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Recent advancements in large language models (LLMs) have shown impressive versatility across various tasks. To eliminate their hallucinations, retrieval-augmented generation (RAG) has emerged as a powerful approach, leveraging external…

The parallel alternating direction method of multipliers (ADMM) algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical…

Graph-language models (GLMs) have demonstrated great potential in graph-based semi-supervised learning. A typical GLM consists of two key stages: graph generation and text embedding, which are usually implemented by inferring a latent graph…

Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal…

There is an increased interest in building data analytics frameworks with advanced algebraic capabilities both in industry and academia. Many of these frameworks, e.g., TensorFlow and BIDMach, implement their compute-intensive primitives in…

We present Selective Non-Gaussian Refinement (SNGR), a SLAM framework that augments iSAM2 with targeted nested sampling on windows where Gaussian approximations are likely to fail. We detect such regions using the condition number of joint…

Generative sequence modeling faces a fundamental tension between the expressivity of Transformers and the efficiency of linear sequence models. Existing efficient architectures are theoretically bounded by shallow, single-step linear…

The embedding-based architecture has become the dominant approach in modern recommender systems, mapping users and items into a compact vector space. It then employs predefined similarity metrics, such as the inner product, to calculate…

The ability for an agent to localize itself within an environment is crucial for many real-world applications. For unknown environments, Simultaneous Localization and Mapping (SLAM) enables incremental and concurrent building of and…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

We study the problem of image alignment for panoramic stitching. Unlike most existing approaches that are feature-based, our algorithm works on pixels directly, and accounts for errors across the whole images globally. Technically, we…

In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…

An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…

We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…

The increasing scale and complexity of large language models (LLMs) pose significant inference latency challenges, primarily due to their autoregressive decoding paradigm characterized by the sequential nature of next-token prediction. By…

Mars exploration requires precise and reliable terrain models to ensure safe rover navigation across its unpredictable and often hazardous landscapes. Stereoscopic vision serves a critical role in the rover's perception, allowing scene…

To operate effectively in the real world, agents should be able to act from high-dimensional raw sensory input such as images and achieve diverse goals across long time-horizons. Current deep reinforcement and imitation learning methods can…

Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least…

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…