相关论文: Complexity of Zeroth- and First-order Stochastic T…

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians…

Training large language models (LLMs) with open-domain instruction data has yielded remarkable success in aligning to end tasks and human preferences. Extensive research has highlighted the importance of the quality and diversity of…

Metric learning is central to retrieval, yet its effects on embedding geometry and optimization dynamics are not well understood. We introduce a diagnostic framework, VARIANCE (intra-/inter-class variance) and GREEDINESS (active ratio and…

Many real-world systems can be studied in terms of pattern recognition tasks, so that proper use (and understanding) of machine learning methods in practical applications becomes essential. While a myriad of classification methods have been…

Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and…

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain…

We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…

We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) $x_1...x_n$ is the sum of terms over intervals $[i,j]$ where each term is non-zero only if the…

The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothness and strong convexity. These metrics are used to tune the hyperparameters of FOA. We introduce a…

In this paper, numerical simulations of four-mode continuous-variable cluster states with different topologies in the framework of measurement-based quantum computation are presented. By utilizing the symplectic representation and…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

Extracting associations that recur across multiple studies while controlling the false discovery rate is a fundamental challenge. Here, we consider an extension of Efron's single-study two-groups model to allow joint analysis of multiple…

Distributionally Robust Reinforcement Learning (DR-RL) aims to derive a policy optimizing the worst-case performance within a predefined uncertainty set. Despite extensive research, previous DR-RL algorithms have predominantly favored…

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…

Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. This makes them applicable to practically important use-cases where training data is…

CUR decompositions approximate a matrix using selected columns, rows, and their intersection. Classical CUR theory provides exactness results for low-rank matrices and perturbation bounds controlled by the size of the noise. In this work we…

The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit…