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Transformer is a transformative framework that models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention mechanism. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way. Based on the equivalence between the inner product of binary codes and the Hamming distance as well as the associative property of matrix multiplication, we can approximate the attention in linear complexity by expressing it as a dot-product of binary codes. Moreover, the compact binary representations of queries and keys enable us to replace most of the expensive multiply-accumulate operations in attention with simple accumulations to save considerable on-chip energy footprint on edge devices. Extensive experiments on both vision and language tasks show that EcoFormer consistently achieves comparable performance with standard attentions while consuming much fewer resources. For example, based on PVTv2-B0 and ImageNet-1K, Ecoformer achieves a 73% energy footprint reduction with only a 0.33% performance drop compared to the standard attention. Code is available at //github.com/ziplab/EcoFormer.

Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.

Well-designed simultaneously transmitting and reflecting RIS (STAR-RIS), which extends the half-space coverage to full-space coverage, incurs wireless communication environments to be smart and reconfigurable. In this paper, we survey how STAR-RIS affects the performance of full-duplex communication systems with the presence of full-duplex users, wherein the base station (BS) and the uplink users are subject to maximum transmission power constraints. Firstly, the weighted sum-rate (WSR) is derived as a system performance metric. Then, we formulate the resource allocation design into an equivalent weighted minimum mean-square-error form and then transform it into several convex sub-problems to maximize the WSR as an optimization problem which jointly optimizes the beamforming and the combining vectors at the BS, the transmit powers of the uplink users, and phase shifts of STAR-RIS. Although the WSR optimization is non-convex, an efficient iterative alternating procedure is proposed to achieve a sub-optimal solution for the optimization problem. Secondly, the STAR-RIS's phase shifts are optimized via the successive convex approximation technique. Finally, numerical results are provided to explain how STAR-RIS improves the performance metric with the presence of full-duplex users.

Different from traditional reflection-only reconfigurable intelligent surfaces (RISs), simultaneously transmitting and reflecting RISs (STAR-RISs) represent a novel technology, which extends the half-space coverage to full-space coverage by simultaneously transmitting and reflecting incident signals. STAR-RISs provide new degrees-of-freedom (DoF) for manipulating signal propagation. Motivated by the above, a novel STAR-RIS assisted non-orthogonal multiple access (NOMA) (STAR-RIS-NOMA) system is proposed in this paper. Our objective is to maximize the achievable sum rate by jointly optimizing the decoding order, power allocation coefficients, active beamforming, and transmission and reflection beamforming. However, the formulated problem is non-convex with intricately coupled variables. To tackle this challenge, a suboptimal two-layer iterative algorithm is proposed. Specifically, in the inner-layer iteration, for a given decoding order, the power allocation coefficients, active beamforming, transmission and reflection beamforming are optimized alternatingly. For the outer-layer iteration, the decoding order of NOMA users in each cluster is updated with the solutions obtained from the inner-layer iteration. Moreover, an efficient decoding order determination scheme is proposed based on the equivalent-combined channel gains. Simulation results are provided to demonstrate that the proposed STAR-RIS-NOMA system, aided by our proposed algorithm, outperforms conventional RIS-NOMA and RIS assisted orthogonal multiple access (RIS-OMA) systems.

In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart process prior to handle within-image dependency, and propose a general global-local spatial selection prior that extends a rich class of well-studied selection priors. Unlike existing constructions, we achieve simultaneous global (i.e, at covariate-level) and local (i.e., at pixel/voxel-level) selection by introducing `participation rate' parameters that measure the probability for the individual covariates to affect the observed images. This along with a hard-thresholding strategy leads to dependency between selections at the two levels, introduces extra sparsity at the local level, and allows the global selection to be informed by the local selection, all in a model-based manner. We design an efficient Gibbs sampler that allows inference for large image data. We show on simulated data that parameters are interpretable and lead to efficient selection. Finally, we demonstrate performance of the proposed model by using data from the Autism Brain Imaging Data Exchange (ABIDE) study. To the best of our knowledge, the proposed model construction is the first in the Bayesian literature to simultaneously achieve image smoothing, parameter estimation and a two-level variable selection for image-on-scalar regression.

The notion of omnipredictors (Gopalan, Kalai, Reingold, Sharan and Wieder ITCS 2021), suggested a new paradigm for loss minimization. Rather than learning a predictor based on a known loss function, omnipredictors can easily be post-processed to minimize any one of a rich family of loss functions compared with the loss of a class $C$. It has been shown that such omnipredictors exist and are implied (for all convex and Lipschitz loss functions) by the notion of multicalibration from the algorithmic fairness literature. Nevertheless, it is often the case that the action selected must obey some additional constraints (such as capacity or parity constraints). In itself, the original notion of omnipredictors does not apply in this well-motivated and heavily studied the context of constrained loss minimization. In this paper, we introduce omnipredictors for constrained optimization and study their complexity and implications. The notion that we introduce allows the learner to be unaware of the loss function that will be later assigned as well as the constraints that will be later imposed, as long as the subpopulations that are used to define these constraints are known. The paper shows how to obtain omnipredictors for constrained optimization problems, relying on appropriate variants of multicalibration. For some interesting constraints and general loss functions and for general constraints and some interesting loss functions, we show how omnipredictors are implied by a variant of multicalibration that is similar in complexity to standard multicalibration. We demonstrate that in the general case, standard multicalibration is insufficient and show that omnipredictors are implied by multicalibration with respect to a class containing all the level sets of hypotheses in $C$. We also investigate the implications when the constraints are group fairness notions.

Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper, we propose to view the time series classification problem from the distribution perspective. We argue that the temporal complexity attributes to the unknown latent distributions within. To this end, we propose DIVERSIFY to learn generalized representations for time series classification. DIVERSIFY takes an iterative process: it first obtains the worst-case distribution scenario via adversarial training, then matches the distributions of the obtained sub-domains. We also present some theoretical insights. We conduct experiments on gesture recognition, speech commands recognition, wearable stress and affect detection, and sensor-based human activity recognition with a total of seven datasets in different settings. Results demonstrate that DIVERSIFY significantly outperforms other baselines and effectively characterizes the latent distributions by qualitative and quantitative analysis.

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.

The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks). Yet, despite its long history, current approaches mostly focus on the optimization of graphs themselves, rather than on directly inferring learning strategies, such as detection, estimation, statistical and probabilistic inference, clustering and separation from signals and data acquired on graphs. To fill this void, we first revisit graph topologies from a Data Analytics point of view, and establish a taxonomy of graph networks through a linear algebraic formalism of graph topology (vertices, connections, directivity). This serves as a basis for spectral analysis of graphs, whereby the eigenvalues and eigenvectors of graph Laplacian and adjacency matrices are shown to convey physical meaning related to both graph topology and higher-order graph properties, such as cuts, walks, paths, and neighborhoods. Next, to illustrate estimation strategies performed on graph signals, spectral analysis of graphs is introduced through eigenanalysis of mathematical descriptors of graphs and in a generic way. Finally, a framework for vertex clustering and graph segmentation is established based on graph spectral representation (eigenanalysis) which illustrates the power of graphs in various data association tasks. The supporting examples demonstrate the promise of Graph Data Analytics in modeling structural and functional/semantic inferences. At the same time, Part I serves as a basis for Part II and Part III which deal with theory, methods and applications of processing Data on Graphs and Graph Topology Learning from data.