and local clipping rules in the special case of average consensus, with tight convergence guarantees. These clipping rules are practical, and yield results that finely characterize the impact of Byzantine nodes, highlighting for instance a qualitative difference in convergence between global and local clipping thresholds. Lastly, we demonstrate that they can serve as a basis for designing efficient attacks.

Multimodal fusion focuses on integrating information from multiple modalities with the goal of more accurate prediction, which has achieved remarkable progress in a wide range of scenarios, including autonomous driving and medical diagnosis. However, the reliability of multimodal fusion remains largely unexplored especially under low-quality data settings. This paper surveys the common challenges and recent advances of multimodal fusion in the wild and presents them in a comprehensive taxonomy. From a data-centric view, we identify four main challenges that are faced by multimodal fusion on low-quality data, namely (1) noisy multimodal data that are contaminated with heterogeneous noises, (2) incomplete multimodal data that some modalities are missing, (3) imbalanced multimodal data that the qualities or properties of different modalities are significantly different and (4) quality-varying multimodal data that the quality of each modality dynamically changes with respect to different samples. This new taxonomy will enable researchers to understand the state of the field and identify several potential directions. We also provide discussion for the open problems in this field together with interesting future research directions.

This study delves into the relationship between emotional trends from X platform data and the market dynamics of well-known cryptocurrencies Cardano, Binance, Fantom, Matic, and Ripple over the period from October 2022 to March 2023. Leveraging SenticNet, we identified emotions like Fear and Anxiety, Rage and Anger, Grief and Sadness, Delight and Pleasantness, Enthusiasm and Eagerness, and Delight and Joy. Following data extraction, we segmented each month into bi-weekly intervals, replicating this process for price data obtained from Finance-Yahoo. Consequently, a comparative analysis was conducted, establishing connections between emotional trends observed across bi-weekly intervals and cryptocurrency prices, uncovering significant correlations between emotional sentiments and coin valuations.

Abstract-- We introduce an advanced, swift pattern recognition strategy for various multiple robotics during curve negotiation. Initially, the paradigm considers robot locations and features as quintessential parameters indicative of divergent robot patterns. The utilization of and underpins the foundational control mechanisms stochastic process theories, particularly the Hidden Markov for sophisticated robot dynamics technologies [1], [2], [3], Model--a form of dynamic Bayesian network--has proven [4], the accurate identification and forecasting of robot's instrumental in elucidating the intricate correlations between group motion and distribution emerge as critical undertakings. Moreover, advanced probabilistic models, including the design of robot dynamics and assistance systems [5], the ARX framework and its stochastic variant [10], the [6]. This necessitates a comprehensive analysis of robotics, SS-ARX model, have been developed to accurately reflect the encompassing both their distribution and feature conditions, unpredictability inherent in robotics status, enabling refined as well as their status patterns (identifiable as functional classification and prediction of robotics distribution.

In safe Reinforcement Learning (RL), safety cost is typically defined as a function dependent on the immediate state and actions. In practice, safety constraints can often be non-Markovian due to the insufficient fidelity of state representation, and safety cost may not be known. We therefore address a general setting where safety labels (e.g., safe or unsafe) are associated with state-action trajectories. Our key contributions are: first, we design a safety model that specifically performs credit assignment to assess contributions of partial state-action trajectories on safety. This safety model is trained using a labeled safety dataset. Second, using RL-as-inference strategy we derive an effective algorithm for optimizing a safe policy using the learned safety model. Finally, we devise a method to dynamically adapt the tradeoff coefficient between reward maximization and safety compliance. We rewrite the constrained optimization problem into its dual problem and derive a gradient-based method to dynamically adjust the tradeoff coefficient during training. Our empirical results demonstrate that this approach is highly scalable and able to satisfy sophisticated non-Markovian safety constraints.

We investigate the impact of the input dimension on the generalization error in generative adversarial networks (GANs). In particular, we first provide both theoretical and practical evidence to validate the existence of an optimal input dimension (OID) that minimizes the generalization error. Then, to identify the OID, we introduce a novel framework called generalized GANs (G-GANs), which includes existing GANs as a special case. By incorporating the group penalty and the architecture penalty developed in the paper, G-GANs have several intriguing features. First, our framework offers adaptive dimensionality reduction from the initial dimension to a dimension necessary for generating the target distribution. Second, this reduction in dimensionality also shrinks the required size of the generator network architecture, which is automatically identified by the proposed architecture penalty. Both reductions in dimensionality and the generator network significantly improve the stability and the accuracy of the estimation and prediction. Theoretical support for the consistent selection of the input dimension and the generator network is provided. Third, the proposed algorithm involves an end-to-end training process, and the algorithm allows for dynamic adjustments between the input dimension and the generator network during training, further enhancing the overall performance of G-GANs. Extensive experiments conducted with simulated and benchmark data demonstrate the superior performance of G-GANs. In particular, compared to that of off-the-shelf methods, G-GANs achieves an average improvement of 45.68% in the CT slice dataset, 43.22% in the MNIST dataset and 46.94% in the FashionMNIST dataset in terms of the maximum mean discrepancy or Frechet inception distance. Moreover, the features generated based on the input dimensions identified by G-GANs align with visually significant features.

In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential nonlinear relationships among the variables. To address this limitation, we propose a partially linear structure that incorporates unspecified functions to capture nonlinear relationships. We establish the identifiability of the proposed model under mild conditions and introduce a practical estimation algorithm. We present the performance of our approach through numerical studies, including simulations and real data analysis.

Suppose that we first apply the Lasso to a design matrix, and then update one of its columns. In general, the signs of the Lasso coefficients may change, and there is no closed-form expression for updating the Lasso solution exactly. In this work, we propose an approximate formula for updating a debiased Lasso coefficient. We provide general nonasymptotic error bounds in terms of the norms and correlations of a given design matrix's columns, and then prove asymptotic convergence results for the case of a random design matrix with i.i.d.\ sub-Gaussian row vectors and i.i.d.\ Gaussian noise. Notably, the approximate formula is asymptotically correct for most coordinates in the proportional growth regime, under the mild assumption that each row of the design matrix is sub-Gaussian with a covariance matrix having a bounded condition number. Our proof only requires certain concentration and anti-concentration properties to control various error terms and the number of sign changes. In contrast, rigorously establishing distributional limit properties (e.g.\ Gaussian limits for the debiased Lasso) under similarly general assumptions has been considered open problem in the universality theory. As applications, we show that the approximate formula allows us to reduce the computation complexity of variable selection algorithms that require solving multiple Lasso problems, such as the conditional randomization test and a variant of the knockoff filter.

Learning an ordering of items based on noisy pairwise comparisons is useful when item-specific labels are difficult to assign, for example, when annotators have to make subjective assessments. Algorithms have been proposed for actively sampling comparisons of items to minimize the number of annotations necessary for learning an accurate ordering. However, many ignore shared structure between items, treating them as unrelated, limiting sample efficiency and precluding generalization to new items. In this work, we study active learning with pairwise preference feedback for ordering items with contextual attributes, both in- and out-of-sample. We give an upper bound on the expected ordering error incurred by active learning strategies under a logistic preference model, in terms of the aleatoric and epistemic uncertainty in comparisons, and propose two algorithms designed to greedily minimize this bound. We evaluate these algorithms in two realistic image ordering tasks, including one with comparisons made by human annotators, and demonstrate superior sample efficiency compared to non-contextual ranking approaches and active preference learning baselines.