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We explore the Ziv-Lempel and Crochemore factorizations of some classical automatic sequences making an extensive use of the theorem prover Walnut.

Contemporary makeup approaches primarily hinge on unpaired learning paradigms, yet they grapple with the challenges of inaccurate supervision (e.g., face misalignment) and sophisticated facial prompts (including face parsing, and landmark detection). These challenges prohibit low-cost deployment of facial makeup models, especially on mobile devices. To solve above problems, we propose a brand-new learning paradigm, termed "Data Amplify Learning (DAL)," alongside a compact makeup model named "TinyBeauty." The core idea of DAL lies in employing a Diffusion-based Data Amplifier (DDA) to "amplify" limited images for the model training, thereby enabling accurate pixel-to-pixel supervision with merely a handful of annotations. Two pivotal innovations in DDA facilitate the above training approach: (1) A Residual Diffusion Model (RDM) is designed to generate high-fidelity detail and circumvent the detail vanishing problem in the vanilla diffusion models; (2) A Fine-Grained Makeup Module (FGMM) is proposed to achieve precise makeup control and combination while retaining face identity. Coupled with DAL, TinyBeauty necessitates merely 80K parameters to achieve a state-of-the-art performance without intricate face prompts. Meanwhile, TinyBeauty achieves a remarkable inference speed of up to 460 fps on the iPhone 13. Extensive experiments show that DAL can produce highly competitive makeup models using only 5 image pairs.

We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be implemented to be adaptive, and it uses graph spline approximation to improve accuracy. We illustrate our approach on classes of large sparse matrices.

We present a novel adversarial penalized self-knowledge distillation method, named adversarial learning and implicit regularization for self-knowledge distillation (AI-KD), which regularizes the training procedure by adversarial learning and implicit distillations. Our model not only distills the deterministic and progressive knowledge which are from the pre-trained and previous epoch predictive probabilities but also transfers the knowledge of the deterministic predictive distributions using adversarial learning. The motivation is that the self-knowledge distillation methods regularize the predictive probabilities with soft targets, but the exact distributions may be hard to predict. Our method deploys a discriminator to distinguish the distributions between the pre-trained and student models while the student model is trained to fool the discriminator in the trained procedure. Thus, the student model not only can learn the pre-trained model's predictive probabilities but also align the distributions between the pre-trained and student models. We demonstrate the effectiveness of the proposed method with network architectures on multiple datasets and show the proposed method achieves better performance than state-of-the-art methods.

This paper presents a method for future motion prediction of multi-agent systems by including group formation information and future intent. Formation of groups depends on a physics-based clustering method that follows the agglomerative hierarchical clustering algorithm. We identify clusters that incorporate the minimum cost-to-go function of a relevant optimal control problem as a metric for clustering between the groups among agents, where groups with similar associated costs are assumed to be likely to move together. The cost metric accounts for proximity to other agents as well as the intended goal of each agent. An unscented Kalman filter based approach is used to update the established clusters as well as add new clusters when new information is obtained. Our approach is verified through non-trivial numerical simulations implementing the proposed algorithm on different datasets pertaining to a variety of scenarios and agents.

The Adam optimizer, often used in Machine Learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. This work shows that the classical Adam algorithm is a first order implicit-explicit (IMEX) Euler discretization of the underlying ODE. Employing the time discretization point of view, we propose new extensions of the Adam scheme obtained by using higher order IMEX methods to solve the ODE. Based on this approach, we derive a new optimization algorithm for neural network training that performs better than classical Adam on several regression and classification problems.

Regression models for compositional data are common in several areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in these models using residuals that are approximately standard normally distributed. However, for regression models for compositional data, there has not been any multivariate residual that meets this requirement. In this work, we introduce a class of asymptotically standard normally distributed residuals for compositional data based on bootstrap. Monte Carlo simulation studies indicate that the distributions of the residuals of this class are well approximated by the standard normal distribution in small samples. An application to simulated data also suggests that one of the residuals of the proposed class is better to identify model misspecification than its competitors. Finally, the usefulness of the best residual of the proposed class is illustrated through an application on sleep stages. The class of residuals proposed here can also be used in other classes of multivariate regression models.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

This research's primary motivation of this study is to address the high hardware and computational demands typically associated with LLMs.Therefore,our goal is to find a balance between model lightness and performance,striving to maximize performance while using a comparatively lightweight model. Hyacinth6B was developed with this objective in mind,aiming to fully leverage the core capabilities of LLMs without incurring substantial resource costs, effectively pushing the boundaries of smaller model's performance. The training approach involves parameter efficient finetuning using the LoRA method.

Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment combinations grows exponentially with the number of treatment factors, which motivates the forward selection strategy based on the sparsity, hierarchy, and heredity principles for factorial effects. Although this strategy is intuitive and has been widely used in practice, its rigorous statistical theory has not been formally established. To fill this gap, we establish design-based theory for forward factor selection in factorial designs based on the potential outcome framework. We not only prove a consistency property for the factor selection procedure but also discuss statistical inference after factor selection. In particular, with selection consistency, we quantify the advantages of forward selection based on asymptotic efficiency gain in estimating factorial effects. With inconsistent selection in higher-order interactions, we propose two strategies and investigate their impact on subsequent inference. Our formulation differs from the existing literature on variable selection and post-selection inference because our theory is based solely on the physical randomization of the factorial design and does not rely on a correctly specified outcome model.